/* Subroutine */ int zungrq_(integer *m, integer *n, integer *k,
doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
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
=======
ZUNGRQ generates an M-by-N complex 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 ZGERQF.
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) COMPLEX*16 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 ZGERQF 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) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGERQF.
WORK (workspace/output) COMPLEX*16 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.
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, i__5;
/* Local variables */
static integer i__, j, l, nbmin, iinfo, ib, nb, ii, kk;
extern /* Subroutine */ int zungr2_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer nx;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer lwkopt;
static logical lquery;
static integer iws;
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "ZUNGRQ", " ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1);
lwkopt = max(1,*m) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 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;
} else if (*lwork < max(1,*m) && ! lquery) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNGRQ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m <= 0) {
work[1].r = 1., work[1].i = 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, "ZUNGRQ", " ", 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 = *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, "ZUNGRQ", " ", 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 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__) {
i__3 = a_subscr(i__, j);
a[i__3].r = 0., a[i__3].i = 0.;
/* 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;
zungr2_(&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;
zlarft_("Backward", "Rowwise", &i__3, &ib, &a_ref(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;
zlarfb_("Right", "Conjugate transpose", "Backward", "Rowwise",
&i__3, &i__4, &ib, &a_ref(ii, 1), 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;
zungr2_(&ib, &i__3, &ib, &a_ref(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 <= i__3; ++l) {
i__4 = ii + ib - 1;
for (j = ii; j <= i__4; ++j) {
i__5 = a_subscr(j, l);
a[i__5].r = 0., a[i__5].i = 0.;
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZUNGRQ */
} /* zungrq_ */
/* Subroutine */ int zgelqf_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublecomplex *tau, doublecomplex *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
=======
ZGELQF computes an LQ factorization of a complex 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) COMPLEX*16 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 unitary 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) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) COMPLEX*16 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.
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 complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; conjg(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 */
/* 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 zgelq2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *);
static integer ib, nb, nx;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer lwkopt;
static logical lquery;
static integer iws;
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "ZGELQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)
1);
lwkopt = *m * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 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) {
i__1 = -(*info);
xerbla_("ZGELQF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
k = min(*m,*n);
if (k == 0) {
work[1].r = 1., work[1].i = 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, "ZGELQF", " ", m, n, &c_n1, &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 = *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, "ZGELQF", " ", m, n, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
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;
zgelq2_(&ib, &i__3, &a_ref(i__, i__), 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;
zlarft_("Forward", "Rowwise", &i__3, &ib, &a_ref(i__, i__),
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;
zlarfb_("Right", "No transpose", "Forward", "Rowwise", &i__3,
&i__4, &ib, &a_ref(i__, i__), lda, &work[1], &ldwork,
&a_ref(i__ + ib, i__), 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;
zgelq2_(&i__2, &i__1, &a_ref(i__, i__), lda, &tau[i__], &work[1], &
iinfo);
}
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZGELQF */
} /* zgelqf_ */
/* Subroutine */ int zungqr_(integer *m, integer *n, integer *k,
doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
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, ki, kk, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int zung2r_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
integer 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 */
/* ======= */
/* ZUNGQR generates an M-by-N complex 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 ZGEQRF. */
/* 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) COMPLEX*16 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 ZGEQRF 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) COMPLEX*16 array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by ZGEQRF. */
