/* method: we compute the QR decomposition of a matrix with Gaussian
values */
float *random_orthogonal_basis (int di)
{
FINTEGER d=di;
long i;
/* generate a Gaussian matrix */
float *x = fmat_new_rand_gauss (d, d);
float *tau = NEWA (float, d);
{ /* compute QR decomposition */
/* query work size */
float lwork_query;
FINTEGER lwork = -1, info;
sgeqrf_ (&d, &d, x, &d, tau, &lwork_query, &lwork, &info);
assert (info == 0);
lwork = (int) lwork_query;
float *work = NEWA (float, lwork);
sgeqrf_ (&d, &d, x, &d, tau, work, &lwork, &info);
assert (info == 0);
free (work);
}
/* Decomposition now stored in x and tau. Apply to identity to get
explicit matrix Q */
float *q = NEWAC (float, d * d);
{
float *t = NEWA (float, d * d);
slarft_ ("F", "C", &d, &d, x, &d, tau, t, &d);
for (i = 0; i < d; i++)
q[i + d * i] = 1;
float *work = NEWA (float, d * d);
slarfb_ ("Left", "N", "F", "C",
&d, &d, &d, x, &d, t, &d, q, &d, work, &d);
free (t);
free (work);
}
free (tau);
free (x);
return q;
}
DLLEXPORT MKL_INT s_qr_factor(MKL_INT m, MKL_INT n, float r[], float tau[], float q[], float work[], MKL_INT len)
{
MKL_INT info = 0;
sgeqrf_(&m, &n, r, &m, tau, work, &len, &info);
for (MKL_INT i = 0; i < m; ++i)
{
for (MKL_INT j = 0; j < m && j < n; ++j)
{
if (i > j)
{
q[j * m + i] = r[j * m + i];
}
}
}
//compute the q elements explicitly
if (m <= n)
{
sorgqr_(&m, &m, &m, q, &m, tau, work, &len, &info);
}
else
{
sorgqr_(&m, &n, &n, q, &m, tau, work, &len, &info);
}
return info;
}
/* QR decomposition */
void THLapack_(geqrf)(int m, int n, real *a, int lda, real *tau, real *work, int lwork, int *info)
{
#ifdef USE_LAPACK
#if defined(TH_REAL_IS_DOUBLE)
dgeqrf_(&m, &n, a, &lda, tau, work, &lwork, info);
#else
sgeqrf_(&m, &n, a, &lda, tau, work, &lwork, info);
#endif
#else
THError("geqrf: Lapack library not found in compile time\n");
#endif
}
DLLEXPORT MKL_INT s_qr_thin_factor(MKL_INT m, MKL_INT n, float q[], float tau[], float r[], float work[], MKL_INT len)
{
MKL_INT info = 0;
sgeqrf_(&m, &n, q, &m, tau, work, &len, &info);
for (MKL_INT i = 0; i < n; ++i)
{
for (MKL_INT j = 0; j < n; ++j)
{
if( i <= j) {
r[j * n + i] = q[j * m + i];
}
}
}
sorgqr_(&m, &n, &n, q, &m, tau, work, &len, &info);
return info;
}
DLLEXPORT int s_qr_solve(int m, int n, int bn, float r[], float b[], float x[], float work[], int len)
{
int info = 0;
float* clone_r = new float[m*n];
memcpy(clone_r, r, m*n*sizeof(float));
float* tau = new float[max(1, min(m,n))];
sgeqrf_(&m, &n, clone_r, &m, tau, work, &len, &info);
if (info != 0)
{
delete[] clone_r;
delete[] tau;
return info;
}
float* clone_b = new float[m*bn];
memcpy(clone_b, b, m*bn*sizeof(float));
char side ='L';
char tran = 'T';
sormqr_(&side, &tran, &m, &bn, &n, clone_r, &m, tau, clone_b, &m, work, &len, &info);
cblas_strsm(CblasColMajor, CblasLeft, CblasUpper, CblasNoTrans, CblasNonUnit, n, bn, 1.0, clone_r, m, clone_b, m);
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < bn; ++j)
{
x[j * n + i] = clone_b[j * m + i];
}
}
delete[] clone_r;
delete[] tau;
delete[] clone_b;
return info;
}
/* Subroutine */ int sggqrf_(integer *n, integer *m, integer *p, real *a,
integer *lda, real *taua, real *b, integer *ldb, real *taub, real *
work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
/* Local variables */
integer nb, nb1, nb2, nb3, lopt;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *), sgerqf_(integer *,
integer *, real *, integer *, real *, real *, integer *, integer *
);
integer lwkopt;
logical lquery;
extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SGGQRF computes a generalized QR factorization of an N-by-M matrix A */
/* and an N-by-P matrix B: */
/* A = Q*R, B = Q*T*Z, */
/* where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal */
/* matrix, and R and T assume one of the forms: */
/* if N >= M, R = ( R11 ) M , or if N < M, R = ( R11 R12 ) N, */
/* ( 0 ) N-M N M-N */
/* M */
/* where R11 is upper triangular, and */
/* if N <= P, T = ( 0 T12 ) N, or if N > P, T = ( T11 ) N-P, */
/* P-N N ( T21 ) P */
/* P */
/* where T12 or T21 is upper triangular. */
/* In particular, if B is square and nonsingular, the GQR factorization */
/* of A and B implicitly gives the QR factorization of inv(B)*A: */
/* inv(B)*A = Z'*(inv(T)*R) */
/* where inv(B) denotes the inverse of the matrix B, and Z' denotes the */
/* transpose of the matrix Z. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The number of rows of the matrices A and B. N >= 0. */
/* M (input) INTEGER */
/* The number of columns of the matrix A. M >= 0. */
/* P (input) INTEGER */
/* The number of columns of the matrix B. P >= 0. */
/* A (input/output) REAL array, dimension (LDA,M) */
/* On entry, the N-by-M matrix A. */
/* On exit, the elements on and above the diagonal of the array */
/* contain the min(N,M)-by-M upper trapezoidal matrix R (R is */
/* upper triangular if N >= M); the elements below the diagonal, */
/* with the array TAUA, represent the orthogonal matrix Q as a */
/* product of min(N,M) elementary reflectors (see Further */
/* Details). */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* TAUA (output) REAL array, dimension (min(N,M)) */
/* The scalar factors of the elementary reflectors which */
/* represent the orthogonal matrix Q (see Further Details). */
/* B (input/output) REAL array, dimension (LDB,P) */
/* On entry, the N-by-P matrix B. */
/* On exit, if N <= P, the upper triangle of the subarray */
/* B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T; */
/* if N > P, the elements on and above the (N-P)-th subdiagonal */
/* contain the N-by-P upper trapezoidal matrix T; the remaining */
/* elements, with the array TAUB, represent the orthogonal */
/* matrix Z as a product of elementary reflectors (see Further */
/* Details). */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* TAUB (output) REAL array, dimension (min(N,P)) */
/* The scalar factors of the elementary reflectors which */
/* represent the orthogonal matrix Z (see Further Details). */
/* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= max(1,N,M,P). */
/* For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3), */
/* where NB1 is the optimal blocksize for the QR factorization */
/* of an N-by-M matrix, NB2 is the optimal blocksize for the */
/* RQ factorization of an N-by-P matrix, and NB3 is the optimal */
/* blocksize for a call of SORMQR. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* Further Details */
/* =============== */
/* The matrix Q is represented as a product of elementary reflectors */
/* Q = H(1) H(2) . . . H(k), where k = min(n,m). */
/* Each H(i) has the form */
/* H(i) = I - taua * v * v' */
/* where taua is a real scalar, and v is a real vector with */
/* v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */
/* and taua in TAUA(i). */
/* To form Q explicitly, use LAPACK subroutine SORGQR. */
/* To use Q to update another matrix, use LAPACK subroutine SORMQR. */
/* The matrix Z is represented as a product of elementary reflectors */
/* Z = H(1) H(2) . . . H(k), where k = min(n,p). */
/* Each H(i) has the form */
/* H(i) = I - taub * v * v' */
/* where taub is a real scalar, and v is a real vector with */
/* v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in */
/* B(n-k+i,1:p-k+i-1), and taub in TAUB(i). */
/* To form Z explicitly, use LAPACK subroutine SORGRQ. */
/* To use Z to update another matrix, use LAPACK subroutine SORMRQ. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--taua;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--taub;
--work;
/* Function Body */
*info = 0;
nb1 = ilaenv_(&c__1, "SGEQRF", " ", n, m, &c_n1, &c_n1);
nb2 = ilaenv_(&c__1, "SGERQF", " ", n, p, &c_n1, &c_n1);
nb3 = ilaenv_(&c__1, "SORMQR", " ", n, m, p, &c_n1);
/* Computing MAX */
i__1 = max(nb1,nb2);
nb = max(i__1,nb3);
/* Computing MAX */
i__1 = max(*n,*m);
lwkopt = max(i__1,*p) * nb;
work[1] = (real) lwkopt;
lquery = *lwork == -1;
if (*n < 0) {
*info = -1;
} else if (*m < 0) {
*info = -2;
} else if (*p < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -8;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = max(1,*n), i__1 = max(i__1,*m);
if (*lwork < max(i__1,*p) && ! lquery) {
*info = -11;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGGQRF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* QR factorization of N-by-M matrix A: A = Q*R */
sgeqrf_(n, m, &a[a_offset], lda, &taua[1], &work[1], lwork, info);
lopt = work[1];
/* Update B := Q'*B. */
i__1 = min(*n,*m);
sormqr_("Left", "Transpose", n, p, &i__1, &a[a_offset], lda, &taua[1], &b[
b_offset], ldb, &work[1], lwork, info);
/* Computing MAX */
i__1 = lopt, i__2 = (integer) work[1];
lopt = max(i__1,i__2);
/* RQ factorization of N-by-P matrix B: B = T*Z. */
sgerqf_(n, p, &b[b_offset], ldb, &taub[1], &work[1], lwork, info);
/* Computing MAX */
i__1 = lopt, i__2 = (integer) work[1];
work[1] = (real) max(i__1,i__2);
return 0;
/* End of SGGQRF */
} /* sggqrf_ */
/* Subroutine */ int sgges_(char *jobvsl, char *jobvsr, char *sort, L_fp
selctg, integer *n, real *a, integer *lda, real *b, integer *ldb,
integer *sdim, real *alphar, real *alphai, real *beta, real *vsl,
integer *ldvsl, real *vsr, integer *ldvsr, real *work, integer *lwork,
logical *bwork, integer *info)
{
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
SGGES computes for a pair of N-by-N real nonsymmetric matrices (A,B),
the generalized eigenvalues, the generalized real Schur form (S,T),
optionally, the left and/or right matrices of Schur vectors (VSL and
VSR). This gives the generalized Schur factorization
(A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**T )
Optionally, it also orders the eigenvalues so that a selected cluster
of eigenvalues appears in the leading diagonal blocks of the upper
quasi-triangular matrix S and the upper triangular matrix T.The
leading columns of VSL and VSR then form an orthonormal basis for the
corresponding left and right eigenspaces (deflating subspaces).
(If only the generalized eigenvalues are needed, use the driver
SGGEV instead, which is faster.)
A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
or a ratio alpha/beta = w, such that A - w*B is singular. It is
usually represented as the pair (alpha,beta), as there is a
reasonable interpretation for beta=0 or both being zero.
A pair of matrices (S,T) is in generalized real Schur form if T is
upper triangular with non-negative diagonal and S is block upper
triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond
to real generalized eigenvalues, while 2-by-2 blocks of S will be
"standardized" by making the corresponding elements of T have the
form:
[ a 0 ]
[ 0 b ]
and the pair of corresponding 2-by-2 blocks in S and T will have a
complex conjugate pair of generalized eigenvalues.
Arguments
=========
JOBVSL (input) CHARACTER*1
= 'N': do not compute the left Schur vectors;
= 'V': compute the left Schur vectors.
JOBVSR (input) CHARACTER*1
= 'N': do not compute the right Schur vectors;
= 'V': compute the right Schur vectors.
SORT (input) CHARACTER*1
Specifies whether or not to order the eigenvalues on the
diagonal of the generalized Schur form.
= 'N': Eigenvalues are not ordered;
= 'S': Eigenvalues are ordered (see SELCTG);
SELCTG (input) LOGICAL FUNCTION of three REAL arguments
SELCTG must be declared EXTERNAL in the calling subroutine.
If SORT = 'N', SELCTG is not referenced.
If SORT = 'S', SELCTG is used to select eigenvalues to sort
to the top left of the Schur form.
An eigenvalue (ALPHAR(j)+ALPHAI(j))/BETA(j) is selected if
SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) is true; i.e. if either
one of a complex conjugate pair of eigenvalues is selected,
then both complex eigenvalues are selected.
Note that in the ill-conditioned case, a selected complex
eigenvalue may no longer satisfy SELCTG(ALPHAR(j),ALPHAI(j),
BETA(j)) = .TRUE. after ordering. INFO is to be set to N+2
in this case.
N (input) INTEGER
The order of the matrices A, B, VSL, and VSR. N >= 0.
A (input/output) REAL array, dimension (LDA, N)
On entry, the first of the pair of matrices.
On exit, A has been overwritten by its generalized Schur
form S.
LDA (input) INTEGER
The leading dimension of A. LDA >= max(1,N).
B (input/output) REAL array, dimension (LDB, N)
On entry, the second of the pair of matrices.
On exit, B has been overwritten by its generalized Schur
form T.
LDB (input) INTEGER
The leading dimension of B. LDB >= max(1,N).
SDIM (output) INTEGER
If SORT = 'N', SDIM = 0.
If SORT = 'S', SDIM = number of eigenvalues (after sorting)
for which SELCTG is true. (Complex conjugate pairs for which
SELCTG is true for either eigenvalue count as 2.)
ALPHAR (output) REAL array, dimension (N)
ALPHAI (output) REAL array, dimension (N)
BETA (output) REAL array, dimension (N)
On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
be the generalized eigenvalues. ALPHAR(j) + ALPHAI(j)*i,
and BETA(j),j=1,...,N are the diagonals of the complex Schur
form (S,T) that would result if the 2-by-2 diagonal blocks of
the real Schur form of (A,B) were further reduced to
triangular form using 2-by-2 complex unitary transformations.
If ALPHAI(j) is zero, then the j-th eigenvalue is real; if
positive, then the j-th and (j+1)-st eigenvalues are a
complex conjugate pair, with ALPHAI(j+1) negative.
Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
may easily over- or underflow, and BETA(j) may even be zero.
Thus, the user should avoid naively computing the ratio.
However, ALPHAR and ALPHAI will be always less than and
usually comparable with norm(A) in magnitude, and BETA always
less than and usually comparable with norm(B).
VSL (output) REAL array, dimension (LDVSL,N)
If JOBVSL = 'V', VSL will contain the left Schur vectors.
Not referenced if JOBVSL = 'N'.
LDVSL (input) INTEGER
The leading dimension of the matrix VSL. LDVSL >=1, and
if JOBVSL = 'V', LDVSL >= N.
VSR (output) REAL array, dimension (LDVSR,N)
If JOBVSR = 'V', VSR will contain the right Schur vectors.
Not referenced if JOBVSR = 'N'.
LDVSR (input) INTEGER
The leading dimension of the matrix VSR. LDVSR >= 1, and
if JOBVSR = 'V', LDVSR >= N.
WORK (workspace/output) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= 8*N+16.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
BWORK (workspace) LOGICAL array, dimension (N)
Not referenced if SORT = 'N'.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
= 1,...,N:
The QZ iteration failed. (A,B) are not in Schur
form, but ALPHAR(j), ALPHAI(j), and BETA(j) should
be correct for j=INFO+1,...,N.
> N: =N+1: other than QZ iteration failed in SHGEQZ.
=N+2: after reordering, roundoff changed values of
some complex eigenvalues so that leading
eigenvalues in the Generalized Schur form no
longer satisfy SELCTG=.TRUE. This could also
be caused due to scaling.
=N+3: reordering failed in STGSEN.
=====================================================================
Decode the input arguments
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static integer c__0 = 0;
static integer c_n1 = -1;
static real c_b33 = 0.f;
static real c_b34 = 1.f;
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset,
vsr_dim1, vsr_offset, i__1, i__2;
real r__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static real anrm, bnrm;
static integer idum[1], ierr, itau, iwrk;
static real pvsl, pvsr;
static integer i__;
extern logical lsame_(char *, char *);
static integer ileft, icols;
static logical cursl, ilvsl, ilvsr;
static integer irows;
static logical lst2sl;
extern /* Subroutine */ int slabad_(real *, real *);
static integer ip;
extern /* Subroutine */ int sggbak_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, real *, integer *, integer *
), sggbal_(char *, integer *, real *, integer *,
real *, integer *, integer *, integer *, real *, real *, real *,
integer *);
static logical ilascl, ilbscl;
extern doublereal slamch_(char *), slange_(char *, integer *,
integer *, real *, integer *, real *);
static real safmin;
extern /* Subroutine */ int sgghrd_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, integer *, real *, integer *
, real *, integer *, integer *);
static real safmax;
extern /* Subroutine */ int xerbla_(char *, integer *);
static real bignum;
extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, real *, integer *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static integer ijobvl, iright;
extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *);
static integer ijobvr;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), slaset_(char *, integer *,
integer *, real *, real *, real *, integer *);
static real anrmto, bnrmto;
static logical lastsl;
extern /* Subroutine */ int shgeqz_(char *, char *, char *, integer *,
integer *, integer *, real *, integer *, real *, integer *, real *
, real *, real *, real *, integer *, real *, integer *, real *,
integer *, integer *), stgsen_(integer *,
logical *, logical *, logical *, integer *, real *, integer *,
real *, integer *, real *, real *, real *, real *, integer *,
real *, integer *, integer *, real *, real *, real *, real *,
integer *, integer *, integer *, integer *);
static integer minwrk, maxwrk;
static real smlnum;
extern /* Subroutine */ int sorgqr_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *, integer *);
static logical wantst, lquery;
extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
static real dif[2];
static integer ihi, ilo;
static real eps;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
#define vsl_ref(a_1,a_2) vsl[(a_2)*vsl_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--alphar;
--alphai;
--beta;
vsl_dim1 = *ldvsl;
vsl_offset = 1 + vsl_dim1 * 1;
vsl -= vsl_offset;
vsr_dim1 = *ldvsr;
vsr_offset = 1 + vsr_dim1 * 1;
vsr -= vsr_offset;
--work;
--bwork;
/* Function Body */
if (lsame_(jobvsl, "N")) {
ijobvl = 1;
ilvsl = FALSE_;
} else if (lsame_(jobvsl, "V")) {
ijobvl = 2;
ilvsl = TRUE_;
} else {
ijobvl = -1;
ilvsl = FALSE_;
}
if (lsame_(jobvsr, "N")) {
ijobvr = 1;
ilvsr = FALSE_;
} else if (lsame_(jobvsr, "V")) {
ijobvr = 2;
ilvsr = TRUE_;
} else {
ijobvr = -1;
ilvsr = FALSE_;
}
wantst = lsame_(sort, "S");
/* Test the input arguments */
*info = 0;
lquery = *lwork == -1;
if (ijobvl <= 0) {
*info = -1;
} else if (ijobvr <= 0) {
*info = -2;
} else if (! wantst && ! lsame_(sort, "N")) {
*info = -3;
} else if (*n < 0) {
*info = -5;
} else if (*lda < max(1,*n)) {
*info = -7;
} else if (*ldb < max(1,*n)) {
*info = -9;
} else if (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
*info = -15;
} else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
*info = -17;
}
/* Compute workspace
(Note: Comments in the code beginning "Workspace:" describe the
minimal amount of workspace needed at that point in the code,
as well as the preferred amount for good performance.
NB refers to the optimal block size for the immediately
following subroutine, as returned by ILAENV.) */
minwrk = 1;
if (*info == 0 && (*lwork >= 1 || lquery)) {
minwrk = (*n + 1) * 7 + 16;
maxwrk = (*n + 1) * 7 + *n * ilaenv_(&c__1, "SGEQRF", " ", n, &c__1,
n, &c__0, (ftnlen)6, (ftnlen)1) + 16;
if (ilvsl) {
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n + 1) * 7 + *n * ilaenv_(&c__1, "SORGQR",
" ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
}
work[1] = (real) maxwrk;
}
if (*lwork < minwrk && ! lquery) {
*info = -19;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGGES ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
*sdim = 0;
return 0;
}
/* Get machine constants */
eps = slamch_("P");
safmin = slamch_("S");
safmax = 1.f / safmin;
slabad_(&safmin, &safmax);
smlnum = sqrt(safmin) / eps;
bignum = 1.f / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = slange_("M", n, n, &a[a_offset], lda, &work[1]);
ilascl = FALSE_;
if (anrm > 0.f && anrm < smlnum) {
anrmto = smlnum;
ilascl = TRUE_;
} else if (anrm > bignum) {
anrmto = bignum;
ilascl = TRUE_;
}
if (ilascl) {
slascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
ierr);
}
/* Scale B if max element outside range [SMLNUM,BIGNUM] */
bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]);
ilbscl = FALSE_;
if (bnrm > 0.f && bnrm < smlnum) {
bnrmto = smlnum;
ilbscl = TRUE_;
} else if (bnrm > bignum) {
bnrmto = bignum;
ilbscl = TRUE_;
}
if (ilbscl) {
slascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
ierr);
}
/* Permute the matrix to make it more nearly triangular
(Workspace: need 6*N + 2*N space for storing balancing factors) */
ileft = 1;
iright = *n + 1;
iwrk = iright + *n;
sggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
ileft], &work[iright], &work[iwrk], &ierr);
/* Reduce B to triangular form (QR decomposition of B)
(Workspace: need N, prefer N*NB) */
irows = ihi + 1 - ilo;
icols = *n + 1 - ilo;
itau = iwrk;
iwrk = itau + irows;
i__1 = *lwork + 1 - iwrk;
sgeqrf_(&irows, &icols, &b_ref(ilo, ilo), ldb, &work[itau], &work[iwrk], &
i__1, &ierr);
/* Apply the orthogonal transformation to matrix A
(Workspace: need N, prefer N*NB) */
i__1 = *lwork + 1 - iwrk;
sormqr_("L", "T", &irows, &icols, &irows, &b_ref(ilo, ilo), ldb, &work[
itau], &a_ref(ilo, ilo), lda, &work[iwrk], &i__1, &ierr);
/* Initialize VSL
(Workspace: need N, prefer N*NB) */
if (ilvsl) {
slaset_("Full", n, n, &c_b33, &c_b34, &vsl[vsl_offset], ldvsl);
i__1 = irows - 1;
i__2 = irows - 1;
slacpy_("L", &i__1, &i__2, &b_ref(ilo + 1, ilo), ldb, &vsl_ref(ilo +
1, ilo), ldvsl);
i__1 = *lwork + 1 - iwrk;
sorgqr_(&irows, &irows, &irows, &vsl_ref(ilo, ilo), ldvsl, &work[itau]
, &work[iwrk], &i__1, &ierr);
}
/* Initialize VSR */
if (ilvsr) {
slaset_("Full", n, n, &c_b33, &c_b34, &vsr[vsr_offset], ldvsr);
}
/* Reduce to generalized Hessenberg form
(Workspace: none needed) */
sgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &ierr);
/* Perform QZ algorithm, computing Schur vectors if desired
(Workspace: need N) */
iwrk = itau;
i__1 = *lwork + 1 - iwrk;
shgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[
b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[vsl_offset]
, ldvsl, &vsr[vsr_offset], ldvsr, &work[iwrk], &i__1, &ierr);
if (ierr != 0) {
if (ierr > 0 && ierr <= *n) {
*info = ierr;
} else if (ierr > *n && ierr <= *n << 1) {
*info = ierr - *n;
} else {
*info = *n + 1;
}
goto L40;
}
/* Sort eigenvalues ALPHA/BETA if desired
(Workspace: need 4*N+16 ) */
*sdim = 0;
if (wantst) {
/* Undo scaling on eigenvalues before SELCTGing */
if (ilascl) {
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1],
n, &ierr);
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1],
n, &ierr);
}
if (ilbscl) {
slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n,
&ierr);
}
/* Select eigenvalues */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
bwork[i__] = (*selctg)(&alphar[i__], &alphai[i__], &beta[i__]);
/* L10: */
}
i__1 = *lwork - iwrk + 1;
stgsen_(&c__0, &ilvsl, &ilvsr, &bwork[1], n, &a[a_offset], lda, &b[
b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[
vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, sdim, &pvsl, &
pvsr, dif, &work[iwrk], &i__1, idum, &c__1, &ierr);
if (ierr == 1) {
*info = *n + 3;
}
}
/* Apply back-permutation to VSL and VSR
(Workspace: none needed) */
if (ilvsl) {
sggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsl[
vsl_offset], ldvsl, &ierr);
}
if (ilvsr) {
sggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsr[
vsr_offset], ldvsr, &ierr);
}
/* Check if unscaling would cause over/underflow, if so, rescale
(ALPHAR(I),ALPHAI(I),BETA(I)) so BETA(I) is on the order of
B(I,I) and ALPHAR(I) and ALPHAI(I) are on the order of A(I,I) */
if (ilascl) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (alphai[i__] != 0.f) {
if (alphar[i__] / safmax > anrmto / anrm || safmin / alphar[
i__] > anrm / anrmto) {
work[1] = (r__1 = a_ref(i__, i__) / alphar[i__], dabs(
r__1));
beta[i__] *= work[1];
alphar[i__] *= work[1];
alphai[i__] *= work[1];
} else if (alphai[i__] / safmax > anrmto / anrm || safmin /
alphai[i__] > anrm / anrmto) {
work[1] = (r__1 = a_ref(i__, i__ + 1) / alphai[i__], dabs(
r__1));
beta[i__] *= work[1];
alphar[i__] *= work[1];
alphai[i__] *= work[1];
}
}
/* L50: */
}
}
if (ilbscl) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (alphai[i__] != 0.f) {
if (beta[i__] / safmax > bnrmto / bnrm || safmin / beta[i__]
> bnrm / bnrmto) {
work[1] = (r__1 = b_ref(i__, i__) / beta[i__], dabs(r__1))
;
beta[i__] *= work[1];
alphar[i__] *= work[1];
alphai[i__] *= work[1];
}
}
/* L60: */
}
}
/* Undo scaling */
if (ilascl) {
slascl_("H", &c__0, &c__0, &anrmto, &anrm, n, n, &a[a_offset], lda, &
ierr);
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
ierr);
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
ierr);
}
if (ilbscl) {
slascl_("U", &c__0, &c__0, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
ierr);
slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
ierr);
}
if (wantst) {
/* Check if reordering is correct */
lastsl = TRUE_;
lst2sl = TRUE_;
*sdim = 0;
ip = 0;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
cursl = (*selctg)(&alphar[i__], &alphai[i__], &beta[i__]);
if (alphai[i__] == 0.f) {
if (cursl) {
++(*sdim);
}
ip = 0;
if (cursl && ! lastsl) {
*info = *n + 2;
}
} else {
if (ip == 1) {
/* Last eigenvalue of conjugate pair */
cursl = cursl || lastsl;
lastsl = cursl;
if (cursl) {
*sdim += 2;
}
ip = -1;
if (cursl && ! lst2sl) {
*info = *n + 2;
}
} else {
/* First eigenvalue of conjugate pair */
ip = 1;
}
}
lst2sl = lastsl;
lastsl = cursl;
/* L30: */
}
}
L40:
work[1] = (real) maxwrk;
return 0;
/* End of SGGES */
} /* sgges_ */
/* Subroutine */ int stimqr_(char *line, integer *nm, integer *mval, integer *
nval, integer *nk, integer *kval, integer *nnb, integer *nbval,
integer *nxval, integer *nlda, integer *ldaval, real *timmin, real *a,
real *tau, real *b, real *work, real *reslts, integer *ldr1, integer
*ldr2, integer *ldr3, integer *nout, ftnlen line_len)
{
/* Initialized data */
static char subnam[6*3] = "SGEQRF" "SORGQR" "SORMQR";
static char sides[1*2] = "L" "R";
static char transs[1*2] = "N" "T";
static integer iseed[4] = { 0,0,0,1 };
/* Format strings */
static char fmt_9999[] = "(1x,a6,\002 timing run not attempted\002,/)";
static char fmt_9998[] = "(/\002 *** Speed of \002,a6,\002 in megaflops "
"***\002)";
static char fmt_9997[] = "(5x,\002line \002,i2,\002 with LDA = \002,i5)";
static char fmt_9996[] = "(5x,\002K = min(M,N)\002,/)";
static char fmt_9995[] = "(/5x,a6,\002 with SIDE = '\002,a1,\002', TRANS"
" = '\002,a1,\002', \002,a1,\002 =\002,i6,/)";
static char fmt_9994[] = "(\002 *** No pairs (M,N) found with M >= N: "
" \002,a6,\002 not timed\002)";
/* System generated locals */
integer reslts_dim1, reslts_dim2, reslts_dim3, reslts_offset, i__1, i__2,
i__3, i__4, i__5, i__6;
/* Builtin functions
Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void),
s_wsle(cilist *), e_wsle(void);
/* Local variables */
static integer ilda;
static char labm[1], side[1];
static integer info;
static char path[3];
static real time;
static integer isub, muse[12], nuse[12], i__, k, m, n;
static char cname[6];
static integer iside, itoff, itran, minmn;
extern doublereal sopla_(char *, integer *, integer *, integer *, integer
*, integer *);
extern /* Subroutine */ int icopy_(integer *, integer *, integer *,
integer *, integer *);
static char trans[1];
static integer k1, i4, m1, n1;
static real s1, s2;
static integer ic;
extern /* Subroutine */ int sprtb4_(char *, char *, char *, integer *,
integer *, integer *, integer *, integer *, integer *, integer *,
real *, integer *, integer *, integer *, ftnlen, ftnlen, ftnlen),
sprtb5_(char *, char *, char *, integer *, integer *, integer *,
integer *, integer *, integer *, real *, integer *, integer *,
integer *, ftnlen, ftnlen, ftnlen);
static integer nb, ik, im, lw, nx, reseed[4];
extern /* Subroutine */ int atimck_(integer *, char *, integer *, integer
*, integer *, integer *, integer *, integer *, ftnlen);
extern doublereal second_(void);
extern /* Subroutine */ int atimin_(char *, char *, integer *, char *,
logical *, integer *, integer *, ftnlen, ftnlen, ftnlen), sgeqrf_(
integer *, integer *, real *, integer *, real *, real *, integer *
, integer *), slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), xlaenv_(integer *, integer
*);
extern doublereal smflop_(real *, real *, integer *);
static real untime;
extern /* Subroutine */ int stimmg_(integer *, integer *, integer *, real
*, integer *, integer *, integer *);
static logical timsub[3];
extern /* Subroutine */ int slatms_(integer *, integer *, char *, integer
*, char *, real *, integer *, real *, real *, integer *, integer *
, char *, real *, integer *, real *, integer *), sorgqr_(integer *, integer *, integer *, real *, integer
*, real *, real *, integer *, integer *), sormqr_(char *, char *,
integer *, integer *, integer *, real *, integer *, real *, real *
, integer *, real *, integer *, integer *);
static integer lda, icl, inb, imx;
static real ops;
/* Fortran I/O blocks */
static cilist io___9 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___29 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___31 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___32 = { 0, 0, 0, 0, 0 };
static cilist io___33 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___34 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___49 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___53 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___54 = { 0, 0, 0, fmt_9994, 0 };
#define subnam_ref(a_0,a_1) &subnam[(a_1)*6 + a_0 - 6]
#define reslts_ref(a_1,a_2,a_3,a_4) reslts[(((a_4)*reslts_dim3 + (a_3))*\
reslts_dim2 + (a_2))*reslts_dim1 + a_1]
/* -- LAPACK timing routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
March 31, 1993
Purpose
=======
STIMQR times the LAPACK routines to perform the QR factorization of
a REAL general matrix.
Arguments
=========
LINE (input) CHARACTER*80
The input line that requested this routine. The first six
characters contain either the name of a subroutine or a
generic path name. The remaining characters may be used to
specify the individual routines to be timed. See ATIMIN for
a full description of the format of the input line.
NM (input) INTEGER
The number of values of M and N contained in the vectors
MVAL and NVAL. The matrix sizes are used in pairs (M,N).
MVAL (input) INTEGER array, dimension (NM)
The values of the matrix row dimension M.
NVAL (input) INTEGER array, dimension (NM)
The values of the matrix column dimension N.
NK (input) INTEGER
The number of values of K in the vector KVAL.
KVAL (input) INTEGER array, dimension (NK)
The values of the matrix dimension K, used in SORMQR.
NNB (input) INTEGER
The number of values of NB and NX contained in the
vectors NBVAL and NXVAL. The blocking parameters are used
in pairs (NB,NX).
NBVAL (input) INTEGER array, dimension (NNB)
The values of the blocksize NB.
NXVAL (input) INTEGER array, dimension (NNB)
The values of the crossover point NX.
NLDA (input) INTEGER
The number of values of LDA contained in the vector LDAVAL.
LDAVAL (input) INTEGER array, dimension (NLDA)
The values of the leading dimension of the array A.
TIMMIN (input) REAL
The minimum time a subroutine will be timed.
A (workspace) REAL array, dimension (LDAMAX*NMAX)
where LDAMAX and NMAX are the maximum values of LDA and N.
TAU (workspace) REAL array, dimension (min(M,N))
B (workspace) REAL array, dimension (LDAMAX*NMAX)
WORK (workspace) REAL array, dimension (LDAMAX*NBMAX)
where NBMAX is the maximum value of NB.
RESLTS (workspace) REAL array, dimension
(LDR1,LDR2,LDR3,2*NK)
The timing results for each subroutine over the relevant
values of (M,N), (NB,NX), and LDA.
LDR1 (input) INTEGER
The first dimension of RESLTS. LDR1 >= max(1,NNB).
