/* 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;
}
/* Subroutine */ int sgelqf_(integer *m, integer *n, real *a, integer *lda,
real *tau, real *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
integer i__, k, ib, nb, nx, iws, nbmin, iinfo;
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* SGELQF computes an LQ factorization of a real M-by-N matrix A: */
/* A = L * Q. */
/* 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 elements on and below the diagonal of the array */
/* contain the m-by-min(m,n) lower trapezoidal matrix L (L is */
/* lower triangular if m <= n); the elements above the diagonal, */
/* with the array TAU, represent the orthogonal matrix Q as a */
/* product of elementary reflectors (see Further Details). */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* TAU (output) REAL array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors (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,M). */
/* For optimum performance LWORK >= M*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(k) . . . H(2) H(1), where k = min(m,n). */
/* Each H(i) has the form */
/* H(i) = I - tau * v * v' */
/* where tau 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,i+1:n), */
/* and tau in TAU(i). */
/* ===================================================================== */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "SGELQF", " ", m, n, &c_n1, &c_n1);
lwkopt = *m * nb;
work[1] = (real) lwkopt;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
} else if (*lwork < max(1,*m) && ! lquery) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGELQF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
k = min(*m,*n);
if (k == 0) {
work[1] = 1.f;
return 0;
}
nbmin = 2;
nx = 0;
iws = *m;
if (nb > 1 && nb < k) {
/* Determine when to cross over from blocked to unblocked code. */
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "SGELQF", " ", m, n, &c_n1, &c_n1);
nx = max(i__1,i__2);
if (nx < k) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *m;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduce NB and */
/* determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "SGELQF", " ", m, n, &c_n1, &
c_n1);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < k && nx < k) {
/* Use blocked code initially */
i__1 = k - nx;
i__2 = nb;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__3 = k - i__ + 1;
ib = min(i__3,nb);
/* Compute the LQ factorization of the current block */
/* A(i:i+ib-1,i:n) */
i__3 = *n - i__ + 1;
sgelq2_(&ib, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[
1], &iinfo);
if (i__ + ib <= *m) {
/* Form the triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
i__3 = *n - i__ + 1;
slarft_("Forward", "Rowwise", &i__3, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H to A(i+ib:m,i:n) from the right */
i__3 = *m - i__ - ib + 1;
i__4 = *n - i__ + 1;
slarfb_("Right", "No transpose", "Forward", "Rowwise", &i__3,
&i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], &
ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib +
1], &ldwork);
}
}
} else {
i__ = 1;
}
/* Use unblocked code to factor the last or only block. */
if (i__ <= k) {
i__2 = *m - i__ + 1;
i__1 = *n - i__ + 1;
sgelq2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1]
, &iinfo);
}
work[1] = (real) iws;
return 0;
/* End of SGELQF */
} /* sgelqf_ */
/* Subroutine */ int sormrq_(char *side, char *trans, integer *m, integer *n,
integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc,
real *work, integer *lwork, integer *info)
{
/* System generated locals */
address a__1[2];
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4,
i__5;
char ch__1[2];
/* Builtin functions */
/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
integer i__;
real t[4160] /* was [65][64] */;
integer i1, i2, i3, ib, nb, mi, ni, nq, nw, iws;
logical left;
extern logical lsame_(char *, char *);
integer nbmin, iinfo;
extern /* Subroutine */ int sormr2_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *), slarfb_(char *, char *, char *, char *
, integer *, integer *, integer *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int slarft_(char *, char *, integer *, integer *,
real *, integer *, real *, real *, integer *);
logical notran;
integer ldwork;
char transt[1];
integer lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SORMRQ overwrites the general real M-by-N matrix C with */
/* SIDE = 'L' SIDE = 'R' */
/* TRANS = 'N': Q * C C * Q */
/* TRANS = 'T': Q**T * C C * Q**T */
/* where Q is a real orthogonal matrix defined as the product of k */
/* elementary reflectors */
/* Q = H(1) H(2) . . . H(k) */
/* as returned by SGERQF. Q is of order M if SIDE = 'L' and of order N */
/* if SIDE = 'R'. */
/* Arguments */
/* ========= */
/* SIDE (input) CHARACTER*1 */
/* = 'L': apply Q or Q**T from the Left; */
/* = 'R': apply Q or Q**T from the Right. */
/* TRANS (input) CHARACTER*1 */
/* = 'N': No transpose, apply Q; */
/* = 'T': Transpose, apply Q**T. */
/* M (input) INTEGER */
/* The number of rows of the matrix C. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix C. N >= 0. */
/* K (input) INTEGER */
/* The number of elementary reflectors whose product defines */
/* the matrix Q. */
/* If SIDE = 'L', M >= K >= 0; */
/* if SIDE = 'R', N >= K >= 0. */
/* A (input) REAL array, dimension */
/* (LDA,M) if SIDE = 'L', */
/* (LDA,N) if SIDE = 'R' */
/* The i-th row must contain the vector which defines the */
/* elementary reflector H(i), for i = 1,2,...,k, as returned by */
/* SGERQF in the last k rows of its array argument A. */
/* A is modified by the routine but restored on exit. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,K). */
/* TAU (input) REAL array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by SGERQF. */
/* C (input/output) REAL array, dimension (LDC,N) */
/* On entry, the M-by-N matrix C. */
/* On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */
/* LDC (input) INTEGER */
/* The leading dimension of the array C. LDC >= max(1,M). */
/* 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 SIDE = 'L', LWORK >= max(1,N); */
/* if SIDE = 'R', LWORK >= max(1,M). */
/* For optimum performance LWORK >= N*NB if SIDE = 'L', and */
/* LWORK >= M*NB if SIDE = 'R', 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 */
/* ===================================================================== */
/* .. 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;
--tau;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
left = lsame_(side, "L");
notran = lsame_(trans, "N");
lquery = *lwork == -1;
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = *m;
nw = max(1,*n);
} else {
nq = *n;
nw = max(1,*m);
}
if (! left && ! lsame_(side, "R")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "T")) {
*info = -2;
} else if (*m < 0) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*k < 0 || *k > nq) {
*info = -5;
} else if (*lda < max(1,*k)) {
*info = -7;
} else if (*ldc < max(1,*m)) {
*info = -10;
}
if (*info == 0) {
if (*m == 0 || *n == 0) {
lwkopt = 1;
} else {
/* Determine the block size. NB may be at most NBMAX, where */
/* NBMAX is used to define the local array T. */
/* Computing MIN */
/* Writing concatenation */
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
i__1 = 64, i__2 = ilaenv_(&c__1, "SORMRQ", ch__1, m, n, k, &c_n1);
nb = min(i__1,i__2);
lwkopt = nw * nb;
}
work[1] = (real) lwkopt;
if (*lwork < nw && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SORMRQ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
return 0;
}
nbmin = 2;
ldwork = nw;
if (nb > 1 && nb < *k) {
iws = nw * nb;
if (*lwork < iws) {
nb = *lwork / ldwork;
/* Computing MAX */
/* Writing concatenation */
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
i__1 = 2, i__2 = ilaenv_(&c__2, "SORMRQ", ch__1, m, n, k, &c_n1);
nbmin = max(i__1,i__2);
}
} else {
iws = nw;
}
if (nb < nbmin || nb >= *k) {
/* Use unblocked code */
sormr2_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[
c_offset], ldc, &work[1], &iinfo);
} else {
/* Use blocked code */
if (left && ! notran || ! left && notran) {
i1 = 1;
i2 = *k;
i3 = nb;
} else {
i1 = (*k - 1) / nb * nb + 1;
i2 = 1;
i3 = -nb;
}
if (left) {
ni = *n;
} else {
mi = *m;
}
if (notran) {
*(unsigned char *)transt = 'T';
} else {
*(unsigned char *)transt = 'N';
}
i__1 = i2;
i__2 = i3;
for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__4 = nb, i__5 = *k - i__ + 1;
ib = min(i__4,i__5);
/* Form the triangular factor of the block reflector */
/* H = H(i+ib-1) . . . H(i+1) H(i) */
i__4 = nq - *k + i__ + ib - 1;
slarft_("Backward", "Rowwise", &i__4, &ib, &a[i__ + a_dim1], lda,
&tau[i__], t, &c__65);
if (left) {
/* H or H' is applied to C(1:m-k+i+ib-1,1:n) */
mi = *m - *k + i__ + ib - 1;
} else {
/* H or H' is applied to C(1:m,1:n-k+i+ib-1) */
ni = *n - *k + i__ + ib - 1;
}
/* Apply H or H' */
slarfb_(side, transt, "Backward", "Rowwise", &mi, &ni, &ib, &a[
i__ + a_dim1], lda, t, &c__65, &c__[c_offset], ldc, &work[
1], &ldwork);
/* L10: */
}
}
work[1] = (real) lwkopt;
return 0;
/* End of SORMRQ */
} /* sormrq_ */
/* Subroutine */ int sgeqrf_(integer *m, integer *n, real *a, integer *lda,
real *tau, real *work, integer *lwork, integer *info)
{
/* -- LAPACK 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
=======
SGEQRF computes a QR factorization of a real M-by-N matrix A:
A = Q * R.