/* WORK (workspace/output) COMPLEX*16 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, "ZUNGQR", " ", m, n, k, &c_n1);
lwkopt = max(1,*n) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 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;
} else if (*lwork < max(1,*n) && ! lquery) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNGQR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n <= 0) {
work[1].r = 1., work[1].i = 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, "ZUNGQR", " ", 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, "ZUNGQR", " ", 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__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* 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;
zung2r_(&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;
zlarft_("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;
zlarfb_("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;
zung2r_(&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) {
i__4 = l + j * a_dim1;
a[i__4].r = 0., a[i__4].i = 0.;
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZUNGQR */
} /* zungqr_ */
/*< SUBROUTINE ZGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) >*/
/* Subroutine */ int zgehrd_(integer *n, integer *ilo, integer *ihi,
doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
doublecomplex z__1;
/* Local variables */
integer i__;
doublecomplex t[4160] /* was [65][64] */;
integer ib;
doublecomplex ei;
integer nb, nh, nx=0, iws, nbmin, iinfo;
extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, ftnlen, ftnlen), zgehd2_(integer *, integer *, integer
*, doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen),
zlahrd_(integer *, integer *, integer *, doublecomplex *, integer
*, doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *);
integer ldwork, lwkopt;
logical lquery;
/* -- 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 */
/* .. Scalar Arguments .. */
/*< INTEGER IHI, ILO, INFO, LDA, LWORK, N >*/
/* .. */
/* .. Array Arguments .. */
/*< COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* ZGEHRD reduces a complex general matrix A to upper Hessenberg form H */
/* by a unitary similarity transformation: Q' * A * Q = H . */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* ILO (input) INTEGER */
/* IHI (input) INTEGER */
/* It is assumed that A is already upper triangular in rows */
/* and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally */
/* set by a previous call to ZGEBAL; otherwise they should be */
/* set to 1 and N respectively. See Further Details. */
/* 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the N-by-N general matrix to be reduced. */
/* On exit, the upper triangle and the first subdiagonal of A */
/* are overwritten with the upper Hessenberg matrix H, and the */
/* elements below the first subdiagonal, with the array TAU, */
/* represent the unitary matrix Q as a product of elementary */
/* reflectors. See Further Details. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* TAU (output) COMPLEX*16 array, dimension (N-1) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to */
/* zero. */
/* WORK (workspace/output) COMPLEX*16 array, dimension (LWORK) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The length 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 had an illegal value. */
/* Further Details */
/* =============== */
/* The matrix Q is represented as a product of (ihi-ilo) elementary */
/* reflectors */
/* Q = H(ilo) H(ilo+1) . . . H(ihi-1). */
/* Each H(i) has the form */
/* H(i) = I - tau * v * v' */
/* where tau is a complex scalar, and v is a complex vector with */
/* v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on */
/* exit in A(i+2:ihi,i), and tau in TAU(i). */
/* The contents of A are illustrated by the following example, with */
/* n = 7, ilo = 2 and ihi = 6: */
/* on entry, on exit, */
/* ( a a a a a a a ) ( a a h h h h a ) */
/* ( a a a a a a ) ( a h h h h a ) */
/* ( a a a a a a ) ( h h h h h h ) */
/* ( a a a a a a ) ( v2 h h h h h ) */
/* ( a a a a a a ) ( v2 v3 h h h h ) */
/* ( a a a a a a ) ( v2 v3 v4 h h h ) */
/* ( a ) ( a ) */
/* where a denotes an element of the original matrix A, h denotes a */
/* modified element of the upper Hessenberg matrix H, and vi denotes an */
/* element of the vector defining H(i). */
/* ===================================================================== */
/* .. Parameters .. */
/*< INTEGER NBMAX, LDT >*/
/*< PARAMETER ( NBMAX = 64, LDT = NBMAX+1 ) >*/
/*< COMPLEX*16 ZERO, ONE >*/
/*< >*/
/* .. */
/* .. Local Scalars .. */
/*< LOGICAL LQUERY >*/
/*< >*/
/*< COMPLEX*16 EI >*/
/* .. */
/* .. Local Arrays .. */
/*< COMPLEX*16 T( LDT, NBMAX ) >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL XERBLA, ZGEHD2, ZGEMM, ZLAHRD, ZLARFB >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC MAX, MIN >*/
/* .. */
/* .. External Functions .. */
/*< INTEGER ILAENV >*/
/*< EXTERNAL ILAENV >*/
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters */
/*< INFO = 0 >*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
/*< NB = MIN( NBMAX, ILAENV( 1, 'ZGEHRD', ' ', N, ILO, IHI, -1 ) ) >*/
/* Computing MIN */
i__1 = 64, i__2 = ilaenv_(&c__1, "ZGEHRD", " ", n, ilo, ihi, &c_n1, (
