/* Subroutine */ int sormtr_(char *side, char *uplo, char *trans, integer *m,
integer *n, 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[2], i__2, i__3;
char ch__1[2];
/* Local variables */
integer i1, i2, nb, mi, ni, nq, nw;
logical left;
integer iinfo;
logical upper;
integer lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* SORMTR 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 of order nq, with nq = m if */
/* SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of */
/* nq-1 elementary reflectors, as returned by SSYTRD: */
/* if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); */
/* if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). */
/* Arguments */
/* ========= */
/* SIDE (input) CHARACTER*1 */
/* = 'L': apply Q or Q**T from the Left; */
/* = 'R': apply Q or Q**T from the Right. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A contains elementary reflectors */
/* from SSYTRD; */
/* = 'L': Lower triangle of A contains elementary reflectors */
/* from SSYTRD. */
/* 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. */
/* A (input) REAL array, dimension */
/* (LDA,M) if SIDE = 'L' */
/* (LDA,N) if SIDE = 'R' */
/* The vectors which define the elementary reflectors, as */
/* returned by SSYTRD. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. */
/* LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. */
/* TAU (input) REAL array, dimension */
/* (M-1) if SIDE = 'L' */
/* (N-1) if SIDE = 'R' */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by SSYTRD. */
/* 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 */
/* ===================================================================== */
/* 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");
upper = lsame_(uplo, "U");
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 (! upper && ! lsame_(uplo, "L")) {
*info = -2;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T")) {
*info = -3;
} else if (*m < 0) {
*info = -4;
} else if (*n < 0) {
*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) {
if (upper) {
if (left) {
/* Writing concatenation */
i__1[0] = 1, a__1[0] = side;
i__1[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
i__2 = *m - 1;
i__3 = *m - 1;
nb = ilaenv_(&c__1, "SORMQL", ch__1, &i__2, n, &i__3, &c_n1);
} else {
/* Writing concatenation */
i__1[0] = 1, a__1[0] = side;
i__1[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
i__2 = *n - 1;
i__3 = *n - 1;
nb = ilaenv_(&c__1, "SORMQL", ch__1, m, &i__2, &i__3, &c_n1);
}
} else {
if (left) {
/* Writing concatenation */
i__1[0] = 1, a__1[0] = side;
i__1[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
i__2 = *m - 1;
i__3 = *m - 1;
nb = ilaenv_(&c__1, "SORMQR", ch__1, &i__2, n, &i__3, &c_n1);
} else {
/* Writing concatenation */
i__1[0] = 1, a__1[0] = side;
i__1[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
i__2 = *n - 1;
i__3 = *n - 1;
nb = ilaenv_(&c__1, "SORMQR", ch__1, m, &i__2, &i__3, &c_n1);
}
}
lwkopt = max(1,nw) * nb;
work[1] = (real) lwkopt;
}
if (*info != 0) {
i__2 = -(*info);
xerbla_("SORMTR", &i__2);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || nq == 1) {
work[1] = 1.f;
return 0;
}
if (left) {
mi = *m - 1;
ni = *n;
} else {
mi = *m;
ni = *n - 1;
}
if (upper) {
/* Q was determined by a call to SSYTRD with UPLO = 'U' */
i__2 = nq - 1;
sormql_(side, trans, &mi, &ni, &i__2, &a[(a_dim1 << 1) + 1], lda, &
tau[1], &c__[c_offset], ldc, &work[1], lwork, &iinfo);
} else {
/* Q was determined by a call to SSYTRD with UPLO = 'L' */
if (left) {
i1 = 2;
i2 = 1;
} else {
i1 = 1;
i2 = 2;
}
i__2 = nq - 1;
sormqr_(side, trans, &mi, &ni, &i__2, &a[a_dim1 + 2], lda, &tau[1], &
c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo);
}
work[1] = (real) lwkopt;
return 0;
/* End of SORMTR */
} /* sormtr_ */
/* Subroutine */ int sormtr_(char *side, char *uplo, char *trans, int *m,
int *n, real *a, int *lda, real *tau, real *c, int *ldc,
real *work, int *lwork, int *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
=======
SORMTR 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 of order nq, with nq = m if
SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
nq-1 elementary reflectors, as returned by SSYTRD:
if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A contains elementary reflectors
from SSYTRD;
= 'L': Lower triangle of A contains elementary reflectors
from SSYTRD.
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.