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 elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
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,N).
For optimum performance LWORK >= N*NB, where NB is
the optimal blocksize.
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 scalar, and v is a real 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).
=====================================================================
Test the input arguments
Parameter adjustments
Function Body */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer i, k, nbmin, iinfo;
extern /* Subroutine */ int sgeqr2_(integer *, integer *, real *, integer
*, real *, real *, integer *);
static integer ib, nb, nx;
extern /* Subroutine */ int slarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int slarft_(char *, char *, integer *, integer *,
real *, integer *, real *, real *, integer *);
static integer ldwork, iws;
#define TAU(I) tau[(I)-1]
#define WORK(I) work[(I)-1]
#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
} else if (*lwork < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGEQRF", &i__1);
return 0;
}
/* Quick return if possible */
k = min(*m,*n);
if (k == 0) {
WORK(1) = 1.f;
return 0;
}
/* Determine the block size. */
nb = ilaenv_(&c__1, "SGEQRF", " ", m, n, &c_n1, &c_n1, 6L, 1L);
nbmin = 2;
nx = 0;
iws = *n;
if (nb > 1 && nb < k) {
/* Determine when to cross over from blocked to unblocked code.
Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "SGEQRF", " ", m, n, &c_n1, &c_n1, 6L,
1L);
nx = max(i__1,i__2);
if (nx < k) {
/* Determine if workspace is large enough for blocked co
de. */
ldwork = *n;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduc
e NB and
determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "SGEQRF", " ", m, n, &c_n1, &
c_n1, 6L, 1L);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < k && nx < k) {
/* Use blocked code initially */
i__1 = k - nx;
i__2 = nb;
for (i = 1; nb < 0 ? i >= k-nx : i <= k-nx; i += nb) {
/* Computing MIN */
i__3 = k - i + 1;
ib = min(i__3,nb);
/* Compute the QR factorization of the current block
A(i:m,i:i+ib-1) */
i__3 = *m - i + 1;
sgeqr2_(&i__3, &ib, &A(i,i), lda, &TAU(i), &WORK(1), &
iinfo);
if (i + ib <= *n) {
/* Form the triangular factor of the block reflec
tor
H = H(i) H(i+1) . . . H(i+ib-1) */
i__3 = *m - i + 1;
slarft_("Forward", "Columnwise", &i__3, &ib, &A(i,i), lda, &TAU(i), &WORK(1), &ldwork);
/* Apply H' to A(i:m,i+ib:n) from the left */
i__3 = *m - i + 1;
i__4 = *n - i - ib + 1;
slarfb_("Left", "Transpose", "Forward", "Columnwise", &i__3, &
i__4, &ib, &A(i,i), lda, &WORK(1), &ldwork,
&A(i,i+ib), lda, &WORK(ib + 1), &
ldwork);
}
/* L10: */
}
} else {
i = 1;
}
/* Use unblocked code to factor the last or only block. */
if (i <= k) {
i__2 = *m - i + 1;
i__1 = *n - i + 1;
sgeqr2_(&i__2, &i__1, &A(i,i), lda, &TAU(i), &WORK(1), &
iinfo);
}
WORK(1) = (real) iws;
return 0;
/* End of SGEQRF */
} /* sgeqrf_ */
/* Subroutine */ int sorgrq_(integer *m, integer *n, integer *k, real *a,
integer *lda, real *tau, real *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
integer i__, j, l, ib, nb, ii, kk, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int sorgr2_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *), slarfb_(char *, char *,
char *, char *, integer *, integer *, integer *, real *, integer *
, real *, integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int slarft_(char *, char *, integer *, integer *,
real *, integer *, real *, real *, integer *);
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SORGRQ generates an M-by-N real matrix Q with orthonormal rows, */
/* which is defined as the last M rows of a product of K elementary */
/* reflectors of order N */
/* Q = H(1) H(2) . . . H(k) */
/* as returned by SGERQF. */
/* Arguments */
/* ========= */
/* M (input) INTEGER */
/* The number of rows of the matrix Q. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix Q. N >= M. */
/* K (input) INTEGER */
/* The number of elementary reflectors whose product defines the */
/* matrix Q. M >= K >= 0. */
/* A (input/output) REAL array, dimension (LDA,N) */
/* On entry, the (m-k+i)-th row must contain the vector which */
/* defines the elementary reflector H(i), for i = 1,2,...,k, as */
/* returned by SGERQF in the last k rows of its array argument */
/* A. */
/* On exit, the M-by-N matrix Q. */
/* LDA (input) INTEGER */
/* The first dimension of the array A. LDA >= max(1,M). */
/* TAU (input) REAL array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by SGERQF. */
/* 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,M). */
/* For optimum performance LWORK >= M*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 has an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < *m) {
*info = -2;
} else if (*k < 0 || *k > *m) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
}
if (*info == 0) {
if (*m <= 0) {
lwkopt = 1;
} else {
nb = ilaenv_(&c__1, "SORGRQ", " ", m, n, k, &c_n1);
lwkopt = *m * nb;
}
work[1] = (real) lwkopt;
if (*lwork < max(1,*m) && ! lquery) {
*info = -8;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SORGRQ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m <= 0) {