LDR2 (input) INTEGER
The second dimension of RESLTS. LDR2 >= max(1,NM).
LDR3 (input) INTEGER
The third dimension of RESLTS. LDR3 >= max(1,NLDA).
NOUT (input) INTEGER
The unit number for output.
Internal Parameters
===================
MODE INTEGER
The matrix type. MODE = 3 is a geometric distribution of
eigenvalues. See SLATMS for further details.
COND REAL
The condition number of the matrix. The singular values are
set to values from DMAX to DMAX/COND.
DMAX REAL
The magnitude of the largest singular value.
=====================================================================
Parameter adjustments */
--mval;
--nval;
--kval;
--nbval;
--nxval;
--ldaval;
--a;
--tau;
--b;
--work;
reslts_dim1 = *ldr1;
reslts_dim2 = *ldr2;
reslts_dim3 = *ldr3;
reslts_offset = 1 + reslts_dim1 * (1 + reslts_dim2 * (1 + reslts_dim3 * 1)
);
reslts -= reslts_offset;
/* Function Body
Extract the timing request from the input line. */
s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16);
s_copy(path + 1, "QR", (ftnlen)2, (ftnlen)2);
atimin_(path, line, &c__3, subnam, timsub, nout, &info, (ftnlen)3, (
ftnlen)80, (ftnlen)6);
if (info != 0) {
goto L230;
}
/* Check that M <= LDA for the input values. */
s_copy(cname, line, (ftnlen)6, (ftnlen)6);
atimck_(&c__1, cname, nm, &mval[1], nlda, &ldaval[1], nout, &info, (
ftnlen)6);
if (info > 0) {
io___9.ciunit = *nout;
s_wsfe(&io___9);
do_fio(&c__1, cname, (ftnlen)6);
e_wsfe();
goto L230;
}
/* Do for each pair of values (M,N): */
i__1 = *nm;
for (im = 1; im <= i__1; ++im) {
m = mval[im];
n = nval[im];
minmn = min(m,n);
icopy_(&c__4, iseed, &c__1, reseed, &c__1);
/* Do for each value of LDA: */
i__2 = *nlda;
for (ilda = 1; ilda <= i__2; ++ilda) {
lda = ldaval[ilda];
/* Do for each pair of values (NB, NX) in NBVAL and NXVAL. */
i__3 = *nnb;
for (inb = 1; inb <= i__3; ++inb) {
nb = nbval[inb];
xlaenv_(&c__1, &nb);
nx = nxval[inb];
xlaenv_(&c__3, &nx);
/* Computing MAX */
i__4 = 1, i__5 = n * max(1,nb);
lw = max(i__4,i__5);
/* Generate a test matrix of size M by N. */
icopy_(&c__4, reseed, &c__1, iseed, &c__1);
slatms_(&m, &n, "Uniform", iseed, "Nonsymm", &tau[1], &c__3, &
c_b24, &c_b25, &m, &n, "No packing", &b[1], &lda, &
work[1], &info);
if (timsub[0]) {
/* SGEQRF: QR factorization */
slacpy_("Full", &m, &n, &b[1], &lda, &a[1], &lda);
ic = 0;
s1 = second_();
L10:
sgeqrf_(&m, &n, &a[1], &lda, &tau[1], &work[1], &lw, &
info);
s2 = second_();
time = s2 - s1;
++ic;
if (time < *timmin) {
slacpy_("Full", &m, &n, &b[1], &lda, &a[1], &lda);
goto L10;
}
/* Subtract the time used in SLACPY. */
icl = 1;
s1 = second_();
L20:
s2 = second_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
slacpy_("Full", &m, &n, &a[1], &lda, &b[1], &lda);
goto L20;
}
time = (time - untime) / (real) ic;
ops = sopla_("SGEQRF", &m, &n, &c__0, &c__0, &nb);
reslts_ref(inb, im, ilda, 1) = smflop_(&ops, &time, &info)
;
} else {
/* If SGEQRF was not timed, generate a matrix and factor
it using SGEQRF anyway so that the factored form of
the matrix can be used in timing the other routines. */
slacpy_("Full", &m, &n, &b[1], &lda, &a[1], &lda);
sgeqrf_(&m, &n, &a[1], &lda, &tau[1], &work[1], &lw, &
info);
}
if (timsub[1]) {
/* SORGQR: Generate orthogonal matrix Q from the QR
factorization */
slacpy_("Full", &m, &minmn, &a[1], &lda, &b[1], &lda);
ic = 0;
s1 = second_();
L30:
sorgqr_(&m, &minmn, &minmn, &b[1], &lda, &tau[1], &work[1]
, &lw, &info);
s2 = second_();
time = s2 - s1;
++ic;
if (time < *timmin) {
slacpy_("Full", &m, &minmn, &a[1], &lda, &b[1], &lda);
goto L30;
}
/* Subtract the time used in SLACPY. */
icl = 1;
s1 = second_();
L40:
s2 = second_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
slacpy_("Full", &m, &minmn, &a[1], &lda, &b[1], &lda);
goto L40;
}
time = (time - untime) / (real) ic;
ops = sopla_("SORGQR", &m, &minmn, &minmn, &c__0, &nb);
reslts_ref(inb, im, ilda, 2) = smflop_(&ops, &time, &info)
;
}
/* L50: */
}
/* L60: */
}
/* L70: */
}
/* Print tables of results */
for (isub = 1; isub <= 2; ++isub) {
if (! timsub[isub - 1]) {
goto L90;
}
io___29.ciunit = *nout;
s_wsfe(&io___29);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
e_wsfe();
if (*nlda > 1) {
i__1 = *nlda;
for (i__ = 1; i__ <= i__1; ++i__) {
io___31.ciunit = *nout;
s_wsfe(&io___31);
do_fio(&c__1, (char *)&i__, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ldaval[i__], (ftnlen)sizeof(integer));
e_wsfe();
/* L80: */
}
}
io___32.ciunit = *nout;
s_wsle(&io___32);
e_wsle();
if (isub == 2) {
io___33.ciunit = *nout;
s_wsfe(&io___33);
e_wsfe();
}
sprtb4_("( NB, NX)", "M", "N", nnb, &nbval[1], &nxval[1], nm, &mval[
1], &nval[1], nlda, &reslts_ref(1, 1, 1, isub), ldr1, ldr2,
nout, (ftnlen)11, (ftnlen)1, (ftnlen)1);
L90:
;
}
/* Time SORMQR separately. Here the starting matrix is M by N, and
K is the free dimension of the matrix multiplied by Q. */
if (timsub[2]) {
/* Check that K <= LDA for the input values. */
atimck_(&c__3, cname, nk, &kval[1], nlda, &ldaval[1], nout, &info, (
ftnlen)6);
if (info > 0) {
io___34.ciunit = *nout;
s_wsfe(&io___34);
do_fio(&c__1, subnam_ref(0, 3), (ftnlen)6);
e_wsfe();
goto L230;
}
/* Use only the pairs (M,N) where M >= N. */
imx = 0;
i__1 = *nm;
for (im = 1; im <= i__1; ++im) {
if (mval[im] >= nval[im]) {
++imx;
muse[imx - 1] = mval[im];
nuse[imx - 1] = nval[im];
}
/* L100: */
}
/* SORMQR: Multiply by Q stored as a product of elementary
transformations
Do for each pair of values (M,N): */
i__1 = imx;
for (im = 1; im <= i__1; ++im) {
m = muse[im - 1];
n = nuse[im - 1];
/* Do for each value of LDA: */
i__2 = *nlda;
for (ilda = 1; ilda <= i__2; ++ilda) {
lda = ldaval[ilda];
/* Generate an M by N matrix and form its QR decomposition. */
slatms_(&m, &n, "Uniform", iseed, "Nonsymm", &tau[1], &c__3, &
c_b24, &c_b25, &m, &n, "No packing", &a[1], &lda, &
work[1], &info);
/* Computing MAX */
i__3 = 1, i__4 = n * max(1,nb);
lw = max(i__3,i__4);
sgeqrf_(&m, &n, &a[1], &lda, &tau[1], &work[1], &lw, &info);
/* Do first for SIDE = 'L', then for SIDE = 'R' */
i4 = 0;
for (iside = 1; iside <= 2; ++iside) {
*(unsigned char *)side = *(unsigned char *)&sides[iside -
1];
/* Do for each pair of values (NB, NX) in NBVAL and
NXVAL. */
i__3 = *nnb;
for (inb = 1; inb <= i__3; ++inb) {
nb = nbval[inb];
xlaenv_(&c__1, &nb);
nx = nxval[inb];
xlaenv_(&c__3, &nx);
/* Do for each value of K in KVAL */
i__4 = *nk;
for (ik = 1; ik <= i__4; ++ik) {
k = kval[ik];
/* Sort out which variable is which */
if (iside == 1) {
m1 = m;
k1 = n;
n1 = k;
/* Computing MAX */
i__5 = 1, i__6 = n1 * max(1,nb);
lw = max(i__5,i__6);
} else {
n1 = m;
k1 = n;
m1 = k;
/* Computing MAX */
i__5 = 1, i__6 = m1 * max(1,nb);
lw = max(i__5,i__6);
}
/* Do first for TRANS = 'N', then for TRANS = 'T' */
itoff = 0;
for (itran = 1; itran <= 2; ++itran) {
*(unsigned char *)trans = *(unsigned char *)&
transs[itran - 1];
stimmg_(&c__0, &m1, &n1, &b[1], &lda, &c__0, &
c__0);
ic = 0;
s1 = second_();
L110:
sormqr_(side, trans, &m1, &n1, &k1, &a[1], &
lda, &tau[1], &b[1], &lda, &work[1], &
lw, &info);
s2 = second_();
time = s2 - s1;
++ic;
if (time < *timmin) {
stimmg_(&c__0, &m1, &n1, &b[1], &lda, &
c__0, &c__0);
goto L110;
}
/* Subtract the time used in STIMMG. */
icl = 1;
s1 = second_();
L120:
s2 = second_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
stimmg_(&c__0, &m1, &n1, &b[1], &lda, &
c__0, &c__0);
goto L120;
}
time = (time - untime) / (real) ic;
i__5 = iside - 1;
ops = sopla_("SORMQR", &m1, &n1, &k1, &i__5, &
nb);
reslts_ref(inb, im, ilda, i4 + itoff + ik) =
smflop_(&ops, &time, &info);
itoff = *nk;
/* L130: */
}
/* L140: */
}
/* L150: */
}
i4 = *nk << 1;
/* L160: */
}
/* L170: */
}
/* L180: */
}
/* Print tables of results */
isub = 3;
i4 = 1;
if (imx >= 1) {
for (iside = 1; iside <= 2; ++iside) {
*(unsigned char *)side = *(unsigned char *)&sides[iside - 1];
if (iside == 1) {
io___49.ciunit = *nout;
s_wsfe(&io___49);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
e_wsfe();
if (*nlda > 1) {
i__1 = *nlda;
for (i__ = 1; i__ <= i__1; ++i__) {
io___50.ciunit = *nout;
s_wsfe(&io___50);
do_fio(&c__1, (char *)&i__, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&ldaval[i__], (ftnlen)
sizeof(integer));
e_wsfe();
/* L190: */
}
}
}
for (itran = 1; itran <= 2; ++itran) {
*(unsigned char *)trans = *(unsigned char *)&transs[itran
- 1];
i__1 = *nk;
for (ik = 1; ik <= i__1; ++ik) {
if (iside == 1) {
n = kval[ik];
io___51.ciunit = *nout;
s_wsfe(&io___51);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
do_fio(&c__1, side, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, "N", (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
e_wsfe();
*(unsigned char *)labm = 'M';
} else {
m = kval[ik];
io___53.ciunit = *nout;
s_wsfe(&io___53);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
do_fio(&c__1, side, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, "M", (ftnlen)1);
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer))
;
e_wsfe();
*(unsigned char *)labm = 'N';
}
sprtb5_("NB", labm, "K", nnb, &nbval[1], &imx, muse,
nuse, nlda, &reslts_ref(1, 1, 1, i4), ldr1,
ldr2, nout, (ftnlen)2, (ftnlen)1, (ftnlen)1);
++i4;
/* L200: */
}
/* L210: */
}
/* L220: */
}
} else {
io___54.ciunit = *nout;
s_wsfe(&io___54);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
e_wsfe();
}
}
L230:
return 0;
/* End of STIMQR */
} /* stimqr_ */
/* Subroutine */ int sgels_(char *trans, integer *m, integer *n, integer *
nrhs, real *a, integer *lda, real *b, integer *ldb, real *work,
integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
/* Local variables */
integer i__, j, nb, mn;
real anrm, bnrm;
integer brow;
logical tpsd;
integer iascl, ibscl;
extern logical lsame_(char *, char *);
integer wsize;
real rwork[1];
extern /* Subroutine */ int slabad_(real *, real *);
extern doublereal slamch_(char *), slange_(char *, integer *,
integer *, real *, integer *, real *);
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
integer scllen;
real bignum;
extern /* Subroutine */ int sgelqf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *), slascl_(char *, integer
*, integer *, real *, real *, integer *, integer *, real *,
integer *, integer *), sgeqrf_(integer *, integer *, real
*, integer *, real *, real *, integer *, integer *), slaset_(char
*, integer *, integer *, real *, real *, real *, integer *);
real smlnum;
extern /* Subroutine */ int sormlq_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
logical lquery;
extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *), strtrs_(char *, char *,
char *, integer *, integer *, real *, integer *, real *, integer *
, integer *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SGELS solves overdetermined or underdetermined real linear systems */
/* involving an M-by-N matrix A, or its transpose, using a QR or LQ */
/* factorization of A. It is assumed that A has full rank. */
/* The following options are provided: */
/* 1. If TRANS = 'N' and m >= n: find the least squares solution of */
/* an overdetermined system, i.e., solve the least squares problem */
/* minimize || B - A*X ||. */
/* 2. If TRANS = 'N' and m < n: find the minimum norm solution of */
/* an underdetermined system A * X = B. */
/* 3. If TRANS = 'T' and m >= n: find the minimum norm solution of */
/* an undetermined system A**T * X = B. */
/* 4. If TRANS = 'T' and m < n: find the least squares solution of */
/* an overdetermined system, i.e., solve the least squares problem */
/* minimize || B - A**T * X ||. */
/* Several right hand side vectors b and solution vectors x can be */
/* handled in a single call; they are stored as the columns of the */
/* M-by-NRHS right hand side matrix B and the N-by-NRHS solution */
/* matrix X. */
/* Arguments */
/* ========= */
/* TRANS (input) CHARACTER*1 */
/* = 'N': the linear system involves A; */
/* = 'T': the linear system involves A**T. */
/* M (input) INTEGER */
/* The number of rows of the matrix A. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of */
/* columns of the matrices B and X. NRHS >=0. */
/* A (input/output) REAL array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, */
/* if M >= N, A is overwritten by details of its QR */
/* factorization as returned by SGEQRF; */
/* if M < N, A is overwritten by details of its LQ */
/* factorization as returned by SGELQF. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* B (input/output) REAL array, dimension (LDB,NRHS) */
/* On entry, the matrix B of right hand side vectors, stored */
/* columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS */
/* if TRANS = 'T'. */
/* On exit, if INFO = 0, B is overwritten by the solution */
/* vectors, stored columnwise: */
/* if TRANS = 'N' and m >= n, rows 1 to n of B contain the least */
/* squares solution vectors; the residual sum of squares for the */
/* solution in each column is given by the sum of squares of */
/* elements N+1 to M in that column; */
/* if TRANS = 'N' and m < n, rows 1 to N of B contain the */
/* minimum norm solution vectors; */
/* if TRANS = 'T' and m >= n, rows 1 to M of B contain the */
/* minimum norm solution vectors; */
/* if TRANS = 'T' and m < n, rows 1 to M of B contain the */
/* least squares solution vectors; the residual sum of squares */
/* for the solution in each column is given by the sum of */
/* squares of elements M+1 to N in that column. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= MAX(1,M,N). */
/* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. */
/* LWORK >= max( 1, MN + max( MN, NRHS ) ). */
/* For optimal performance, */
/* LWORK >= max( 1, MN + max( MN, NRHS )*NB ). */
/* where MN = min(M,N) and NB is the optimum block size. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, the i-th diagonal element of the */
/* triangular factor of A is zero, so that A does not have */
/* full rank; the least squares solution could not be */
/* computed. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--work;
/* Function Body */
*info = 0;
mn = min(*m,*n);
lquery = *lwork == -1;
if (! (lsame_(trans, "N") || lsame_(trans, "T"))) {
*info = -1;
} else if (*m < 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*lda < max(1,*m)) {
*info = -6;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = max(1,*m);
if (*ldb < max(i__1,*n)) {
*info = -8;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = 1, i__2 = mn + max(mn,*nrhs);
if (*lwork < max(i__1,i__2) && ! lquery) {
*info = -10;
}
}
}
/* Figure out optimal block size */
if (*info == 0 || *info == -10) {
tpsd = TRUE_;
if (lsame_(trans, "N")) {
tpsd = FALSE_;
}
if (*m >= *n) {
nb = ilaenv_(&c__1, "SGEQRF", " ", m, n, &c_n1, &c_n1);
if (tpsd) {
/* Computing MAX */
i__1 = nb, i__2 = ilaenv_(&c__1, "SORMQR", "LN", m, nrhs, n, &
c_n1);
nb = max(i__1,i__2);
} else {
/* Computing MAX */
i__1 = nb, i__2 = ilaenv_(&c__1, "SORMQR", "LT", m, nrhs, n, &
c_n1);
nb = max(i__1,i__2);
}
} else {
nb = ilaenv_(&c__1, "SGELQF", " ", m, n, &c_n1, &c_n1);
if (tpsd) {
/* Computing MAX */
i__1 = nb, i__2 = ilaenv_(&c__1, "SORMLQ", "LT", n, nrhs, m, &
c_n1);
nb = max(i__1,i__2);
} else {
/* Computing MAX */
i__1 = nb, i__2 = ilaenv_(&c__1, "SORMLQ", "LN", n, nrhs, m, &
c_n1);
nb = max(i__1,i__2);
}
}
/* Computing MAX */
i__1 = 1, i__2 = mn + max(mn,*nrhs) * nb;
wsize = max(i__1,i__2);
work[1] = (real) wsize;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGELS ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
/* Computing MIN */
i__1 = min(*m,*n);
if (min(i__1,*nrhs) == 0) {
i__1 = max(*m,*n);
slaset_("Full", &i__1, nrhs, &c_b33, &c_b33, &b[b_offset], ldb);
return 0;
}
/* Get machine parameters */
smlnum = slamch_("S") / slamch_("P");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
/* Scale A, B if max element outside range [SMLNUM,BIGNUM] */
anrm = slange_("M", m, n, &a[a_offset], lda, rwork);
iascl = 0;
if (anrm > 0.f && anrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
slascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda,
info);
iascl = 1;
} else if (anrm > bignum) {
/* Scale matrix norm down to BIGNUM */
slascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
info);
iascl = 2;
} else if (anrm == 0.f) {
/* Matrix all zero. Return zero solution. */
i__1 = max(*m,*n);
slaset_("F", &i__1, nrhs, &c_b33, &c_b33, &b[b_offset], ldb);
goto L50;
}
brow = *m;
if (tpsd) {
brow = *n;
}
bnrm = slange_("M", &brow, nrhs, &b[b_offset], ldb, rwork);
ibscl = 0;
if (bnrm > 0.f && bnrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
slascl_("G", &c__0, &c__0, &bnrm, &smlnum, &brow, nrhs, &b[b_offset],
ldb, info);
ibscl = 1;
} else if (bnrm > bignum) {
/* Scale matrix norm down to BIGNUM */
slascl_("G", &c__0, &c__0, &bnrm, &bignum, &brow, nrhs, &b[b_offset],
ldb, info);
ibscl = 2;
}
if (*m >= *n) {
/* compute QR factorization of A */
i__1 = *lwork - mn;
sgeqrf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info)
;
/* workspace at least N, optimally N*NB */
if (! tpsd) {
/* Least-Squares Problem min || A * X - B || */
/* B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS) */
i__1 = *lwork - mn;
sormqr_("Left", "Transpose", m, nrhs, n, &a[a_offset], lda, &work[
1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
/* workspace at least NRHS, optimally NRHS*NB */
/* B(1:N,1:NRHS) := inv(R) * B(1:N,1:NRHS) */
strtrs_("Upper", "No transpose", "Non-unit", n, nrhs, &a[a_offset]
, lda, &b[b_offset], ldb, info);
if (*info > 0) {
return 0;
}
scllen = *n;
} else {
/* Overdetermined system of equations A' * X = B */
/* B(1:N,1:NRHS) := inv(R') * B(1:N,1:NRHS) */
strtrs_("Upper", "Transpose", "Non-unit", n, nrhs, &a[a_offset],
lda, &b[b_offset], ldb, info);
if (*info > 0) {
return 0;
}
/* B(N+1:M,1:NRHS) = ZERO */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = *n + 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = 0.f;
/* L10: */
}
/* L20: */
}
/* B(1:M,1:NRHS) := Q(1:N,:) * B(1:N,1:NRHS) */
i__1 = *lwork - mn;
sormqr_("Left", "No transpose", m, nrhs, n, &a[a_offset], lda, &
work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
/* workspace at least NRHS, optimally NRHS*NB */
scllen = *m;
}
} else {
/* Compute LQ factorization of A */
i__1 = *lwork - mn;
sgelqf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info)
;
/* workspace at least M, optimally M*NB. */
if (! tpsd) {
/* underdetermined system of equations A * X = B */
/* B(1:M,1:NRHS) := inv(L) * B(1:M,1:NRHS) */
strtrs_("Lower", "No transpose", "Non-unit", m, nrhs, &a[a_offset]
, lda, &b[b_offset], ldb, info);
if (*info > 0) {
return 0;
}
/* B(M+1:N,1:NRHS) = 0 */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = *m + 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = 0.f;
/* L30: */
}
/* L40: */
}
/* B(1:N,1:NRHS) := Q(1:N,:)' * B(1:M,1:NRHS) */
i__1 = *lwork - mn;
sormlq_("Left", "Transpose", n, nrhs, m, &a[a_offset], lda, &work[
1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
/* workspace at least NRHS, optimally NRHS*NB */
scllen = *n;
} else {
/* overdetermined system min || A' * X - B || */
/* B(1:N,1:NRHS) := Q * B(1:N,1:NRHS) */
i__1 = *lwork - mn;
sormlq_("Left", "No transpose", n, nrhs, m, &a[a_offset], lda, &
work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
/* workspace at least NRHS, optimally NRHS*NB */
/* B(1:M,1:NRHS) := inv(L') * B(1:M,1:NRHS) */
strtrs_("Lower", "Transpose", "Non-unit", m, nrhs, &a[a_offset],
lda, &b[b_offset], ldb, info);
if (*info > 0) {
return 0;
}
scllen = *m;
}
}
/* Undo scaling */
if (iascl == 1) {
slascl_("G", &c__0, &c__0, &anrm, &smlnum, &scllen, nrhs, &b[b_offset]
, ldb, info);
} else if (iascl == 2) {
slascl_("G", &c__0, &c__0, &anrm, &bignum, &scllen, nrhs, &b[b_offset]
, ldb, info);
}
if (ibscl == 1) {
slascl_("G", &c__0, &c__0, &smlnum, &bnrm, &scllen, nrhs, &b[b_offset]
, ldb, info);
} else if (ibscl == 2) {
slascl_("G", &c__0, &c__0, &bignum, &bnrm, &scllen, nrhs, &b[b_offset]
, ldb, info);
}
L50:
work[1] = (real) wsize;
return 0;
/* End of SGELS */
} /* sgels_ */
/* Subroutine */ int sgelsd_(integer *m, integer *n, integer *nrhs, real *a,
integer *lda, real *b, integer *ldb, real *s, real *rcond, integer *
rank, real *work, integer *lwork, integer *iwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
/* Builtin functions */
double log(doublereal);
/* Local variables */
static real anrm, bnrm;
static integer itau, nlvl, iascl, ibscl;
static real sfmin;
static integer minmn, maxmn, itaup, itauq, mnthr, nwork, ie, il;
extern /* Subroutine */ int slabad_(real *, real *);
static integer mm;
extern /* Subroutine */ int sgebrd_(integer *, integer *, real *, integer
*, real *, real *, real *, real *, real *, integer *, integer *);
extern doublereal slamch_(char *), slange_(char *, integer *,
integer *, real *, integer *, real *);
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static real bignum;
extern /* Subroutine */ int sgelqf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *), slalsd_(char *, integer
*, integer *, integer *, real *, real *, real *, integer *, real *
, integer *, real *, integer *, integer *), slascl_(char *
, integer *, integer *, real *, real *, integer *, integer *,
real *, integer *, integer *);
static integer wlalsd;
extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *), slacpy_(char *, integer
*, integer *, real *, integer *, real *, integer *),
slaset_(char *, integer *, integer *, real *, real *, real *,
integer *);
static integer ldwork;
extern /* Subroutine */ int sormbr_(char *, char *, char *, integer *,
integer *, integer *, real *, integer *, real *, real *, integer *
, real *, integer *, integer *);
static integer minwrk, maxwrk;
static real smlnum;
extern /* Subroutine */ int sormlq_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
static logical lquery;
static integer smlsiz;
extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
static real eps;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1999
Purpose
=======
SGELSD computes the minimum-norm solution to a real linear least
squares problem:
minimize 2-norm(| b - A*x |)
using the singular value decomposition (SVD) of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
The problem is solved in three steps:
(1) Reduce the coefficient matrix A to bidiagonal form with
Householder transformations, reducing the original problem
into a "bidiagonal least squares problem" (BLS)
(2) Solve the BLS using a divide and conquer approach.
(3) Apply back all the Householder tranformations to solve
the original least squares problem.
The effective rank of A is determined by treating as zero those
singular values which are less than RCOND times the largest singular
value.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
M (input) INTEGER
The number of rows of A. M >= 0.
N (input) INTEGER
The number of columns of A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A (input) REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, A has been destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B (input/output) REAL array, dimension (LDB,NRHS)
On entry, the M-by-NRHS right hand side matrix B.
On exit, B is overwritten by the N-by-NRHS solution
matrix X. If m >= n and RANK = n, the residual
sum-of-squares for the solution in the i-th column is given
by the sum of squares of elements n+1:m in that column.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,max(M,N)).
S (output) REAL array, dimension (min(M,N))
The singular values of A in decreasing order.
The condition number of A in the 2-norm = S(1)/S(min(m,n)).
RCOND (input) REAL
RCOND is used to determine the effective rank of A.
Singular values S(i) <= RCOND*S(1) are treated as zero.
If RCOND < 0, machine precision is used instead.
RANK (output) INTEGER
The effective rank of A, i.e., the number of singular values
which are greater than RCOND*S(1).
WORK (workspace/output) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK must be at least 1.
The exact minimum amount of workspace needed depends on M,
N and NRHS. As long as LWORK is at least
12*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2,
if M is greater than or equal to N or
12*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS + (SMLSIZ+1)**2,
if M is less than N, the code will execute correctly.
SMLSIZ is returned by ILAENV and is equal to the maximum
size of the subproblems at the bottom of the computation
tree (usually about 25), and
NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
For good performance, LWORK should generally be larger.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
IWORK (workspace) INTEGER array, dimension (LIWORK)
LIWORK >= 3 * MINMN * NLVL + 11 * MINMN,
where MINMN = MIN( M,N ).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: the algorithm for computing the SVD failed to converge;
if INFO = i, i off-diagonal elements of an intermediate
bidiagonal form did not converge to zero.
Further Details
===============
Based on contributions by
Ming Gu and Ren-Cang Li, Computer Science Division, University of
California at Berkeley, USA
Osni Marques, LBNL/NERSC, USA
=====================================================================
Test the input arguments.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--s;
--work;
--iwork;
/* Function Body */
*info = 0;
minmn = min(*m,*n);
maxmn = max(*m,*n);
mnthr = ilaenv_(&c__6, "SGELSD", " ", m, n, nrhs, &c_n1, (ftnlen)6, (
ftnlen)1);
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*ldb < max(1,maxmn)) {
*info = -7;
}
smlsiz = ilaenv_(&c__9, "SGELSD", " ", &c__0, &c__0, &c__0, &c__0, (
ftnlen)6, (ftnlen)1);
/* Compute workspace.
(Note: Comments in the code beginning "Workspace:" describe the
minimal amount of workspace needed at that point in the code,
as well as the preferred amount for good performance.
NB refers to the optimal block size for the immediately
following subroutine, as returned by ILAENV.) */
minwrk = 1;
minmn = max(1,minmn);
/* Computing MAX */
i__1 = (integer) (log((real) minmn / (real) (smlsiz + 1)) / log(2.f)) + 1;
nlvl = max(i__1,0);
if (*info == 0) {
maxwrk = 0;
mm = *m;
if (*m >= *n && *m >= mnthr) {
/* Path 1a - overdetermined, with many more rows than columns. */
mm = *n;
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "SGEQRF", " ", m,
n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + *nrhs * ilaenv_(&c__1, "SORMQR", "LT",
m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)2);
maxwrk = max(i__1,i__2);
}
if (*m >= *n) {
/* Path 1 - overdetermined or exactly determined.
Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + (mm + *n) * ilaenv_(&c__1, "SGEBRD"
, " ", &mm, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + *nrhs * ilaenv_(&c__1, "SORMBR",
"QLT", &mm, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + (*n - 1) * ilaenv_(&c__1, "SORMBR",
"PLN", n, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing 2nd power */
i__1 = smlsiz + 1;
wlalsd = *n * 9 + (*n << 1) * smlsiz + (*n << 3) * nlvl + *n * *
nrhs + i__1 * i__1;
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + wlalsd;
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1,i__2),
i__2 = *n * 3 + wlalsd;
minwrk = max(i__1,i__2);
}
if (*n > *m) {
/* Computing 2nd power */
i__1 = smlsiz + 1;
wlalsd = *m * 9 + (*m << 1) * smlsiz + (*m << 3) * nlvl + *m * *
nrhs + i__1 * i__1;
if (*n >= mnthr) {
/* Path 2a - underdetermined, with many more columns
than rows. */
maxwrk = *m + *m * ilaenv_(&c__1, "SGELQF", " ", m, n, &c_n1,
&c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) *
ilaenv_(&c__1, "SGEBRD", " ", m, m, &c_n1, &c_n1, (
ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs * ilaenv_(&
c__1, "SORMBR", "QLT", m, nrhs, m, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) *
ilaenv_(&c__1, "SORMBR", "PLN", m, nrhs, m, &c_n1, (
ftnlen)6, (ftnlen)3);
maxwrk = max(i__1,i__2);
if (*nrhs > 1) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs;
maxwrk = max(i__1,i__2);
} else {
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 1);
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = maxwrk, i__2 = *m + *nrhs * ilaenv_(&c__1, "SORMLQ",
"LT", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)2);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + wlalsd;
maxwrk = max(i__1,i__2);
} else {
/* Path 2 - remaining underdetermined cases. */
maxwrk = *m * 3 + (*n + *m) * ilaenv_(&c__1, "SGEBRD", " ", m,
n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * 3 + *nrhs * ilaenv_(&c__1, "SORMBR"
, "QLT", m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORMBR",
"PLN", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * 3 + wlalsd;
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *m, i__1 = max(i__1,i__2),
i__2 = *m * 3 + wlalsd;
minwrk = max(i__1,i__2);
}
minwrk = min(minwrk,maxwrk);
work[1] = (real) maxwrk;
if (*lwork < minwrk && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGELSD", &i__1);
return 0;
} else if (lquery) {
goto L10;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0) {
*rank = 0;
return 0;
}
/* Get machine parameters. */
eps = slamch_("P");
sfmin = slamch_("S");
smlnum = sfmin / eps;
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
/* Scale A if max entry outside range [SMLNUM,BIGNUM]. */
anrm = slange_("M", m, n, &a[a_offset], lda, &work[1]);
iascl = 0;
if (anrm > 0.f && anrm < smlnum) {
/* Scale matrix norm up to SMLNUM. */
slascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda,
info);
iascl = 1;
} else if (anrm > bignum) {
/* Scale matrix norm down to BIGNUM. */
slascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
info);
iascl = 2;
} else if (anrm == 0.f) {
/* Matrix all zero. Return zero solution. */
i__1 = max(*m,*n);
slaset_("F", &i__1, nrhs, &c_b82, &c_b82, &b[b_offset], ldb);
slaset_("F", &minmn, &c__1, &c_b82, &c_b82, &s[1], &c__1);
*rank = 0;
goto L10;
}
/* Scale B if max entry outside range [SMLNUM,BIGNUM]. */
bnrm = slange_("M", m, nrhs, &b[b_offset], ldb, &work[1]);
ibscl = 0;
if (bnrm > 0.f && bnrm < smlnum) {
/* Scale matrix norm up to SMLNUM. */
slascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
info);
ibscl = 1;
} else if (bnrm > bignum) {
/* Scale matrix norm down to BIGNUM. */
slascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
info);
ibscl = 2;
}
/* If M < N make sure certain entries of B are zero. */
if (*m < *n) {
i__1 = *n - *m;
slaset_("F", &i__1, nrhs, &c_b82, &c_b82, &b_ref(*m + 1, 1), ldb);
}
/* Overdetermined case. */
if (*m >= *n) {
/* Path 1 - overdetermined or exactly determined. */
mm = *m;
if (*m >= mnthr) {
/* Path 1a - overdetermined, with many more rows than columns. */
mm = *n;
itau = 1;
nwork = itau + *n;
/* Compute A=Q*R.
(Workspace: need 2*N, prefer N+N*NB) */
i__1 = *lwork - nwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1,
info);
/* Multiply B by transpose(Q).