A (input) REAL array, dimension
(LDA,M) if SIDE = 'L'
(LDA,N) if SIDE = 'R'
The vectors which define the elementary reflectors, as
returned by SSYTRD.
LDA (input) INTEGER
The leading dimension of the array A.
LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
TAU (input) REAL array, dimension
(M-1) if SIDE = 'L'
(N-1) if SIDE = 'R'
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SSYTRD.
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 */
/* System generated locals */
/* Unused variables commented out by MDG on 03-09-05
int a_dim1, a_offset, c_dim1, c_offset;
*/
int i__1;
/* Local variables */
static logical left;
extern logical lsame_(char *, char *);
static int iinfo, i1;
static logical upper;
static int i2, mi, ni, nq, nw;
extern /* Subroutine */ int xerbla_(char *, int *), sormql_(
char *, char *, int *, int *, int *, real *, int *
, real *, real *, int *, real *, int *, int *), sormqr_(char *, char *, int *, int *, int *,
real *, int *, real *, real *, int *, real *, int *,
int *);
#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");
upper = lsame_(uplo, "U");
/* 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 (! upper && ! lsame_(uplo, "L")) {
*info = -2;
} else if (! lsame_(trans, "N") && ! lsame_(trans, "T")) {
*info = -3;
} else if (*m < 0) {
*info = -4;
} else if (*n < 0) {
*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_("SORMTR", &i__1);
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || nq == 1) {
WORK(1) = 1.f;
return 0;
}
if (left) {
mi = *m - 1;
ni = *n;
} else {
mi = *m;
ni = *n - 1;
}
if (upper) {
/* Q was determined by a call to SSYTRD with UPLO = 'U' */
i__1 = nq - 1;
sormql_(side, trans, &mi, &ni, &i__1, &A(1,2), lda, &
TAU(1), &C(1,1), ldc, &WORK(1), lwork, &iinfo);
} else {
/* Q was determined by a call to SSYTRD with UPLO = 'L' */
if (left) {
i1 = 2;
i2 = 1;
} else {
i1 = 1;
i2 = 2;
}
i__1 = nq - 1;
sormqr_(side, trans, &mi, &ni, &i__1, &A(2,1), lda, &TAU(1), &
C(i1,i2), ldc, &WORK(1), lwork, &iinfo);
}
return 0;
/* End of SORMTR */
} /* sormtr_ */
/* Subroutine */ int sgeqls_(integer *m, integer *n, integer *nrhs, real *a,
integer *lda, real *tau, real *b, integer *ldb, real *work, integer *
lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1;
/* Local variables */
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* Solve the least squares problem */
/* min || A*X - B || */
/* using the QL factorization */
/* A = Q*L */
/* computed by SGEQLF. */
/* 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. M >= N >= 0. */
/* NRHS (input) INTEGER */
/* The number of columns of B. NRHS >= 0. */
/* A (input) REAL array, dimension (LDA,N) */
/* Details of the QL factorization of the original matrix A as */
/* returned by SGEQLF. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= M. */
/* TAU (input) REAL array, dimension (N) */
/* Details of the orthogonal matrix Q. */
/* B (input/output) REAL array, dimension (LDB,NRHS) */
/* On entry, the m-by-nrhs right hand side matrix B. */
/* On exit, the n-by-nrhs solution matrix X, stored in rows */
/* m-n+1:m. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= M. */
/* WORK (workspace) REAL array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The length of the array WORK. LWORK must be at least NRHS, */
/* and should be at least NRHS*NB, where NB is the block size */
/* for this environment. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--work;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0 || *n > *m) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*ldb < max(1,*m)) {
*info = -8;
} else if (*lwork < 1 || *lwork < *nrhs && *m > 0 && *n > 0) {
*info = -10;
}
if (*info != 0) {
i__1 = -(*info);
this_xerbla_("SGEQLS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0 || *m == 0) {
return 0;
}
/* B := Q' * B */
sormql_("Left", "Transpose", m, nrhs, n, &a[a_offset], lda, &tau[1], &b[
b_offset], ldb, &work[1], lwork, info);
/* Solve L*X = B(m-n+1:m,:) */
strsm_("Left", "Lower", "No transpose", "Non-unit", n, nrhs, &c_b9, &a[*m
- *n + 1 + a_dim1], lda, &b[*m - *n + 1 + b_dim1], ldb);
return 0;
/* End of SGEQLS */
} /* sgeqls_ */