return 0;
}
nbmin = 2;
nx = 0;
iws = *m;
if (nb > 1 && nb < *k) {
/* Determine when to cross over from blocked to unblocked code. */
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "SORGRQ", " ", m, n, k, &c_n1);
nx = max(i__1,i__2);
if (nx < *k) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *m;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduce NB and */
/* determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "SORGRQ", " ", m, n, k, &c_n1);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < *k && nx < *k) {
/* Use blocked code after the first block. */
/* The last kk rows are handled by the block method. */
/* Computing MIN */
i__1 = *k, i__2 = (*k - nx + nb - 1) / nb * nb;
kk = min(i__1,i__2);
/* Set A(1:m-kk,n-kk+1:n) to zero. */
i__1 = *n;
for (j = *n - kk + 1; j <= i__1; ++j) {
i__2 = *m - kk;
for (i__ = 1; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] = 0.f;
/* L10: */
}
/* L20: */
}
} else {
kk = 0;
}
/* Use unblocked code for the first or only block. */
i__1 = *m - kk;
i__2 = *n - kk;
i__3 = *k - kk;
sorgr2_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], &iinfo)
;
if (kk > 0) {
/* Use blocked code */
i__1 = *k;
i__2 = nb;
for (i__ = *k - kk + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
i__2) {
/* Computing MIN */
i__3 = nb, i__4 = *k - i__ + 1;
ib = min(i__3,i__4);
ii = *m - *k + i__;
if (ii > 1) {
/* Form the triangular factor of the block reflector */
/* H = H(i+ib-1) . . . H(i+1) H(i) */
i__3 = *n - *k + i__ + ib - 1;
slarft_("Backward", "Rowwise", &i__3, &ib, &a[ii + a_dim1],
lda, &tau[i__], &work[1], &ldwork);
/* Apply H' to A(1:m-k+i-1,1:n-k+i+ib-1) from the right */
i__3 = ii - 1;
i__4 = *n - *k + i__ + ib - 1;
slarfb_("Right", "Transpose", "Backward", "Rowwise", &i__3, &
i__4, &ib, &a[ii + a_dim1], lda, &work[1], &ldwork, &
a[a_offset], lda, &work[ib + 1], &ldwork);
}
/* Apply H' to columns 1:n-k+i+ib-1 of current block */
i__3 = *n - *k + i__ + ib - 1;
sorgr2_(&ib, &i__3, &ib, &a[ii + a_dim1], lda, &tau[i__], &work[1]
, &iinfo);
/* Set columns n-k+i+ib:n of current block to zero */
i__3 = *n;
for (l = *n - *k + i__ + ib; l <= i__3; ++l) {
i__4 = ii + ib - 1;
for (j = ii; j <= i__4; ++j) {
a[j + l * a_dim1] = 0.f;
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
work[1] = (real) iws;
return 0;
/* End of SORGRQ */
} /* sorgrq_ */
/* Subroutine */ int sorgrq_(integer *m, integer *n, integer *k, real *a,
integer *lda, real *tau, real *work, integer *lwork, integer *info)
{
/* -- LAPACK 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
=======
SORGRQ generates an M-by-N real matrix Q with orthonormal rows,
which is defined as the last M rows of a product of K elementary
reflectors of order N
Q = H(1) H(2) . . . H(k)
as returned by SGERQF.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix Q. M >= 0.
N (input) INTEGER
The number of columns of the matrix Q. N >= M.
K (input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
A (input/output) REAL array, dimension (LDA,N)
On entry, the (m-k+i)-th row must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by SGERQF in the last k rows of its array argument
A.
On exit, the M-by-N matrix Q.
LDA (input) INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU (input) REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SGERQF.
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,M).
For optimum performance LWORK >= M*NB, where NB is the
optimal blocksize.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
=====================================================================
Test the input arguments
Parameter adjustments
Function Body */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer i, j, l, nbmin, iinfo, ib;
extern /* Subroutine */ int sorgr2_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *);
static integer nb, ii, kk, nx;
extern /* Subroutine */ int slarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int slarft_(char *, char *, integer *, integer *,
real *, integer *, real *, real *, integer *);
static integer ldwork, iws;
#define TAU(I) tau[(I)-1]
#define WORK(I) work[(I)-1]
#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < *m) {
*info = -2;
} else if (*k < 0 || *k > *m) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*lwork < max(1,*m)) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SORGRQ", &i__1);
return 0;
}
/* Quick return if possible */
if (*m <= 0) {
WORK(1) = 1.f;
return 0;
}
/* Determine the block size. */
nb = ilaenv_(&c__1, "SORGRQ", " ", m, n, k, &c_n1, 6L, 1L);
nbmin = 2;
nx = 0;
iws = *m;
if (nb > 1 && nb < *k) {
/* Determine when to cross over from blocked to unblocked code.
Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "SORGRQ", " ", m, n, k, &c_n1, 6L, 1L)
;
nx = max(i__1,i__2);
if (nx < *k) {
/* Determine if workspace is large enough for blocked co
de. */
ldwork = *m;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduc
e NB and
determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "SORGRQ", " ", m, n, k, &c_n1,
6L, 1L);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < *k && nx < *k) {
/* Use blocked code after the first block.
The last kk rows are handled by the block method.