ftnlen)6, (ftnlen)1);
nb = min(i__1,i__2);
/*< LWKOPT = N*NB >*/
lwkopt = *n * nb;
/*< WORK( 1 ) = LWKOPT >*/
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
/*< LQUERY = ( LWORK.EQ.-1 ) >*/
lquery = *lwork == -1;
/*< IF( N.LT.0 ) THEN >*/
if (*n < 0) {
/*< INFO = -1 >*/
*info = -1;
/*< ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN >*/
} else if (*ilo < 1 || *ilo > max(1,*n)) {
/*< INFO = -2 >*/
*info = -2;
/*< ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN >*/
} else if (*ihi < min(*ilo,*n) || *ihi > *n) {
/*< INFO = -3 >*/
*info = -3;
/*< ELSE IF( LDA.LT.MAX( 1, N ) ) THEN >*/
} else if (*lda < max(1,*n)) {
/*< INFO = -5 >*/
*info = -5;
/*< ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN >*/
} else if (*lwork < max(1,*n) && ! lquery) {
/*< INFO = -8 >*/
*info = -8;
/*< END IF >*/
}
/*< IF( INFO.NE.0 ) THEN >*/
if (*info != 0) {
/*< CALL XERBLA( 'ZGEHRD', -INFO ) >*/
i__1 = -(*info);
xerbla_("ZGEHRD", &i__1, (ftnlen)6);
/*< RETURN >*/
return 0;
/*< ELSE IF( LQUERY ) THEN >*/
} else if (lquery) {
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/* Set elements 1:ILO-1 and IHI:N-1 of TAU to zero */
/*< DO 10 I = 1, ILO - 1 >*/
i__1 = *ilo - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< TAU( I ) = ZERO >*/
i__2 = i__;
tau[i__2].r = 0., tau[i__2].i = 0.;
/*< 10 CONTINUE >*/
/* L10: */
}
/*< DO 20 I = MAX( 1, IHI ), N - 1 >*/
i__1 = *n - 1;
for (i__ = max(1,*ihi); i__ <= i__1; ++i__) {
/*< TAU( I ) = ZERO >*/
i__2 = i__;
tau[i__2].r = 0., tau[i__2].i = 0.;
/*< 20 CONTINUE >*/
/* L20: */
}
/* Quick return if possible */
/*< NH = IHI - ILO + 1 >*/
nh = *ihi - *ilo + 1;
/*< IF( NH.LE.1 ) THEN >*/
if (nh <= 1) {
/*< WORK( 1 ) = 1 >*/
work[1].r = 1., work[1].i = 0.;
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/*< NBMIN = 2 >*/
nbmin = 2;
/*< IWS = 1 >*/
iws = 1;
/*< IF( NB.GT.1 .AND. NB.LT.NH ) THEN >*/
if (nb > 1 && nb < nh) {
/* Determine when to cross over from blocked to unblocked code */
/* (last block is always handled by unblocked code). */
/*< NX = MAX( NB, ILAENV( 3, 'ZGEHRD', ' ', N, ILO, IHI, -1 ) ) >*/
/* Computing MAX */
i__1 = nb, i__2 = ilaenv_(&c__3, "ZGEHRD", " ", n, ilo, ihi, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
/*< IF( NX.LT.NH ) THEN >*/
if (nx < nh) {
/* Determine if workspace is large enough for blocked code. */
/*< IWS = N*NB >*/
iws = *n * nb;
/*< IF( LWORK.LT.IWS ) THEN >*/
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: determine the */
/* minimum value of NB, and reduce NB or force use of */
/* unblocked code. */
/*< >*/
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "ZGEHRD", " ", n, ilo, ihi, &
c_n1, (ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
/*< IF( LWORK.GE.N*NBMIN ) THEN >*/
if (*lwork >= *n * nbmin) {
/*< NB = LWORK / N >*/
nb = *lwork / *n;
/*< ELSE >*/
} else {
/*< NB = 1 >*/
nb = 1;
/*< END IF >*/
}
/*< END IF >*/
}
/*< END IF >*/
}
/*< END IF >*/
}
/*< LDWORK = N >*/
ldwork = *n;
/*< IF( NB.LT.NBMIN .OR. NB.GE.NH ) THEN >*/
if (nb < nbmin || nb >= nh) {
/* Use unblocked code below */
/*< I = ILO >*/
i__ = *ilo;
/*< ELSE >*/
} else {
/* Use blocked code */
/*< DO 30 I = ILO, IHI - 1 - NX, NB >*/
i__1 = *ihi - 1 - nx;
i__2 = nb;
for (i__ = *ilo; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/*< IB = MIN( NB, IHI-I ) >*/
/* Computing MIN */
i__3 = nb, i__4 = *ihi - i__;
ib = min(i__3,i__4);
/* Reduce columns i:i+ib-1 to Hessenberg form, returning the */
/* matrices V and T of the block reflector H = I - V*T*V' */
/* which performs the reduction, and also the matrix Y = A*V*T */
/*< >*/
zlahrd_(ihi, &i__, &ib, &a[i__ * a_dim1 + 1], lda, &tau[i__], t, &
c__65, &work[1], &ldwork);
/* Apply the block reflector H to A(1:ihi,i+ib:ihi) from the */
/* right, computing A := A - Y * V'. V(i+ib,ib-1) must be set */
/* to 1. */
/*< EI = A( I+IB, I+IB-1 ) >*/
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
ei.r = a[i__3].r, ei.i = a[i__3].i;
/*< A( I+IB, I+IB-1 ) = ONE >*/
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
a[i__3].r = 1., a[i__3].i = 0.;
/*< >*/
i__3 = *ihi - i__ - ib + 1;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "Conjugate transpose", ihi, &i__3, &ib, &
z__1, &work[1], &ldwork, &a[i__ + ib + i__ * a_dim1], lda,
&c_b2, &a[(i__ + ib) * a_dim1 + 1], lda, (ftnlen)12, (
ftnlen)19);
/*< A( I+IB, I+IB-1 ) = EI >*/
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
a[i__3].r = ei.r, a[i__3].i = ei.i;
/* Apply the block reflector H to A(i+1:ihi,i+ib:n) from the */
/* left */
/*< >*/
i__3 = *ihi - i__;
i__4 = *n - i__ - ib + 1;
zlarfb_("Left", "Conjugate transpose", "Forward", "Columnwise", &
i__3, &i__4, &ib, &a[i__ + 1 + i__ * a_dim1], lda, t, &
c__65, &a[i__ + 1 + (i__ + ib) * a_dim1], lda, &work[1], &
ldwork, (ftnlen)4, (ftnlen)19, (ftnlen)7, (ftnlen)10);
/*< 30 CONTINUE >*/
/* L30: */
}
/*< END IF >*/
}
/* Use unblocked code to reduce the rest of the matrix */
/*< CALL ZGEHD2( N, I, IHI, A, LDA, TAU, WORK, IINFO ) >*/
zgehd2_(n, &i__, ihi, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
/*< WORK( 1 ) = IWS >*/
work[1].r = (doublereal) iws, work[1].i = 0.;
/*< RETURN >*/
return 0;
/* End of ZGEHRD */
/*< END >*/
} /* zgehrd_ */
/* Subroutine */ int zgeqrf_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublecomplex *tau, doublecomplex *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;