(Workspace: need N+NRHS, prefer N+NRHS*NB) */
i__1 = *lwork - nwork + 1;
sormqr_("L", "T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[
b_offset], ldb, &work[nwork], &i__1, info);
/* Zero out below R. */
if (*n > 1) {
i__1 = *n - 1;
i__2 = *n - 1;
slaset_("L", &i__1, &i__2, &c_b82, &c_b82, &a_ref(2, 1), lda);
}
}
ie = 1;
itauq = ie + *n;
itaup = itauq + *n;
nwork = itaup + *n;
/* Bidiagonalize R in A.
(Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */
i__1 = *lwork - nwork + 1;
sgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[nwork], &i__1, info);
/* Multiply B by transpose of left bidiagonalizing vectors of R.
(Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */
i__1 = *lwork - nwork + 1;
sormbr_("Q", "L", "T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq],
&b[b_offset], ldb, &work[nwork], &i__1, info);
/* Solve the bidiagonal least squares problem. */
slalsd_("U", &smlsiz, n, nrhs, &s[1], &work[ie], &b[b_offset], ldb,
rcond, rank, &work[nwork], &iwork[1], info);
if (*info != 0) {
goto L10;
}
/* Multiply B by right bidiagonalizing vectors of R. */
i__1 = *lwork - nwork + 1;
sormbr_("P", "L", "N", n, nrhs, n, &a[a_offset], lda, &work[itaup], &
b[b_offset], ldb, &work[nwork], &i__1, info);
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = *m, i__2 = (*m << 1) - 4, i__1 = max(i__1,i__2), i__1 = max(
i__1,*nrhs), i__2 = *n - *m * 3;
if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__1,i__2)) {
/* Path 2a - underdetermined, with many more columns than rows
and sufficient workspace for an efficient algorithm. */
ldwork = *m;
/* Computing MAX
Computing MAX */
i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 =
max(i__3,*nrhs), i__4 = *n - *m * 3;
i__1 = (*m << 2) + *m * *lda + max(i__3,i__4), i__2 = *m * *lda +
*m + *m * *nrhs;
if (*lwork >= max(i__1,i__2)) {
ldwork = *lda;
}
itau = 1;
nwork = *m + 1;
/* Compute A=L*Q.
(Workspace: need 2*M, prefer M+M*NB) */
i__1 = *lwork - nwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1,
info);
il = nwork;
/* Copy L to WORK(IL), zeroing out above its diagonal. */
slacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwork);
i__1 = *m - 1;
i__2 = *m - 1;
slaset_("U", &i__1, &i__2, &c_b82, &c_b82, &work[il + ldwork], &
ldwork);
ie = il + ldwork * *m;
itauq = ie + *m;
itaup = itauq + *m;
nwork = itaup + *m;
/* Bidiagonalize L in WORK(IL).
(Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */
i__1 = *lwork - nwork + 1;
sgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq],
&work[itaup], &work[nwork], &i__1, info);
/* Multiply B by transpose of left bidiagonalizing vectors of L.
(Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */
i__1 = *lwork - nwork + 1;
sormbr_("Q", "L", "T", m, nrhs, m, &work[il], &ldwork, &work[
itauq], &b[b_offset], ldb, &work[nwork], &i__1, info);
/* Solve the bidiagonal least squares problem. */
slalsd_("U", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset],
ldb, rcond, rank, &work[nwork], &iwork[1], info);
if (*info != 0) {
goto L10;
}
/* Multiply B by right bidiagonalizing vectors of L. */
i__1 = *lwork - nwork + 1;
sormbr_("P", "L", "N", m, nrhs, m, &work[il], &ldwork, &work[
itaup], &b[b_offset], ldb, &work[nwork], &i__1, info);
/* Zero out below first M rows of B. */
i__1 = *n - *m;
slaset_("F", &i__1, nrhs, &c_b82, &c_b82, &b_ref(*m + 1, 1), ldb);
nwork = itau + *m;
/* Multiply transpose(Q) by B.
(Workspace: need M+NRHS, prefer M+NRHS*NB) */
i__1 = *lwork - nwork + 1;
sormlq_("L", "T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[
b_offset], ldb, &work[nwork], &i__1, info);
} else {
/* Path 2 - remaining underdetermined cases. */
ie = 1;
itauq = ie + *m;
itaup = itauq + *m;
nwork = itaup + *m;
/* Bidiagonalize A.
(Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */
i__1 = *lwork - nwork + 1;
sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[nwork], &i__1, info);
/* Multiply B by transpose of left bidiagonalizing vectors.
(Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */
i__1 = *lwork - nwork + 1;
sormbr_("Q", "L", "T", m, nrhs, n, &a[a_offset], lda, &work[itauq]
, &b[b_offset], ldb, &work[nwork], &i__1, info);
/* Solve the bidiagonal least squares problem. */
slalsd_("L", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset],
ldb, rcond, rank, &work[nwork], &iwork[1], info);
if (*info != 0) {
goto L10;
}
/* Multiply B by right bidiagonalizing vectors of A. */
i__1 = *lwork - nwork + 1;
sormbr_("P", "L", "N", n, nrhs, m, &a[a_offset], lda, &work[itaup]
, &b[b_offset], ldb, &work[nwork], &i__1, info);
}
}
/* Undo scaling. */
if (iascl == 1) {
slascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
info);
slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
minmn, info);
} else if (iascl == 2) {
slascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
info);
slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
minmn, info);
}
if (ibscl == 1) {
slascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
} else if (ibscl == 2) {
slascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
}
L10:
work[1] = (real) maxwrk;
return 0;
/* End of SGELSD */
} /* sgelsd_ */
/* Subroutine */ int serrqr_(char *path, integer *nunit)
{
/* Local variables */
real a[4] /* was [2][2] */, b[2];
integer i__, j;
real w[2], x[2], af[4] /* was [2][2] */;
integer info;
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SERRQR tests the error exits for the REAL routines */
/* that use the QR decomposition of a general matrix. */
/* Arguments */
/* ========= */
/* PATH (input) CHARACTER*3 */
/* The LAPACK path name for the routines to be tested. */
/* NUNIT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
/* Set the variables to innocuous values. */
for (j = 1; j <= 2; ++j) {
for (i__ = 1; i__ <= 2; ++i__) {
a[i__ + (j << 1) - 3] = 1.f / (real) (i__ + j);
af[i__ + (j << 1) - 3] = 1.f / (real) (i__ + j);
/* L10: */
}
b[j - 1] = 0.f;
w[j - 1] = 0.f;
x[j - 1] = 0.f;
/* L20: */
}
infoc_1.ok = TRUE_;
/* Error exits for QR factorization */
/* SGEQRF */
s_copy(srnamc_1.srnamt, "SGEQRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgeqrf_(&c_n1, &c__0, a, &c__1, b, w, &c__1, &info);
chkxer_("SGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeqrf_(&c__0, &c_n1, a, &c__1, b, w, &c__1, &info);
chkxer_("SGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgeqrf_(&c__2, &c__1, a, &c__1, b, w, &c__1, &info);
chkxer_("SGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sgeqrf_(&c__1, &c__2, a, &c__1, b, w, &c__1, &info);
chkxer_("SGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGEQR2 */
s_copy(srnamc_1.srnamt, "SGEQR2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgeqr2_(&c_n1, &c__0, a, &c__1, b, w, &info);
chkxer_("SGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeqr2_(&c__0, &c_n1, a, &c__1, b, w, &info);
chkxer_("SGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgeqr2_(&c__2, &c__1, a, &c__1, b, w, &info);
chkxer_("SGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGEQRS */
s_copy(srnamc_1.srnamt, "SGEQRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgeqrs_(&c_n1, &c__0, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeqrs_(&c__0, &c_n1, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeqrs_(&c__1, &c__2, &c__0, a, &c__2, x, b, &c__2, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgeqrs_(&c__0, &c__0, &c_n1, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sgeqrs_(&c__2, &c__1, &c__0, a, &c__1, x, b, &c__2, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
sgeqrs_(&c__2, &c__1, &c__0, a, &c__2, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sgeqrs_(&c__1, &c__1, &c__2, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SORGQR */
s_copy(srnamc_1.srnamt, "SORGQR", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sorgqr_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorgqr_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorgqr_(&c__1, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorgqr_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorgqr_(&c__1, &c__1, &c__2, a, &c__1, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorgqr_(&c__2, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
sorgqr_(&c__2, &c__2, &c__0, a, &c__2, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SORG2R */
s_copy(srnamc_1.srnamt, "SORG2R", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sorg2r_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorg2r_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorg2r_(&c__1, &c__2, &c__0, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorg2r_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorg2r_(&c__2, &c__1, &c__2, a, &c__2, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorg2r_(&c__2, &c__1, &c__0, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SORMQR */
s_copy(srnamc_1.srnamt, "SORMQR", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sormqr_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sormqr_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sormqr_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sormqr_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sormqr_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sormqr_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sormqr_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sormqr_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sormqr_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sormqr_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
sormqr_("L", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
sormqr_("R", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SORM2R */
s_copy(srnamc_1.srnamt, "SORM2R", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sorm2r_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorm2r_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorm2r_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sorm2r_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorm2r_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorm2r_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorm2r_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sorm2r_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sorm2r_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sorm2r_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* Print a summary line. */
alaesm_(path, &infoc_1.ok, &infoc_1.nout);
return 0;
/* End of SERRQR */
} /* serrqr_ */
/* Subroutine */ int sgegv_(char *jobvl, char *jobvr, integer *n, real *a,
integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real
*beta, real *vl, integer *ldvl, real *vr, integer *ldvr, real *work,
integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1,
vr_offset, i__1, i__2;
real r__1, r__2, r__3, r__4;
/* Local variables */
integer jc, nb, in, jr, nb1, nb2, nb3, ihi, ilo;
real eps;
logical ilv;
real absb, anrm, bnrm;
integer itau;
real temp;
logical ilvl, ilvr;
integer lopt;
real anrm1, anrm2, bnrm1, bnrm2, absai, scale, absar, sbeta;
integer ileft, iinfo, icols, iwork, irows;
real salfai;
real salfar;
real safmin;
real safmax;
char chtemp[1];
logical ldumma[1];
integer ijobvl, iright;
logical ilimit;
integer ijobvr;
real onepls;
integer lwkmin;
integer lwkopt;
logical lquery;
/* -- LAPACK driver routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* This routine is deprecated and has been replaced by routine SGGEV. */
/* SGEGV computes the eigenvalues and, optionally, the left and/or right */
/* eigenvectors of a real matrix pair (A,B). */
/* Given two square matrices A and B, */
/* the generalized nonsymmetric eigenvalue problem (GNEP) is to find the */
/* eigenvalues lambda and corresponding (non-zero) eigenvectors x such */
/* that */
/* A*x = lambda*B*x. */
/* An alternate form is to find the eigenvalues mu and corresponding */
/* eigenvectors y such that */
/* mu*A*y = B*y. */
/* These two forms are equivalent with mu = 1/lambda and x = y if */
/* neither lambda nor mu is zero. In order to deal with the case that */
/* lambda or mu is zero or small, two values alpha and beta are returned */
/* for each eigenvalue, such that lambda = alpha/beta and */
/* mu = beta/alpha. */
/* The vectors x and y in the above equations are right eigenvectors of */
/* the matrix pair (A,B). Vectors u and v satisfying */
/* u**H*A = lambda*u**H*B or mu*v**H*A = v**H*B */
/* are left eigenvectors of (A,B). */
/* Note: this routine performs "full balancing" on A and B -- see */
/* "Further Details", below. */
/* Arguments */
/* ========= */
/* JOBVL (input) CHARACTER*1 */
/* = 'N': do not compute the left generalized eigenvectors; */
/* = 'V': compute the left generalized eigenvectors (returned */
/* in VL). */
/* JOBVR (input) CHARACTER*1 */
/* = 'N': do not compute the right generalized eigenvectors; */
/* = 'V': compute the right generalized eigenvectors (returned */
/* in VR). */
/* N (input) INTEGER */
/* The order of the matrices A, B, VL, and VR. N >= 0. */
/* A (input/output) REAL array, dimension (LDA, N) */
/* On entry, the matrix A. */
/* If JOBVL = 'V' or JOBVR = 'V', then on exit A */
/* contains the real Schur form of A from the generalized Schur */
/* factorization of the pair (A,B) after balancing. */
/* If no eigenvectors were computed, then only the diagonal */
/* blocks from the Schur form will be correct. See SGGHRD and */
/* SHGEQZ for details. */
/* LDA (input) INTEGER */
/* The leading dimension of A. LDA >= max(1,N). */
/* B (input/output) REAL array, dimension (LDB, N) */
/* On entry, the matrix B. */
/* If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the */
/* upper triangular matrix obtained from B in the generalized */
/* Schur factorization of the pair (A,B) after balancing. */
/* If no eigenvectors were computed, then only those elements of */
/* B corresponding to the diagonal blocks from the Schur form of */
/* A will be correct. See SGGHRD and SHGEQZ for details. */
/* LDB (input) INTEGER */
/* The leading dimension of B. LDB >= max(1,N). */
/* ALPHAR (output) REAL array, dimension (N) */
/* The real parts of each scalar alpha defining an eigenvalue of */
/* GNEP. */
/* ALPHAI (output) REAL array, dimension (N) */
/* The imaginary parts of each scalar alpha defining an */
/* eigenvalue of GNEP. If ALPHAI(j) is zero, then the j-th */
/* eigenvalue is real; if positive, then the j-th and */
/* (j+1)-st eigenvalues are a complex conjugate pair, with */
/* ALPHAI(j+1) = -ALPHAI(j). */
/* BETA (output) REAL array, dimension (N) */
/* The scalars beta that define the eigenvalues of GNEP. */
/* Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and */
/* beta = BETA(j) represent the j-th eigenvalue of the matrix */
/* pair (A,B), in one of the forms lambda = alpha/beta or */
/* mu = beta/alpha. Since either lambda or mu may overflow, */
/* they should not, in general, be computed. */
/* VL (output) REAL array, dimension (LDVL,N) */
/* If JOBVL = 'V', the left eigenvectors u(j) are stored */
/* in the columns of VL, in the same order as their eigenvalues. */
/* If the j-th eigenvalue is real, then u(j) = VL(:,j). */
/* If the j-th and (j+1)-st eigenvalues form a complex conjugate */
/* pair, then */
/* u(j) = VL(:,j) + i*VL(:,j+1) */
/* and */
/* u(j+1) = VL(:,j) - i*VL(:,j+1). */
/* Each eigenvector is scaled so that its largest component has */
/* abs(real part) + abs(imag. part) = 1, except for eigenvectors */
/* corresponding to an eigenvalue with alpha = beta = 0, which */
/* are set to zero. */
/* Not referenced if JOBVL = 'N'. */
/* LDVL (input) INTEGER */
/* The leading dimension of the matrix VL. LDVL >= 1, and */
/* if JOBVL = 'V', LDVL >= N. */
/* VR (output) REAL array, dimension (LDVR,N) */
/* If JOBVR = 'V', the right eigenvectors x(j) are stored */
/* in the columns of VR, in the same order as their eigenvalues. */
/* If the j-th eigenvalue is real, then x(j) = VR(:,j). */
/* If the j-th and (j+1)-st eigenvalues form a complex conjugate */
/* pair, then */
/* x(j) = VR(:,j) + i*VR(:,j+1) */
/* and */
/* x(j+1) = VR(:,j) - i*VR(:,j+1). */
/* Each eigenvector is scaled so that its largest component has */
/* abs(real part) + abs(imag. part) = 1, except for eigenvalues */
/* corresponding to an eigenvalue with alpha = beta = 0, which */
/* are set to zero. */
/* Not referenced if JOBVR = 'N'. */
/* LDVR (input) INTEGER */
/* The leading dimension of the matrix VR. LDVR >= 1, and */
/* if JOBVR = 'V', LDVR >= N. */
/* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= max(1,8*N). */
/* For good performance, LWORK must generally be larger. */
/* To compute the optimal value of LWORK, call ILAENV to get */
/* blocksizes (for SGEQRF, SORMQR, and SORGQR.) Then compute: */
/* NB -- MAX of the blocksizes for SGEQRF, SORMQR, and SORGQR; */
/* The optimal LWORK is: */
/* 2*N + MAX( 6*N, N*(NB+1) ). */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* The QZ iteration failed. No eigenvectors have been */
/* calculated, but ALPHAR(j), ALPHAI(j), and BETA(j) */
/* > N: errors that usually indicate LAPACK problems: */
/* =N+1: error return from SGGBAL */
/* =N+2: error return from SGEQRF */
/* =N+3: error return from SORMQR */
/* =N+4: error return from SORGQR */
/* =N+5: error return from SGGHRD */
/* =N+6: error return from SHGEQZ (other than failed */
/* iteration) */
/* =N+7: error return from STGEVC */
/* =N+8: error return from SGGBAK (computing VL) */
/* =N+9: error return from SGGBAK (computing VR) */
/* =N+10: error return from SLASCL (various calls) */
/* Further Details */
/* =============== */
/* Balancing */
/* --------- */
/* This driver calls SGGBAL to both permute and scale rows and columns */
/* of A and B. The permutations PL and PR are chosen so that PL*A*PR */
/* and PL*B*R will be upper triangular except for the diagonal blocks */
/* A(i:j,i:j) and B(i:j,i:j), with i and j as close together as */
/* possible. The diagonal scaling matrices DL and DR are chosen so */
/* that the pair DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to */
/* one (except for the elements that start out zero.) */
/* After the eigenvalues and eigenvectors of the balanced matrices */
/* have been computed, SGGBAK transforms the eigenvectors back to what */
/* they would have been (in perfect arithmetic) if they had not been */
/* balanced. */
/* Contents of A and B on Exit */
/* -------- -- - --- - -- ---- */
/* If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or */
/* both), then on exit the arrays A and B will contain the real Schur */
/* form[*] of the "balanced" versions of A and B. If no eigenvectors */
/* are computed, then only the diagonal blocks will be correct. */
/* [*] See SHGEQZ, SGEGS, or read the book "Matrix Computations", */
/* by Golub & van Loan, pub. by Johns Hopkins U. Press. */
/* ===================================================================== */
/* Decode the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--alphar;
--alphai;
--beta;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--work;
/* Function Body */
if (lsame_(jobvl, "N")) {
ijobvl = 1;
ilvl = FALSE_;
} else if (lsame_(jobvl, "V")) {
ijobvl = 2;
ilvl = TRUE_;
} else {
ijobvl = -1;
ilvl = FALSE_;
}
if (lsame_(jobvr, "N")) {
ijobvr = 1;
ilvr = FALSE_;
} else if (lsame_(jobvr, "V")) {
ijobvr = 2;
ilvr = TRUE_;
} else {
ijobvr = -1;
ilvr = FALSE_;
}
ilv = ilvl || ilvr;
/* Test the input arguments */
/* Computing MAX */
i__1 = *n << 3;
lwkmin = max(i__1,1);
lwkopt = lwkmin;
work[1] = (real) lwkopt;
lquery = *lwork == -1;
*info = 0;
if (ijobvl <= 0) {
*info = -1;
} else if (ijobvr <= 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -7;
} else if (*ldvl < 1 || ilvl && *ldvl < *n) {
*info = -12;
} else if (*ldvr < 1 || ilvr && *ldvr < *n) {
*info = -14;
} else if (*lwork < lwkmin && ! lquery) {
*info = -16;
}
if (*info == 0) {
nb1 = ilaenv_(&c__1, "SGEQRF", " ", n, n, &c_n1, &c_n1);
nb2 = ilaenv_(&c__1, "SORMQR", " ", n, n, n, &c_n1);
nb3 = ilaenv_(&c__1, "SORGQR", " ", n, n, n, &c_n1);
/* Computing MAX */
i__1 = max(nb1,nb2);
nb = max(i__1,nb3);
/* Computing MAX */
i__1 = *n * 6, i__2 = *n * (nb + 1);
lopt = (*n << 1) + max(i__1,i__2);
work[1] = (real) lopt;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGEGV ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Get machine constants */
eps = slamch_("E") * slamch_("B");
safmin = slamch_("S");
safmin += safmin;
safmax = 1.f / safmin;
onepls = eps * 4 + 1.f;
/* Scale A */
anrm = slange_("M", n, n, &a[a_offset], lda, &work[1]);
anrm1 = anrm;
anrm2 = 1.f;
if (anrm < 1.f) {
if (safmax * anrm < 1.f) {
anrm1 = safmin;
anrm2 = safmax * anrm;
}
}
if (anrm > 0.f) {
slascl_("G", &c_n1, &c_n1, &anrm, &c_b27, n, n, &a[a_offset], lda, &
iinfo);
if (iinfo != 0) {
*info = *n + 10;
return 0;
}
}
/* Scale B */
bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]);
bnrm1 = bnrm;
bnrm2 = 1.f;
if (bnrm < 1.f) {
if (safmax * bnrm < 1.f) {
bnrm1 = safmin;
bnrm2 = safmax * bnrm;
}
}
if (bnrm > 0.f) {
slascl_("G", &c_n1, &c_n1, &bnrm, &c_b27, n, n, &b[b_offset], ldb, &
iinfo);
if (iinfo != 0) {
*info = *n + 10;
return 0;
}
}
/* Permute the matrix to make it more nearly triangular */
/* Workspace layout: (8*N words -- "work" requires 6*N words) */
ileft = 1;
iright = *n + 1;
iwork = iright + *n;
sggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
ileft], &work[iright], &work[iwork], &iinfo);
if (iinfo != 0) {
*info = *n + 1;
goto L120;
}
/* Reduce B to triangular form, and initialize VL and/or VR */
irows = ihi + 1 - ilo;
if (ilv) {
icols = *n + 1 - ilo;
} else {
icols = irows;
}
itau = iwork;
iwork = itau + irows;
i__1 = *lwork + 1 - iwork;
sgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 2;
goto L120;
}
i__1 = *lwork + 1 - iwork;
sormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwork], &i__1, &
iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 3;
goto L120;
}
if (ilvl) {
slaset_("Full", n, n, &c_b38, &c_b27, &vl[vl_offset], ldvl)
;
i__1 = irows - 1;
i__2 = irows - 1;
slacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vl[ilo +
1 + ilo * vl_dim1], ldvl);
i__1 = *lwork + 1 - iwork;
sorgqr_(&irows, &irows, &irows, &vl[ilo + ilo * vl_dim1], ldvl, &work[
itau], &work[iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 4;
goto L120;
}
}
if (ilvr) {
slaset_("Full", n, n, &c_b38, &c_b27, &vr[vr_offset], ldvr)
;
}
/* Reduce to generalized Hessenberg form */
if (ilv) {
/* Eigenvectors requested -- work on whole matrix. */
sgghrd_(jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &iinfo);
} else {
sgghrd_("N", "N", &irows, &c__1, &irows, &a[ilo + ilo * a_dim1], lda,
&b[ilo + ilo * b_dim1], ldb, &vl[vl_offset], ldvl, &vr[
vr_offset], ldvr, &iinfo);
}
if (iinfo != 0) {
*info = *n + 5;
goto L120;
}
/* Perform QZ algorithm */
iwork = itau;
if (ilv) {
*(unsigned char *)chtemp = 'S';
} else {
*(unsigned char *)chtemp = 'E';
}
i__1 = *lwork + 1 - iwork;
shgeqz_(chtemp, jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[
b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vl[vl_offset],
ldvl, &vr[vr_offset], ldvr, &work[iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
if (iinfo > 0 && iinfo <= *n) {
*info = iinfo;
} else if (iinfo > *n && iinfo <= *n << 1) {
*info = iinfo - *n;
} else {
*info = *n + 6;
}
goto L120;
}
if (ilv) {
/* Compute Eigenvectors (STGEVC requires 6*N words of workspace) */
if (ilvl) {
if (ilvr) {
*(unsigned char *)chtemp = 'B';
} else {
*(unsigned char *)chtemp = 'L';
}
} else {
*(unsigned char *)chtemp = 'R';
}
stgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], ldb,
&vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &work[
iwork], &iinfo);
if (iinfo != 0) {
*info = *n + 7;
goto L120;
}
/* Undo balancing on VL and VR, rescale */
if (ilvl) {
sggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
vl[vl_offset], ldvl, &iinfo);
if (iinfo != 0) {
*info = *n + 8;
goto L120;
}
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
if (alphai[jc] < 0.f) {
goto L50;
}
temp = 0.f;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__2 = temp, r__3 = (r__1 = vl[jr + jc * vl_dim1],
dabs(r__1));
temp = dmax(r__2,r__3);
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__3 = temp, r__4 = (r__1 = vl[jr + jc * vl_dim1],
dabs(r__1)) + (r__2 = vl[jr + (jc + 1) *
vl_dim1], dabs(r__2));
temp = dmax(r__3,r__4);
}
}
if (temp < safmin) {
goto L50;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vl[jr + jc * vl_dim1] *= temp;
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vl[jr + jc * vl_dim1] *= temp;
vl[jr + (jc + 1) * vl_dim1] *= temp;
}
}
L50:
;
}
}
if (ilvr) {
sggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
vr[vr_offset], ldvr, &iinfo);
if (iinfo != 0) {
*info = *n + 9;
goto L120;
}
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
if (alphai[jc] < 0.f) {
goto L100;
}
temp = 0.f;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__2 = temp, r__3 = (r__1 = vr[jr + jc * vr_dim1],
dabs(r__1));
temp = dmax(r__2,r__3);
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__3 = temp, r__4 = (r__1 = vr[jr + jc * vr_dim1],
dabs(r__1)) + (r__2 = vr[jr + (jc + 1) *
vr_dim1], dabs(r__2));
temp = dmax(r__3,r__4);
}
}
if (temp < safmin) {
goto L100;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vr[jr + jc * vr_dim1] *= temp;
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vr[jr + jc * vr_dim1] *= temp;
vr[jr + (jc + 1) * vr_dim1] *= temp;
}
}
L100:
;
}
}
/* End of eigenvector calculation */
}
/* Undo scaling in alpha, beta */
/* Note: this does not give the alpha and beta for the unscaled */
/* problem. */
/* Un-scaling is limited to avoid underflow in alpha and beta */
/* if they are significant. */
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
absar = (r__1 = alphar[jc], dabs(r__1));
absai = (r__1 = alphai[jc], dabs(r__1));
absb = (r__1 = beta[jc], dabs(r__1));
salfar = anrm * alphar[jc];
salfai = anrm * alphai[jc];
sbeta = bnrm * beta[jc];
ilimit = FALSE_;
scale = 1.f;
/* Check for significant underflow in ALPHAI */
/* Computing MAX */
r__1 = safmin, r__2 = eps * absar, r__1 = max(r__1,r__2), r__2 = eps *
absb;
if (dabs(salfai) < safmin && absai >= dmax(r__1,r__2)) {
ilimit = TRUE_;
/* Computing MAX */
r__1 = onepls * safmin, r__2 = anrm2 * absai;
scale = onepls * safmin / anrm1 / dmax(r__1,r__2);
} else if (salfai == 0.f) {
/* If insignificant underflow in ALPHAI, then make the */
/* conjugate eigenvalue real. */
if (alphai[jc] < 0.f && jc > 1) {
alphai[jc - 1] = 0.f;
} else if (alphai[jc] > 0.f && jc < *n) {
alphai[jc + 1] = 0.f;
}
}
/* Check for significant underflow in ALPHAR */
/* Computing MAX */
r__1 = safmin, r__2 = eps * absai, r__1 = max(r__1,r__2), r__2 = eps *
absb;
if (dabs(salfar) < safmin && absar >= dmax(r__1,r__2)) {
ilimit = TRUE_;
/* Computing MAX */
/* Computing MAX */
r__3 = onepls * safmin, r__4 = anrm2 * absar;
r__1 = scale, r__2 = onepls * safmin / anrm1 / dmax(r__3,r__4);
scale = dmax(r__1,r__2);
}
/* Check for significant underflow in BETA */
/* Computing MAX */
r__1 = safmin, r__2 = eps * absar, r__1 = max(r__1,r__2), r__2 = eps *
absai;
if (dabs(sbeta) < safmin && absb >= dmax(r__1,r__2)) {
ilimit = TRUE_;
/* Computing MAX */
/* Computing MAX */
r__3 = onepls * safmin, r__4 = bnrm2 * absb;
r__1 = scale, r__2 = onepls * safmin / bnrm1 / dmax(r__3,r__4);
scale = dmax(r__1,r__2);
}
/* Check for possible overflow when limiting scaling */
if (ilimit) {
/* Computing MAX */
r__1 = dabs(salfar), r__2 = dabs(salfai), r__1 = max(r__1,r__2),
r__2 = dabs(sbeta);
temp = scale * safmin * dmax(r__1,r__2);
if (temp > 1.f) {
scale /= temp;
}
if (scale < 1.f) {
ilimit = FALSE_;
}
}
/* Recompute un-scaled ALPHAR, ALPHAI, BETA if necessary. */
if (ilimit) {
salfar = scale * alphar[jc] * anrm;
salfai = scale * alphai[jc] * anrm;
sbeta = scale * beta[jc] * bnrm;
}
alphar[jc] = salfar;
alphai[jc] = salfai;
beta[jc] = sbeta;
}
L120:
work[1] = (real) lwkopt;
return 0;
/* End of SGEGV */
} /* sgegv_ */
/* Subroutine */ int sgegs_(char *jobvsl, char *jobvsr, integer *n, real *a,
integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real
*beta, real *vsl, integer *ldvsl, real *vsr, integer *ldvsr, real *
work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset,
vsr_dim1, vsr_offset, i__1, i__2;
/* Local variables */
integer nb, nb1, nb2, nb3, ihi, ilo;
real eps, anrm, bnrm;
integer itau, lopt;
extern logical lsame_(char *, char *);
integer ileft, iinfo, icols;
logical ilvsl;
integer iwork;
logical ilvsr;
integer irows;
extern /* Subroutine */ int sggbak_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, real *, integer *, integer *
), sggbal_(char *, integer *, real *, integer *,
real *, integer *, integer *, integer *, real *, real *, real *,
integer *);
logical ilascl, ilbscl;
extern doublereal slamch_(char *), slange_(char *, integer *,
integer *, real *, integer *, real *);
real safmin;
extern /* Subroutine */ int sgghrd_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, integer *, real *, integer *
, real *, integer *, integer *), xerbla_(char *,
integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
real bignum;
extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, real *, integer *, integer *);
integer ijobvl, iright;
extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *);
integer ijobvr;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), slaset_(char *, integer *,
integer *, real *, real *, real *, integer *);
real anrmto;
integer lwkmin;
real bnrmto;
extern /* Subroutine */ int shgeqz_(char *, char *, char *, integer *,
integer *, integer *, real *, integer *, real *, integer *, real *
, real *, real *, real *, integer *, real *, integer *, real *,
integer *, integer *);
real smlnum;
extern /* Subroutine */ int sorgqr_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *, integer *);
integer lwkopt;
logical lquery;
extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* This routine is deprecated and has been replaced by routine SGGES. */
/* SGEGS computes the eigenvalues, real Schur form, and, optionally, */
/* left and or/right Schur vectors of a real matrix pair (A,B). */
/* Given two square matrices A and B, the generalized real Schur */
/* factorization has the form */
/* A = Q*S*Z**T, B = Q*T*Z**T */
/* where Q and Z are orthogonal matrices, T is upper triangular, and S */
/* is an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal */
/* blocks, the 2-by-2 blocks corresponding to complex conjugate pairs */
/* of eigenvalues of (A,B). The columns of Q are the left Schur vectors */
/* and the columns of Z are the right Schur vectors. */
/* If only the eigenvalues of (A,B) are needed, the driver routine */
/* SGEGV should be used instead. See SGEGV for a description of the */
/* eigenvalues of the generalized nonsymmetric eigenvalue problem */
/* (GNEP). */
/* Arguments */
