/* 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)
{
/* 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 sorm2l_(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 routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* 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 (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,nq)) {
*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, "SORMQL", 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_("SORMQL", &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, "SORMQL", ch__1, m, n, k, &c_n1);
nbmin = max(i__1,i__2);
}
} else {
iws = nw;
}
if (nb < nbmin || nb >= *k) {
/* Use unblocked code */
sorm2l_(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;
}
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", "Columnwise", &i__4, &ib, &a[i__ * a_dim1 + 1]
, 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[
i__ * a_dim1 + 1], lda, t, &c__65, &c__[c_offset], ldc, &
work[1], &ldwork);
/* L10: */
}
}
work[1] = (real) lwkopt;
return 0;
/* End of SORMQL */
} /* sormql_ */
/* 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_ */