Computing MIN */
i__1 = *k, i__2 = (*k - nx + nb - 1) / nb * nb;
kk = min(i__1,i__2);
/* Set A(1:m-kk,n-kk+1:n) to zero. */
i__1 = *n;
for (j = *n - kk + 1; j <= *n; ++j) {
i__2 = *m - kk;
for (i = 1; i <= *m-kk; ++i) {
A(i,j) = 0.f;
/* L10: */
}
/* L20: */
}
} else {
kk = 0;
}
/* Use unblocked code for the first or only block. */
i__1 = *m - kk;
i__2 = *n - kk;
i__3 = *k - kk;
sorgr2_(&i__1, &i__2, &i__3, &A(1,1), lda, &TAU(1), &WORK(1), &iinfo)
;
if (kk > 0) {
/* Use blocked code */
i__1 = *k;
i__2 = nb;
for (i = *k - kk + 1; nb < 0 ? i >= *k : i <= *k; i += nb) {
/* Computing MIN */
i__3 = nb, i__4 = *k - i + 1;
ib = min(i__3,i__4);
ii = *m - *k + i;
if (ii > 1) {
/* Form the triangular factor of the block reflec
tor
H = H(i+ib-1) . . . H(i+1) H(i) */
i__3 = *n - *k + i + ib - 1;
slarft_("Backward", "Rowwise", &i__3, &ib, &A(ii,1),
lda, &TAU(i), &WORK(1), &ldwork);
/* Apply H' to A(1:m-k+i-1,1:n-k+i+ib-1) from the
right */
i__3 = ii - 1;
i__4 = *n - *k + i + ib - 1;
slarfb_("Right", "Transpose", "Backward", "Rowwise", &i__3, &
i__4, &ib, &A(ii,1), lda, &WORK(1), &ldwork, &
A(1,1), lda, &WORK(ib + 1), &ldwork);
}
/* Apply H' to columns 1:n-k+i+ib-1 of current block */
i__3 = *n - *k + i + ib - 1;
sorgr2_(&ib, &i__3, &ib, &A(ii,1), lda, &TAU(i), &WORK(1),
&iinfo);
/* Set columns n-k+i+ib:n of current block to zero */
i__3 = *n;
for (l = *n - *k + i + ib; l <= *n; ++l) {
i__4 = ii + ib - 1;
for (j = ii; j <= ii+ib-1; ++j) {
A(j,l) = 0.f;
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
WORK(1) = (real) iws;
return 0;
/* End of SORGRQ */
} /* sorgrq_ */
/* Subroutine */
int sgerqf_(integer *m, integer *n, real *a, integer *lda, real *tau, real *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
integer i__, k, ib, nb, ki, kk, mu, nu, nx, iws, nbmin, iinfo;
extern /* Subroutine */
int sgerq2_(integer *, integer *, real *, integer *, real *, real *, integer *), slarfb_(char *, char *, char *, char *, integer *, integer *, integer *, real *, integer *, real * , integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
extern /* Subroutine */
int slarft_(char *, char *, integer *, integer *, real *, integer *, real *, real *, integer *);
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK computational 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 .. */
/* .. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--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;
}
else if (*lwork < max(1,*m) && ! lquery)
{
*info = -7;
}
if (*info == 0)
{
k = min(*m,*n);
if (k == 0)
{
lwkopt = 1;
}
else
{
nb = ilaenv_(&c__1, "SGERQF", " ", m, n, &c_n1, &c_n1);
lwkopt = *m * nb;
work[1] = (real) lwkopt;
}
work[1] = (real) lwkopt;
if (*lwork < max(1,*m) && ! lquery)
{
*info = -7;
}
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("SGERQF", &i__1);
return 0;
}
else if (lquery)
{
return 0;
}
/* Quick return if possible */
if (k == 0)
{
return 0;
}
nbmin = 2;
nx = 1;
iws = *m;
if (nb > 1 && nb < k)
{
/* Determine when to cross over from blocked to unblocked code. */
/* Computing MAX */
i__1 = 0;
i__2 = ilaenv_(&c__3, "SGERQF", " ", m, n, &c_n1, &c_n1); // , expr subst
nx = max(i__1,i__2);
if (nx < k)
{
/* Determine if workspace is large enough for blocked code. */
ldwork = *m;
iws = ldwork * nb;
if (*lwork < iws)
{
/* Not enough workspace to use optimal NB: reduce NB and */
/* determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2;
i__2 = ilaenv_(&c__2, "SGERQF", " ", m, n, &c_n1, & c_n1); // , expr subst
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < k && nx < k)
{
/* Use blocked code initially. */
/* The last kk rows are handled by the block method. */
ki = (k - nx - 1) / nb * nb;
/* Computing MIN */
i__1 = k;
i__2 = ki + nb; // , expr subst
kk = min(i__1,i__2);
i__1 = k - kk + 1;
i__2 = -nb;
for (i__ = k - kk + ki + 1;
i__2 < 0 ? i__ >= i__1 : i__ <= i__1;
i__ += i__2)
{
/* Computing MIN */
i__3 = k - i__ + 1;
ib = min(i__3,nb);
/* Compute the RQ factorization of the current block */
/* A(m-k+i:m-k+i+ib-1,1:n-k+i+ib-1) */
i__3 = *n - k + i__ + ib - 1;
sgerq2_(&ib, &i__3, &a[*m - k + i__ + a_dim1], lda, &tau[i__], & work[1], &iinfo);
if (*m - k + i__ > 1)
{
/* Form the triangular factor of the block reflector */
/* H = H(i+ib-1) . . . H(i+1) H(i) */
i__3 = *n - k + i__ + ib - 1;
slarft_("Backward", "Rowwise", &i__3, &ib, &a[*m - k + i__ + a_dim1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H to A(1:m-k+i-1,1:n-k+i+ib-1) from the right */
i__3 = *m - k + i__ - 1;
i__4 = *n - k + i__ + ib - 1;
slarfb_("Right", "No transpose", "Backward", "Rowwise", &i__3, &i__4, &ib, &a[*m - k + i__ + a_dim1], lda, &work[1], &ldwork, &a[a_offset], lda, &work[ib + 1], &ldwork);
}
/* L10: */
}
mu = *m - k + i__ + nb - 1;
nu = *n - k + i__ + nb - 1;
}
else
{
mu = *m;
nu = *n;
}
/* Use unblocked code to factor the last or only block */
if (mu > 0 && nu > 0)
{
sgerq2_(&mu, &nu, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
}
work[1] = (real) iws;
return 0;
/* End of SGERQF */
}
/* Subroutine */ int sormql_(char *side, char *trans, integer *m, integer *n,
integer *k, real *a, integer *lda, real *tau, real *c, integer *ldc,
real *work, integer *lwork, integer *info)
{
/* -- LAPACK 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
=======
SORMQL overwrites the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q**T * C C * Q**T
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
Q = H(k) . . . H(2) H(1)
as returned by SGEQLF. Q is of order M if SIDE = 'L' and of order N
if SIDE = 'R'.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
A (input) REAL array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
SGEQLF in the last k columns of its array argument A.
A is modified by the routine but restored on exit.
LDA (input) INTEGER
The leading dimension of the array A.
If SIDE = 'L', LDA >= max(1,M);
if SIDE = 'R', LDA >= max(1,N).
TAU (input) REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SGEQLF.
C (input/output) REAL array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
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.
If SIDE = 'L', LWORK >= max(1,N);
if SIDE = 'R', LWORK >= max(1,M).
For optimum performance LWORK >= N*NB if SIDE = 'L', and
LWORK >= M*NB if SIDE = 'R', where NB is the optimal
blocksize.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input arguments
Parameter adjustments
Function Body */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__2 = 2;
static integer c__65 = 65;
/* System generated locals */
address a__1[2];
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4,
i__5;
char ch__1[2];
/* Builtin functions
Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
static logical left;
static integer i;
static real t[4160] /* was [65][64] */;
extern logical lsame_(char *, char *);
static integer nbmin, iinfo, i1, i2, i3, ib;
extern /* Subroutine */ int sorm2l_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *);
static integer nb, mi, ni, nq, nw;
extern /* Subroutine */ int slarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int slarft_(char *, char *, integer *, integer *,
real *, integer *, real *, real *, integer *);
static logical notran;
static integer ldwork, iws;
#define TAU(I) tau[(I)-1]
#define WORK(I) work[(I)-1]
#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
#define C(I,J) c[(I)-1 + ((J)-1)* ( *ldc)]
*info = 0;
left = lsame_(side, "L");
notran = lsame_(trans, "N");
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = *m;
nw = *n;
} else {
nq = *n;
nw = *m;
}
if (! left && ! lsame_(side, "R")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "T")) {
*info = -2;
} else if (*m < 0) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*k < 0 || *k > nq) {
*info = -5;
} else if (*lda < max(1,nq)) {
*info = -7;
} else if (*ldc < max(1,*m)) {
*info = -10;
} else if (*lwork < max(1,nw)) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SORMQL", &i__1);
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || *k == 0) {
WORK(1) = 1.f;
return 0;
}
/* Determine the block size. NB may be at most NBMAX, where NBMAX
is used to define the local array T.