/* ========= */
/* JOBVSL (input) CHARACTER*1 */
/* = 'N': do not compute the left Schur vectors; */
/* = 'V': compute the left Schur vectors (returned in VSL). */
/* JOBVSR (input) CHARACTER*1 */
/* = 'N': do not compute the right Schur vectors; */
/* = 'V': compute the right Schur vectors (returned in VSR). */
/* N (input) INTEGER */
/* The order of the matrices A, B, VSL, and VSR. N >= 0. */
/* A (input/output) REAL array, dimension (LDA, N) */
/* On entry, the matrix A. */
/* On exit, the upper quasi-triangular matrix S from the */
/* generalized real Schur factorization. */
/* LDA (input) INTEGER */
/* The leading dimension of A. LDA >= max(1,N). */
/* B (input/output) REAL array, dimension (LDB, N) */
/* On entry, the matrix B. */
/* On exit, the upper triangular matrix T from the generalized */
/* real Schur factorization. */
/* LDB (input) INTEGER */
/* The leading dimension of B. LDB >= max(1,N). */
/* ALPHAR (output) REAL array, dimension (N) */
/* The real parts of each scalar alpha defining an eigenvalue */
/* of GNEP. */
/* ALPHAI (output) REAL array, dimension (N) */
/* The imaginary parts of each scalar alpha defining an */
/* eigenvalue of GNEP. If ALPHAI(j) is zero, then the j-th */
/* eigenvalue is real; if positive, then the j-th and (j+1)-st */
/* eigenvalues are a complex conjugate pair, with */
/* ALPHAI(j+1) = -ALPHAI(j). */
/* BETA (output) REAL array, dimension (N) */
/* The scalars beta that define the eigenvalues of GNEP. */
/* Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and */
/* beta = BETA(j) represent the j-th eigenvalue of the matrix */
/* pair (A,B), in one of the forms lambda = alpha/beta or */
/* mu = beta/alpha. Since either lambda or mu may overflow, */
/* they should not, in general, be computed. */
/* VSL (output) REAL array, dimension (LDVSL,N) */
/* If JOBVSL = 'V', the matrix of left Schur vectors Q. */
/* Not referenced if JOBVSL = 'N'. */
/* LDVSL (input) INTEGER */
/* The leading dimension of the matrix VSL. LDVSL >=1, and */
/* if JOBVSL = 'V', LDVSL >= N. */
/* VSR (output) REAL array, dimension (LDVSR,N) */
/* If JOBVSR = 'V', the matrix of right Schur vectors Z. */
/* Not referenced if JOBVSR = 'N'. */
/* LDVSR (input) INTEGER */
/* The leading dimension of the matrix VSR. LDVSR >= 1, and */
/* if JOBVSR = 'V', LDVSR >= N. */
/* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= max(1,4*N). */
/* For good performance, LWORK must generally be larger. */
/* To compute the optimal value of LWORK, call ILAENV to get */
/* blocksizes (for SGEQRF, SORMQR, and SORGQR.) Then compute: */
/* NB -- MAX of the blocksizes for SGEQRF, SORMQR, and SORGQR */
/* The optimal LWORK is 2*N + N*(NB+1). */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* = 1,...,N: */
/* The QZ iteration failed. (A,B) are not in Schur */
/* form, but ALPHAR(j), ALPHAI(j), and BETA(j) should */
/* be correct for j=INFO+1,...,N. */
/* > N: errors that usually indicate LAPACK problems: */
/* =N+1: error return from SGGBAL */
/* =N+2: error return from SGEQRF */
/* =N+3: error return from SORMQR */
/* =N+4: error return from SORGQR */
/* =N+5: error return from SGGHRD */
/* =N+6: error return from SHGEQZ (other than failed */
/* iteration) */
/* =N+7: error return from SGGBAK (computing VSL) */
/* =N+8: error return from SGGBAK (computing VSR) */
/* =N+9: error return from SLASCL (various places) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--alphar;
--alphai;
--beta;
vsl_dim1 = *ldvsl;
vsl_offset = 1 + vsl_dim1;
vsl -= vsl_offset;
vsr_dim1 = *ldvsr;
vsr_offset = 1 + vsr_dim1;
vsr -= vsr_offset;
--work;
/* Function Body */
if (lsame_(jobvsl, "N")) {
ijobvl = 1;
ilvsl = FALSE_;
} else if (lsame_(jobvsl, "V")) {
ijobvl = 2;
ilvsl = TRUE_;
} else {
ijobvl = -1;
ilvsl = FALSE_;
}
if (lsame_(jobvsr, "N")) {
ijobvr = 1;
ilvsr = FALSE_;
} else if (lsame_(jobvsr, "V")) {
ijobvr = 2;
ilvsr = TRUE_;
} else {
ijobvr = -1;
ilvsr = FALSE_;
}
/* Test the input arguments */
/* Computing MAX */
i__1 = *n << 2;
lwkmin = max(i__1,1);
lwkopt = lwkmin;
work[1] = (real) lwkopt;
lquery = *lwork == -1;
*info = 0;
if (ijobvl <= 0) {
*info = -1;
} else if (ijobvr <= 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -7;
} else if (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
*info = -12;
} else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
*info = -14;
} else if (*lwork < lwkmin && ! lquery) {
*info = -16;
}
if (*info == 0) {
nb1 = ilaenv_(&c__1, "SGEQRF", " ", n, n, &c_n1, &c_n1);
nb2 = ilaenv_(&c__1, "SORMQR", " ", n, n, n, &c_n1);
nb3 = ilaenv_(&c__1, "SORGQR", " ", n, n, n, &c_n1);
/* Computing MAX */
i__1 = max(nb1,nb2);
nb = max(i__1,nb3);
lopt = (*n << 1) + *n * (nb + 1);
work[1] = (real) lopt;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGEGS ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Get machine constants */
eps = slamch_("E") * slamch_("B");
safmin = slamch_("S");
smlnum = *n * safmin / eps;
bignum = 1.f / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = slange_("M", n, n, &a[a_offset], lda, &work[1]);
ilascl = FALSE_;
if (anrm > 0.f && anrm < smlnum) {
anrmto = smlnum;
ilascl = TRUE_;
} else if (anrm > bignum) {
anrmto = bignum;
ilascl = TRUE_;
}
if (ilascl) {
slascl_("G", &c_n1, &c_n1, &anrm, &anrmto, n, n, &a[a_offset], lda, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
}
/* Scale B if max element outside range [SMLNUM,BIGNUM] */
bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]);
ilbscl = FALSE_;
if (bnrm > 0.f && bnrm < smlnum) {
bnrmto = smlnum;
ilbscl = TRUE_;
} else if (bnrm > bignum) {
bnrmto = bignum;
ilbscl = TRUE_;
}
if (ilbscl) {
slascl_("G", &c_n1, &c_n1, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
}
/* Permute the matrix to make it more nearly triangular */
/* Workspace layout: (2*N words -- "work..." not actually used) */
/* left_permutation, right_permutation, work... */
ileft = 1;
iright = *n + 1;
iwork = iright + *n;
sggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
ileft], &work[iright], &work[iwork], &iinfo);
if (iinfo != 0) {
*info = *n + 1;
goto L10;
}
/* Reduce B to triangular form, and initialize VSL and/or VSR */
/* Workspace layout: ("work..." must have at least N words) */
/* left_permutation, right_permutation, tau, work... */
irows = ihi + 1 - ilo;
icols = *n + 1 - ilo;
itau = iwork;
iwork = itau + irows;
i__1 = *lwork + 1 - iwork;
sgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 2;
goto L10;
}
i__1 = *lwork + 1 - iwork;
sormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwork], &i__1, &
iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 3;
goto L10;
}
if (ilvsl) {
slaset_("Full", n, n, &c_b36, &c_b37, &vsl[vsl_offset], ldvsl);
i__1 = irows - 1;
i__2 = irows - 1;
slacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vsl[ilo
+ 1 + ilo * vsl_dim1], ldvsl);
i__1 = *lwork + 1 - iwork;
sorgqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, &
work[itau], &work[iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 4;
goto L10;
}
}
if (ilvsr) {
slaset_("Full", n, n, &c_b36, &c_b37, &vsr[vsr_offset], ldvsr);
}
/* Reduce to generalized Hessenberg form */
sgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &iinfo);
if (iinfo != 0) {
*info = *n + 5;
goto L10;
}
/* Perform QZ algorithm, computing Schur vectors if desired */
/* Workspace layout: ("work..." must have at least 1 word) */
/* left_permutation, right_permutation, work... */
iwork = itau;
i__1 = *lwork + 1 - iwork;
shgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[
b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[vsl_offset]
, ldvsl, &vsr[vsr_offset], ldvsr, &work[iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
if (iinfo > 0 && iinfo <= *n) {
*info = iinfo;
} else if (iinfo > *n && iinfo <= *n << 1) {
*info = iinfo - *n;
} else {
*info = *n + 6;
}
goto L10;
}
/* Apply permutation to VSL and VSR */
if (ilvsl) {
sggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsl[
vsl_offset], ldvsl, &iinfo);
if (iinfo != 0) {
*info = *n + 7;
goto L10;
}
}
if (ilvsr) {
sggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsr[
vsr_offset], ldvsr, &iinfo);
if (iinfo != 0) {
*info = *n + 8;
goto L10;
}
}
/* Undo scaling */
if (ilascl) {
slascl_("H", &c_n1, &c_n1, &anrmto, &anrm, n, n, &a[a_offset], lda, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
slascl_("G", &c_n1, &c_n1, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
slascl_("G", &c_n1, &c_n1, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
}
if (ilbscl) {
slascl_("U", &c_n1, &c_n1, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
slascl_("G", &c_n1, &c_n1, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
}
L10:
work[1] = (real) lwkopt;
return 0;
/* End of SGEGS */
} /* sgegs_ */
/* Subroutine */ int sggesx_(char *jobvsl, char *jobvsr, char *sort, L_fp
selctg, char *sense, integer *n, real *a, integer *lda, real *b,
integer *ldb, integer *sdim, real *alphar, real *alphai, real *beta,
real *vsl, integer *ldvsl, real *vsr, integer *ldvsr, real *rconde,
real *rcondv, real *work, integer *lwork, integer *iwork, integer *
liwork, logical *bwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset,
vsr_dim1, vsr_offset, i__1, i__2;
real r__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, ip;
real pl, pr, dif[2];
integer ihi, ilo;
real eps;
integer ijob;
real anrm, bnrm;
integer ierr, itau, iwrk, lwrk;
extern logical lsame_(char *, char *);
integer ileft, icols;
logical cursl, ilvsl, ilvsr;
integer irows;
logical lst2sl;
extern /* Subroutine */ int slabad_(real *, real *), sggbak_(char *, char
*, integer *, integer *, integer *, real *, real *, integer *,
real *, integer *, integer *), sggbal_(char *,
integer *, real *, integer *, real *, integer *, integer *,
integer *, real *, real *, real *, integer *);
logical ilascl, ilbscl;
extern doublereal slamch_(char *), slange_(char *, integer *,
integer *, real *, integer *, real *);
real safmin;
extern /* Subroutine */ int sgghrd_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, integer *, real *, integer *
, real *, integer *, integer *);
real safmax;
extern /* Subroutine */ int xerbla_(char *, integer *);
real bignum;
extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, real *, integer *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
integer ijobvl, iright;
extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *);
integer ijobvr;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *);
logical wantsb, wantse, lastsl;
integer liwmin;
real anrmto, bnrmto;
integer minwrk, maxwrk;
logical wantsn;
real smlnum;
extern /* Subroutine */ int shgeqz_(char *, char *, char *, integer *,
integer *, integer *, real *, integer *, real *, integer *, real *
, real *, real *, real *, integer *, real *, integer *, real *,
integer *, integer *), slaset_(char *,
integer *, integer *, real *, real *, real *, integer *),
sorgqr_(integer *, integer *, integer *, real *, integer *, real *
, real *, integer *, integer *), stgsen_(integer *, logical *,
logical *, logical *, integer *, real *, integer *, real *,
integer *, real *, real *, real *, real *, integer *, real *,
integer *, integer *, real *, real *, real *, real *, integer *,
integer *, integer *, integer *);
logical wantst, lquery, wantsv;
extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* .. Function Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SGGESX computes for a pair of N-by-N real nonsymmetric matrices */
/* (A,B), the generalized eigenvalues, the real Schur form (S,T), and, */
/* optionally, the left and/or right matrices of Schur vectors (VSL and */
/* VSR). This gives the generalized Schur factorization */
/* (A,B) = ( (VSL) S (VSR)**T, (VSL) T (VSR)**T ) */
/* Optionally, it also orders the eigenvalues so that a selected cluster */
/* of eigenvalues appears in the leading diagonal blocks of the upper */
/* quasi-triangular matrix S and the upper triangular matrix T; computes */
/* a reciprocal condition number for the average of the selected */
/* eigenvalues (RCONDE); and computes a reciprocal condition number for */
/* the right and left deflating subspaces corresponding to the selected */
/* eigenvalues (RCONDV). The leading columns of VSL and VSR then form */
/* an orthonormal basis for the corresponding left and right eigenspaces */
/* (deflating subspaces). */
/* A generalized eigenvalue for a pair of matrices (A,B) is a scalar w */
/* or a ratio alpha/beta = w, such that A - w*B is singular. It is */
/* usually represented as the pair (alpha,beta), as there is a */
/* reasonable interpretation for beta=0 or for both being zero. */
/* A pair of matrices (S,T) is in generalized real Schur form if T is */
/* upper triangular with non-negative diagonal and S is block upper */
/* triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond */
/* to real generalized eigenvalues, while 2-by-2 blocks of S will be */
/* "standardized" by making the corresponding elements of T have the */
/* form: */
/* [ a 0 ] */
/* [ 0 b ] */
/* and the pair of corresponding 2-by-2 blocks in S and T will have a */
/* complex conjugate pair of generalized eigenvalues. */
/* Arguments */
/* ========= */
/* JOBVSL (input) CHARACTER*1 */
/* = 'N': do not compute the left Schur vectors; */
/* = 'V': compute the left Schur vectors. */
/* JOBVSR (input) CHARACTER*1 */
/* = 'N': do not compute the right Schur vectors; */
/* = 'V': compute the right Schur vectors. */
/* SORT (input) CHARACTER*1 */
/* Specifies whether or not to order the eigenvalues on the */
/* diagonal of the generalized Schur form. */
/* = 'N': Eigenvalues are not ordered; */
/* = 'S': Eigenvalues are ordered (see SELCTG). */
/* SELCTG (external procedure) LOGICAL FUNCTION of three REAL arguments */
/* SELCTG must be declared EXTERNAL in the calling subroutine. */
/* If SORT = 'N', SELCTG is not referenced. */
/* If SORT = 'S', SELCTG is used to select eigenvalues to sort */
/* to the top left of the Schur form. */
/* An eigenvalue (ALPHAR(j)+ALPHAI(j))/BETA(j) is selected if */
/* SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) is true; i.e. if either */
/* one of a complex conjugate pair of eigenvalues is selected, */
/* then both complex eigenvalues are selected. */
/* Note that a selected complex eigenvalue may no longer satisfy */
/* SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) = .TRUE. after ordering, */
/* since ordering may change the value of complex eigenvalues */
/* (especially if the eigenvalue is ill-conditioned), in this */
/* case INFO is set to N+3. */
/* SENSE (input) CHARACTER*1 */
/* Determines which reciprocal condition numbers are computed. */
/* = 'N' : None are computed; */
/* = 'E' : Computed for average of selected eigenvalues only; */
/* = 'V' : Computed for selected deflating subspaces only; */
/* = 'B' : Computed for both. */
/* If SENSE = 'E', 'V', or 'B', SORT must equal 'S'. */
/* N (input) INTEGER */
/* The order of the matrices A, B, VSL, and VSR. N >= 0. */
/* A (input/output) REAL array, dimension (LDA, N) */
/* On entry, the first of the pair of matrices. */
/* On exit, A has been overwritten by its generalized Schur */
/* form S. */
/* LDA (input) INTEGER */
/* The leading dimension of A. LDA >= max(1,N). */
/* B (input/output) REAL array, dimension (LDB, N) */
/* On entry, the second of the pair of matrices. */
/* On exit, B has been overwritten by its generalized Schur */
/* form T. */
/* LDB (input) INTEGER */
/* The leading dimension of B. LDB >= max(1,N). */
/* SDIM (output) INTEGER */
/* If SORT = 'N', SDIM = 0. */
/* If SORT = 'S', SDIM = number of eigenvalues (after sorting) */
/* for which SELCTG is true. (Complex conjugate pairs for which */
/* SELCTG is true for either eigenvalue count as 2.) */
/* ALPHAR (output) REAL array, dimension (N) */
/* ALPHAI (output) REAL array, dimension (N) */
/* BETA (output) REAL array, dimension (N) */
/* On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will */
/* be the generalized eigenvalues. ALPHAR(j) + ALPHAI(j)*i */
/* and BETA(j),j=1,...,N are the diagonals of the complex Schur */
/* form (S,T) that would result if the 2-by-2 diagonal blocks of */
/* the real Schur form of (A,B) were further reduced to */
/* triangular form using 2-by-2 complex unitary transformations. */
/* If ALPHAI(j) is zero, then the j-th eigenvalue is real; if */
/* positive, then the j-th and (j+1)-st eigenvalues are a */
/* complex conjugate pair, with ALPHAI(j+1) negative. */
/* Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) */
/* may easily over- or underflow, and BETA(j) may even be zero. */
/* Thus, the user should avoid naively computing the ratio. */
/* However, ALPHAR and ALPHAI will be always less than and */
/* usually comparable with norm(A) in magnitude, and BETA always */
/* less than and usually comparable with norm(B). */
/* VSL (output) REAL array, dimension (LDVSL,N) */
/* If JOBVSL = 'V', VSL will contain the left Schur vectors. */
/* Not referenced if JOBVSL = 'N'. */
/* LDVSL (input) INTEGER */
/* The leading dimension of the matrix VSL. LDVSL >=1, and */
/* if JOBVSL = 'V', LDVSL >= N. */
/* VSR (output) REAL array, dimension (LDVSR,N) */
/* If JOBVSR = 'V', VSR will contain the right Schur vectors. */
/* Not referenced if JOBVSR = 'N'. */
/* LDVSR (input) INTEGER */
/* The leading dimension of the matrix VSR. LDVSR >= 1, and */
/* if JOBVSR = 'V', LDVSR >= N. */
/* RCONDE (output) REAL array, dimension ( 2 ) */
/* If SENSE = 'E' or 'B', RCONDE(1) and RCONDE(2) contain the */
/* reciprocal condition numbers for the average of the selected */
/* eigenvalues. */
/* Not referenced if SENSE = 'N' or 'V'. */
/* RCONDV (output) REAL array, dimension ( 2 ) */
/* If SENSE = 'V' or 'B', RCONDV(1) and RCONDV(2) contain the */
/* reciprocal condition numbers for the selected deflating */
/* subspaces. */
/* Not referenced if SENSE = 'N' or 'E'. */
/* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. */
/* If N = 0, LWORK >= 1, else if SENSE = 'E', 'V', or 'B', */
/* LWORK >= max( 8*N, 6*N+16, 2*SDIM*(N-SDIM) ), else */
/* LWORK >= max( 8*N, 6*N+16 ). */
/* Note that 2*SDIM*(N-SDIM) <= N*N/2. */
/* Note also that an error is only returned if */
/* LWORK < max( 8*N, 6*N+16), but if SENSE = 'E' or 'V' or 'B' */
/* this may not be large enough. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the bound on the optimal size of the WORK */
/* array and the minimum size of the IWORK array, returns these */
/* values as the first entries of the WORK and IWORK arrays, and */
/* no error message related to LWORK or LIWORK is issued by */
/* XERBLA. */
/* IWORK (workspace) INTEGER array, dimension (MAX(1,LIWORK)) */
/* On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK. */
/* LIWORK (input) INTEGER */
/* The dimension of the array IWORK. */
/* If SENSE = 'N' or N = 0, LIWORK >= 1, otherwise */
/* LIWORK >= N+6. */
/* If LIWORK = -1, then a workspace query is assumed; the */
/* routine only calculates the bound on the optimal size of the */
/* WORK array and the minimum size of the IWORK array, returns */
/* these values as the first entries of the WORK and IWORK */
/* arrays, and no error message related to LWORK or LIWORK is */
/* issued by XERBLA. */
/* BWORK (workspace) LOGICAL array, dimension (N) */
/* Not referenced if SORT = 'N'. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* = 1,...,N: */
/* The QZ iteration failed. (A,B) are not in Schur */
/* form, but ALPHAR(j), ALPHAI(j), and BETA(j) should */
/* be correct for j=INFO+1,...,N. */
/* > N: =N+1: other than QZ iteration failed in SHGEQZ */
/* =N+2: after reordering, roundoff changed values of */
/* some complex eigenvalues so that leading */
/* eigenvalues in the Generalized Schur form no */
/* longer satisfy SELCTG=.TRUE. This could also */
/* be caused due to scaling. */
/* =N+3: reordering failed in STGSEN. */
/* Further details */
/* =============== */
/* An approximate (asymptotic) bound on the average absolute error of */
/* the selected eigenvalues is */
/* EPS * norm((A, B)) / RCONDE( 1 ). */
/* An approximate (asymptotic) bound on the maximum angular error in */
/* the computed deflating subspaces is */
/* EPS * norm((A, B)) / RCONDV( 2 ). */
/* See LAPACK User's Guide, section 4.11 for more information. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--alphar;
--alphai;
--beta;
vsl_dim1 = *ldvsl;
vsl_offset = 1 + vsl_dim1;
vsl -= vsl_offset;
vsr_dim1 = *ldvsr;
vsr_offset = 1 + vsr_dim1;
vsr -= vsr_offset;
--rconde;
--rcondv;
--work;
--iwork;
--bwork;
/* Function Body */
if (lsame_(jobvsl, "N")) {
ijobvl = 1;
ilvsl = FALSE_;
} else if (lsame_(jobvsl, "V")) {
ijobvl = 2;
ilvsl = TRUE_;
} else {
ijobvl = -1;
ilvsl = FALSE_;
}
if (lsame_(jobvsr, "N")) {
ijobvr = 1;
ilvsr = FALSE_;
} else if (lsame_(jobvsr, "V")) {
ijobvr = 2;
ilvsr = TRUE_;
} else {
ijobvr = -1;
ilvsr = FALSE_;
}
wantst = lsame_(sort, "S");
wantsn = lsame_(sense, "N");
wantse = lsame_(sense, "E");
wantsv = lsame_(sense, "V");
wantsb = lsame_(sense, "B");
lquery = *lwork == -1 || *liwork == -1;
if (wantsn) {
ijob = 0;
} else if (wantse) {
ijob = 1;
} else if (wantsv) {
ijob = 2;
} else if (wantsb) {
ijob = 4;
}
/* Test the input arguments */
*info = 0;
if (ijobvl <= 0) {
*info = -1;
} else if (ijobvr <= 0) {
*info = -2;
} else if (! wantst && ! lsame_(sort, "N")) {
*info = -3;
} else if (! (wantsn || wantse || wantsv || wantsb) || ! wantst && !
wantsn) {
*info = -5;
} else if (*n < 0) {
*info = -6;
} else if (*lda < max(1,*n)) {
*info = -8;
} else if (*ldb < max(1,*n)) {
*info = -10;
} else if (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
*info = -16;
} else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
*info = -18;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV.) */
if (*info == 0) {
if (*n > 0) {
/* Computing MAX */
i__1 = *n << 3, i__2 = *n * 6 + 16;
minwrk = max(i__1,i__2);
maxwrk = minwrk - *n + *n * ilaenv_(&c__1, "SGEQRF", " ", n, &
c__1, n, &c__0);
/* Computing MAX */
i__1 = maxwrk, i__2 = minwrk - *n + *n * ilaenv_(&c__1, "SORMQR",
" ", n, &c__1, n, &c_n1);
maxwrk = max(i__1,i__2);
if (ilvsl) {
/* Computing MAX */
i__1 = maxwrk, i__2 = minwrk - *n + *n * ilaenv_(&c__1, "SOR"
"GQR", " ", n, &c__1, n, &c_n1);
maxwrk = max(i__1,i__2);
}
lwrk = maxwrk;
if (ijob >= 1) {
/* Computing MAX */
i__1 = lwrk, i__2 = *n * *n / 2;
lwrk = max(i__1,i__2);
}
} else {
minwrk = 1;
maxwrk = 1;
lwrk = 1;
}
work[1] = (real) lwrk;
if (wantsn || *n == 0) {
liwmin = 1;
} else {
liwmin = *n + 6;
}
iwork[1] = liwmin;
if (*lwork < minwrk && ! lquery) {
*info = -22;
} else if (*liwork < liwmin && ! lquery) {
*info = -24;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGGESX", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
*sdim = 0;
return 0;
}
/* Get machine constants */
eps = slamch_("P");
safmin = slamch_("S");
safmax = 1.f / safmin;
slabad_(&safmin, &safmax);
smlnum = sqrt(safmin) / eps;
bignum = 1.f / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = slange_("M", n, n, &a[a_offset], lda, &work[1]);
ilascl = FALSE_;
if (anrm > 0.f && anrm < smlnum) {
anrmto = smlnum;
ilascl = TRUE_;
} else if (anrm > bignum) {
anrmto = bignum;
ilascl = TRUE_;
}
if (ilascl) {
slascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
ierr);
}
/* Scale B if max element outside range [SMLNUM,BIGNUM] */
bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]);
ilbscl = FALSE_;
if (bnrm > 0.f && bnrm < smlnum) {
bnrmto = smlnum;
ilbscl = TRUE_;
} else if (bnrm > bignum) {
bnrmto = bignum;
ilbscl = TRUE_;
}
if (ilbscl) {
slascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
ierr);
}
/* Permute the matrix to make it more nearly triangular */
/* (Workspace: need 6*N + 2*N for permutation parameters) */
ileft = 1;
iright = *n + 1;
iwrk = iright + *n;
sggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
ileft], &work[iright], &work[iwrk], &ierr);
/* Reduce B to triangular form (QR decomposition of B) */
/* (Workspace: need N, prefer N*NB) */
irows = ihi + 1 - ilo;
icols = *n + 1 - ilo;
itau = iwrk;
iwrk = itau + irows;
i__1 = *lwork + 1 - iwrk;
sgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
iwrk], &i__1, &ierr);
/* Apply the orthogonal transformation to matrix A */
/* (Workspace: need N, prefer N*NB) */
i__1 = *lwork + 1 - iwrk;
sormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwrk], &i__1, &
ierr);
/* Initialize VSL */
/* (Workspace: need N, prefer N*NB) */
if (ilvsl) {
slaset_("Full", n, n, &c_b42, &c_b43, &vsl[vsl_offset], ldvsl);
if (irows > 1) {
i__1 = irows - 1;
i__2 = irows - 1;
slacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vsl[
ilo + 1 + ilo * vsl_dim1], ldvsl);
}
i__1 = *lwork + 1 - iwrk;
sorgqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, &
work[itau], &work[iwrk], &i__1, &ierr);
}
/* Initialize VSR */
if (ilvsr) {
slaset_("Full", n, n, &c_b42, &c_b43, &vsr[vsr_offset], ldvsr);
}
/* Reduce to generalized Hessenberg form */
/* (Workspace: none needed) */
sgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &ierr);
*sdim = 0;
/* Perform QZ algorithm, computing Schur vectors if desired */
/* (Workspace: need N) */
iwrk = itau;
i__1 = *lwork + 1 - iwrk;
shgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[
b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[vsl_offset]
, ldvsl, &vsr[vsr_offset], ldvsr, &work[iwrk], &i__1, &ierr);
if (ierr != 0) {
if (ierr > 0 && ierr <= *n) {
*info = ierr;
} else if (ierr > *n && ierr <= *n << 1) {
*info = ierr - *n;
} else {
*info = *n + 1;
}
goto L50;
}
/* Sort eigenvalues ALPHA/BETA and compute the reciprocal of */
/* condition number(s) */
/* (Workspace: If IJOB >= 1, need MAX( 8*(N+1), 2*SDIM*(N-SDIM) ) */
/* otherwise, need 8*(N+1) ) */
if (wantst) {
/* Undo scaling on eigenvalues before SELCTGing */
if (ilascl) {
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1],
n, &ierr);
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1],
n, &ierr);
}
if (ilbscl) {
slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n,
&ierr);
}
/* Select eigenvalues */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
bwork[i__] = (*selctg)(&alphar[i__], &alphai[i__], &beta[i__]);
/* L10: */
}
/* Reorder eigenvalues, transform Generalized Schur vectors, and */
/* compute reciprocal condition numbers */
i__1 = *lwork - iwrk + 1;
stgsen_(&ijob, &ilvsl, &ilvsr, &bwork[1], n, &a[a_offset], lda, &b[
b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[
vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, sdim, &pl, &pr,
dif, &work[iwrk], &i__1, &iwork[1], liwork, &ierr);
if (ijob >= 1) {
/* Computing MAX */
i__1 = maxwrk, i__2 = (*sdim << 1) * (*n - *sdim);
maxwrk = max(i__1,i__2);
}
if (ierr == -22) {
/* not enough real workspace */
*info = -22;
} else {
if (ijob == 1 || ijob == 4) {
rconde[1] = pl;
rconde[2] = pr;
}
if (ijob == 2 || ijob == 4) {
rcondv[1] = dif[0];
rcondv[2] = dif[1];
}
if (ierr == 1) {
*info = *n + 3;
}
}
}
/* Apply permutation to VSL and VSR */
/* (Workspace: none needed) */
if (ilvsl) {
sggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsl[
vsl_offset], ldvsl, &ierr);
}
if (ilvsr) {
sggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsr[
vsr_offset], ldvsr, &ierr);
}
/* Check if unscaling would cause over/underflow, if so, rescale */
/* (ALPHAR(I),ALPHAI(I),BETA(I)) so BETA(I) is on the order of */
/* B(I,I) and ALPHAR(I) and ALPHAI(I) are on the order of A(I,I) */
if (ilascl) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (alphai[i__] != 0.f) {
if (alphar[i__] / safmax > anrmto / anrm || safmin / alphar[
i__] > anrm / anrmto) {
work[1] = (r__1 = a[i__ + i__ * a_dim1] / alphar[i__],
dabs(r__1));
beta[i__] *= work[1];
alphar[i__] *= work[1];
alphai[i__] *= work[1];
} else if (alphai[i__] / safmax > anrmto / anrm || safmin /
alphai[i__] > anrm / anrmto) {
work[1] = (r__1 = a[i__ + (i__ + 1) * a_dim1] / alphai[
i__], dabs(r__1));
beta[i__] *= work[1];
alphar[i__] *= work[1];
alphai[i__] *= work[1];
}
}
/* L20: */
}
}
if (ilbscl) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (alphai[i__] != 0.f) {
if (beta[i__] / safmax > bnrmto / bnrm || safmin / beta[i__]
> bnrm / bnrmto) {
work[1] = (r__1 = b[i__ + i__ * b_dim1] / beta[i__], dabs(
r__1));
beta[i__] *= work[1];
alphar[i__] *= work[1];
alphai[i__] *= work[1];
}
}
/* L25: */
}
}
/* Undo scaling */
if (ilascl) {
slascl_("H", &c__0, &c__0, &anrmto, &anrm, n, n, &a[a_offset], lda, &
ierr);
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
ierr);
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
ierr);
}
if (ilbscl) {
slascl_("U", &c__0, &c__0, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
ierr);
slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
ierr);
}
if (wantst) {
/* Check if reordering is correct */
lastsl = TRUE_;
lst2sl = TRUE_;
*sdim = 0;
ip = 0;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
cursl = (*selctg)(&alphar[i__], &alphai[i__], &beta[i__]);
if (alphai[i__] == 0.f) {
if (cursl) {
++(*sdim);
}
ip = 0;
if (cursl && ! lastsl) {
*info = *n + 2;
}
} else {
if (ip == 1) {
/* Last eigenvalue of conjugate pair */
cursl = cursl || lastsl;
lastsl = cursl;
if (cursl) {
*sdim += 2;
}
ip = -1;
if (cursl && ! lst2sl) {
*info = *n + 2;
}
} else {
/* First eigenvalue of conjugate pair */
ip = 1;
}
}
lst2sl = lastsl;
lastsl = cursl;
/* L40: */
}
}
L50:
work[1] = (real) maxwrk;
iwork[1] = liwmin;
return 0;
/* End of SGGESX */
} /* sggesx_ */
/* Subroutine */ int serrqr_(char *path, integer *nunit)
{
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
static integer info;
static real a[4] /* was [2][2] */, b[2];
static integer i__, j;
static real w[2], x[2];
extern /* Subroutine */ int sgeqr2_(integer *, integer *, real *, integer
*, real *, real *, integer *);
static real af[4] /* was [2][2] */;
extern /* Subroutine */ int sorg2r_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *), sorm2r_(char *, char *,
integer *, integer *, integer *, real *, integer *, real *, real *
, integer *, real *, integer *), alaesm_(char *,
logical *, integer *), chkxer_(char *, integer *, integer
*, logical *, logical *), sgeqrf_(integer *, integer *,
real *, integer *, real *, real *, integer *, integer *), sgeqrs_(
integer *, integer *, integer *, real *, integer *, real *, real *
, integer *, real *, integer *, integer *), sorgqr_(integer *,
integer *, integer *, real *, integer *, real *, real *, integer *
, integer *), sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
#define a_ref(a_1,a_2) a[(a_2)*2 + a_1 - 3]
#define af_ref(a_1,a_2) af[(a_2)*2 + a_1 - 3]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
SERRQR tests the error exits for the REAL routines
that use the QR decomposition of a general matrix.
Arguments
=========
PATH (input) CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT (input) INTEGER
The unit number for output.
