/* Subroutine */ int sopgtr_(char *uplo, integer *n, real *ap, real *tau,
real *q, integer *ldq, real *work, integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
SOPGTR generates a real orthogonal matrix Q which is defined as the
product of n-1 elementary reflectors H(i) of order n, as returned by
SSPTRD using packed storage:
if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangular packed storage used in previous
call to SSPTRD;
= 'L': Lower triangular packed storage used in previous
call to SSPTRD.
N (input) INTEGER
The order of the matrix Q. N >= 0.
AP (input) REAL array, dimension (N*(N+1)/2)
The vectors which define the elementary reflectors, as
returned by SSPTRD.
TAU (input) REAL array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SSPTRD.
Q (output) REAL array, dimension (LDQ,N)
The N-by-N orthogonal matrix Q.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
WORK (workspace) REAL array, dimension (N-1)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input arguments
Parameter adjustments */
/* System generated locals */
integer q_dim1, q_offset, i__1, i__2, i__3;
/* Local variables */
static integer i__, j;
extern logical lsame_(char *, char *);
static integer iinfo;
static logical upper;
extern /* Subroutine */ int sorg2l_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *), sorg2r_(integer *,
integer *, integer *, real *, integer *, real *, real *, integer *
);
static integer ij;
extern /* Subroutine */ int xerbla_(char *, integer *);
#define q_ref(a_1,a_2) q[(a_2)*q_dim1 + a_1]
--ap;
--tau;
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
--work;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*ldq < max(1,*n)) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SOPGTR", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (upper) {
/* Q was determined by a call to SSPTRD with UPLO = 'U'
Unpack the vectors which define the elementary reflectors and
set the last row and column of Q equal to those of the unit
matrix */
ij = 2;
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
q_ref(i__, j) = ap[ij];
++ij;
/* L10: */
}
ij += 2;
q_ref(*n, j) = 0.f;
/* L20: */
}
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
q_ref(i__, *n) = 0.f;
/* L30: */
}
q_ref(*n, *n) = 1.f;
/* Generate Q(1:n-1,1:n-1) */
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
sorg2l_(&i__1, &i__2, &i__3, &q[q_offset], ldq, &tau[1], &work[1], &
iinfo);
} else {
/* Q was determined by a call to SSPTRD with UPLO = 'L'.
Unpack the vectors which define the elementary reflectors and
set the first row and column of Q equal to those of the unit
matrix */
q_ref(1, 1) = 1.f;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
q_ref(i__, 1) = 0.f;
/* L40: */
}
ij = 3;
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
q_ref(1, j) = 0.f;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
q_ref(i__, j) = ap[ij];
++ij;
/* L50: */
}
ij += 2;
/* L60: */
}
if (*n > 1) {
/* Generate Q(2:n,2:n) */
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
sorg2r_(&i__1, &i__2, &i__3, &q_ref(2, 2), ldq, &tau[1], &work[1],
&iinfo);
}
}
return 0;
/* End of SOPGTR */
} /* sopgtr_ */
/* Subroutine */ int sopgtr_(char *uplo, integer *n, real *ap, real *tau,
real *q, integer *ldq, real *work, integer *info)
{
/* System generated locals */
integer q_dim1, q_offset, i__1, i__2, i__3;
/* Local variables */
integer i__, j, ij;
integer iinfo;
logical upper;
/* -- LAPACK routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* SOPGTR generates a real orthogonal matrix Q which is defined as the */
/* product of n-1 elementary reflectors H(i) of order n, as returned by */
/* SSPTRD using packed storage: */
/* if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), */
/* if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangular packed storage used in previous */
/* call to SSPTRD; */
/* = 'L': Lower triangular packed storage used in previous */
/* call to SSPTRD. */
/* N (input) INTEGER */
/* The order of the matrix Q. N >= 0. */
/* AP (input) REAL array, dimension (N*(N+1)/2) */
/* The vectors which define the elementary reflectors, as */
/* returned by SSPTRD. */
/* TAU (input) REAL array, dimension (N-1) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by SSPTRD. */
/* Q (output) REAL array, dimension (LDQ,N) */
/* The N-by-N orthogonal matrix Q. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. LDQ >= max(1,N). */
/* WORK (workspace) REAL array, dimension (N-1) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* Test the input arguments */
/* Parameter adjustments */
--ap;
--tau;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--work;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*ldq < max(1,*n)) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SOPGTR", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (upper) {
/* Q was determined by a call to SSPTRD with UPLO = 'U' */
/* Unpack the vectors which define the elementary reflectors and */
/* set the last row and column of Q equal to those of the unit */
/* matrix */
ij = 2;
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
q[i__ + j * q_dim1] = ap[ij];
++ij;
}
ij += 2;
q[*n + j * q_dim1] = 0.f;
}
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
q[i__ + *n * q_dim1] = 0.f;
}
q[*n + *n * q_dim1] = 1.f;
/* Generate Q(1:n-1,1:n-1) */
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
sorg2l_(&i__1, &i__2, &i__3, &q[q_offset], ldq, &tau[1], &work[1], &
iinfo);
} else {
/* Q was determined by a call to SSPTRD with UPLO = 'L'. */
/* Unpack the vectors which define the elementary reflectors and */
/* set the first row and column of Q equal to those of the unit */
/* matrix */
q[q_dim1 + 1] = 1.f;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
q[i__ + q_dim1] = 0.f;
}
ij = 3;
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
q[j * q_dim1 + 1] = 0.f;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
q[i__ + j * q_dim1] = ap[ij];
++ij;
}
ij += 2;
}
if (*n > 1) {
/* Generate Q(2:n,2:n) */
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
sorg2r_(&i__1, &i__2, &i__3, &q[(q_dim1 << 1) + 2], ldq, &tau[1],
&work[1], &iinfo);
}
}
return 0;
/* End of SOPGTR */
} /* sopgtr_ */
/* Subroutine */ int sorgql_(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, kk, nx, iws, nbmin, iinfo;
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* November 2006 */
/* 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 */
/* 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 (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 */
/* ===================================================================== */
/* 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 || *n > *m) {
*info = -2;
} else if (*k < 0 || *k > *n) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
}
if (*info == 0) {
if (*n == 0) {
lwkopt = 1;
} else {
nb = ilaenv_(&c__1, "SORGQL", " ", m, n, k, &c_n1);
lwkopt = *n * nb;
}
work[1] = (real) lwkopt;
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) {
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);
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);
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[i__ + j * a_dim1] = 0.f;
}
}
} 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[(*n - *k +
i__) * a_dim1 + 1], 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[(*n - *k + i__) * a_dim1 + 1],
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[(*n - *k + i__) * a_dim1 + 1], 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[l + j * a_dim1] = 0.f;
}
}
}
}
work[1] = (real) iws;
return 0;
/* End of SORGQL */
} /* sorgql_ */
/* 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_ */