Computing MIN
Writing concatenation */
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, 2L);
i__1 = 64, i__2 = ilaenv_(&c__1, "SORMQL", ch__1, m, n, k, &c_n1, 6L, 2L);
nb = min(i__1,i__2);
nbmin = 2;
ldwork = nw;
if (nb > 1 && nb < *k) {
iws = nw * nb;
if (*lwork < iws) {
nb = *lwork / ldwork;
/* Computing MAX
Writing concatenation */
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, 2L);
i__1 = 2, i__2 = ilaenv_(&c__2, "SORMQL", ch__1, m, n, k, &c_n1,
6L, 2L);
nbmin = max(i__1,i__2);
}
} else {
iws = nw;
}
if (nb < nbmin || nb >= *k) {
/* Use unblocked code */
sorm2l_(side, trans, m, n, k, &A(1,1), lda, &TAU(1), &C(1,1)
, ldc, &WORK(1), &iinfo);
} else {
/* Use blocked code */
if (left && notran || ! left && ! notran) {
i1 = 1;
i2 = *k;
i3 = nb;
} else {
i1 = (*k - 1) / nb * nb + 1;
i2 = 1;
i3 = -nb;
}
if (left) {
ni = *n;
} else {
mi = *m;
}
i__1 = i2;
i__2 = i3;
for (i = i1; i3 < 0 ? i >= i2 : i <= i2; i += i3) {
/* Computing MIN */
i__4 = nb, i__5 = *k - i + 1;
ib = min(i__4,i__5);
/* Form the triangular factor of the block reflector
H = H(i+ib-1) . . . H(i+1) H(i) */
i__4 = nq - *k + i + ib - 1;
slarft_("Backward", "Columnwise", &i__4, &ib, &A(1,i),
lda, &TAU(i), t, &c__65);
if (left) {
/* H or H' is applied to C(1:m-k+i+ib-1,1:n) */
mi = *m - *k + i + ib - 1;
} else {
/* H or H' is applied to C(1:m,1:n-k+i+ib-1) */
ni = *n - *k + i + ib - 1;
}
/* Apply H or H' */
slarfb_(side, trans, "Backward", "Columnwise", &mi, &ni, &ib, &A(1,i), lda, t, &c__65, &C(1,1), ldc, &WORK(
1), &ldwork);
/* L10: */
}
}
WORK(1) = (real) iws;
return 0;
/* End of SORMQL */
} /* sormql_ */
/* Subroutine */ int sorgql_(integer *m, integer *n, integer *k, real *a,
integer *lda, real *tau, real *work, integer *lwork, integer *info)
{
/* -- LAPACK 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
=======
SORGQL generates an M-by-N real matrix Q with orthonormal columns,
which is defined as the last N columns of a product of K elementary
reflectors of order M
Q = H(k) . . . H(2) H(1)
as returned by SGEQLF.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix Q. M >= 0.
N (input) INTEGER
The number of columns of the matrix Q. M >= N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A (input/output) REAL array, dimension (LDA,N)
On entry, the (n-k+i)-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by SGEQLF in the last k columns of its array
argument A.
On exit, the M-by-N matrix Q.
LDA (input) INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU (input) REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SGEQLF.
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,N).
For optimum performance LWORK >= N*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 has an illegal value
=====================================================================
Test the input arguments
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer i__, j, l, nbmin, iinfo;
extern /* Subroutine */ int sorg2l_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *);
static integer ib, nb, kk, nx;
extern /* Subroutine */ int slarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int slarft_(char *, char *, integer *, integer *,
real *, integer *, real *, real *, integer *);
static integer ldwork, lwkopt;
static logical lquery;
static integer iws;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "SORGQL", " ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1);
lwkopt = max(1,*n) * nb;
work[1] = (real) lwkopt;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0 || *n > *m) {
*info = -2;
} else if (*k < 0 || *k > *n) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*lwork < max(1,*n) && ! lquery) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SORGQL", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n <= 0) {
work[1] = 1.f;
return 0;
}
nbmin = 2;
nx = 0;
iws = *n;
if (nb > 1 && nb < *k) {
/* Determine when to cross over from blocked to unblocked code.
Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "SORGQL", " ", m, n, k, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
if (nx < *k) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *n;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduce NB and
determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "SORGQL", " ", m, n, k, &c_n1,
(ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < *k && nx < *k) {
/* Use blocked code after the first block.
The last kk columns are handled by the block method.
Computing MIN */
i__1 = *k, i__2 = (*k - nx + nb - 1) / nb * nb;
kk = min(i__1,i__2);
/* Set A(m-kk+1:m,1:n-kk) to zero. */
i__1 = *n - kk;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = *m - kk + 1; i__ <= i__2; ++i__) {
a_ref(i__, j) = 0.f;
/* L10: */
}
/* L20: */
}
} else {
kk = 0;
}
/* Use unblocked code for the first or only block. */
i__1 = *m - kk;
i__2 = *n - kk;
i__3 = *k - kk;
sorg2l_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], &iinfo)
;
if (kk > 0) {
/* Use blocked code */
i__1 = *k;
i__2 = nb;
for (i__ = *k - kk + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
i__2) {
/* Computing MIN */
i__3 = nb, i__4 = *k - i__ + 1;
ib = min(i__3,i__4);
if (*n - *k + i__ > 1) {
/* Form the triangular factor of the block reflector
H = H(i+ib-1) . . . H(i+1) H(i) */
i__3 = *m - *k + i__ + ib - 1;
slarft_("Backward", "Columnwise", &i__3, &ib, &a_ref(1, *n - *
k + i__), lda, &tau[i__], &work[1], &ldwork);
/* Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left */
i__3 = *m - *k + i__ + ib - 1;
i__4 = *n - *k + i__ - 1;
slarfb_("Left", "No transpose", "Backward", "Columnwise", &
i__3, &i__4, &ib, &a_ref(1, *n - *k + i__), lda, &
work[1], &ldwork, &a[a_offset], lda, &work[ib + 1], &
ldwork);
}
/* Apply H to rows 1:m-k+i+ib-1 of current block */
i__3 = *m - *k + i__ + ib - 1;
sorg2l_(&i__3, &ib, &ib, &a_ref(1, *n - *k + i__), lda, &tau[i__],
&work[1], &iinfo);
/* Set rows m-k+i+ib:m of current block to zero */
i__3 = *n - *k + i__ + ib - 1;
for (j = *n - *k + i__; j <= i__3; ++j) {
i__4 = *m;
for (l = *m - *k + i__ + ib; l <= i__4; ++l) {
a_ref(l, j) = 0.f;
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
work[1] = (real) iws;
return 0;
/* End of SORGQL */
} /* sorgql_ */
/* Subroutine */
int sormqr_fla(char *side, char *trans, integer *m, integer *n, integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc, real *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__4, i__5;
char ch__1[2];
/* Builtin functions */
/* Subroutine */
/* Local variables */
integer i__;
real t[4160] /* was [65][64] */
;
integer i1, i2, i3, ib, ic, jc, nb, mi, ni, nq, nw, iws;
logical left;
extern logical lsame_(char *, char *);
integer nbmin, iinfo;
extern /* Subroutine */
int sorm2r_fla(char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *), slarfb_(char *, char *, char *, char * , integer *, integer *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
extern /* Subroutine */
int slarft_(char *, char *, integer *, integer *, real *, integer *, real *, real *, integer *);
logical notran;
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK computational 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 Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