===================================================================== */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
/* Set the variables to innocuous values. */
for (j = 1; j <= 2; ++j) {
for (i__ = 1; i__ <= 2; ++i__) {
a_ref(i__, j) = 1.f / (real) (i__ + j);
af_ref(i__, j) = 1.f / (real) (i__ + j);
/* L10: */
}
b[j - 1] = 0.f;
w[j - 1] = 0.f;
x[j - 1] = 0.f;
/* L20: */
}
infoc_1.ok = TRUE_;
/* Error exits for QR factorization
SGEQRF */
s_copy(srnamc_1.srnamt, "SGEQRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgeqrf_(&c_n1, &c__0, a, &c__1, b, w, &c__1, &info);
chkxer_("SGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeqrf_(&c__0, &c_n1, a, &c__1, b, w, &c__1, &info);
chkxer_("SGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgeqrf_(&c__2, &c__1, a, &c__1, b, w, &c__1, &info);
chkxer_("SGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sgeqrf_(&c__1, &c__2, a, &c__1, b, w, &c__1, &info);
chkxer_("SGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGEQR2 */
s_copy(srnamc_1.srnamt, "SGEQR2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgeqr2_(&c_n1, &c__0, a, &c__1, b, w, &info);
chkxer_("SGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeqr2_(&c__0, &c_n1, a, &c__1, b, w, &info);
chkxer_("SGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgeqr2_(&c__2, &c__1, a, &c__1, b, w, &info);
chkxer_("SGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGEQRS */
s_copy(srnamc_1.srnamt, "SGEQRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgeqrs_(&c_n1, &c__0, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeqrs_(&c__0, &c_n1, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeqrs_(&c__1, &c__2, &c__0, a, &c__2, x, b, &c__2, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgeqrs_(&c__0, &c__0, &c_n1, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sgeqrs_(&c__2, &c__1, &c__0, a, &c__1, x, b, &c__2, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
sgeqrs_(&c__2, &c__1, &c__0, a, &c__2, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sgeqrs_(&c__1, &c__1, &c__2, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("SGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SORGQR */
s_copy(srnamc_1.srnamt, "SORGQR", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sorgqr_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorgqr_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorgqr_(&c__1, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorgqr_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorgqr_(&c__1, &c__1, &c__2, a, &c__1, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorgqr_(&c__2, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
sorgqr_(&c__2, &c__2, &c__0, a, &c__2, x, w, &c__1, &info);
chkxer_("SORGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SORG2R */
s_copy(srnamc_1.srnamt, "SORG2R", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sorg2r_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorg2r_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorg2r_(&c__1, &c__2, &c__0, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorg2r_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorg2r_(&c__2, &c__1, &c__2, a, &c__2, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorg2r_(&c__2, &c__1, &c__0, a, &c__1, x, w, &info);
chkxer_("SORG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SORMQR */
s_copy(srnamc_1.srnamt, "SORMQR", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sormqr_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sormqr_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sormqr_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sormqr_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sormqr_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sormqr_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sormqr_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sormqr_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sormqr_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sormqr_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
sormqr_("L", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
sormqr_("R", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("SORMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SORM2R */
s_copy(srnamc_1.srnamt, "SORM2R", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sorm2r_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sorm2r_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sorm2r_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sorm2r_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorm2r_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorm2r_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sorm2r_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sorm2r_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sorm2r_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sorm2r_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &info);
chkxer_("SORM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* Print a summary line. */
alaesm_(path, &infoc_1.ok, &infoc_1.nout);
return 0;
/* End of SERRQR */
} /* serrqr_ */
/* Subroutine */
int sgegv_(char *jobvl, char *jobvr, integer *n, real *a, integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real *beta, real *vl, integer *ldvl, real *vr, integer *ldvr, real *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, i__2;
real r__1, r__2, r__3, r__4;
/* Local variables */
integer jc, nb, in, jr, nb1, nb2, nb3, ihi, ilo;
real eps;
logical ilv;
real absb, anrm, bnrm;
integer itau;
real temp;
logical ilvl, ilvr;
integer lopt;
real anrm1, anrm2, bnrm1, bnrm2, absai, scale, absar, sbeta;
extern logical lsame_(char *, char *);
integer ileft, iinfo, icols, iwork, irows;
real salfai;
extern /* Subroutine */
int sggbak_(char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, integer * ), sggbal_(char *, integer *, real *, integer *, real *, integer *, integer *, integer *, real *, real *, real *, integer *);
real salfar;
extern real slamch_(char *), slange_(char *, integer *, integer *, real *, integer *, real *);
real safmin;
extern /* Subroutine */
int sgghrd_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, integer *, real *, integer * , real *, integer *, integer *);
real safmax;
char chtemp[1];
logical ldumma[1];
extern /* Subroutine */
int slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
integer ijobvl, iright;
logical ilimit;
extern /* Subroutine */
int sgeqrf_(integer *, integer *, real *, integer *, real *, real *, integer *, integer *);
integer ijobvr;
extern /* Subroutine */
int slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, real *, integer *), stgevc_( char *, char *, logical *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, integer *, integer *, integer *, real *, integer *);
real onepls;
integer lwkmin;
extern /* Subroutine */
int shgeqz_(char *, char *, char *, integer *, integer *, integer *, real *, integer *, real *, integer *, real * , real *, real *, real *, integer *, real *, integer *, real *, integer *, integer *), sorgqr_(integer *, integer *, integer *, real *, integer *, real *, real *, integer * , integer *);
integer lwkopt;
logical lquery;
extern /* Subroutine */
int sormqr_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *, integer *);
/* -- LAPACK driver routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--alphar;
--alphai;
--beta;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--work;
/* Function Body */
if (lsame_(jobvl, "N"))
{
ijobvl = 1;
ilvl = FALSE_;
}
else if (lsame_(jobvl, "V"))
{
ijobvl = 2;
ilvl = TRUE_;
}
else
{
ijobvl = -1;
ilvl = FALSE_;
}
if (lsame_(jobvr, "N"))
{
ijobvr = 1;
ilvr = FALSE_;
}
else if (lsame_(jobvr, "V"))
{
ijobvr = 2;
ilvr = TRUE_;
}
else
{
ijobvr = -1;
ilvr = FALSE_;
}
ilv = ilvl || ilvr;
/* Test the input arguments */
/* Computing MAX */
i__1 = *n << 3;
lwkmin = max(i__1,1);
lwkopt = lwkmin;
work[1] = (real) lwkopt;
lquery = *lwork == -1;
*info = 0;
if (ijobvl <= 0)
{
*info = -1;
}
else if (ijobvr <= 0)
{
*info = -2;
}
else if (*n < 0)
{
*info = -3;
}
else if (*lda < max(1,*n))
{
*info = -5;
}
else if (*ldb < max(1,*n))
{
*info = -7;
}
else if (*ldvl < 1 || ilvl && *ldvl < *n)
{
*info = -12;
}
else if (*ldvr < 1 || ilvr && *ldvr < *n)
{
*info = -14;
}
else if (*lwork < lwkmin && ! lquery)
{
*info = -16;
}
if (*info == 0)
{
nb1 = ilaenv_(&c__1, "SGEQRF", " ", n, n, &c_n1, &c_n1);
nb2 = ilaenv_(&c__1, "SORMQR", " ", n, n, n, &c_n1);
nb3 = ilaenv_(&c__1, "SORGQR", " ", n, n, n, &c_n1);
/* Computing MAX */
i__1 = max(nb1,nb2);
nb = max(i__1,nb3);
/* Computing MAX */
i__1 = *n * 6;
i__2 = *n * (nb + 1); // , expr subst
lopt = (*n << 1) + max(i__1,i__2);
work[1] = (real) lopt;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("SGEGV ", &i__1);
return 0;
}
else if (lquery)
{
return 0;
}
/* Quick return if possible */
if (*n == 0)
{
return 0;
}
/* Get machine constants */
eps = slamch_("E") * slamch_("B");
safmin = slamch_("S");
safmin += safmin;
safmax = 1.f / safmin;
onepls = eps * 4 + 1.f;
/* Scale A */
anrm = slange_("M", n, n, &a[a_offset], lda, &work[1]);
anrm1 = anrm;
anrm2 = 1.f;
if (anrm < 1.f)
{
if (safmax * anrm < 1.f)
{
anrm1 = safmin;
anrm2 = safmax * anrm;
}
}
if (anrm > 0.f)
{
slascl_("G", &c_n1, &c_n1, &anrm, &c_b27, n, n, &a[a_offset], lda, & iinfo);
if (iinfo != 0)
{
*info = *n + 10;
return 0;
}
}
/* Scale B */
bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]);
bnrm1 = bnrm;
bnrm2 = 1.f;
if (bnrm < 1.f)
{
if (safmax * bnrm < 1.f)
{
bnrm1 = safmin;
bnrm2 = safmax * bnrm;
}
}
if (bnrm > 0.f)
{
slascl_("G", &c_n1, &c_n1, &bnrm, &c_b27, n, n, &b[b_offset], ldb, & iinfo);
if (iinfo != 0)
{
*info = *n + 10;
return 0;
}
}
/* Permute the matrix to make it more nearly triangular */
/* Workspace layout: (8*N words -- "work" requires 6*N words) */
/* left_permutation, right_permutation, work... */
ileft = 1;
iright = *n + 1;
iwork = iright + *n;
sggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[ ileft], &work[iright], &work[iwork], &iinfo);
if (iinfo != 0)
{
*info = *n + 1;
goto L120;
}
/* Reduce B to triangular form, and initialize VL and/or VR */
/* Workspace layout: ("work..." must have at least N words) */
/* left_permutation, right_permutation, tau, work... */
irows = ihi + 1 - ilo;
if (ilv)
{
icols = *n + 1 - ilo;
}
else
{
icols = irows;
}
itau = iwork;
iwork = itau + irows;
i__1 = *lwork + 1 - iwork;
sgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[ iwork], &i__1, &iinfo);
if (iinfo >= 0)
{
/* Computing MAX */
i__1 = lwkopt;
i__2 = (integer) work[iwork] + iwork - 1; // , expr subst
lwkopt = max(i__1,i__2);
}
if (iinfo != 0)
{
*info = *n + 2;
goto L120;
}
i__1 = *lwork + 1 - iwork;
sormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, & work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwork], &i__1, & iinfo);
if (iinfo >= 0)
{
/* Computing MAX */
i__1 = lwkopt;
i__2 = (integer) work[iwork] + iwork - 1; // , expr subst
lwkopt = max(i__1,i__2);
}
if (iinfo != 0)
{
*info = *n + 3;
goto L120;
}
if (ilvl)
{
slaset_("Full", n, n, &c_b38, &c_b27, &vl[vl_offset], ldvl) ;
i__1 = irows - 1;
i__2 = irows - 1;
slacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vl[ilo + 1 + ilo * vl_dim1], ldvl);
i__1 = *lwork + 1 - iwork;
sorgqr_(&irows, &irows, &irows, &vl[ilo + ilo * vl_dim1], ldvl, &work[ itau], &work[iwork], &i__1, &iinfo);
if (iinfo >= 0)
{
/* Computing MAX */
i__1 = lwkopt;
i__2 = (integer) work[iwork] + iwork - 1; // , expr subst
lwkopt = max(i__1,i__2);
}
if (iinfo != 0)
{
*info = *n + 4;
goto L120;
}
}
if (ilvr)
{
slaset_("Full", n, n, &c_b38, &c_b27, &vr[vr_offset], ldvr) ;
}
/* Reduce to generalized Hessenberg form */
if (ilv)
{
/* Eigenvectors requested -- work on whole matrix. */
sgghrd_(jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset], ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &iinfo);
}
else
{
sgghrd_("N", "N", &irows, &c__1, &irows, &a[ilo + ilo * a_dim1], lda, &b[ilo + ilo * b_dim1], ldb, &vl[vl_offset], ldvl, &vr[ vr_offset], ldvr, &iinfo);
}
if (iinfo != 0)
{
*info = *n + 5;
goto L120;
}
/* Perform QZ algorithm */
/* Workspace layout: ("work..." must have at least 1 word) */
/* left_permutation, right_permutation, work... */
iwork = itau;
if (ilv)
{
*(unsigned char *)chtemp = 'S';
}
else
{
*(unsigned char *)chtemp = 'E';
}
i__1 = *lwork + 1 - iwork;
shgeqz_(chtemp, jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[ b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &work[iwork], &i__1, &iinfo);
if (iinfo >= 0)
{
/* Computing MAX */
i__1 = lwkopt;
i__2 = (integer) work[iwork] + iwork - 1; // , expr subst
lwkopt = max(i__1,i__2);
}
if (iinfo != 0)
{
if (iinfo > 0 && iinfo <= *n)
{
*info = iinfo;
}
else if (iinfo > *n && iinfo <= *n << 1)
{
*info = iinfo - *n;
}
else
{
*info = *n + 6;
}
goto L120;
}
if (ilv)
{
/* Compute Eigenvectors (STGEVC requires 6*N words of workspace) */
if (ilvl)
{
if (ilvr)
{
*(unsigned char *)chtemp = 'B';
}
else
{
*(unsigned char *)chtemp = 'L';
}
}
else
{
*(unsigned char *)chtemp = 'R';
}
stgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &work[ iwork], &iinfo);
if (iinfo != 0)
{
*info = *n + 7;
goto L120;
}
/* Undo balancing on VL and VR, rescale */
if (ilvl)
{
sggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, & vl[vl_offset], ldvl, &iinfo);
if (iinfo != 0)
{
*info = *n + 8;
goto L120;
}
i__1 = *n;
for (jc = 1;
jc <= i__1;
++jc)
{
if (alphai[jc] < 0.f)
{
goto L50;
}
temp = 0.f;
if (alphai[jc] == 0.f)
{
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
/* Computing MAX */
r__2 = temp;
r__3 = (r__1 = vl[jr + jc * vl_dim1], f2c_abs(r__1)); // , expr subst
temp = max(r__2,r__3);
/* L10: */
}
}
else
{
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
/* Computing MAX */
r__3 = temp;
r__4 = (r__1 = vl[jr + jc * vl_dim1], f2c_abs(r__1)) + (r__2 = vl[jr + (jc + 1) * vl_dim1], f2c_abs(r__2)); // , expr subst
temp = max(r__3,r__4);
/* L20: */
}
}
if (temp < safmin)
{
goto L50;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f)
{
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
vl[jr + jc * vl_dim1] *= temp;
/* L30: */
}
}
else
{
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
vl[jr + jc * vl_dim1] *= temp;
vl[jr + (jc + 1) * vl_dim1] *= temp;
/* L40: */
}
}
L50:
;
}
}
if (ilvr)
{
sggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, & vr[vr_offset], ldvr, &iinfo);
if (iinfo != 0)
{
*info = *n + 9;
goto L120;
}
i__1 = *n;
for (jc = 1;
jc <= i__1;
++jc)
{
if (alphai[jc] < 0.f)
{
goto L100;
}
temp = 0.f;
if (alphai[jc] == 0.f)
{
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
/* Computing MAX */
r__2 = temp;
r__3 = (r__1 = vr[jr + jc * vr_dim1], f2c_abs(r__1)); // , expr subst
temp = max(r__2,r__3);
/* L60: */
}
}
else
{
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
/* Computing MAX */
r__3 = temp;
r__4 = (r__1 = vr[jr + jc * vr_dim1], f2c_abs(r__1)) + (r__2 = vr[jr + (jc + 1) * vr_dim1], f2c_abs(r__2)); // , expr subst
temp = max(r__3,r__4);
/* L70: */
}
}
if (temp < safmin)
{
goto L100;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f)
{
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
vr[jr + jc * vr_dim1] *= temp;
/* L80: */
}
}
else
{
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
vr[jr + jc * vr_dim1] *= temp;
vr[jr + (jc + 1) * vr_dim1] *= temp;
/* L90: */
}
}
L100:
;
}
}
/* End of eigenvector calculation */
}
/* Undo scaling in alpha, beta */
/* Note: this does not give the alpha and beta for the unscaled */
/* problem. */
/* Un-scaling is limited to avoid underflow in alpha and beta */
/* if they are significant. */
i__1 = *n;
for (jc = 1;
jc <= i__1;
++jc)
{
absar = (r__1 = alphar[jc], f2c_abs(r__1));
absai = (r__1 = alphai[jc], f2c_abs(r__1));
absb = (r__1 = beta[jc], f2c_abs(r__1));
salfar = anrm * alphar[jc];
salfai = anrm * alphai[jc];
sbeta = bnrm * beta[jc];
ilimit = FALSE_;
scale = 1.f;
/* Check for significant underflow in ALPHAI */
/* Computing MAX */
r__1 = safmin, r__2 = eps * absar;
r__1 = max(r__1,r__2);
r__2 = eps * absb; // ; expr subst
if (f2c_abs(salfai) < safmin && absai >= max(r__1,r__2))
{
ilimit = TRUE_;
/* Computing MAX */
r__1 = onepls * safmin;
r__2 = anrm2 * absai; // , expr subst
scale = onepls * safmin / anrm1 / max(r__1,r__2);
}
else if (salfai == 0.f)
{
/* If insignificant underflow in ALPHAI, then make the */
/* conjugate eigenvalue real. */
if (alphai[jc] < 0.f && jc > 1)
{
alphai[jc - 1] = 0.f;
}
else if (alphai[jc] > 0.f && jc < *n)
{
alphai[jc + 1] = 0.f;
}
}
/* Check for significant underflow in ALPHAR */
/* Computing MAX */
r__1 = safmin, r__2 = eps * absai;
r__1 = max(r__1,r__2);
r__2 = eps * absb; // ; expr subst
if (f2c_abs(salfar) < safmin && absar >= max(r__1,r__2))
{
ilimit = TRUE_;
/* Computing MAX */
/* Computing MAX */
r__3 = onepls * safmin;
r__4 = anrm2 * absar; // , expr subst
r__1 = scale;
r__2 = onepls * safmin / anrm1 / max(r__3,r__4); // , expr subst
scale = max(r__1,r__2);
}
/* Check for significant underflow in BETA */
/* Computing MAX */
r__1 = safmin, r__2 = eps * absar;
r__1 = max(r__1,r__2);
r__2 = eps * absai; // ; expr subst
if (f2c_abs(sbeta) < safmin && absb >= max(r__1,r__2))
{
ilimit = TRUE_;
/* Computing MAX */
/* Computing MAX */
r__3 = onepls * safmin;
r__4 = bnrm2 * absb; // , expr subst
r__1 = scale;
r__2 = onepls * safmin / bnrm1 / max(r__3,r__4); // , expr subst
scale = max(r__1,r__2);
}
/* Check for possible overflow when limiting scaling */
if (ilimit)
{
/* Computing MAX */
r__1 = f2c_abs(salfar), r__2 = f2c_abs(salfai);
r__1 = max(r__1,r__2);
r__2 = f2c_abs(sbeta); // ; expr subst
temp = scale * safmin * max(r__1,r__2);
if (temp > 1.f)
{
scale /= temp;
}
if (scale < 1.f)
{
ilimit = FALSE_;
}
}
/* Recompute un-scaled ALPHAR, ALPHAI, BETA if necessary. */
if (ilimit)
{
salfar = scale * alphar[jc] * anrm;
salfai = scale * alphai[jc] * anrm;
sbeta = scale * beta[jc] * bnrm;
}
alphar[jc] = salfar;
alphai[jc] = salfai;
beta[jc] = sbeta;
/* L110: */
}
L120:
work[1] = (real) lwkopt;
return 0;
/* End of SGEGV */
}
/* Subroutine */ int sggev_(char *jobvl, char *jobvr, integer *n, real *a,
integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real
*beta, real *vl, integer *ldvl, real *vr, integer *ldvr, real *work,
integer *lwork, integer *info)
{
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
SGGEV computes for a pair of N-by-N real nonsymmetric matrices (A,B)
the generalized eigenvalues, and optionally, the left and/or right
generalized eigenvectors.
A generalized eigenvalue for a pair of matrices (A,B) is a scalar
lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
singular. It is usually represented as the pair (alpha,beta), as
there is a reasonable interpretation for beta=0, and even for both
being zero.
The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
of (A,B) satisfies
A * v(j) = lambda(j) * B * v(j).
The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
of (A,B) satisfies
u(j)**H * A = lambda(j) * u(j)**H * B .
where u(j)**H is the conjugate-transpose of u(j).
Arguments
=========
JOBVL (input) CHARACTER*1
= 'N': do not compute the left generalized eigenvectors;
= 'V': compute the left generalized eigenvectors.
JOBVR (input) CHARACTER*1
= 'N': do not compute the right generalized eigenvectors;
= 'V': compute the right generalized eigenvectors.
N (input) INTEGER
The order of the matrices A, B, VL, and VR. N >= 0.
A (input/output) REAL array, dimension (LDA, N)
On entry, the matrix A in the pair (A,B).
On exit, A has been overwritten.
LDA (input) INTEGER
The leading dimension of A. LDA >= max(1,N).
B (input/output) REAL array, dimension (LDB, N)
On entry, the matrix B in the pair (A,B).
On exit, B has been overwritten.
LDB (input) INTEGER
The leading dimension of B. LDB >= max(1,N).
ALPHAR (output) REAL array, dimension (N)
ALPHAI (output) REAL array, dimension (N)
BETA (output) REAL array, dimension (N)
On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
be the generalized eigenvalues. If ALPHAI(j) is zero, then
the j-th eigenvalue is real; if positive, then the j-th and
(j+1)-st eigenvalues are a complex conjugate pair, with
ALPHAI(j+1) negative.
Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
may easily over- or underflow, and BETA(j) may even be zero.
Thus, the user should avoid naively computing the ratio
alpha/beta. However, ALPHAR and ALPHAI will be always less
than and usually comparable with norm(A) in magnitude, and
BETA always less than and usually comparable with norm(B).
VL (output) REAL array, dimension (LDVL,N)
If JOBVL = 'V', the left eigenvectors u(j) are stored one
after another in the columns of VL, in the same order as
their eigenvalues. If the j-th eigenvalue is real, then
u(j) = VL(:,j), the j-th column of VL. If the j-th and
(j+1)-th eigenvalues form a complex conjugate pair, then
u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1).
Each eigenvector will be scaled so the largest component have
abs(real part)+abs(imag. part)=1.
Not referenced if JOBVL = 'N'.
LDVL (input) INTEGER
The leading dimension of the matrix VL. LDVL >= 1, and
if JOBVL = 'V', LDVL >= N.
VR (output) REAL array, dimension (LDVR,N)
If JOBVR = 'V', the right eigenvectors v(j) are stored one
after another in the columns of VR, in the same order as
their eigenvalues. If the j-th eigenvalue is real, then
v(j) = VR(:,j), the j-th column of VR. If the j-th and
(j+1)-th eigenvalues form a complex conjugate pair, then
v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1).
Each eigenvector will be scaled so the largest component have
abs(real part)+abs(imag. part)=1.
Not referenced if JOBVR = 'N'.
LDVR (input) INTEGER
The leading dimension of the matrix VR. LDVR >= 1, and
if JOBVR = 'V', LDVR >= N.
WORK (workspace/output) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,8*N).
For good performance, LWORK must generally be larger.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
= 1,...,N:
The QZ iteration failed. No eigenvectors have been
calculated, but ALPHAR(j), ALPHAI(j), and BETA(j)
should be correct for j=INFO+1,...,N.
> N: =N+1: other than QZ iteration failed in SHGEQZ.
=N+2: error return from STGEVC.
=====================================================================
Decode the input arguments
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static integer c__0 = 0;
static real c_b26 = 0.f;
static real c_b27 = 1.f;
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1,
vr_offset, i__1, i__2;
real r__1, r__2, r__3, r__4;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static real anrm, bnrm;
static integer ierr, itau;
static real temp;
static logical ilvl, ilvr;
static integer iwrk;
extern logical lsame_(char *, char *);
static integer ileft, icols, irows, jc;
extern /* Subroutine */ int slabad_(real *, real *);
static integer in, jr;
extern /* Subroutine */ int sggbak_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, real *, integer *, integer *
), sggbal_(char *, integer *, real *, integer *,
real *, integer *, integer *, integer *, real *, real *, real *,
integer *);
static logical ilascl, ilbscl;
extern doublereal slamch_(char *), slange_(char *, integer *,
integer *, real *, integer *, real *);
extern /* Subroutine */ int xerbla_(char *, integer *), sgghrd_(
char *, char *, integer *, integer *, integer *, real *, integer *
, real *, integer *, real *, integer *, real *, integer *,
integer *);
static logical ldumma[1];
static char chtemp[1];
static real bignum;
extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, real *, integer *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static integer ijobvl, iright;
extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *);
static integer ijobvr;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), slaset_(char *, integer *,
integer *, real *, real *, real *, integer *), stgevc_(
char *, char *, logical *, integer *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *, integer *,
integer *, real *, integer *);
static real anrmto, bnrmto;
extern /* Subroutine */ int shgeqz_(char *, char *, char *, integer *,
integer *, integer *, real *, integer *, real *, integer *, real *
, real *, real *, real *, integer *, real *, integer *, real *,
integer *, integer *);
static integer minwrk, maxwrk;
static real smlnum;
extern /* Subroutine */ int sorgqr_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *, integer *);
static logical lquery;
extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
static integer ihi, ilo;
static real eps;
static logical ilv;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
#define vl_ref(a_1,a_2) vl[(a_2)*vl_dim1 + a_1]
#define vr_ref(a_1,a_2) vr[(a_2)*vr_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--alphar;
--alphai;
--beta;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1 * 1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1 * 1;
vr -= vr_offset;
--work;
/* Function Body */
if (lsame_(jobvl, "N")) {
ijobvl = 1;
ilvl = FALSE_;
} else if (lsame_(jobvl, "V")) {
ijobvl = 2;
ilvl = TRUE_;
} else {
ijobvl = -1;
ilvl = FALSE_;
}
if (lsame_(jobvr, "N")) {
ijobvr = 1;
ilvr = FALSE_;
} else if (lsame_(jobvr, "V")) {
ijobvr = 2;
ilvr = TRUE_;
} else {
ijobvr = -1;
ilvr = FALSE_;
}
ilv = ilvl || ilvr;
/* Test the input arguments */
*info = 0;
lquery = *lwork == -1;
if (ijobvl <= 0) {
*info = -1;
} else if (ijobvr <= 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -7;
} else if (*ldvl < 1 || ilvl && *ldvl < *n) {
*info = -12;
} else if (*ldvr < 1 || ilvr && *ldvr < *n) {
*info = -14;
}
/* Compute workspace
(Note: Comments in the code beginning "Workspace:" describe the
minimal amount of workspace needed at that point in the code,
as well as the preferred amount for good performance.
NB refers to the optimal block size for the immediately
following subroutine, as returned by ILAENV. The workspace is
computed assuming ILO = 1 and IHI = N, the worst case.) */
minwrk = 1;
if (*info == 0 && (*lwork >= 1 || lquery)) {
maxwrk = *n * 7 + *n * ilaenv_(&c__1, "SGEQRF", " ", n, &c__1, n, &
c__0, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = 1, i__2 = *n << 3;
minwrk = max(i__1,i__2);
work[1] = (real) maxwrk;
}
if (*lwork < minwrk && ! lquery) {
*info = -16;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGGEV ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Get machine constants */
eps = slamch_("P");
smlnum = slamch_("S");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1.f / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = slange_("M", n, n, &a[a_offset], lda, &work[1]);
ilascl = FALSE_;
if (anrm > 0.f && anrm < smlnum) {
anrmto = smlnum;
ilascl = TRUE_;
} else if (anrm > bignum) {
anrmto = bignum;
ilascl = TRUE_;
}
if (ilascl) {
slascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
ierr);
}
/* Scale B if max element outside range [SMLNUM,BIGNUM] */
bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]);
ilbscl = FALSE_;
if (bnrm > 0.f && bnrm < smlnum) {
bnrmto = smlnum;
ilbscl = TRUE_;
} else if (bnrm > bignum) {
bnrmto = bignum;
ilbscl = TRUE_;
}
if (ilbscl) {
slascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
ierr);
}
/* Permute the matrices A, B to isolate eigenvalues if possible
(Workspace: need 6*N) */
ileft = 1;
iright = *n + 1;
iwrk = iright + *n;
sggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
ileft], &work[iright], &work[iwrk], &ierr);
/* Reduce B to triangular form (QR decomposition of B)
(Workspace: need N, prefer N*NB) */
irows = ihi + 1 - ilo;
if (ilv) {
icols = *n + 1 - ilo;
} else {
icols = irows;
}
itau = iwrk;
iwrk = itau + irows;
i__1 = *lwork + 1 - iwrk;
sgeqrf_(&irows, &icols, &b_ref(ilo, ilo), ldb, &work[itau], &work[iwrk], &
i__1, &ierr);
/* Apply the orthogonal transformation to matrix A
(Workspace: need N, prefer N*NB) */
i__1 = *lwork + 1 - iwrk;
sormqr_("L", "T", &irows, &icols, &irows, &b_ref(ilo, ilo), ldb, &work[
itau], &a_ref(ilo, ilo), lda, &work[iwrk], &i__1, &ierr);
/* Initialize VL
(Workspace: need N, prefer N*NB) */
if (ilvl) {
slaset_("Full", n, n, &c_b26, &c_b27, &vl[vl_offset], ldvl)
;
i__1 = irows - 1;
i__2 = irows - 1;
slacpy_("L", &i__1, &i__2, &b_ref(ilo + 1, ilo), ldb, &vl_ref(ilo + 1,
ilo), ldvl);
i__1 = *lwork + 1 - iwrk;
sorgqr_(&irows, &irows, &irows, &vl_ref(ilo, ilo), ldvl, &work[itau],
&work[iwrk], &i__1, &ierr);
}
/* Initialize VR */
if (ilvr) {
slaset_("Full", n, n, &c_b26, &c_b27, &vr[vr_offset], ldvr)
;
}
/* Reduce to generalized Hessenberg form
(Workspace: none needed) */
if (ilv) {
/* Eigenvectors requested -- work on whole matrix. */
sgghrd_(jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &ierr);
} else {
sgghrd_("N", "N", &irows, &c__1, &irows, &a_ref(ilo, ilo), lda, &
b_ref(ilo, ilo), ldb, &vl[vl_offset], ldvl, &vr[vr_offset],
ldvr, &ierr);
}
/* Perform QZ algorithm (Compute eigenvalues, and optionally, the
Schur forms and Schur vectors)
(Workspace: need N) */
iwrk = itau;
if (ilv) {
*(unsigned char *)chtemp = 'S';
} else {
*(unsigned char *)chtemp = 'E';
}
i__1 = *lwork + 1 - iwrk;
shgeqz_(chtemp, jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[
b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vl[vl_offset],
ldvl, &vr[vr_offset], ldvr, &work[iwrk], &i__1, &ierr);
if (ierr != 0) {
if (ierr > 0 && ierr <= *n) {
*info = ierr;
} else if (ierr > *n && ierr <= *n << 1) {
*info = ierr - *n;
} else {
*info = *n + 1;
}
goto L110;
}
/* Compute Eigenvectors
(Workspace: need 6*N) */
if (ilv) {
if (ilvl) {
if (ilvr) {
*(unsigned char *)chtemp = 'B';
} else {
*(unsigned char *)chtemp = 'L';
}
} else {
*(unsigned char *)chtemp = 'R';
}
stgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], ldb,
&vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &work[
iwrk], &ierr);
if (ierr != 0) {
*info = *n + 2;
goto L110;
}
/* Undo balancing on VL and VR and normalization
(Workspace: none needed) */
if (ilvl) {
sggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
vl[vl_offset], ldvl, &ierr);
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
if (alphai[jc] < 0.f) {
goto L50;
}
temp = 0.f;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__2 = temp, r__3 = (r__1 = vl_ref(jr, jc), dabs(r__1)
);
temp = dmax(r__2,r__3);
/* L10: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__3 = temp, r__4 = (r__1 = vl_ref(jr, jc), dabs(r__1)
) + (r__2 = vl_ref(jr, jc + 1), dabs(r__2));
temp = dmax(r__3,r__4);
/* L20: */
}
}
if (temp < smlnum) {
goto L50;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vl_ref(jr, jc) = vl_ref(jr, jc) * temp;
/* L30: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vl_ref(jr, jc) = vl_ref(jr, jc) * temp;
vl_ref(jr, jc + 1) = vl_ref(jr, jc + 1) * temp;
/* L40: */
}
}
L50:
;
}
}
if (ilvr) {
sggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
vr[vr_offset], ldvr, &ierr);
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
if (alphai[jc] < 0.f) {
goto L100;
}
temp = 0.f;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__2 = temp, r__3 = (r__1 = vr_ref(jr, jc), dabs(r__1)
);
temp = dmax(r__2,r__3);
/* L60: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__3 = temp, r__4 = (r__1 = vr_ref(jr, jc), dabs(r__1)
) + (r__2 = vr_ref(jr, jc + 1), dabs(r__2));
temp = dmax(r__3,r__4);
/* L70: */
}
}
if (temp < smlnum) {
goto L100;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vr_ref(jr, jc) = vr_ref(jr, jc) * temp;
/* L80: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vr_ref(jr, jc) = vr_ref(jr, jc) * temp;
vr_ref(jr, jc + 1) = vr_ref(jr, jc + 1) * temp;
/* L90: */
}
}
L100:
;
}
}
/* End of eigenvector calculation */
}
/* Undo scaling if necessary */
if (ilascl) {
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
ierr);
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
ierr);
}
if (ilbscl) {
slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
ierr);
}
L110:
work[1] = (real) maxwrk;
return 0;
/* End of SGGEV */
} /* sggev_ */
/* Subroutine */ int sgelss_(integer *m, integer *n, integer *nrhs, real *a,
integer *lda, real *b, integer *ldb, real *s, real *rcond, integer *
rank, real *work, integer *lwork, integer *info)
{
/* -- LAPACK driver routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
SGELSS computes the minimum norm solution to a real linear least
squares problem:
Minimize 2-norm(| b - A*x |).
using the singular value decomposition (SVD) of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix
X.
The effective rank of A is determined by treating as zero those
singular values which are less than RCOND times the largest singular
value.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A (input/output) REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the first min(m,n) rows of A are overwritten with
its right singular vectors, stored rowwise.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B (input/output) REAL array, dimension (LDB,NRHS)
On entry, the M-by-NRHS right hand side matrix B.
On exit, B is overwritten by the N-by-NRHS solution
matrix X. If m >= n and RANK = n, the residual
sum-of-squares for the solution in the i-th column is given
by the sum of squares of elements n+1:m in that column.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,max(M,N)).
S (output) REAL array, dimension (min(M,N))
The singular values of A in decreasing order.
The condition number of A in the 2-norm = S(1)/S(min(m,n)).
RCOND (input) REAL
RCOND is used to determine the effective rank of A.
Singular values S(i) <= RCOND*S(1) are treated as zero.
If RCOND < 0, machine precision is used instead.
RANK (output) INTEGER
The effective rank of A, i.e., the number of singular values
which are greater than RCOND*S(1).
WORK (workspace/output) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= 1, and also:
LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS )
For good performance, LWORK should generally be larger.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: the algorithm for computing the SVD failed to converge;
if INFO = i, i off-diagonal elements of an intermediate
bidiagonal form did not converge to zero.
=====================================================================
Test the input arguments
Parameter adjustments
Function Body */
/* Table of constant values */
static integer c__6 = 6;
static integer c_n1 = -1;
static integer c__1 = 1;
static integer c__0 = 0;
static real c_b74 = 0.f;
static real c_b108 = 1.f;
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
real r__1;
/* Local variables */
static real anrm, bnrm;
static integer itau;
static real vdum[1];
static integer i, iascl, ibscl, chunk;
extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, real *, integer *, real *,
real *, integer *);
static real sfmin;
static integer minmn, maxmn;
extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *,
real *, integer *, real *, integer *, real *, real *, integer *);
static integer itaup, itauq;
extern /* Subroutine */ int srscl_(integer *, real *, real *, integer *);
static integer mnthr, iwork;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *);
static integer bl, ie, il;
extern /* Subroutine */ int slabad_(real *, real *);
static integer mm, bdspac;
extern /* Subroutine */ int sgebrd_(integer *, integer *, real *, integer
*, real *, real *, real *, real *, real *, integer *, integer *);
extern doublereal slamch_(char *), slange_(char *, integer *,
integer *, real *, integer *, real *);
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static real bignum;
extern /* Subroutine */ int sgelqf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *), slascl_(char *, integer
*, integer *, real *, real *, integer *, integer *, real *,
integer *, integer *), sgeqrf_(integer *, integer *, real
*, integer *, real *, real *, integer *, integer *), slacpy_(char
*, integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *,
real *, integer *), sbdsqr_(char *, integer *, integer *,
integer *, integer *, real *, real *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *), sorgbr_(
char *, integer *, integer *, integer *, real *, integer *, real *
, real *, integer *, integer *);
static integer ldwork;
extern /* Subroutine */ int sormbr_(char *, char *, char *, integer *,
integer *, integer *, real *, integer *, real *, real *, integer *
, real *, integer *, integer *);
static integer minwrk, maxwrk;
static real smlnum;
extern /* Subroutine */ int sormlq_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *), sormqr_(char *, char *,
integer *, integer *, integer *, real *, integer *, real *, real *
, integer *, real *, integer *, integer *);
static real eps, thr;
#define S(I) s[(I)-1]
#define WORK(I) work[(I)-1]
#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
#define B(I,J) b[(I)-1 + ((J)-1)* ( *ldb)]
*info = 0;
minmn = min(*m,*n);
maxmn = max(*m,*n);
mnthr = ilaenv_(&c__6, "SGELSS", " ", m, n, nrhs, &c_n1, 6L, 1L);
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*ldb < max(1,maxmn)) {
*info = -7;
}
/* Compute workspace
(Note: Comments in the code beginning "Workspace:" describe the
minimal amount of workspace needed at that point in the code,
as well as the preferred amount for good performance.
NB refers to the optimal block size for the immediately
following subroutine, as returned by ILAENV.) */
minwrk = 1;
if (*info == 0 && *lwork >= 1) {
maxwrk = 0;
mm = *m;
if (*m >= *n && *m >= mnthr) {
/* Path 1a - overdetermined, with many more rows than co
lumns */
mm = *n;
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "SGEQRF", " ", m,
n, &c_n1, &c_n1, 6L, 1L);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + *nrhs * ilaenv_(&c__1, "SORMQR", "LT",
m, nrhs, n, &c_n1, 6L, 2L);
maxwrk = max(i__1,i__2);
}
if (*m >= *n) {
/* Path 1 - overdetermined or exactly determined
Compute workspace neede for SBDSQR
Computing MAX */
i__1 = 1, i__2 = *n * 5 - 4;
bdspac = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + (mm + *n) * ilaenv_(&c__1, "SGEBRD"
, " ", &mm, n, &c_n1, &c_n1, 6L, 1L);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + *nrhs * ilaenv_(&c__1, "SORMBR",
"QLT", &mm, nrhs, n, &c_n1, 6L, 3L);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + (*n - 1) * ilaenv_(&c__1, "SORGBR",
"P", n, n, n, &c_n1, 6L, 1L);
maxwrk = max(i__1,i__2);
maxwrk = max(maxwrk,bdspac);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * *nrhs;
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1,i__2);
minwrk = max(i__1,bdspac);
maxwrk = max(minwrk,maxwrk);
}
if (*n > *m) {
/* Compute workspace neede for SBDSQR
Computing MAX */
i__1 = 1, i__2 = *m * 5 - 4;
bdspac = max(i__1,i__2);
/* Computing MAX */
i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *n, i__1 = max(i__1,i__2);
minwrk = max(i__1,bdspac);
if (*n >= mnthr) {
/* Path 2a - underdetermined, with many more colu
mns
than rows */
maxwrk = *m + *m * ilaenv_(&c__1, "SGELQF", " ", m, n, &c_n1,
&c_n1, 6L, 1L);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) *
ilaenv_(&c__1, "SGEBRD", " ", m, m, &c_n1, &c_n1, 6L,
1L);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs * ilaenv_(&
c__1, "SORMBR", "QLT", m, nrhs, m, &c_n1, 6L, 3L);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) *
ilaenv_(&c__1, "SORGBR", "P", m, m, m, &c_n1, 6L, 1L);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + *m + bdspac;
maxwrk = max(i__1,i__2);
if (*nrhs > 1) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs;
maxwrk = max(i__1,i__2);
} else {
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 1);
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = maxwrk, i__2 = *m + *nrhs * ilaenv_(&c__1, "SORMLQ",
"LT", n, nrhs, m, &c_n1, 6L, 2L);
maxwrk = max(i__1,i__2);
} else {
/* Path 2 - underdetermined */
maxwrk = *m * 3 + (*n + *m) * ilaenv_(&c__1, "SGEBRD", " ", m,
n, &c_n1, &c_n1, 6L, 1L);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * 3 + *nrhs * ilaenv_(&c__1, "SORMBR"
, "QLT", m, nrhs, m, &c_n1, 6L, 3L);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORGBR",
"P", m, n, m, &c_n1, 6L, 1L);
maxwrk = max(i__1,i__2);
maxwrk = max(maxwrk,bdspac);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * *nrhs;
maxwrk = max(i__1,i__2);
}
}
maxwrk = max(minwrk,maxwrk);
WORK(1) = (real) maxwrk;
}
minwrk = max(minwrk,1);
if (*lwork < minwrk) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGELSS", &i__1);
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
*rank = 0;
return 0;
}
/* Get machine parameters */
eps = slamch_("P");
sfmin = slamch_("S");
smlnum = sfmin / eps;
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = slange_("M", m, n, &A(1,1), lda, &WORK(1));
iascl = 0;
if (anrm > 0.f && anrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
slascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &A(1,1), lda,
info);
iascl = 1;
} else if (anrm > bignum) {
/* Scale matrix norm down to BIGNUM */
slascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &A(1,1), lda,
info);
iascl = 2;
} else if (anrm == 0.f) {
/* VISMatrix all zero. Return zero solution. */
i__1 = max(*m,*n);
slaset_("F", &i__1, nrhs, &c_b74, &c_b74, &B(1,1), ldb);
slaset_("F", &minmn, &c__1, &c_b74, &c_b74, &S(1), &c__1);
*rank = 0;
goto L70;
}
/* Scale B if max element outside range [SMLNUM,BIGNUM] */
bnrm = slange_("M", m, nrhs, &B(1,1), ldb, &WORK(1));
ibscl = 0;
if (bnrm > 0.f && bnrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
slascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &B(1,1), ldb,
info);
ibscl = 1;
} else if (bnrm > bignum) {
/* Scale matrix norm down to BIGNUM */
slascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &B(1,1), ldb,
info);
ibscl = 2;
}
/* Overdetermined case */
if (*m >= *n) {
/* Path 1 - overdetermined or exactly determined */
mm = *m;
if (*m >= mnthr) {
/* Path 1a - overdetermined, with many more rows than co
lumns */
mm = *n;
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R
(Workspace: need 2*N, prefer N+N*NB) */
i__1 = *lwork - iwork + 1;
sgeqrf_(m, n, &A(1,1), lda, &WORK(itau), &WORK(iwork), &i__1,
info);
/* Multiply B by transpose(Q)
(Workspace: need N+NRHS, prefer N+NRHS*NB) */
i__1 = *lwork - iwork + 1;
sormqr_("L", "T", m, nrhs, n, &A(1,1), lda, &WORK(itau), &B(1,1), ldb, &WORK(iwork), &i__1, info);
/* Zero out below R */
if (*n > 1) {
i__1 = *n - 1;
i__2 = *n - 1;
slaset_("L", &i__1, &i__2, &c_b74, &c_b74, &A(2,1),
lda);
}
}
ie = 1;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in A
(Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */
i__1 = *lwork - iwork + 1;
sgebrd_(&mm, n, &A(1,1), lda, &S(1), &WORK(ie), &WORK(itauq), &
WORK(itaup), &WORK(iwork), &i__1, info);
/* Multiply B by transpose of left bidiagonalizing vectors of R
(Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */
i__1 = *lwork - iwork + 1;
sormbr_("Q", "L", "T", &mm, nrhs, n, &A(1,1), lda, &WORK(itauq),
&B(1,1), ldb, &WORK(iwork), &i__1, info);
/* Generate right bidiagonalizing vectors of R in A
(Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
i__1 = *lwork - iwork + 1;
sorgbr_("P", n, n, n, &A(1,1), lda, &WORK(itaup), &WORK(iwork), &
i__1, info);
iwork = ie + *n;
/* Perform bidiagonal QR iteration
multiply B by transpose of left singular vectors
compute right singular vectors in A
(Workspace: need BDSPAC) */
sbdsqr_("U", n, n, &c__0, nrhs, &S(1), &WORK(ie), &A(1,1), lda,
vdum, &c__1, &B(1,1), ldb, &WORK(iwork), info);
if (*info != 0) {
goto L70;
}
/* Multiply B by reciprocals of singular values
Computing MAX */
r__1 = *rcond * S(1);
thr = dmax(r__1,sfmin);
if (*rcond < 0.f) {
/* Computing MAX */
r__1 = eps * S(1);
thr = dmax(r__1,sfmin);
}
*rank = 0;
i__1 = *n;
for (i = 1; i <= *n; ++i) {
if (S(i) > thr) {
srscl_(nrhs, &S(i), &B(i,1), ldb);
++(*rank);
} else {
slaset_("F", &c__1, nrhs, &c_b74, &c_b74, &B(i,1), ldb);
}
/* L10: */
}
/* Multiply B by right singular vectors
(Workspace: need N, prefer N*NRHS) */
if (*lwork >= *ldb * *nrhs && *nrhs > 1) {
sgemm_("T", "N", n, nrhs, n, &c_b108, &A(1,1), lda, &B(1,1), ldb, &c_b74, &WORK(1), ldb);
slacpy_("G", n, nrhs, &WORK(1), ldb, &B(1,1), ldb);
} else if (*nrhs > 1) {
chunk = *lwork / *n;
i__1 = *nrhs;
i__2 = chunk;
for (i = 1; chunk < 0 ? i >= *nrhs : i <= *nrhs; i += chunk) {
/* Computing MIN */
i__3 = *nrhs - i + 1;
bl = min(i__3,chunk);
sgemm_("T", "N", n, &bl, n, &c_b108, &A(1,1), lda, &B(1,1), ldb, &c_b74, &WORK(1), n);
slacpy_("G", n, &bl, &WORK(1), n, &B(1,1), ldb);
/* L20: */
}
} else {
sgemv_("T", n, n, &c_b108, &A(1,1), lda, &B(1,1), &c__1,
&c_b74, &WORK(1), &c__1);
scopy_(n, &WORK(1), &c__1, &B(1,1), &c__1);
}
} else /* if(complicated condition) */ {
/* Computing MAX */
i__2 = *m, i__1 = (*m << 1) - 4, i__2 = max(i__2,i__1), i__2 = max(
i__2,*nrhs), i__1 = *n - *m * 3;
if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__2,i__1)) {
/* Path 2a - underdetermined, with many more columns than r
ows
and sufficient workspace for an efficient algorithm */
ldwork = *m;
/* Computing MAX
Computing MAX */
i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 =
max(i__3,*nrhs), i__4 = *n - *m * 3;
i__2 = (*m << 2) + *m * *lda + max(i__3,i__4), i__1 = *m * *lda +
*m + *m * *nrhs;
if (*lwork >= max(i__2,i__1)) {
ldwork = *lda;
}
itau = 1;
iwork = *m + 1;
/* Compute A=L*Q
(Workspace: need 2*M, prefer M+M*NB) */
i__2 = *lwork - iwork + 1;
sgelqf_(m, n, &A(1,1), lda, &WORK(itau), &WORK(iwork), &i__2,
info);
il = iwork;
/* Copy L to WORK(IL), zeroing out above it */
slacpy_("L", m, m, &A(1,1), lda, &WORK(il), &ldwork);
i__2 = *m - 1;
i__1 = *m - 1;
slaset_("U", &i__2, &i__1, &c_b74, &c_b74, &WORK(il + ldwork), &
ldwork);
ie = il + ldwork * *m;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in WORK(IL)
(Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, m, &WORK(il), &ldwork, &S(1), &WORK(ie), &WORK(itauq),
&WORK(itaup), &WORK(iwork), &i__2, info);
/* Multiply B by transpose of left bidiagonalizing vectors
of L
(Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB)
*/
i__2 = *lwork - iwork + 1;
sormbr_("Q", "L", "T", m, nrhs, m, &WORK(il), &ldwork, &WORK(
itauq), &B(1,1), ldb, &WORK(iwork), &i__2, info);
/* Generate right bidiagonalizing vectors of R in WORK(IL)
(Workspace: need M*M+5*M-1, prefer M*M+4*M+(M-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", m, m, m, &WORK(il), &ldwork, &WORK(itaup), &WORK(
iwork), &i__2, info);
iwork = ie + *m;
/* Perform bidiagonal QR iteration,
computing right singular vectors of L in WORK(IL) and
multiplying B by transpose of left singular vectors
(Workspace: need M*M+M+BDSPAC) */
sbdsqr_("U", m, m, &c__0, nrhs, &S(1), &WORK(ie), &WORK(il), &
ldwork, &A(1,1), lda, &B(1,1), ldb, &WORK(iwork)
, info);
if (*info != 0) {
goto L70;
}
/* Multiply B by reciprocals of singular values
Computing MAX */
r__1 = *rcond * S(1);
thr = dmax(r__1,sfmin);
if (*rcond < 0.f) {
/* Computing MAX */
r__1 = eps * S(1);
thr = dmax(r__1,sfmin);
}
*rank = 0;
i__2 = *m;
for (i = 1; i <= *m; ++i) {
if (S(i) > thr) {
srscl_(nrhs, &S(i), &B(i,1), ldb);
++(*rank);
} else {
slaset_("F", &c__1, nrhs, &c_b74, &c_b74, &B(i,1),
ldb);
}
/* L30: */
}
iwork = ie;
/* Multiply B by right singular vectors of L in WORK(IL)
(Workspace: need M*M+2*M, prefer M*M+M+M*NRHS) */
if (*lwork >= *ldb * *nrhs + iwork - 1 && *nrhs > 1) {
sgemm_("T", "N", m, nrhs, m, &c_b108, &WORK(il), &ldwork, &B(1,1), ldb, &c_b74, &WORK(iwork), ldb);
slacpy_("G", m, nrhs, &WORK(iwork), ldb, &B(1,1), ldb);
} else if (*nrhs > 1) {
chunk = (*lwork - iwork + 1) / *m;
i__2 = *nrhs;
i__1 = chunk;
for (i = 1; chunk < 0 ? i >= *nrhs : i <= *nrhs; i += chunk) {
/* Computing MIN */
i__3 = *nrhs - i + 1;
bl = min(i__3,chunk);
sgemm_("T", "N", m, &bl, m, &c_b108, &WORK(il), &ldwork, &
B(1,i), ldb, &c_b74, &WORK(iwork), n);
slacpy_("G", m, &bl, &WORK(iwork), n, &B(1,1), ldb);
/* L40: */
}
} else {
sgemv_("T", m, m, &c_b108, &WORK(il), &ldwork, &B(1,1),
&c__1, &c_b74, &WORK(iwork), &c__1);
scopy_(m, &WORK(iwork), &c__1, &B(1,1), &c__1);
}
/* Zero out below first M rows of B */
i__1 = *n - *m;
slaset_("F", &i__1, nrhs, &c_b74, &c_b74, &B(*m+1,1),
ldb);
iwork = itau + *m;
/* Multiply transpose(Q) by B
(Workspace: need M+NRHS, prefer M+NRHS*NB) */
i__1 = *lwork - iwork + 1;
sormlq_("L", "T", n, nrhs, m, &A(1,1), lda, &WORK(itau), &B(1,1), ldb, &WORK(iwork), &i__1, info);
} else {
/* Path 2 - remaining underdetermined cases */
ie = 1;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize A
(Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */
i__1 = *lwork - iwork + 1;
sgebrd_(m, n, &A(1,1), lda, &S(1), &WORK(ie), &WORK(itauq), &
WORK(itaup), &WORK(iwork), &i__1, info);
/* Multiply B by transpose of left bidiagonalizing vectors
(Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */
i__1 = *lwork - iwork + 1;
sormbr_("Q", "L", "T", m, nrhs, n, &A(1,1), lda, &WORK(itauq)
, &B(1,1), ldb, &WORK(iwork), &i__1, info);
/* Generate right bidiagonalizing vectors in A
(Workspace: need 4*M, prefer 3*M+M*NB) */
i__1 = *lwork - iwork + 1;
sorgbr_("P", m, n, m, &A(1,1), lda, &WORK(itaup), &WORK(
iwork), &i__1, info);
iwork = ie + *m;
/* Perform bidiagonal QR iteration,
computing right singular vectors of A in A and
multiplying B by transpose of left singular vectors
(Workspace: need BDSPAC) */
sbdsqr_("L", m, n, &c__0, nrhs, &S(1), &WORK(ie), &A(1,1),
lda, vdum, &c__1, &B(1,1), ldb, &WORK(iwork), info);
if (*info != 0) {
goto L70;
}
/* Multiply B by reciprocals of singular values
Computing MAX */
r__1 = *rcond * S(1);
thr = dmax(r__1,sfmin);
if (*rcond < 0.f) {
/* Computing MAX */
r__1 = eps * S(1);
thr = dmax(r__1,sfmin);
}
*rank = 0;
i__1 = *m;
for (i = 1; i <= *m; ++i) {
if (S(i) > thr) {
srscl_(nrhs, &S(i), &B(i,1), ldb);
++(*rank);
} else {
slaset_("F", &c__1, nrhs, &c_b74, &c_b74, &B(i,1),
ldb);
}
/* L50: */
}
/* Multiply B by right singular vectors of A
(Workspace: need N, prefer N*NRHS) */
if (*lwork >= *ldb * *nrhs && *nrhs > 1) {
sgemm_("T", "N", n, nrhs, m, &c_b108, &A(1,1), lda, &B(1,1), ldb, &c_b74, &WORK(1), ldb);
slacpy_("F", n, nrhs, &WORK(1), ldb, &B(1,1), ldb);
} else if (*nrhs > 1) {
chunk = *lwork / *n;
i__1 = *nrhs;
i__2 = chunk;
for (i = 1; chunk < 0 ? i >= *nrhs : i <= *nrhs; i += chunk) {
/* Computing MIN */
i__3 = *nrhs - i + 1;
bl = min(i__3,chunk);
sgemm_("T", "N", n, &bl, m, &c_b108, &A(1,1), lda, &
B(1,i), ldb, &c_b74, &WORK(1), n);
slacpy_("F", n, &bl, &WORK(1), n, &B(1,i), ldb);
/* L60: */
}
} else {
sgemv_("T", m, n, &c_b108, &A(1,1), lda, &B(1,1), &
c__1, &c_b74, &WORK(1), &c__1);
scopy_(n, &WORK(1), &c__1, &B(1,1), &c__1);
}
}
}
/* Undo scaling */
if (iascl == 1) {
slascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &B(1,1), ldb,
info);
slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &S(1), &
minmn, info);
} else if (iascl == 2) {
slascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &B(1,1), ldb,
info);
slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &S(1), &
minmn, info);
}
if (ibscl == 1) {
slascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &B(1,1), ldb,
info);
} else if (ibscl == 2) {
slascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &B(1,1), ldb,
info);
}
L70:
WORK(1) = (real) maxwrk;
return 0;
/* End of SGELSS */
} /* sgelss_ */
/* Subroutine */ int sgegv_(char *jobvl, char *jobvr, integer *n, real *a,
integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real
*beta, real *vl, integer *ldvl, real *vr, integer *ldvr, real *work,
integer *lwork, integer *info)
{
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
This routine is deprecated and has been replaced by routine SGGEV.
SGEGV computes for a pair of n-by-n real nonsymmetric matrices A and
B, the generalized eigenvalues (alphar +/- alphai*i, beta), and
optionally, the left and/or right generalized eigenvectors (VL and
VR).
A generalized eigenvalue for a pair of matrices (A,B) is, roughly
speaking, a scalar w or a ratio alpha/beta = w, such that A - w*B
is singular. It is usually represented as the pair (alpha,beta),
as there is a reasonable interpretation for beta=0, and even for
both being zero. A good beginning reference is the book, "Matrix
Computations", by G. Golub & C. van Loan (Johns Hopkins U. Press)
A right generalized eigenvector corresponding to a generalized
eigenvalue w for a pair of matrices (A,B) is a vector r such
that (A - w B) r = 0 . A left generalized eigenvector is a vector
l such that l**H * (A - w B) = 0, where l**H is the
conjugate-transpose of l.
Note: this routine performs "full balancing" on A and B -- see
"Further Details", below.
Arguments
=========
JOBVL (input) CHARACTER*1
= 'N': do not compute the left generalized eigenvectors;
= 'V': compute the left generalized eigenvectors.
JOBVR (input) CHARACTER*1
= 'N': do not compute the right generalized eigenvectors;
= 'V': compute the right generalized eigenvectors.
N (input) INTEGER
The order of the matrices A, B, VL, and VR. N >= 0.
A (input/output) REAL array, dimension (LDA, N)
On entry, the first of the pair of matrices whose
generalized eigenvalues and (optionally) generalized
eigenvectors are to be computed.
On exit, the contents will have been destroyed. (For a
description of the contents of A on exit, see "Further
Details", below.)
LDA (input) INTEGER
The leading dimension of A. LDA >= max(1,N).
B (input/output) REAL array, dimension (LDB, N)
On entry, the second of the pair of matrices whose
generalized eigenvalues and (optionally) generalized
eigenvectors are to be computed.
On exit, the contents will have been destroyed. (For a
description of the contents of B on exit, see "Further
Details", below.)
LDB (input) INTEGER
The leading dimension of B. LDB >= max(1,N).
ALPHAR (output) REAL array, dimension (N)
ALPHAI (output) REAL array, dimension (N)
BETA (output) REAL array, dimension (N)
On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
be the generalized eigenvalues. If ALPHAI(j) is zero, then
the j-th eigenvalue is real; if positive, then the j-th and
(j+1)-st eigenvalues are a complex conjugate pair, with
ALPHAI(j+1) negative.
Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
may easily over- or underflow, and BETA(j) may even be zero.
Thus, the user should avoid naively computing the ratio
alpha/beta. However, ALPHAR and ALPHAI will be always less
than and usually comparable with norm(A) in magnitude, and
BETA always less than and usually comparable with norm(B).
VL (output) REAL array, dimension (LDVL,N)
If JOBVL = 'V', the left generalized eigenvectors. (See
"Purpose", above.) Real eigenvectors take one column,
complex take two columns, the first for the real part and
the second for the imaginary part. Complex eigenvectors
correspond to an eigenvalue with positive imaginary part.
Each eigenvector will be scaled so the largest component
will have abs(real part) + abs(imag. part) = 1, *except*
that for eigenvalues with alpha=beta=0, a zero vector will
be returned as the corresponding eigenvector.
Not referenced if JOBVL = 'N'.
LDVL (input) INTEGER
The leading dimension of the matrix VL. LDVL >= 1, and
if JOBVL = 'V', LDVL >= N.
VR (output) REAL array, dimension (LDVR,N)
If JOBVR = 'V', the right generalized eigenvectors. (See
"Purpose", above.) Real eigenvectors take one column,
complex take two columns, the first for the real part and
the second for the imaginary part. Complex eigenvectors
correspond to an eigenvalue with positive imaginary part.
Each eigenvector will be scaled so the largest component
will have abs(real part) + abs(imag. part) = 1, *except*
that for eigenvalues with alpha=beta=0, a zero vector will
be returned as the corresponding eigenvector.
Not referenced if JOBVR = 'N'.
LDVR (input) INTEGER
The leading dimension of the matrix VR. LDVR >= 1, and
if JOBVR = 'V', LDVR >= N.
WORK (workspace/output) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,8*N).
For good performance, LWORK must generally be larger.
To compute the optimal value of LWORK, call ILAENV to get
blocksizes (for SGEQRF, SORMQR, and SORGQR.) Then compute:
NB -- MAX of the blocksizes for SGEQRF, SORMQR, and SORGQR;
The optimal LWORK is:
2*N + MAX( 6*N, N*(NB+1) ).
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
= 1,...,N:
The QZ iteration failed. No eigenvectors have been
calculated, but ALPHAR(j), ALPHAI(j), and BETA(j)
should be correct for j=INFO+1,...,N.
> N: errors that usually indicate LAPACK problems:
=N+1: error return from SGGBAL
=N+2: error return from SGEQRF
=N+3: error return from SORMQR
=N+4: error return from SORGQR
=N+5: error return from SGGHRD
=N+6: error return from SHGEQZ (other than failed
iteration)
=N+7: error return from STGEVC
=N+8: error return from SGGBAK (computing VL)
=N+9: error return from SGGBAK (computing VR)
=N+10: error return from SLASCL (various calls)
Further Details
===============
Balancing
---------
This driver calls SGGBAL to both permute and scale rows and columns
of A and B. The permutations PL and PR are chosen so that PL*A*PR
and PL*B*R will be upper triangular except for the diagonal blocks
A(i:j,i:j) and B(i:j,i:j), with i and j as close together as
possible. The diagonal scaling matrices DL and DR are chosen so
that the pair DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to
one (except for the elements that start out zero.)
After the eigenvalues and eigenvectors of the balanced matrices
have been computed, SGGBAK transforms the eigenvectors back to what
they would have been (in perfect arithmetic) if they had not been
balanced.
Contents of A and B on Exit
-------- -- - --- - -- ----
If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or
both), then on exit the arrays A and B will contain the real Schur
form[*] of the "balanced" versions of A and B. If no eigenvectors
are computed, then only the diagonal blocks will be correct.
[*] See SHGEQZ, SGEGS, or read the book "Matrix Computations",
by Golub & van Loan, pub. by Johns Hopkins U. Press.
=====================================================================
Decode the input arguments
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static real c_b27 = 1.f;
static real c_b38 = 0.f;
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1,
vr_offset, i__1, i__2;
real r__1, r__2, r__3, r__4;
/* Local variables */
static real absb, anrm, bnrm;
static integer itau;
static real temp;
static logical ilvl, ilvr;
static integer lopt;
static real anrm1, anrm2, bnrm1, bnrm2, absai, scale, absar, sbeta;
extern logical lsame_(char *, char *);
static integer ileft, iinfo, icols, iwork, irows, jc, nb, in, jr;
static real salfai;
extern /* Subroutine */ int sggbak_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, real *, integer *, integer *
), sggbal_(char *, integer *, real *, integer *,
real *, integer *, integer *, integer *, real *, real *, real *,
integer *);
static real salfar;
extern doublereal slamch_(char *), slange_(char *, integer *,
integer *, real *, integer *, real *);
static real safmin;
extern /* Subroutine */ int sgghrd_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, integer *, real *, integer *
, real *, integer *, integer *);
static real safmax;
static char chtemp[1];
static logical ldumma[1];
extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, real *, integer *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static integer ijobvl, iright;
static logical ilimit;
extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *);
static integer ijobvr;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), slaset_(char *, integer *,
integer *, real *, real *, real *, integer *), stgevc_(
char *, char *, logical *, integer *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *, integer *,
integer *, real *, integer *);
static real onepls;
static integer lwkmin, nb1, nb2, nb3;
extern /* Subroutine */ int shgeqz_(char *, char *, char *, integer *,
integer *, integer *, real *, integer *, real *, integer *, real *
, real *, real *, real *, integer *, real *, integer *, real *,
integer *, integer *), sorgqr_(integer *,
integer *, integer *, real *, integer *, real *, real *, integer *
, integer *);
static integer lwkopt;
static logical lquery;
extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
static integer ihi, ilo;
static real eps;
static logical ilv;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
#define vl_ref(a_1,a_2) vl[(a_2)*vl_dim1 + a_1]
#define vr_ref(a_1,a_2) vr[(a_2)*vr_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--alphar;
--alphai;
--beta;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1 * 1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1 * 1;
vr -= vr_offset;
--work;
/* Function Body */
if (lsame_(jobvl, "N")) {
ijobvl = 1;
ilvl = FALSE_;
} else if (lsame_(jobvl, "V")) {
ijobvl = 2;
ilvl = TRUE_;
} else {
ijobvl = -1;
ilvl = FALSE_;
}
if (lsame_(jobvr, "N")) {
ijobvr = 1;
ilvr = FALSE_;
} else if (lsame_(jobvr, "V")) {
ijobvr = 2;
ilvr = TRUE_;
} else {
ijobvr = -1;
ilvr = FALSE_;
}
ilv = ilvl || ilvr;
/* Test the input arguments
Computing MAX */
i__1 = *n << 3;
lwkmin = max(i__1,1);
lwkopt = lwkmin;
work[1] = (real) lwkopt;
lquery = *lwork == -1;
*info = 0;
if (ijobvl <= 0) {
*info = -1;
} else if (ijobvr <= 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -7;
} else if (*ldvl < 1 || ilvl && *ldvl < *n) {
*info = -12;
} else if (*ldvr < 1 || ilvr && *ldvr < *n) {
*info = -14;
} else if (*lwork < lwkmin && ! lquery) {
*info = -16;
}
if (*info == 0) {
nb1 = ilaenv_(&c__1, "SGEQRF", " ", n, n, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
nb2 = ilaenv_(&c__1, "SORMQR", " ", n, n, n, &c_n1, (ftnlen)6, (
ftnlen)1);
nb3 = ilaenv_(&c__1, "SORGQR", " ", n, n, n, &c_n1, (ftnlen)6, (
ftnlen)1);
/* Computing MAX */
i__1 = max(nb1,nb2);
nb = max(i__1,nb3);
/* Computing MAX */
i__1 = *n * 6, i__2 = *n * (nb + 1);
lopt = (*n << 1) + max(i__1,i__2);
work[1] = (real) lopt;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGEGV ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Get machine constants */
eps = slamch_("E") * slamch_("B");
safmin = slamch_("S");
safmin += safmin;
safmax = 1.f / safmin;
onepls = eps * 4 + 1.f;
/* Scale A */
anrm = slange_("M", n, n, &a[a_offset], lda, &work[1]);
anrm1 = anrm;
anrm2 = 1.f;
if (anrm < 1.f) {
if (safmax * anrm < 1.f) {
anrm1 = safmin;
anrm2 = safmax * anrm;
}
}
if (anrm > 0.f) {
slascl_("G", &c_n1, &c_n1, &anrm, &c_b27, n, n, &a[a_offset], lda, &
iinfo);
if (iinfo != 0) {
*info = *n + 10;
return 0;
}
}
/* Scale B */
bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]);
bnrm1 = bnrm;
bnrm2 = 1.f;
if (bnrm < 1.f) {
if (safmax * bnrm < 1.f) {
bnrm1 = safmin;
bnrm2 = safmax * bnrm;
}
}
if (bnrm > 0.f) {
slascl_("G", &c_n1, &c_n1, &bnrm, &c_b27, n, n, &b[b_offset], ldb, &
iinfo);
if (iinfo != 0) {
*info = *n + 10;
return 0;
}
}
/* Permute the matrix to make it more nearly triangular
Workspace layout: (8*N words -- "work" requires 6*N words)
left_permutation, right_permutation, work... */
ileft = 1;
iright = *n + 1;
iwork = iright + *n;
sggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
ileft], &work[iright], &work[iwork], &iinfo);
if (iinfo != 0) {
*info = *n + 1;
goto L120;
}
/* Reduce B to triangular form, and initialize VL and/or VR
Workspace layout: ("work..." must have at least N words)
left_permutation, right_permutation, tau, work... */
irows = ihi + 1 - ilo;
if (ilv) {
icols = *n + 1 - ilo;
} else {
icols = irows;
}
itau = iwork;
iwork = itau + irows;
i__1 = *lwork + 1 - iwork;
sgeqrf_(&irows, &icols, &b_ref(ilo, ilo), ldb, &work[itau], &work[iwork],
&i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 2;
goto L120;
}
i__1 = *lwork + 1 - iwork;
sormqr_("L", "T", &irows, &icols, &irows, &b_ref(ilo, ilo), ldb, &work[
itau], &a_ref(ilo, ilo), lda, &work[iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 3;
goto L120;
}
if (ilvl) {
slaset_("Full", n, n, &c_b38, &c_b27, &vl[vl_offset], ldvl)
;
i__1 = irows - 1;
i__2 = irows - 1;
slacpy_("L", &i__1, &i__2, &b_ref(ilo + 1, ilo), ldb, &vl_ref(ilo + 1,
ilo), ldvl);
i__1 = *lwork + 1 - iwork;
sorgqr_(&irows, &irows, &irows, &vl_ref(ilo, ilo), ldvl, &work[itau],
&work[iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 4;
goto L120;
}
}
if (ilvr) {
slaset_("Full", n, n, &c_b38, &c_b27, &vr[vr_offset], ldvr)
;
}
/* Reduce to generalized Hessenberg form */
if (ilv) {
/* Eigenvectors requested -- work on whole matrix. */
sgghrd_(jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &iinfo);
} else {
sgghrd_("N", "N", &irows, &c__1, &irows, &a_ref(ilo, ilo), lda, &
b_ref(ilo, ilo), ldb, &vl[vl_offset], ldvl, &vr[vr_offset],
ldvr, &iinfo);
}
if (iinfo != 0) {
*info = *n + 5;
goto L120;
}
/* Perform QZ algorithm
Workspace layout: ("work..." must have at least 1 word)
left_permutation, right_permutation, work... */
iwork = itau;
if (ilv) {
*(unsigned char *)chtemp = 'S';
} else {
*(unsigned char *)chtemp = 'E';
}
i__1 = *lwork + 1 - iwork;
shgeqz_(chtemp, jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[
b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vl[vl_offset],
ldvl, &vr[vr_offset], ldvr, &work[iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
if (iinfo > 0 && iinfo <= *n) {
*info = iinfo;
} else if (iinfo > *n && iinfo <= *n << 1) {
*info = iinfo - *n;
} else {
*info = *n + 6;
}
goto L120;
}
if (ilv) {
/* Compute Eigenvectors (STGEVC requires 6*N words of workspace) */
if (ilvl) {
if (ilvr) {
*(unsigned char *)chtemp = 'B';
} else {
*(unsigned char *)chtemp = 'L';
}
} else {
*(unsigned char *)chtemp = 'R';
}
stgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], ldb,
&vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &work[
iwork], &iinfo);
if (iinfo != 0) {
*info = *n + 7;
goto L120;
}
/* Undo balancing on VL and VR, rescale */
if (ilvl) {
sggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
vl[vl_offset], ldvl, &iinfo);
if (iinfo != 0) {
*info = *n + 8;
goto L120;
}
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
if (alphai[jc] < 0.f) {
goto L50;
}
temp = 0.f;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__2 = temp, r__3 = (r__1 = vl_ref(jr, jc), dabs(r__1)
);
temp = dmax(r__2,r__3);
/* L10: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__3 = temp, r__4 = (r__1 = vl_ref(jr, jc), dabs(r__1)
) + (r__2 = vl_ref(jr, jc + 1), dabs(r__2));
temp = dmax(r__3,r__4);
/* L20: */
}
}
if (temp < safmin) {
goto L50;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vl_ref(jr, jc) = vl_ref(jr, jc) * temp;
/* L30: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vl_ref(jr, jc) = vl_ref(jr, jc) * temp;
vl_ref(jr, jc + 1) = vl_ref(jr, jc + 1) * temp;
/* L40: */
}
}
L50:
;
}
}
if (ilvr) {
sggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
vr[vr_offset], ldvr, &iinfo);
if (iinfo != 0) {
*info = *n + 9;
goto L120;
}
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
if (alphai[jc] < 0.f) {
goto L100;
}
temp = 0.f;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__2 = temp, r__3 = (r__1 = vr_ref(jr, jc), dabs(r__1)
);
temp = dmax(r__2,r__3);
/* L60: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__3 = temp, r__4 = (r__1 = vr_ref(jr, jc), dabs(r__1)
) + (r__2 = vr_ref(jr, jc + 1), dabs(r__2));
temp = dmax(r__3,r__4);
/* L70: */
}
}
if (temp < safmin) {
goto L100;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vr_ref(jr, jc) = vr_ref(jr, jc) * temp;
/* L80: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vr_ref(jr, jc) = vr_ref(jr, jc) * temp;
vr_ref(jr, jc + 1) = vr_ref(jr, jc + 1) * temp;
/* L90: */
}
}
L100:
;
}
}
/* End of eigenvector calculation */
}
/* Undo scaling in alpha, beta
Note: this does not give the alpha and beta for the unscaled
problem.