left = lsame_(side, "L");
notran = lsame_(trans, "N");
lquery = *lwork == -1;
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left)
{
nq = *m;
nw = *n;
}
else
{
nq = *n;
nw = *m;
}
if (! left && ! lsame_(side, "R"))
{
*info = -1;
}
else if (! notran && ! lsame_(trans, "T"))
{
*info = -2;
}
else if (*m < 0)
{
*info = -3;
}
else if (*n < 0)
{
*info = -4;
}
else if (*k < 0 || *k > nq)
{
*info = -5;
}
else if (*lda < max(1,nq))
{
*info = -7;
}
else if (*ldc < max(1,*m))
{
*info = -10;
}
else if (*lwork < max(1,nw) && ! lquery)
{
*info = -12;
}
if (*info == 0)
{
/* Determine the block size. NB may be at most NBMAX, where NBMAX */
/* is used to define the local array T. */
/* Computing MIN */
i__1 = 64;
i__2 = ilaenv_(&c__1, "SORMQR", ch__1, m, n, k, &c_n1); // , expr subst
nb = min(i__1,i__2);
lwkopt = max(1,nw) * nb;
work[1] = (real) lwkopt;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("SORMQR", &i__1);
return 0;
}
else if (lquery)
{
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || *k == 0)
{
work[1] = 1.f;
return 0;
}
nbmin = 2;
ldwork = nw;
if (nb > 1 && nb < *k)
{
iws = nw * nb;
if (*lwork < iws)
{
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2;
i__2 = ilaenv_(&c__2, "SORMQR", ch__1, m, n, k, &c_n1); // , expr subst
nbmin = max(i__1,i__2);
}
}
else
{
iws = nw;
}
if (nb < nbmin || nb >= *k)
{
/* Use unblocked code */
sorm2r_fla(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ c_offset], ldc, &work[1], &iinfo);
}
else
{
/* Use blocked code */
if (left && ! notran || ! left && notran)
{
i1 = 1;
i2 = *k;
i3 = nb;
}
else
{
i1 = (*k - 1) / nb * nb + 1;
i2 = 1;
i3 = -nb;
}
if (left)
{
ni = *n;
jc = 1;
}
else
{
mi = *m;
ic = 1;
}
i__1 = i2;
i__2 = i3;
for (i__ = i1;
i__2 < 0 ? i__ >= i__1 : i__ <= i__1;
i__ += i__2)
{
/* Computing MIN */
i__4 = nb;
i__5 = *k - i__ + 1; // , expr subst
ib = min(i__4,i__5);
/* Form the triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
i__4 = nq - i__ + 1;
slarft_("Forward", "Columnwise", &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], t, &c__65) ;
if (left)
{
/* H or H**T is applied to C(i:m,1:n) */
mi = *m - i__ + 1;
ic = i__;
}
else
{
/* H or H**T is applied to C(1:m,i:n) */
ni = *n - i__ + 1;
jc = i__;
}
/* Apply H or H**T */
slarfb_(side, trans, "Forward", "Columnwise", &mi, &ni, &ib, &a[ i__ + i__ * a_dim1], lda, t, &c__65, &c__[ic + jc * c_dim1], ldc, &work[1], &ldwork);
/* L10: */
}
}
work[1] = (real) lwkopt;
return 0;
/* End of SORMQR */
}
/* Subroutine */ int sgerqf_(integer *m, integer *n, real *a, integer *lda,
real *tau, real *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
integer i__, k, ib, nb, ki, kk, mu, nu, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int sgerq2_(integer *, integer *, real *, integer
*, real *, real *, integer *), slarfb_(char *, char *, char *,
char *, integer *, integer *, integer *, real *, integer *, real *
, integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int slarft_(char *, char *, integer *, integer *,
real *, integer *, real *, real *, integer *);
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SGERQF computes an RQ factorization of a real M-by-N matrix A: */
/* A = R * Q. */
/* 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, */
/* if m <= n, the upper triangle of the subarray */
/* A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; */
/* if m >= n, the elements on and above the (m-n)-th subdiagonal */
/* contain the M-by-N upper trapezoidal matrix R; */
/* the remaining elements, with the array TAU, represent the */
/* orthogonal matrix Q as a product of min(m,n) elementary */
/* reflectors (see Further Details). */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* TAU (output) REAL array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors (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,M). */
/* For optimum performance LWORK >= M*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 scalar, and v is a real vector with */
/* v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in */
/* A(m-k+i,1:n-k+i-1), and tau in TAU(i). */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--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;
} else if (*lwork < max(1,*m) && ! lquery) {
*info = -7;
}
if (*info == 0) {
k = min(*m,*n);
if (k == 0) {
lwkopt = 1;
} else {
nb = ilaenv_(&c__1, "SGERQF", " ", m, n, &c_n1, &c_n1);
lwkopt = *m * nb;
work[1] = (real) lwkopt;
}
work[1] = (real) lwkopt;
if (*lwork < max(1,*m) && ! lquery) {
*info = -7;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGERQF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (k == 0) {
return 0;
}
nbmin = 2;
nx = 1;
iws = *m;
if (nb > 1 && nb < k) {
/* Determine when to cross over from blocked to unblocked code. */
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "SGERQF", " ", m, n, &c_n1, &c_n1);
nx = max(i__1,i__2);
if (nx < k) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *m;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduce NB and */
/* determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "SGERQF", " ", m, n, &c_n1, &
c_n1);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < k && nx < k) {
/* Use blocked code initially. */
/* The last kk rows are handled by the block method. */
ki = (k - nx - 1) / nb * nb;
/* Computing MIN */
i__1 = k, i__2 = ki + nb;
kk = min(i__1,i__2);
i__1 = k - kk + 1;
i__2 = -nb;
for (i__ = k - kk + ki + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__
+= i__2) {
/* Computing MIN */
i__3 = k - i__ + 1;
ib = min(i__3,nb);
/* Compute the RQ factorization of the current block */
/* A(m-k+i:m-k+i+ib-1,1:n-k+i+ib-1) */
i__3 = *n - k + i__ + ib - 1;
sgerq2_(&ib, &i__3, &a[*m - k + i__ + a_dim1], lda, &tau[i__], &
work[1], &iinfo);
if (*m - k + i__ > 1) {
/* Form the triangular factor of the block reflector */
/* H = H(i+ib-1) . . . H(i+1) H(i) */
i__3 = *n - k + i__ + ib - 1;
slarft_("Backward", "Rowwise", &i__3, &ib, &a[*m - k + i__ +
a_dim1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H to A(1:m-k+i-1,1:n-k+i+ib-1) from the right */
i__3 = *m - k + i__ - 1;
i__4 = *n - k + i__ + ib - 1;
slarfb_("Right", "No transpose", "Backward", "Rowwise", &i__3,
&i__4, &ib, &a[*m - k + i__ + a_dim1], lda, &work[1],
&ldwork, &a[a_offset], lda, &work[ib + 1], &ldwork);
}
/* L10: */
}
mu = *m - k + i__ + nb - 1;
nu = *n - k + i__ + nb - 1;
} else {
mu = *m;
nu = *n;
}
/* Use unblocked code to factor the last or only block */
if (mu > 0 && nu > 0) {
sgerq2_(&mu, &nu, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
}
work[1] = (real) iws;
return 0;
/* End of SGERQF */
} /* sgerqf_ */
int sorgqr_(int *m, int *n, int *k, float *a,
int *lda, float *tau, float *work, int *lwork, int *info)
{
/* System generated locals */
int a_dim1, a_offset, i__1, i__2, i__3;
/* Local variables */
int i__, j, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo;
extern int sorg2r_(int *, int *, int *, float
*, int *, float *, float *, int *), slarfb_(char *, char *,
char *, char *, int *, int *, int *, float *, int *
, float *, int *, float *, int *, float *, int *), xerbla_(char *, int *);
extern int ilaenv_(int *, char *, char *, int *, int *,
int *, int *);