Un-scaling is limited to avoid underflow in alpha and beta
if they are significant. */
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
absar = (r__1 = alphar[jc], dabs(r__1));
absai = (r__1 = alphai[jc], dabs(r__1));
absb = (r__1 = beta[jc], dabs(r__1));
salfar = anrm * alphar[jc];
salfai = anrm * alphai[jc];
sbeta = bnrm * beta[jc];
ilimit = FALSE_;
scale = 1.f;
/* Check for significant underflow in ALPHAI
Computing MAX */
r__1 = safmin, r__2 = eps * absar, r__1 = max(r__1,r__2), r__2 = eps *
absb;
if (dabs(salfai) < safmin && absai >= dmax(r__1,r__2)) {
ilimit = TRUE_;
/* Computing MAX */
r__1 = onepls * safmin, r__2 = anrm2 * absai;
scale = onepls * safmin / anrm1 / dmax(r__1,r__2);
} else if (salfai == 0.f) {
/* If insignificant underflow in ALPHAI, then make the
conjugate eigenvalue real. */
if (alphai[jc] < 0.f && jc > 1) {
alphai[jc - 1] = 0.f;
} else if (alphai[jc] > 0.f && jc < *n) {
alphai[jc + 1] = 0.f;
}
}
/* Check for significant underflow in ALPHAR
Computing MAX */
r__1 = safmin, r__2 = eps * absai, r__1 = max(r__1,r__2), r__2 = eps *
absb;
if (dabs(salfar) < safmin && absar >= dmax(r__1,r__2)) {
ilimit = TRUE_;
/* Computing MAX
Computing MAX */
r__3 = onepls * safmin, r__4 = anrm2 * absar;
r__1 = scale, r__2 = onepls * safmin / anrm1 / dmax(r__3,r__4);
scale = dmax(r__1,r__2);
}
/* Check for significant underflow in BETA
Computing MAX */
r__1 = safmin, r__2 = eps * absar, r__1 = max(r__1,r__2), r__2 = eps *
absai;
if (dabs(sbeta) < safmin && absb >= dmax(r__1,r__2)) {
ilimit = TRUE_;
/* Computing MAX
Computing MAX */
r__3 = onepls * safmin, r__4 = bnrm2 * absb;
r__1 = scale, r__2 = onepls * safmin / bnrm1 / dmax(r__3,r__4);
scale = dmax(r__1,r__2);
}
/* Check for possible overflow when limiting scaling */
if (ilimit) {
/* Computing MAX */
r__1 = dabs(salfar), r__2 = dabs(salfai), r__1 = max(r__1,r__2),
r__2 = dabs(sbeta);
temp = scale * safmin * dmax(r__1,r__2);
if (temp > 1.f) {
scale /= temp;
}
if (scale < 1.f) {
ilimit = FALSE_;
}
}
/* Recompute un-scaled ALPHAR, ALPHAI, BETA if necessary. */
if (ilimit) {
salfar = scale * alphar[jc] * anrm;
salfai = scale * alphai[jc] * anrm;
sbeta = scale * beta[jc] * bnrm;
}
alphar[jc] = salfar;
alphai[jc] = salfai;
beta[jc] = sbeta;
/* L110: */
}
L120:
work[1] = (real) lwkopt;
return 0;
/* End of SGEGV */
} /* sgegv_ */
inline void geqrf( const int & m, const int & n, float da[], const int & lda, float dtau[], float dwork[], const int& ldwork, int& info)
{
sgeqrf_(m,n,da,lda,dtau,dwork,ldwork,info);
}
/* Subroutine */ int sgeqp3_(integer *m, integer *n, real *a, integer *lda,
integer *jpvt, real *tau, real *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
/* Local variables */
integer j, jb, na, nb, sm, sn, nx, fjb, iws, nfxd;
extern doublereal snrm2_(integer *, real *, integer *);
integer nbmin, minmn, minws;
extern /* Subroutine */ int sswap_(integer *, real *, integer *, real *,
integer *), slaqp2_(integer *, integer *, integer *, real *,
integer *, integer *, real *, real *, real *, real *), xerbla_(
char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *);
integer topbmn, sminmn;
extern /* Subroutine */ int slaqps_(integer *, integer *, integer *,
integer *, integer *, real *, integer *, integer *, real *, real *
, real *, real *, real *, integer *);
integer lwkopt;
logical lquery;
extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SGEQP3 computes a QR factorization with column pivoting of a */
/* matrix A: A*P = Q*R using Level 3 BLAS. */
/* Arguments */
/* ========= */
/* M (input) INTEGER */
/* The number of rows of the matrix A. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix A. N >= 0. */
/* A (input/output) REAL array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, the upper triangle of the array contains the */
/* min(M,N)-by-N upper trapezoidal matrix R; the elements below */
/* the diagonal, together with the array TAU, represent the */
/* orthogonal matrix Q as a product of min(M,N) elementary */
/* reflectors. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* JPVT (input/output) INTEGER array, dimension (N) */
/* On entry, if JPVT(J).ne.0, the J-th column of A is permuted */
/* to the front of A*P (a leading column); if JPVT(J)=0, */
/* the J-th column of A is a free column. */
/* On exit, if JPVT(J)=K, then the J-th column of A*P was the */
/* the K-th column of A. */
/* TAU (output) REAL array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors. */
/* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO=0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= 3*N+1. */
/* For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB */
/* is the optimal blocksize. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit. */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* Further Details */
/* =============== */
/* The matrix Q is represented as a product of elementary reflectors */
/* Q = H(1) H(2) . . . H(k), where k = min(m,n). */
/* Each H(i) has the form */
/* H(i) = I - tau * v * v' */
/* where tau is a real/complex scalar, and v is a real/complex vector */
/* with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in */
/* A(i+1:m,i), and tau in TAU(i). */
/* Based on contributions by */
/* G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain */
/* X. Sun, Computer Science Dept., Duke University, USA */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--jpvt;
--tau;
--work;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
}
if (*info == 0) {
minmn = min(*m,*n);
if (minmn == 0) {
iws = 1;
lwkopt = 1;
} else {
iws = *n * 3 + 1;
nb = ilaenv_(&c__1, "SGEQRF", " ", m, n, &c_n1, &c_n1);
lwkopt = (*n << 1) + (*n + 1) * nb;
}
work[1] = (real) lwkopt;
if (*lwork < iws && ! lquery) {
*info = -8;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGEQP3", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible. */
if (minmn == 0) {
return 0;
}
/* Move initial columns up front. */
nfxd = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (jpvt[j] != 0) {
if (j != nfxd) {
sswap_(m, &a[j * a_dim1 + 1], &c__1, &a[nfxd * a_dim1 + 1], &
c__1);
jpvt[j] = jpvt[nfxd];
jpvt[nfxd] = j;
} else {
jpvt[j] = j;
}
++nfxd;
} else {
jpvt[j] = j;
}
/* L10: */
}
--nfxd;
/* Factorize fixed columns */
/* ======================= */
/* Compute the QR factorization of fixed columns and update */
/* remaining columns. */
if (nfxd > 0) {
na = min(*m,nfxd);
/* CC CALL SGEQR2( M, NA, A, LDA, TAU, WORK, INFO ) */
sgeqrf_(m, &na, &a[a_offset], lda, &tau[1], &work[1], lwork, info);
/* Computing MAX */
i__1 = iws, i__2 = (integer) work[1];
iws = max(i__1,i__2);
if (na < *n) {
/* CC CALL SORM2R( 'Left', 'Transpose', M, N-NA, NA, A, LDA, */
/* CC $ TAU, A( 1, NA+1 ), LDA, WORK, INFO ) */
i__1 = *n - na;
sormqr_("Left", "Transpose", m, &i__1, &na, &a[a_offset], lda, &
tau[1], &a[(na + 1) * a_dim1 + 1], lda, &work[1], lwork,
info);
/* Computing MAX */
i__1 = iws, i__2 = (integer) work[1];
iws = max(i__1,i__2);
}
}
/* Factorize free columns */
/* ====================== */
if (nfxd < minmn) {
sm = *m - nfxd;
sn = *n - nfxd;
sminmn = minmn - nfxd;
/* Determine the block size. */
nb = ilaenv_(&c__1, "SGEQRF", " ", &sm, &sn, &c_n1, &c_n1);
nbmin = 2;
nx = 0;
if (nb > 1 && nb < sminmn) {
/* Determine when to cross over from blocked to unblocked code. */
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "SGEQRF", " ", &sm, &sn, &c_n1, &
c_n1);
nx = max(i__1,i__2);
if (nx < sminmn) {
/* Determine if workspace is large enough for blocked code. */
minws = (sn << 1) + (sn + 1) * nb;
iws = max(iws,minws);
if (*lwork < minws) {
/* Not enough workspace to use optimal NB: Reduce NB and */
/* determine the minimum value of NB. */
nb = (*lwork - (sn << 1)) / (sn + 1);
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "SGEQRF", " ", &sm, &sn, &
c_n1, &c_n1);
nbmin = max(i__1,i__2);
}
}
}
/* Initialize partial column norms. The first N elements of work */
/* store the exact column norms. */
i__1 = *n;
for (j = nfxd + 1; j <= i__1; ++j) {
work[j] = snrm2_(&sm, &a[nfxd + 1 + j * a_dim1], &c__1);
work[*n + j] = work[j];
/* L20: */
}
if (nb >= nbmin && nb < sminmn && nx < sminmn) {
/* Use blocked code initially. */
j = nfxd + 1;
/* Compute factorization: while loop. */
topbmn = minmn - nx;
L30:
if (j <= topbmn) {
/* Computing MIN */
i__1 = nb, i__2 = topbmn - j + 1;
jb = min(i__1,i__2);
/* Factorize JB columns among columns J:N. */
i__1 = *n - j + 1;
i__2 = j - 1;
i__3 = *n - j + 1;
slaqps_(m, &i__1, &i__2, &jb, &fjb, &a[j * a_dim1 + 1], lda, &
jpvt[j], &tau[j], &work[j], &work[*n + j], &work[(*n
<< 1) + 1], &work[(*n << 1) + jb + 1], &i__3);
j += fjb;
goto L30;
}
} else {
j = nfxd + 1;
}
/* Use unblocked code to factor the last or only block. */
if (j <= minmn) {
i__1 = *n - j + 1;
i__2 = j - 1;
slaqp2_(m, &i__1, &i__2, &a[j * a_dim1 + 1], lda, &jpvt[j], &tau[
j], &work[j], &work[*n + j], &work[(*n << 1) + 1]);
}
}
work[1] = (real) iws;
return 0;
/* End of SGEQP3 */
} /* sgeqp3_ */
/* Subroutine */ int sgegs_(char *jobvsl, char *jobvsr, integer *n, real *a,
integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real
*beta, real *vsl, integer *ldvsl, real *vsr, integer *ldvsr, real *
work, integer *lwork, integer *info)
{
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
This routine is deprecated and has been replaced by routine SGGES.
SGEGS computes for a pair of N-by-N real nonsymmetric matrices A, B:
the generalized eigenvalues (alphar +/- alphai*i, beta), the real
Schur form (A, B), and optionally left and/or right Schur vectors
(VSL and VSR).
(If only the generalized eigenvalues are needed, use the driver SGEGV
instead.)
A generalized eigenvalue for a pair of matrices (A,B) is, roughly
speaking, a scalar w or a ratio alpha/beta = w, such that A - w*B
is singular. It is usually represented as the pair (alpha,beta),
as there is a reasonable interpretation for beta=0, and even for
both being zero. A good beginning reference is the book, "Matrix
Computations", by G. Golub & C. van Loan (Johns Hopkins U. Press)
The (generalized) Schur form of a pair of matrices is the result of
multiplying both matrices on the left by one orthogonal matrix and
both on the right by another orthogonal matrix, these two orthogonal
matrices being chosen so as to bring the pair of matrices into
(real) Schur form.
A pair of matrices A, B is in generalized real Schur form if B is
upper triangular with non-negative diagonal and A is block upper
triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond
to real generalized eigenvalues, while 2-by-2 blocks of A will be
"standardized" by making the corresponding elements of B have the
form:
[ a 0 ]
[ 0 b ]
and the pair of corresponding 2-by-2 blocks in A and B will
have a complex conjugate pair of generalized eigenvalues.
The left and right Schur vectors are the columns of VSL and VSR,
respectively, where VSL and VSR are the orthogonal matrices
which reduce A and B to Schur form:
Schur form of (A,B) = ( (VSL)**T A (VSR), (VSL)**T B (VSR) )
Arguments
=========
JOBVSL (input) CHARACTER*1
= 'N': do not compute the left Schur vectors;
= 'V': compute the left Schur vectors.
JOBVSR (input) CHARACTER*1
= 'N': do not compute the right Schur vectors;
= 'V': compute the right Schur vectors.
N (input) INTEGER
The order of the matrices A, B, VSL, and VSR. N >= 0.
A (input/output) REAL array, dimension (LDA, N)
On entry, the first of the pair of matrices whose generalized
eigenvalues and (optionally) Schur vectors are to be
computed.
On exit, the generalized Schur form of A.
Note: to avoid overflow, the Frobenius norm of the matrix
A should be less than the overflow threshold.
LDA (input) INTEGER
The leading dimension of A. LDA >= max(1,N).
B (input/output) REAL array, dimension (LDB, N)
On entry, the second of the pair of matrices whose
generalized eigenvalues and (optionally) Schur vectors are
to be computed.
On exit, the generalized Schur form of B.
Note: to avoid overflow, the Frobenius norm of the matrix
B should be less than the overflow threshold.
LDB (input) INTEGER
The leading dimension of B. LDB >= max(1,N).
ALPHAR (output) REAL array, dimension (N)
ALPHAI (output) REAL array, dimension (N)
BETA (output) REAL array, dimension (N)
On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
be the generalized eigenvalues. ALPHAR(j) + ALPHAI(j)*i,
j=1,...,N and BETA(j),j=1,...,N are the diagonals of the
complex Schur form (A,B) that would result if the 2-by-2
diagonal blocks of the real Schur form of (A,B) were further
reduced to triangular form using 2-by-2 complex unitary
transformations. If ALPHAI(j) is zero, then the j-th
eigenvalue is real; if positive, then the j-th and (j+1)-st
eigenvalues are a complex conjugate pair, with ALPHAI(j+1)
negative.
Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
may easily over- or underflow, and BETA(j) may even be zero.
Thus, the user should avoid naively computing the ratio
alpha/beta. However, ALPHAR and ALPHAI will be always less
than and usually comparable with norm(A) in magnitude, and
BETA always less than and usually comparable with norm(B).
VSL (output) REAL array, dimension (LDVSL,N)
If JOBVSL = 'V', VSL will contain the left Schur vectors.
(See "Purpose", above.)
Not referenced if JOBVSL = 'N'.
LDVSL (input) INTEGER
The leading dimension of the matrix VSL. LDVSL >=1, and
if JOBVSL = 'V', LDVSL >= N.
VSR (output) REAL array, dimension (LDVSR,N)
If JOBVSR = 'V', VSR will contain the right Schur vectors.
(See "Purpose", above.)
Not referenced if JOBVSR = 'N'.
LDVSR (input) INTEGER
The leading dimension of the matrix VSR. LDVSR >= 1, and
if JOBVSR = 'V', LDVSR >= N.
WORK (workspace/output) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,4*N).
For good performance, LWORK must generally be larger.
To compute the optimal value of LWORK, call ILAENV to get
blocksizes (for SGEQRF, SORMQR, and SORGQR.) Then compute:
NB -- MAX of the blocksizes for SGEQRF, SORMQR, and SORGQR
The optimal LWORK is 2*N + N*(NB+1).
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
= 1,...,N:
The QZ iteration failed. (A,B) are not in Schur
form, but ALPHAR(j), ALPHAI(j), and BETA(j) should
be correct for j=INFO+1,...,N.
> N: errors that usually indicate LAPACK problems:
=N+1: error return from SGGBAL
=N+2: error return from SGEQRF
=N+3: error return from SORMQR
=N+4: error return from SORGQR
=N+5: error return from SGGHRD
=N+6: error return from SHGEQZ (other than failed
iteration)
=N+7: error return from SGGBAK (computing VSL)
=N+8: error return from SGGBAK (computing VSR)
=N+9: error return from SLASCL (various places)
=====================================================================
Decode the input arguments
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static real c_b36 = 0.f;
static real c_b37 = 1.f;
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset,
vsr_dim1, vsr_offset, i__1, i__2;
/* Local variables */
static real anrm, bnrm;
static integer itau, lopt;
extern logical lsame_(char *, char *);
static integer ileft, iinfo, icols;
static logical ilvsl;
static integer iwork;
static logical ilvsr;
static integer irows, nb;
extern /* Subroutine */ int sggbak_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, real *, integer *, integer *
), sggbal_(char *, integer *, real *, integer *,
real *, integer *, integer *, integer *, real *, real *, real *,
integer *);
static logical ilascl, ilbscl;
extern doublereal slamch_(char *), slange_(char *, integer *,
integer *, real *, integer *, real *);
static real safmin;
extern /* Subroutine */ int sgghrd_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, integer *, real *, integer *
, real *, integer *, integer *), xerbla_(char *,
integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static real bignum;
extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, real *, integer *, integer *);
static integer ijobvl, iright;
extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *);
static integer ijobvr;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), slaset_(char *, integer *,
integer *, real *, real *, real *, integer *);
static real anrmto;
static integer lwkmin, nb1, nb2, nb3;
static real bnrmto;
extern /* Subroutine */ int shgeqz_(char *, char *, char *, integer *,
integer *, integer *, real *, integer *, real *, integer *, real *
, real *, real *, real *, integer *, real *, integer *, real *,
integer *, integer *);
static real smlnum;
extern /* Subroutine */ int sorgqr_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *, integer *);
static integer lwkopt;
static logical lquery;
extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
static integer ihi, ilo;
static real eps;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
#define vsl_ref(a_1,a_2) vsl[(a_2)*vsl_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--alphar;
--alphai;
--beta;
vsl_dim1 = *ldvsl;
vsl_offset = 1 + vsl_dim1 * 1;
vsl -= vsl_offset;
vsr_dim1 = *ldvsr;
vsr_offset = 1 + vsr_dim1 * 1;
vsr -= vsr_offset;
--work;
/* Function Body */
if (lsame_(jobvsl, "N")) {
ijobvl = 1;
ilvsl = FALSE_;
} else if (lsame_(jobvsl, "V")) {
ijobvl = 2;
ilvsl = TRUE_;
} else {
ijobvl = -1;
ilvsl = FALSE_;
}
if (lsame_(jobvsr, "N")) {
ijobvr = 1;
ilvsr = FALSE_;
} else if (lsame_(jobvsr, "V")) {
ijobvr = 2;
ilvsr = TRUE_;
} else {
ijobvr = -1;
ilvsr = FALSE_;
}
/* Test the input arguments
Computing MAX */
i__1 = *n << 2;
lwkmin = max(i__1,1);
lwkopt = lwkmin;
work[1] = (real) lwkopt;
lquery = *lwork == -1;
*info = 0;
if (ijobvl <= 0) {
*info = -1;
} else if (ijobvr <= 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -7;
} else if (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
*info = -12;
} else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
*info = -14;
} else if (*lwork < lwkmin && ! lquery) {
*info = -16;
}
if (*info == 0) {
nb1 = ilaenv_(&c__1, "SGEQRF", " ", n, n, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
nb2 = ilaenv_(&c__1, "SORMQR", " ", n, n, n, &c_n1, (ftnlen)6, (
ftnlen)1);
nb3 = ilaenv_(&c__1, "SORGQR", " ", n, n, n, &c_n1, (ftnlen)6, (
ftnlen)1);
/* Computing MAX */
i__1 = max(nb1,nb2);
nb = max(i__1,nb3);
lopt = (*n << 1) + *n * (nb + 1);
work[1] = (real) lopt;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGEGS ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Get machine constants */
eps = slamch_("E") * slamch_("B");
safmin = slamch_("S");
smlnum = *n * safmin / eps;
bignum = 1.f / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = slange_("M", n, n, &a[a_offset], lda, &work[1]);
ilascl = FALSE_;
if (anrm > 0.f && anrm < smlnum) {
anrmto = smlnum;
ilascl = TRUE_;
} else if (anrm > bignum) {
anrmto = bignum;
ilascl = TRUE_;
}
if (ilascl) {
slascl_("G", &c_n1, &c_n1, &anrm, &anrmto, n, n, &a[a_offset], lda, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
}
/* Scale B if max element outside range [SMLNUM,BIGNUM] */
bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]);
ilbscl = FALSE_;
if (bnrm > 0.f && bnrm < smlnum) {
bnrmto = smlnum;
ilbscl = TRUE_;
} else if (bnrm > bignum) {
bnrmto = bignum;
ilbscl = TRUE_;
}
if (ilbscl) {
slascl_("G", &c_n1, &c_n1, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
}
/* Permute the matrix to make it more nearly triangular
Workspace layout: (2*N words -- "work..." not actually used)
left_permutation, right_permutation, work... */
ileft = 1;
iright = *n + 1;
iwork = iright + *n;
sggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
ileft], &work[iright], &work[iwork], &iinfo);
if (iinfo != 0) {
*info = *n + 1;
goto L10;
}
/* Reduce B to triangular form, and initialize VSL and/or VSR
Workspace layout: ("work..." must have at least N words)
left_permutation, right_permutation, tau, work... */
irows = ihi + 1 - ilo;
icols = *n + 1 - ilo;
itau = iwork;
iwork = itau + irows;
i__1 = *lwork + 1 - iwork;
sgeqrf_(&irows, &icols, &b_ref(ilo, ilo), ldb, &work[itau], &work[iwork],
&i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 2;
goto L10;
}
i__1 = *lwork + 1 - iwork;
sormqr_("L", "T", &irows, &icols, &irows, &b_ref(ilo, ilo), ldb, &work[
itau], &a_ref(ilo, ilo), lda, &work[iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 3;
goto L10;
}
if (ilvsl) {
slaset_("Full", n, n, &c_b36, &c_b37, &vsl[vsl_offset], ldvsl);
i__1 = irows - 1;
i__2 = irows - 1;
slacpy_("L", &i__1, &i__2, &b_ref(ilo + 1, ilo), ldb, &vsl_ref(ilo +
1, ilo), ldvsl);
i__1 = *lwork + 1 - iwork;
sorgqr_(&irows, &irows, &irows, &vsl_ref(ilo, ilo), ldvsl, &work[itau]
, &work[iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 4;
goto L10;
}
}
if (ilvsr) {
slaset_("Full", n, n, &c_b36, &c_b37, &vsr[vsr_offset], ldvsr);
}
/* Reduce to generalized Hessenberg form */
sgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &iinfo);
if (iinfo != 0) {
*info = *n + 5;
goto L10;
}
/* Perform QZ algorithm, computing Schur vectors if desired
Workspace layout: ("work..." must have at least 1 word)
left_permutation, right_permutation, work... */
iwork = itau;
i__1 = *lwork + 1 - iwork;
shgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[
b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[vsl_offset]
, ldvsl, &vsr[vsr_offset], ldvsr, &work[iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = max(i__1,i__2);
}
if (iinfo != 0) {
if (iinfo > 0 && iinfo <= *n) {
*info = iinfo;
} else if (iinfo > *n && iinfo <= *n << 1) {
*info = iinfo - *n;
} else {
*info = *n + 6;
}
goto L10;
}
/* Apply permutation to VSL and VSR */
if (ilvsl) {
sggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsl[
vsl_offset], ldvsl, &iinfo);
if (iinfo != 0) {
*info = *n + 7;
goto L10;
}
}
if (ilvsr) {
sggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsr[
vsr_offset], ldvsr, &iinfo);
if (iinfo != 0) {
*info = *n + 8;
goto L10;
}
}
/* Undo scaling */
if (ilascl) {
slascl_("H", &c_n1, &c_n1, &anrmto, &anrm, n, n, &a[a_offset], lda, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
slascl_("G", &c_n1, &c_n1, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
slascl_("G", &c_n1, &c_n1, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
}
if (ilbscl) {
slascl_("U", &c_n1, &c_n1, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
slascl_("G", &c_n1, &c_n1, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
iinfo);
if (iinfo != 0) {
*info = *n + 9;
return 0;
}
}
L10:
work[1] = (real) lwkopt;
return 0;
/* End of SGEGS */
} /* sgegs_ */
int sggevx_(char *balanc, char *jobvl, char *jobvr, char *
sense, int *n, float *a, int *lda, float *b, int *ldb, float
*alphar, float *alphai, float *beta, float *vl, int *ldvl, float *vr,
int *ldvr, int *ilo, int *ihi, float *lscale, float *rscale,
float *abnrm, float *bbnrm, float *rconde, float *rcondv, float *work,
int *lwork, int *iwork, int *bwork, int *info)
{
/* System generated locals */
int a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1,
vr_offset, i__1, i__2;
float r__1, r__2, r__3, r__4;
/* Builtin functions */
double sqrt(double);
/* Local variables */
int i__, j, m, jc, in, mm, jr;
float eps;
int ilv, pair;
float anrm, bnrm;
int ierr, itau;
float temp;
int ilvl, ilvr;
int iwrk, iwrk1;
extern int lsame_(char *, char *);
int icols;
int noscl;
int irows;
extern int slabad_(float *, float *), sggbak_(char *, char
*, int *, int *, int *, float *, float *, int *,
float *, int *, int *), sggbal_(char *,
int *, float *, int *, float *, int *, int *,
int *, float *, float *, float *, int *);
int ilascl, ilbscl;
extern double slamch_(char *);
extern int xerbla_(char *, int *), sgghrd_(
char *, char *, int *, int *, int *, float *, int *
, float *, int *, float *, int *, float *, int *,
int *);
int ldumma[1];
char chtemp[1];
float bignum;
extern int slascl_(char *, int *, int *, float *,
float *, int *, int *, float *, int *, int *);
extern int ilaenv_(int *, char *, char *, int *, int *,
int *, int *);
extern double slange_(char *, int *, int *, float *, int *,
float *);
int ijobvl;
extern int sgeqrf_(int *, int *, float *, int
*, float *, float *, int *, int *);
int ijobvr;
extern int slacpy_(char *, int *, int *, float *,
int *, float *, int *);
int wantsb;
extern int slaset_(char *, int *, int *, float *,
float *, float *, int *);
float anrmto;
int wantse;
float bnrmto;
extern int shgeqz_(char *, char *, char *, int *,
int *, int *, float *, int *, float *, int *, float *
, float *, float *, float *, int *, float *, int *, float *,
int *, int *), stgevc_(char *,
char *, int *, int *, float *, int *, float *, int *
, float *, int *, float *, int *, int *, int *,
float *, int *), stgsna_(char *, char *,
int *, int *, float *, int *, float *, int *, float *
, int *, float *, int *, float *, float *, int *,
int *, float *, int *, int *, int *);
int minwrk, maxwrk;
int wantsn;
float smlnum;
extern int sorgqr_(int *, int *, int *, float
*, int *, float *, float *, int *, int *);
int lquery, wantsv;
extern int sormqr_(char *, char *, int *, int *,
int *, float *, int *, float *, float *, int *, float *,
int *, int *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SGGEVX computes for a pair of N-by-N float nonsymmetric matrices (A,B) */
/* the generalized eigenvalues, and optionally, the left and/or right */
/* generalized eigenvectors. */
/* Optionally also, it computes a balancing transformation to improve */
/* the conditioning of the eigenvalues and eigenvectors (ILO, IHI, */
/* LSCALE, RSCALE, ABNRM, and BBNRM), reciprocal condition numbers for */
/* the eigenvalues (RCONDE), and reciprocal condition numbers for the */
/* right eigenvectors (RCONDV). */
/* A generalized eigenvalue for a pair of matrices (A,B) is a scalar */
/* lambda or a ratio alpha/beta = lambda, such that A - lambda*B is */
/* singular. It is usually represented as the pair (alpha,beta), as */
/* there is a reasonable interpretation for beta=0, and even for both */
/* being zero. */
/* The right eigenvector v(j) corresponding to the eigenvalue lambda(j) */
/* of (A,B) satisfies */
/* A * v(j) = lambda(j) * B * v(j) . */
/* The left eigenvector u(j) corresponding to the eigenvalue lambda(j) */
/* of (A,B) satisfies */
/* u(j)**H * A = lambda(j) * u(j)**H * B. */
/* where u(j)**H is the conjugate-transpose of u(j). */
/* Arguments */
/* ========= */
/* BALANC (input) CHARACTER*1 */
/* Specifies the balance option to be performed. */
/* = 'N': do not diagonally scale or permute; */
/* = 'P': permute only; */
/* = 'S': scale only; */
/* = 'B': both permute and scale. */
/* Computed reciprocal condition numbers will be for the */
/* matrices after permuting and/or balancing. Permuting does */
/* not change condition numbers (in exact arithmetic), but */
/* balancing does. */
/* JOBVL (input) CHARACTER*1 */
/* = 'N': do not compute the left generalized eigenvectors; */
/* = 'V': compute the left generalized eigenvectors. */
/* JOBVR (input) CHARACTER*1 */
/* = 'N': do not compute the right generalized eigenvectors; */
/* = 'V': compute the right generalized eigenvectors. */
/* SENSE (input) CHARACTER*1 */
/* Determines which reciprocal condition numbers are computed. */
/* = 'N': none are computed; */
/* = 'E': computed for eigenvalues only; */
/* = 'V': computed for eigenvectors only; */
/* = 'B': computed for eigenvalues and eigenvectors. */
/* N (input) INTEGER */
/* The order of the matrices A, B, VL, and VR. N >= 0. */
/* A (input/output) REAL array, dimension (LDA, N) */
/* On entry, the matrix A in the pair (A,B). */
/* On exit, A has been overwritten. If JOBVL='V' or JOBVR='V' */
/* or both, then A contains the first part of the float Schur */
/* form of the "balanced" versions of the input A and B. */
/* LDA (input) INTEGER */
/* The leading dimension of A. LDA >= MAX(1,N). */
/* B (input/output) REAL array, dimension (LDB, N) */
/* On entry, the matrix B in the pair (A,B). */
/* On exit, B has been overwritten. If JOBVL='V' or JOBVR='V' */
/* or both, then B contains the second part of the float Schur */
/* form of the "balanced" versions of the input A and B. */
/* LDB (input) INTEGER */
/* The leading dimension of B. LDB >= MAX(1,N). */
/* ALPHAR (output) REAL array, dimension (N) */
/* ALPHAI (output) REAL array, dimension (N) */
/* BETA (output) REAL array, dimension (N) */
/* On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will */
/* be the generalized eigenvalues. If ALPHAI(j) is zero, then */
/* the j-th eigenvalue is float; if positive, then the j-th and */
/* (j+1)-st eigenvalues are a complex conjugate pair, with */
/* ALPHAI(j+1) negative. */
/* Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) */
/* may easily over- or underflow, and BETA(j) may even be zero. */
/* Thus, the user should avoid naively computing the ratio */
/* ALPHA/BETA. However, ALPHAR and ALPHAI will be always less */
/* than and usually comparable with norm(A) in magnitude, and */
/* BETA always less than and usually comparable with norm(B). */
/* VL (output) REAL array, dimension (LDVL,N) */
/* If JOBVL = 'V', the left eigenvectors u(j) are stored one */
/* after another in the columns of VL, in the same order as */
/* their eigenvalues. If the j-th eigenvalue is float, then */
/* u(j) = VL(:,j), the j-th column of VL. If the j-th and */
/* (j+1)-th eigenvalues form a complex conjugate pair, then */
/* u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1). */
/* Each eigenvector will be scaled so the largest component have */
/* ABS(float part) + ABS(imag. part) = 1. */
/* Not referenced if JOBVL = 'N'. */
/* LDVL (input) INTEGER */
/* The leading dimension of the matrix VL. LDVL >= 1, and */
/* if JOBVL = 'V', LDVL >= N. */
/* VR (output) REAL array, dimension (LDVR,N) */
/* If JOBVR = 'V', the right eigenvectors v(j) are stored one */
/* after another in the columns of VR, in the same order as */
/* their eigenvalues. If the j-th eigenvalue is float, then */
/* v(j) = VR(:,j), the j-th column of VR. If the j-th and */
/* (j+1)-th eigenvalues form a complex conjugate pair, then */
/* v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1). */
/* Each eigenvector will be scaled so the largest component have */
/* ABS(float part) + ABS(imag. part) = 1. */
/* Not referenced if JOBVR = 'N'. */
/* LDVR (input) INTEGER */
/* The leading dimension of the matrix VR. LDVR >= 1, and */
/* if JOBVR = 'V', LDVR >= N. */
/* ILO (output) INTEGER */
/* IHI (output) INTEGER */
/* ILO and IHI are int values such that on exit */
/* A(i,j) = 0 and B(i,j) = 0 if i > j and */
/* j = 1,...,ILO-1 or i = IHI+1,...,N. */
/* If BALANC = 'N' or 'S', ILO = 1 and IHI = N. */
/* LSCALE (output) REAL array, dimension (N) */
/* Details of the permutations and scaling factors applied */
/* to the left side of A and B. If PL(j) is the index of the */
/* row interchanged with row j, and DL(j) is the scaling */
/* factor applied to row j, then */
/* LSCALE(j) = PL(j) for j = 1,...,ILO-1 */
/* = DL(j) for j = ILO,...,IHI */
/* = PL(j) for j = IHI+1,...,N. */
/* The order in which the interchanges are made is N to IHI+1, */
/* then 1 to ILO-1. */
/* RSCALE (output) REAL array, dimension (N) */
/* Details of the permutations and scaling factors applied */
/* to the right side of A and B. If PR(j) is the index of the */
/* column interchanged with column j, and DR(j) is the scaling */
/* factor applied to column j, then */
/* RSCALE(j) = PR(j) for j = 1,...,ILO-1 */
/* = DR(j) for j = ILO,...,IHI */
/* = PR(j) for j = IHI+1,...,N */
/* The order in which the interchanges are made is N to IHI+1, */
/* then 1 to ILO-1. */
/* ABNRM (output) REAL */
/* The one-norm of the balanced matrix A. */
/* BBNRM (output) REAL */
/* The one-norm of the balanced matrix B. */
/* RCONDE (output) REAL array, dimension (N) */
/* If SENSE = 'E' or 'B', the reciprocal condition numbers of */
/* the eigenvalues, stored in consecutive elements of the array. */
/* For a complex conjugate pair of eigenvalues two consecutive */
/* elements of RCONDE are set to the same value. Thus RCONDE(j), */
/* RCONDV(j), and the j-th columns of VL and VR all correspond */
/* to the j-th eigenpair. */
/* If SENSE = 'N' or 'V', RCONDE is not referenced. */
/* RCONDV (output) REAL array, dimension (N) */
/* If SENSE = 'V' or 'B', the estimated reciprocal condition */
/* numbers of the eigenvectors, stored in consecutive elements */
/* of the array. For a complex eigenvector two consecutive */
/* elements of RCONDV are set to the same value. If the */
/* eigenvalues cannot be reordered to compute RCONDV(j), */
/* RCONDV(j) is set to 0; this can only occur when the true */
/* value would be very small anyway. */
/* If SENSE = 'N' or 'E', RCONDV is not referenced. */
/* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= MAX(1,2*N). */
/* If BALANC = 'S' or 'B', or JOBVL = 'V', or JOBVR = 'V', */
/* LWORK >= MAX(1,6*N). */
/* If SENSE = 'E', LWORK >= MAX(1,10*N). */
/* If SENSE = 'V' or 'B', LWORK >= 2*N*N+8*N+16. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* IWORK (workspace) INTEGER array, dimension (N+6) */
/* If SENSE = 'E', IWORK is not referenced. */
/* BWORK (workspace) LOGICAL array, dimension (N) */
/* If SENSE = 'N', BWORK is not referenced. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* = 1,...,N: */
/* The QZ iteration failed. No eigenvectors have been */
/* calculated, but ALPHAR(j), ALPHAI(j), and BETA(j) */
/* should be correct for j=INFO+1,...,N. */
/* > N: =N+1: other than QZ iteration failed in SHGEQZ. */
/* =N+2: error return from STGEVC. */
/* Further Details */
/* =============== */
/* Balancing a matrix pair (A,B) includes, first, permuting rows and */
/* columns to isolate eigenvalues, second, applying diagonal similarity */
/* transformation to the rows and columns to make the rows and columns */
/* as close in norm as possible. The computed reciprocal condition */
/* numbers correspond to the balanced matrix. Permuting rows and columns */
/* will not change the condition numbers (in exact arithmetic) but */
/* diagonal scaling will. For further explanation of balancing, see */
/* section 4.11.1.2 of LAPACK Users' Guide. */
/* An approximate error bound on the chordal distance between the i-th */
/* computed generalized eigenvalue w and the corresponding exact */
/* eigenvalue lambda is */
/* chord(w, lambda) <= EPS * norm(ABNRM, BBNRM) / RCONDE(I) */
/* An approximate error bound for the angle between the i-th computed */
/* eigenvector VL(i) or VR(i) is given by */
/* EPS * norm(ABNRM, BBNRM) / DIF(i). */
/* For further explanation of the reciprocal condition numbers RCONDE */
/* and RCONDV, see section 4.11 of LAPACK User's Guide. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--alphar;
--alphai;
--beta;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--lscale;
--rscale;
--rconde;
--rcondv;
--work;
--iwork;
--bwork;
/* Function Body */
if (lsame_(jobvl, "N")) {
ijobvl = 1;
ilvl = FALSE;
} else if (lsame_(jobvl, "V")) {
ijobvl = 2;
ilvl = TRUE;
} else {
ijobvl = -1;
ilvl = FALSE;
}
if (lsame_(jobvr, "N")) {
ijobvr = 1;
ilvr = FALSE;
} else if (lsame_(jobvr, "V")) {
ijobvr = 2;
ilvr = TRUE;
} else {
ijobvr = -1;
ilvr = FALSE;
}
ilv = ilvl || ilvr;
noscl = lsame_(balanc, "N") || lsame_(balanc, "P");
wantsn = lsame_(sense, "N");
wantse = lsame_(sense, "E");
wantsv = lsame_(sense, "V");
wantsb = lsame_(sense, "B");
/* Test the input arguments */
*info = 0;
lquery = *lwork == -1;
if (! (noscl || lsame_(balanc, "S") || lsame_(
balanc, "B"))) {
*info = -1;
} else if (ijobvl <= 0) {
*info = -2;
} else if (ijobvr <= 0) {
*info = -3;
} else if (! (wantsn || wantse || wantsb || wantsv)) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*lda < MAX(1,*n)) {
*info = -7;
} else if (*ldb < MAX(1,*n)) {
*info = -9;
} else if (*ldvl < 1 || ilvl && *ldvl < *n) {
*info = -14;
} else if (*ldvr < 1 || ilvr && *ldvr < *n) {
*info = -16;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV. The workspace is */
/* computed assuming ILO = 1 and IHI = N, the worst case.) */
if (*info == 0) {
if (*n == 0) {
minwrk = 1;
maxwrk = 1;
} else {
if (noscl && ! ilv) {
minwrk = *n << 1;
} else {
minwrk = *n * 6;
}
if (wantse) {
minwrk = *n * 10;
} else if (wantsv || wantsb) {
minwrk = (*n << 1) * (*n + 4) + 16;
}
maxwrk = minwrk;
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "SGEQRF", " ", n, &
c__1, n, &c__0);
maxwrk = MAX(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "SORMQR", " ", n, &
c__1, n, &c__0);
maxwrk = MAX(i__1,i__2);
if (ilvl) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "SORGQR",
" ", n, &c__1, n, &c__0);
maxwrk = MAX(i__1,i__2);
}
}
work[1] = (float) maxwrk;
if (*lwork < minwrk && ! lquery) {
*info = -26;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGGEVX", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Get machine constants */
eps = slamch_("P");
smlnum = slamch_("S");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1.f / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = slange_("M", n, n, &a[a_offset], lda, &work[1]);
ilascl = FALSE;
if (anrm > 0.f && anrm < smlnum) {
anrmto = smlnum;
ilascl = TRUE;
} else if (anrm > bignum) {
anrmto = bignum;
ilascl = TRUE;
}
if (ilascl) {
slascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
ierr);
}
/* Scale B if max element outside range [SMLNUM,BIGNUM] */
bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]);
ilbscl = FALSE;
if (bnrm > 0.f && bnrm < smlnum) {
bnrmto = smlnum;
ilbscl = TRUE;
} else if (bnrm > bignum) {
bnrmto = bignum;
ilbscl = TRUE;
}
if (ilbscl) {
slascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
ierr);
}
/* Permute and/or balance the matrix pair (A,B) */
/* (Workspace: need 6*N if BALANC = 'S' or 'B', 1 otherwise) */
sggbal_(balanc, n, &a[a_offset], lda, &b[b_offset], ldb, ilo, ihi, &
lscale[1], &rscale[1], &work[1], &ierr);
/* Compute ABNRM and BBNRM */
*abnrm = slange_("1", n, n, &a[a_offset], lda, &work[1]);
if (ilascl) {
work[1] = *abnrm;
slascl_("G", &c__0, &c__0, &anrmto, &anrm, &c__1, &c__1, &work[1], &
c__1, &ierr);
*abnrm = work[1];
}
*bbnrm = slange_("1", n, n, &b[b_offset], ldb, &work[1]);
if (ilbscl) {
work[1] = *bbnrm;
slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, &c__1, &c__1, &work[1], &
c__1, &ierr);
*bbnrm = work[1];
}
/* Reduce B to triangular form (QR decomposition of B) */
/* (Workspace: need N, prefer N*NB ) */
irows = *ihi + 1 - *ilo;
if (ilv || ! wantsn) {
icols = *n + 1 - *ilo;
} else {
icols = irows;
}
itau = 1;
iwrk = itau + irows;
i__1 = *lwork + 1 - iwrk;
sgeqrf_(&irows, &icols, &b[*ilo + *ilo * b_dim1], ldb, &work[itau], &work[
iwrk], &i__1, &ierr);
/* Apply the orthogonal transformation to A */
/* (Workspace: need N, prefer N*NB) */
i__1 = *lwork + 1 - iwrk;
sormqr_("L", "T", &irows, &icols, &irows, &b[*ilo + *ilo * b_dim1], ldb, &
work[itau], &a[*ilo + *ilo * a_dim1], lda, &work[iwrk], &i__1, &
ierr);
/* Initialize VL and/or VR */
/* (Workspace: need N, prefer N*NB) */
if (ilvl) {
slaset_("Full", n, n, &c_b57, &c_b58, &vl[vl_offset], ldvl)
;
if (irows > 1) {
i__1 = irows - 1;
i__2 = irows - 1;
slacpy_("L", &i__1, &i__2, &b[*ilo + 1 + *ilo * b_dim1], ldb, &vl[
*ilo + 1 + *ilo * vl_dim1], ldvl);
}
i__1 = *lwork + 1 - iwrk;
sorgqr_(&irows, &irows, &irows, &vl[*ilo + *ilo * vl_dim1], ldvl, &
work[itau], &work[iwrk], &i__1, &ierr);
}
if (ilvr) {
slaset_("Full", n, n, &c_b57, &c_b58, &vr[vr_offset], ldvr)
;
}
/* Reduce to generalized Hessenberg form */
/* (Workspace: none needed) */
if (ilv || ! wantsn) {
/* Eigenvectors requested -- work on whole matrix. */
sgghrd_(jobvl, jobvr, n, ilo, ihi, &a[a_offset], lda, &b[b_offset],
ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &ierr);
} else {
sgghrd_("N", "N", &irows, &c__1, &irows, &a[*ilo + *ilo * a_dim1],
lda, &b[*ilo + *ilo * b_dim1], ldb, &vl[vl_offset], ldvl, &vr[
vr_offset], ldvr, &ierr);
}
/* Perform QZ algorithm (Compute eigenvalues, and optionally, the */
/* Schur forms and Schur vectors) */
/* (Workspace: need N) */
if (ilv || ! wantsn) {
*(unsigned char *)chtemp = 'S';
} else {
*(unsigned char *)chtemp = 'E';
}
shgeqz_(chtemp, jobvl, jobvr, n, ilo, ihi, &a[a_offset], lda, &b[b_offset]
, ldb, &alphar[1], &alphai[1], &beta[1], &vl[vl_offset], ldvl, &
vr[vr_offset], ldvr, &work[1], lwork, &ierr);
if (ierr != 0) {
if (ierr > 0 && ierr <= *n) {
*info = ierr;
} else if (ierr > *n && ierr <= *n << 1) {
*info = ierr - *n;
} else {
*info = *n + 1;
}
goto L130;
}
/* Compute Eigenvectors and estimate condition numbers if desired */
/* (Workspace: STGEVC: need 6*N */
/* STGSNA: need 2*N*(N+2)+16 if SENSE = 'V' or 'B', */
/* need N otherwise ) */
if (ilv || ! wantsn) {
if (ilv) {
if (ilvl) {
if (ilvr) {
*(unsigned char *)chtemp = 'B';
} else {
*(unsigned char *)chtemp = 'L';
}
} else {
*(unsigned char *)chtemp = 'R';
}
stgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset],
ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &
work[1], &ierr);
if (ierr != 0) {
*info = *n + 2;
goto L130;
}
}
if (! wantsn) {
/* compute eigenvectors (STGEVC) and estimate condition */
/* numbers (STGSNA). Note that the definition of the condition */
/* number is not invariant under transformation (u,v) to */
/* (Q*u, Z*v), where (u,v) are eigenvectors of the generalized */
/* Schur form (S,T), Q and Z are orthogonal matrices. In order */
/* to avoid using extra 2*N*N workspace, we have to recalculate */
/* eigenvectors and estimate one condition numbers at a time. */
pair = FALSE;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (pair) {
pair = FALSE;
goto L20;
}
mm = 1;
if (i__ < *n) {
if (a[i__ + 1 + i__ * a_dim1] != 0.f) {
pair = TRUE;
mm = 2;
}
}
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
bwork[j] = FALSE;
/* L10: */
}
if (mm == 1) {
bwork[i__] = TRUE;
} else if (mm == 2) {
bwork[i__] = TRUE;
bwork[i__ + 1] = TRUE;
}
iwrk = mm * *n + 1;
iwrk1 = iwrk + mm * *n;
/* Compute a pair of left and right eigenvectors. */
/* (compute workspace: need up to 4*N + 6*N) */
if (wantse || wantsb) {
stgevc_("B", "S", &bwork[1], n, &a[a_offset], lda, &b[
b_offset], ldb, &work[1], n, &work[iwrk], n, &mm,
&m, &work[iwrk1], &ierr);
if (ierr != 0) {
*info = *n + 2;
goto L130;
}
}
i__2 = *lwork - iwrk1 + 1;
stgsna_(sense, "S", &bwork[1], n, &a[a_offset], lda, &b[
b_offset], ldb, &work[1], n, &work[iwrk], n, &rconde[
i__], &rcondv[i__], &mm, &m, &work[iwrk1], &i__2, &
iwork[1], &ierr);
L20:
;
}
}
}
/* Undo balancing on VL and VR and normalization */
/* (Workspace: none needed) */
if (ilvl) {
sggbak_(balanc, "L", n, ilo, ihi, &lscale[1], &rscale[1], n, &vl[
vl_offset], ldvl, &ierr);
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
if (alphai[jc] < 0.f) {
goto L70;
}
temp = 0.f;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__2 = temp, r__3 = (r__1 = vl[jr + jc * vl_dim1], ABS(
r__1));
temp = MAX(r__2,r__3);
/* L30: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__3 = temp, r__4 = (r__1 = vl[jr + jc * vl_dim1], ABS(
r__1)) + (r__2 = vl[jr + (jc + 1) * vl_dim1],
ABS(r__2));
temp = MAX(r__3,r__4);
/* L40: */
}
}
if (temp < smlnum) {
goto L70;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vl[jr + jc * vl_dim1] *= temp;
/* L50: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vl[jr + jc * vl_dim1] *= temp;
vl[jr + (jc + 1) * vl_dim1] *= temp;
/* L60: */
}
}
L70:
;
}
}
if (ilvr) {
sggbak_(balanc, "R", n, ilo, ihi, &lscale[1], &rscale[1], n, &vr[
vr_offset], ldvr, &ierr);
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
if (alphai[jc] < 0.f) {
goto L120;
}
temp = 0.f;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__2 = temp, r__3 = (r__1 = vr[jr + jc * vr_dim1], ABS(
r__1));
temp = MAX(r__2,r__3);
/* L80: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__3 = temp, r__4 = (r__1 = vr[jr + jc * vr_dim1], ABS(
r__1)) + (r__2 = vr[jr + (jc + 1) * vr_dim1],
ABS(r__2));
temp = MAX(r__3,r__4);
/* L90: */
}
}
if (temp < smlnum) {
goto L120;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vr[jr + jc * vr_dim1] *= temp;
/* L100: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vr[jr + jc * vr_dim1] *= temp;
vr[jr + (jc + 1) * vr_dim1] *= temp;
/* L110: */
}
}
L120:
;
}
}
/* Undo scaling if necessary */
if (ilascl) {
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
ierr);
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
ierr);
}
if (ilbscl) {
slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
ierr);
}
L130:
work[1] = (float) maxwrk;
return 0;
/* End of SGGEVX */
} /* sggevx_ */
/* Subroutine */
int sggevx_(char *balanc, char *jobvl, char *jobvr, char * sense, integer *n, real *a, integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real *beta, real *vl, integer *ldvl, real *vr, integer *ldvr, integer *ilo, integer *ihi, real *lscale, real *rscale, real *abnrm, real *bbnrm, real *rconde, real *rcondv, real *work, integer *lwork, integer *iwork, logical *bwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, i__2;
real r__1, r__2, r__3, r__4;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, m, jc, in, mm, jr;
real eps;
logical ilv, pair;
real anrm, bnrm;
integer ierr, itau;
real temp;
logical ilvl, ilvr;
integer iwrk, iwrk1;
extern logical lsame_(char *, char *);
integer icols;
logical noscl;
integer irows;
extern /* Subroutine */
int slabad_(real *, real *), sggbak_(char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, integer *), sggbal_(char *, integer *, real *, integer *, real *, integer *, integer *, integer *, real *, real *, real *, integer *);
logical ilascl, ilbscl;
extern real slamch_(char *);
extern /* Subroutine */
int xerbla_(char *, integer *), sgghrd_( char *, char *, integer *, integer *, integer *, real *, integer * , real *, integer *, real *, integer *, real *, integer *, integer *);
logical ldumma[1];
char chtemp[1];
real bignum;
extern /* Subroutine */
int slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
extern real slange_(char *, integer *, integer *, real *, integer *, real *);
integer ijobvl;
extern /* Subroutine */
int sgeqrf_(integer *, integer *, real *, integer *, real *, real *, integer *, integer *);
integer ijobvr;
extern /* Subroutine */
int slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *);
logical wantsb;
extern /* Subroutine */
int slaset_(char *, integer *, integer *, real *, real *, real *, integer *);
real anrmto;
logical wantse;
real bnrmto;
extern /* Subroutine */
int shgeqz_(char *, char *, char *, integer *, integer *, integer *, real *, integer *, real *, integer *, real * , real *, real *, real *, integer *, real *, integer *, real *, integer *, integer *), stgevc_(char *, char *, logical *, integer *, real *, integer *, real *, integer * , real *, integer *, real *, integer *, integer *, integer *, real *, integer *), stgsna_(char *, char *, logical *, integer *, real *, integer *, real *, integer *, real * , integer *, real *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *, integer *);
integer minwrk, maxwrk;
logical wantsn;
real smlnum;
extern /* Subroutine */
int sorgqr_(integer *, integer *, integer *, real *, integer *, real *, real *, integer *, integer *);
logical lquery, wantsv;
extern /* Subroutine */
int sormqr_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *, integer *);
/* -- LAPACK driver routine (version 3.4.1) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* April 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--alphar;
--alphai;
--beta;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--lscale;
--rscale;
--rconde;
--rcondv;
--work;
--iwork;
--bwork;
/* Function Body */
if (lsame_(jobvl, "N"))
{
ijobvl = 1;
ilvl = FALSE_;
}
else if (lsame_(jobvl, "V"))
{
ijobvl = 2;
ilvl = TRUE_;
}
else
{
ijobvl = -1;
ilvl = FALSE_;
}
if (lsame_(jobvr, "N"))
{
ijobvr = 1;
ilvr = FALSE_;
}
else if (lsame_(jobvr, "V"))
{
ijobvr = 2;
ilvr = TRUE_;
}
else
{
ijobvr = -1;
ilvr = FALSE_;
}
ilv = ilvl || ilvr;
noscl = lsame_(balanc, "N") || lsame_(balanc, "P");
wantsn = lsame_(sense, "N");
wantse = lsame_(sense, "E");
wantsv = lsame_(sense, "V");
wantsb = lsame_(sense, "B");
/* Test the input arguments */
*info = 0;
lquery = *lwork == -1;
if (! (noscl || lsame_(balanc, "S") || lsame_( balanc, "B")))
{
*info = -1;
}
else if (ijobvl <= 0)
{
*info = -2;
}
else if (ijobvr <= 0)
{
*info = -3;
}
else if (! (wantsn || wantse || wantsb || wantsv))
{
*info = -4;
}
else if (*n < 0)
{
*info = -5;
}
else if (*lda < max(1,*n))
{
*info = -7;
}
else if (*ldb < max(1,*n))
{
*info = -9;
}
else if (*ldvl < 1 || ilvl && *ldvl < *n)
{
*info = -14;
}
else if (*ldvr < 1 || ilvr && *ldvr < *n)
{
*info = -16;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV. The workspace is */
/* computed assuming ILO = 1 and IHI = N, the worst case.) */
if (*info == 0)
{
if (*n == 0)
{
minwrk = 1;
maxwrk = 1;
}
else
{
if (noscl && ! ilv)
{
minwrk = *n << 1;
}
else
{
minwrk = *n * 6;
}
if (wantse)
{
minwrk = *n * 10;
}
else if (wantsv || wantsb)
{
minwrk = (*n << 1) * (*n + 4) + 16;
}
maxwrk = minwrk;
/* Computing MAX */
i__1 = maxwrk;
i__2 = *n + *n * ilaenv_(&c__1, "SGEQRF", " ", n, & c__1, n, &c__0); // , expr subst
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk;
i__2 = *n + *n * ilaenv_(&c__1, "SORMQR", " ", n, & c__1, n, &c__0); // , expr subst
maxwrk = max(i__1,i__2);
if (ilvl)
{
/* Computing MAX */
i__1 = maxwrk;
i__2 = *n + *n * ilaenv_(&c__1, "SORGQR", " ", n, &c__1, n, &c__0); // , expr subst
maxwrk = max(i__1,i__2);
}
}
work[1] = (real) maxwrk;
if (*lwork < minwrk && ! lquery)
{
*info = -26;
}
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("SGGEVX", &i__1);
return 0;
}
else if (lquery)
{
return 0;
}
/* Quick return if possible */
if (*n == 0)
{
return 0;
}
/* Get machine constants */
eps = slamch_("P");
smlnum = slamch_("S");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1.f / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = slange_("M", n, n, &a[a_offset], lda, &work[1]);
ilascl = FALSE_;
if (anrm > 0.f && anrm < smlnum)
{
anrmto = smlnum;
ilascl = TRUE_;
}
else if (anrm > bignum)
{
anrmto = bignum;
ilascl = TRUE_;
}
if (ilascl)
{
slascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, & ierr);
}
/* Scale B if max element outside range [SMLNUM,BIGNUM] */
bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]);
ilbscl = FALSE_;
if (bnrm > 0.f && bnrm < smlnum)
{
bnrmto = smlnum;
ilbscl = TRUE_;
}
else if (bnrm > bignum)
{
bnrmto = bignum;
ilbscl = TRUE_;
}
if (ilbscl)
{
slascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, & ierr);
}
/* Permute and/or balance the matrix pair (A,B) */
/* (Workspace: need 6*N if BALANC = 'S' or 'B', 1 otherwise) */
sggbal_(balanc, n, &a[a_offset], lda, &b[b_offset], ldb, ilo, ihi, & lscale[1], &rscale[1], &work[1], &ierr);
/* Compute ABNRM and BBNRM */
*abnrm = slange_("1", n, n, &a[a_offset], lda, &work[1]);
if (ilascl)
{
work[1] = *abnrm;
slascl_("G", &c__0, &c__0, &anrmto, &anrm, &c__1, &c__1, &work[1], & c__1, &ierr);
*abnrm = work[1];
}
*bbnrm = slange_("1", n, n, &b[b_offset], ldb, &work[1]);
if (ilbscl)
{
work[1] = *bbnrm;
slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, &c__1, &c__1, &work[1], & c__1, &ierr);
*bbnrm = work[1];
}
/* Reduce B to triangular form (QR decomposition of B) */
/* (Workspace: need N, prefer N*NB ) */
irows = *ihi + 1 - *ilo;
if (ilv || ! wantsn)
{
icols = *n + 1 - *ilo;
}
else
{
icols = irows;
}
itau = 1;
iwrk = itau + irows;
i__1 = *lwork + 1 - iwrk;
sgeqrf_(&irows, &icols, &b[*ilo + *ilo * b_dim1], ldb, &work[itau], &work[ iwrk], &i__1, &ierr);
/* Apply the orthogonal transformation to A */
/* (Workspace: need N, prefer N*NB) */
i__1 = *lwork + 1 - iwrk;
sormqr_("L", "T", &irows, &icols, &irows, &b[*ilo + *ilo * b_dim1], ldb, & work[itau], &a[*ilo + *ilo * a_dim1], lda, &work[iwrk], &i__1, & ierr);
/* Initialize VL and/or VR */
/* (Workspace: need N, prefer N*NB) */
if (ilvl)
{
slaset_("Full", n, n, &c_b57, &c_b58, &vl[vl_offset], ldvl) ;
if (irows > 1)
{
i__1 = irows - 1;
i__2 = irows - 1;
slacpy_("L", &i__1, &i__2, &b[*ilo + 1 + *ilo * b_dim1], ldb, &vl[ *ilo + 1 + *ilo * vl_dim1], ldvl);
}
i__1 = *lwork + 1 - iwrk;
sorgqr_(&irows, &irows, &irows, &vl[*ilo + *ilo * vl_dim1], ldvl, & work[itau], &work[iwrk], &i__1, &ierr);
}
if (ilvr)
{
slaset_("Full", n, n, &c_b57, &c_b58, &vr[vr_offset], ldvr) ;
}
/* Reduce to generalized Hessenberg form */
/* (Workspace: none needed) */
if (ilv || ! wantsn)
{
/* Eigenvectors requested -- work on whole matrix. */
sgghrd_(jobvl, jobvr, n, ilo, ihi, &a[a_offset], lda, &b[b_offset], ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &ierr);
}
else
{
sgghrd_("N", "N", &irows, &c__1, &irows, &a[*ilo + *ilo * a_dim1], lda, &b[*ilo + *ilo * b_dim1], ldb, &vl[vl_offset], ldvl, &vr[ vr_offset], ldvr, &ierr);
}
/* Perform QZ algorithm (Compute eigenvalues, and optionally, the */
/* Schur forms and Schur vectors) */
/* (Workspace: need N) */
if (ilv || ! wantsn)
{
*(unsigned char *)chtemp = 'S';
}
else
{
*(unsigned char *)chtemp = 'E';
}
shgeqz_(chtemp, jobvl, jobvr, n, ilo, ihi, &a[a_offset], lda, &b[b_offset] , ldb, &alphar[1], &alphai[1], &beta[1], &vl[vl_offset], ldvl, & vr[vr_offset], ldvr, &work[1], lwork, &ierr);
if (ierr != 0)
{
if (ierr > 0 && ierr <= *n)
{
*info = ierr;
}
else if (ierr > *n && ierr <= *n << 1)
{
*info = ierr - *n;
}
else
{
*info = *n + 1;
}
goto L130;
}
/* Compute Eigenvectors and estimate condition numbers if desired */
/* (Workspace: STGEVC: need 6*N */
/* STGSNA: need 2*N*(N+2)+16 if SENSE = 'V' or 'B', */
/* need N otherwise ) */
if (ilv || ! wantsn)
{
if (ilv)
{
if (ilvl)
{
if (ilvr)
{
*(unsigned char *)chtemp = 'B';
}
else
{
*(unsigned char *)chtemp = 'L';
}
}
else
{
*(unsigned char *)chtemp = 'R';
}
stgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, & work[1], &ierr);
if (ierr != 0)
{
*info = *n + 2;
goto L130;
}
}
if (! wantsn)
{
/* compute eigenvectors (STGEVC) and estimate condition */
/* numbers (STGSNA). Note that the definition of the condition */
/* number is not invariant under transformation (u,v) to */
/* (Q*u, Z*v), where (u,v) are eigenvectors of the generalized */
/* Schur form (S,T), Q and Z are orthogonal matrices. In order */
/* to avoid using extra 2*N*N workspace, we have to recalculate */
/* eigenvectors and estimate one condition numbers at a time. */
pair = FALSE_;
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
if (pair)
{
pair = FALSE_;
goto L20;
}
mm = 1;
if (i__ < *n)
{
if (a[i__ + 1 + i__ * a_dim1] != 0.f)
{
pair = TRUE_;
mm = 2;
}
}
i__2 = *n;
for (j = 1;
j <= i__2;
++j)
{
bwork[j] = FALSE_;
/* L10: */
}
if (mm == 1)
{
bwork[i__] = TRUE_;
}
else if (mm == 2)
{
bwork[i__] = TRUE_;
bwork[i__ + 1] = TRUE_;
}
iwrk = mm * *n + 1;
iwrk1 = iwrk + mm * *n;
/* Compute a pair of left and right eigenvectors. */
/* (compute workspace: need up to 4*N + 6*N) */
if (wantse || wantsb)
{
stgevc_("B", "S", &bwork[1], n, &a[a_offset], lda, &b[ b_offset], ldb, &work[1], n, &work[iwrk], n, &mm, &m, &work[iwrk1], &ierr);
if (ierr != 0)
{
*info = *n + 2;
goto L130;
}
}
i__2 = *lwork - iwrk1 + 1;
stgsna_(sense, "S", &bwork[1], n, &a[a_offset], lda, &b[ b_offset], ldb, &work[1], n, &work[iwrk], n, &rconde[ i__], &rcondv[i__], &mm, &m, &work[iwrk1], &i__2, & iwork[1], &ierr);
L20:
;
}
}
}
/* Undo balancing on VL and VR and normalization */
/* (Workspace: none needed) */
if (ilvl)
{
sggbak_(balanc, "L", n, ilo, ihi, &lscale[1], &rscale[1], n, &vl[ vl_offset], ldvl, &ierr);
i__1 = *n;
for (jc = 1;
jc <= i__1;
++jc)
{
if (alphai[jc] < 0.f)
{
goto L70;
}
temp = 0.f;
if (alphai[jc] == 0.f)
{
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
/* Computing MAX */
r__2 = temp;
r__3 = (r__1 = vl[jr + jc * vl_dim1], abs( r__1)); // , expr subst
temp = max(r__2,r__3);
/* L30: */
}
}
else
{
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
/* Computing MAX */
r__3 = temp;
r__4 = (r__1 = vl[jr + jc * vl_dim1], abs( r__1)) + (r__2 = vl[jr + (jc + 1) * vl_dim1], abs( r__2)); // , expr subst
temp = max(r__3,r__4);
/* L40: */
}
}
if (temp < smlnum)
{
goto L70;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f)
{
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
vl[jr + jc * vl_dim1] *= temp;
/* L50: */
}
}
else
{
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
vl[jr + jc * vl_dim1] *= temp;
vl[jr + (jc + 1) * vl_dim1] *= temp;
/* L60: */
}
}
L70:
;
}
}
if (ilvr)
{
sggbak_(balanc, "R", n, ilo, ihi, &lscale[1], &rscale[1], n, &vr[ vr_offset], ldvr, &ierr);
i__1 = *n;
for (jc = 1;
jc <= i__1;
++jc)
{
if (alphai[jc] < 0.f)
{
goto L120;
}
temp = 0.f;
if (alphai[jc] == 0.f)
{
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
/* Computing MAX */
r__2 = temp;
r__3 = (r__1 = vr[jr + jc * vr_dim1], abs( r__1)); // , expr subst
temp = max(r__2,r__3);
/* L80: */
}
}
else
{
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
/* Computing MAX */
r__3 = temp;
r__4 = (r__1 = vr[jr + jc * vr_dim1], abs( r__1)) + (r__2 = vr[jr + (jc + 1) * vr_dim1], abs( r__2)); // , expr subst
temp = max(r__3,r__4);
/* L90: */
}
}
if (temp < smlnum)
{
goto L120;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f)
{
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
vr[jr + jc * vr_dim1] *= temp;
/* L100: */
}
}
else
{
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
vr[jr + jc * vr_dim1] *= temp;
vr[jr + (jc + 1) * vr_dim1] *= temp;
/* L110: */
}
}
L120:
;
}
}
/* Undo scaling if necessary */
L130:
if (ilascl)
{
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], n, & ierr);
slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], n, & ierr);
}
if (ilbscl)
{
slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, & ierr);
}
work[1] = (real) maxwrk;
return 0;
/* End of SGGEVX */
}