extern int slarft_(char *, char *, int *, int *,
float *, int *, float *, float *, int *);
int ldwork, lwkopt;
int lquery;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SORGQR generates an M-by-N float matrix Q with orthonormal columns, */
/* which is defined as the first N columns of a product of K elementary */
/* reflectors of order M */
/* Q = H(1) H(2) . . . H(k) */
/* as returned by SGEQRF. */
/* Arguments */
/* ========= */
/* M (input) INTEGER */
/* The number of rows of the matrix Q. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix Q. M >= N >= 0. */
/* K (input) INTEGER */
/* The number of elementary reflectors whose product defines the */
/* matrix Q. N >= K >= 0. */
/* A (input/output) REAL array, dimension (LDA,N) */
/* On entry, the i-th column must contain the vector which */
/* defines the elementary reflector H(i), for i = 1,2,...,k, as */
/* returned by SGEQRF in the first k columns of its array */
/* argument A. */
/* On exit, the M-by-N matrix Q. */
/* LDA (input) INTEGER */
/* The first dimension of the array A. LDA >= MAX(1,M). */
/* TAU (input) REAL array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by SGEQRF. */
/* 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). */
/* For optimum performance LWORK >= N*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 has an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "SORGQR", " ", m, n, k, &c_n1);
lwkopt = MAX(1,*n) * nb;
work[1] = (float) lwkopt;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0 || *n > *m) {
*info = -2;
} else if (*k < 0 || *k > *n) {
*info = -3;
} else if (*lda < MAX(1,*m)) {
*info = -5;
} else if (*lwork < MAX(1,*n) && ! lquery) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SORGQR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n <= 0) {
work[1] = 1.f;
return 0;
}
nbmin = 2;
nx = 0;
iws = *n;
if (nb > 1 && nb < *k) {
/* Determine when to cross over from blocked to unblocked code. */
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "SORGQR", " ", m, n, k, &c_n1);
nx = MAX(i__1,i__2);
if (nx < *k) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *n;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduce NB and */
/* determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "SORGQR", " ", m, n, k, &c_n1);
nbmin = MAX(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < *k && nx < *k) {
/* Use blocked code after the last block. */
/* The first kk columns are handled by the block method. */
ki = (*k - nx - 1) / nb * nb;
/* Computing MIN */
i__1 = *k, i__2 = ki + nb;
kk = MIN(i__1,i__2);
/* Set A(1:kk,kk+1:n) to zero. */
i__1 = *n;
for (j = kk + 1; j <= i__1; ++j) {
i__2 = kk;
for (i__ = 1; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] = 0.f;
/* L10: */
}
/* L20: */
}
} else {
kk = 0;
}
/* Use unblocked code for the last or only block. */
if (kk < *n) {
i__1 = *m - kk;
i__2 = *n - kk;
i__3 = *k - kk;
sorg2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, &
tau[kk + 1], &work[1], &iinfo);
}
if (kk > 0) {
/* Use blocked code */
i__1 = -nb;
for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
/* Computing MIN */
i__2 = nb, i__3 = *k - i__ + 1;
ib = MIN(i__2,i__3);
if (i__ + ib <= *n) {
/* Form the triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
i__2 = *m - i__ + 1;
slarft_("Forward", "Columnwise", &i__2, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H to A(i:m,i+ib:n) from the left */
i__2 = *m - i__ + 1;
i__3 = *n - i__ - ib + 1;
slarfb_("Left", "No transpose", "Forward", "Columnwise", &
i__2, &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[
1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, &
work[ib + 1], &ldwork);
}
/* Apply H to rows i:m of current block */
i__2 = *m - i__ + 1;
sorg2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &
work[1], &iinfo);
/* Set rows 1:i-1 of current block to zero */
i__2 = i__ + ib - 1;
for (j = i__; j <= i__2; ++j) {
i__3 = i__ - 1;
for (l = 1; l <= i__3; ++l) {
a[l + j * a_dim1] = 0.f;
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
work[1] = (float) iws;
return 0;
/* End of SORGQR */
} /* sorgqr_ */
/* Subroutine */ int sormlq_(char *side, char *trans, integer *m, integer *n,
integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc,
real *work, integer *lwork, integer *info)
{
/* -- LAPACK 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
=======
SORMLQ overwrites the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q**T * C C * Q**T
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
Q = H(k) . . . H(2) H(1)
as returned by SGELQF. Q is of order M if SIDE = 'L' and of order N
if SIDE = 'R'.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
A (input) REAL array, dimension
(LDA,M) if SIDE = 'L',
(LDA,N) if SIDE = 'R'
The i-th row must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
SGELQF in the first k rows of its array argument A.
A is modified by the routine but restored on exit.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,K).
TAU (input) REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SGELQF.
C (input/output) REAL array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
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.
If SIDE = 'L', LWORK >= max(1,N);
if SIDE = 'R', LWORK >= max(1,M).
For optimum performance LWORK >= N*NB if SIDE = 'L', and
LWORK >= M*NB if SIDE = 'R', 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
=====================================================================
Test the input arguments
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__2 = 2;
static integer c__65 = 65;
/* System generated locals */
address a__1[2];
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4,
i__5;
char ch__1[2];
/* Builtin functions
Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
static logical left;
static integer i__;
static real t[4160] /* was [65][64] */;
extern logical lsame_(char *, char *);
static integer nbmin, iinfo, i1, i2, i3, ib, ic, jc;
extern /* Subroutine */ int sorml2_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *);
static integer nb, mi, ni, nq, nw;
extern /* Subroutine */ int slarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int slarft_(char *, char *, integer *, integer *,
real *, integer *, real *, real *, integer *);
static logical notran;
static integer ldwork;
static char transt[1];
static integer lwkopt;
static logical lquery;
static integer iws;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define c___ref(a_1,a_2) c__[(a_2)*c_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
left = lsame_(side, "L");
notran = lsame_(trans, "N");
lquery = *lwork == -1;
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = *m;
nw = *n;
} else {
nq = *n;
nw = *m;
}
if (! left && ! lsame_(side, "R")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "T")) {
*info = -2;
} else if (*m < 0) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*k < 0 || *k > nq) {
*info = -5;
} else if (*lda < max(1,*k)) {
*info = -7;
} else if (*ldc < max(1,*m)) {
*info = -10;
} else if (*lwork < max(1,nw) && ! lquery) {
*info = -12;
}
if (*info == 0) {
/* Determine the block size. NB may be at most NBMAX, where NBMAX
is used to define the local array T.
Computing MIN
Writing concatenation */
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
i__1 = 64, i__2 = ilaenv_(&c__1, "SORMLQ", ch__1, m, n, k, &c_n1, (
ftnlen)6, (ftnlen)2);
nb = min(i__1,i__2);
lwkopt = max(1,nw) * nb;
work[1] = (real) lwkopt;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SORMLQ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || *k == 0) {
work[1] = 1.f;
return 0;
}
nbmin = 2;
ldwork = nw;
if (nb > 1 && nb < *k) {
iws = nw * nb;
if (*lwork < iws) {
nb = *lwork / ldwork;
/* Computing MAX
Writing concatenation */
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
i__1 = 2, i__2 = ilaenv_(&c__2, "SORMLQ", ch__1, m, n, k, &c_n1, (
ftnlen)6, (ftnlen)2);
nbmin = max(i__1,i__2);
}
} else {
iws = nw;
}
if (nb < nbmin || nb >= *k) {
/* Use unblocked code */
sorml2_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[
c_offset], ldc, &work[1], &iinfo);
} else {
/* Use blocked code */
if (left && notran || ! left && ! notran) {
i1 = 1;
i2 = *k;
i3 = nb;
} else {
i1 = (*k - 1) / nb * nb + 1;
i2 = 1;
i3 = -nb;
}
if (left) {
ni = *n;
jc = 1;
} else {
mi = *m;
ic = 1;
}
if (notran) {
*(unsigned char *)transt = 'T';
} else {
*(unsigned char *)transt = 'N';
}
i__1 = i2;
i__2 = i3;
for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__4 = nb, i__5 = *k - i__ + 1;
ib = min(i__4,i__5);
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
i__4 = nq - i__ + 1;
slarft_("Forward", "Rowwise", &i__4, &ib, &a_ref(i__, i__), lda, &
tau[i__], t, &c__65);
if (left) {
/* H or H' is applied to C(i:m,1:n) */
mi = *m - i__ + 1;
ic = i__;
} else {
/* H or H' is applied to C(1:m,i:n) */
ni = *n - i__ + 1;
jc = i__;
}
/* Apply H or H' */
slarfb_(side, transt, "Forward", "Rowwise", &mi, &ni, &ib, &a_ref(
i__, i__), lda, t, &c__65, &c___ref(ic, jc), ldc, &work[1]
, &ldwork);
/* L10: */
}
}
work[1] = (real) lwkopt;
return 0;
/* End of SORMLQ */
} /* sormlq_ */
/* Subroutine */
int sorglq_fla(integer *m, integer *n, integer *k, real *a, integer *lda, 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 i__, j, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo;
extern /* Subroutine */
int sorgl2_fla(integer *, integer *, integer *, real *, integer *, real *, real *, integer *), slarfb_(char *, char *, char *, char *, integer *, integer *, integer *, real *, integer * , real *, integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
extern /* Subroutine */
int slarft_(char *, char *, integer *, integer *, real *, integer *, real *, real *, integer *);
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK computational 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 .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "SORGLQ", " ", m, n, k, &c_n1);
lwkopt = max(1,*m) * nb;
work[1] = (real) lwkopt;
lquery = *lwork == -1;
if (*m < 0)
{
*info = -1;
}
else if (*n < *m)
{
*info = -2;
}
else if (*k < 0 || *k > *m)
{
*info = -3;
}
else if (*lda < max(1,*m))
{
*info = -5;
}
else if (*lwork < max(1,*m) && ! lquery)
{
*info = -8;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("SORGLQ", &i__1);
return 0;
}
else if (lquery)
{
return 0;
}
/* Quick return if possible */
if (*m <= 0)
{
work[1] = 1.f;
return 0;
}
nbmin = 2;
nx = 0;
iws = *m;
if (nb > 1 && nb < *k)
{
/* Determine when to cross over from blocked to unblocked code. */
/* Computing MAX */
i__1 = 0;
i__2 = ilaenv_(&c__3, "SORGLQ", " ", m, n, k, &c_n1); // , expr subst
nx = max(i__1,i__2);
if (nx < *k)
{
/* Determine if workspace is large enough for blocked code. */
ldwork = *m;
iws = ldwork * nb;
if (*lwork < iws)
{
/* Not enough workspace to use optimal NB: reduce NB and */
/* determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2;
i__2 = ilaenv_(&c__2, "SORGLQ", " ", m, n, k, &c_n1); // , expr subst
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < *k && nx < *k)
{
/* Use blocked code after the last block. */
/* The first kk rows are handled by the block method. */
ki = (*k - nx - 1) / nb * nb;
/* Computing MIN */
i__1 = *k;
i__2 = ki + nb; // , expr subst
kk = min(i__1,i__2);
/* Set A(kk+1:m,1:kk) to zero. */
i__1 = kk;
for (j = 1;
j <= i__1;
++j)
{
i__2 = *m;
for (i__ = kk + 1;
i__ <= i__2;
++i__)
{
a[i__ + j * a_dim1] = 0.f;
/* L10: */
}
/* L20: */
}
}
else
{
kk = 0;
}
/* Use unblocked code for the last or only block. */
if (kk < *m)
{
i__1 = *m - kk;
i__2 = *n - kk;
i__3 = *k - kk;
sorgl2_fla(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, & tau[kk + 1], &work[1], &iinfo);
}
if (kk > 0)
{
/* Use blocked code */
i__1 = -nb;
for (i__ = ki + 1;
i__1 < 0 ? i__ >= 1 : i__ <= 1;
i__ += i__1)
{
/* Computing MIN */
i__2 = nb;
i__3 = *k - i__ + 1; // , expr subst
ib = min(i__2,i__3);
if (i__ + ib <= *m)
{
/* Form the triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
i__2 = *n - i__ + 1;
slarft_("Forward", "Rowwise", &i__2, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H**T to A(i+ib:m,i:n) from the right */
i__2 = *m - i__ - ib + 1;
i__3 = *n - i__ + 1;
slarfb_("Right", "Transpose", "Forward", "Rowwise", &i__2, & i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], & ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib + 1], &ldwork);
}
/* Apply H**T to columns i:n of current block */
i__2 = *n - i__ + 1;
sorgl2_fla(&ib, &i__2, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], & work[1], &iinfo);
/* Set columns 1:i-1 of current block to zero */
i__2 = i__ - 1;
for (j = 1;
j <= i__2;
++j)
{
i__3 = i__ + ib - 1;
for (l = i__;
l <= i__3;
++l)
{
a[l + j * a_dim1] = 0.f;
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
work[1] = (real) iws;
return 0;
/* End of SORGLQ */
}