extern /* Subroutine */ int zgeqr2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *), xerbla_(
char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
integer 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 */
/* ======= */
/* ZGEQRF computes a QR factorization of a complex 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) COMPLEX*16 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 unitary 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) COMPLEX*16 array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). */
/* WORK (workspace/output) COMPLEX*16 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 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 complex scalar, and v is a complex vector with */
/* v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), */
/* and tau in TAU(i). */
/* ===================================================================== */
/* .. 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, "ZGEQRF", " ", m, n, &c_n1, &c_n1);
lwkopt = *n * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 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,*n) && ! lquery) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEQRF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
k = min(*m,*n);
if (k == 0) {
work[1].r = 1., work[1].i = 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, "ZGEQRF", " ", 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 = *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, "ZGEQRF", " ", 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 QR factorization of the current block */
/* A(i:m,i:i+ib-1) */
i__3 = *m - i__ + 1;
zgeqr2_(&i__3, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[
1], &iinfo);
if (i__ + ib <= *n) {
/* Form the triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
i__3 = *m - i__ + 1;
zlarft_("Forward", "Columnwise", &i__3, &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__3 = *m - i__ + 1;
i__4 = *n - i__ - ib + 1;
zlarfb_("Left", "Conjugate transpose", "Forward", "Columnwise"
, &i__3, &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &
work[1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], 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;
zgeqr2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1]
, &iinfo);
}
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZGEQRF */
} /* zgeqrf_ */
/* Subroutine */ int zgerqf_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublecomplex *tau, doublecomplex *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 zgerq2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *), xerbla_(
char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
integer 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 */
/* ======= */
/* ZGERQF computes an RQ factorization of a complex 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) COMPLEX*16 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 */
/* unitary 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) COMPLEX*16 array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). */
/* WORK (workspace/output) COMPLEX*16 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 complex scalar, and v is a complex vector with */
/* v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(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;
}
if (*info == 0) {
k = min(*m,*n);
if (k == 0) {
lwkopt = 1;
} else {
nb = ilaenv_(&c__1, "ZGERQF", " ", m, n, &c_n1, &c_n1);
lwkopt = *m * nb;
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
if (*lwork < max(1,*m) && ! lquery) {
*info = -7;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGERQF", &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, "ZGERQF", " ", 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, "ZGERQF", " ", 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;
zgerq2_(&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;
zlarft_("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;
zlarfb_("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) {
zgerq2_(&mu, &nu, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
}
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZGERQF */
} /* zgerqf_ */
/* Subroutine */ int zungqr_(integer *m, integer *n, integer *k,
doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
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
=======
ZUNGQR generates an M-by-N complex 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 ZGEQRF.
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) COMPLEX*16 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 ZGEQRF 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) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQRF.
WORK (workspace/output) COMPLEX*16 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 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, nb, ki, kk;
extern /* Subroutine */ int zung2r_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer nx;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer 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 || *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)) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNGQR", &i__1);
return 0;
}
/* Quick return if possible */
if (*n <= 0) {
WORK(1).r = 1., WORK(1).i = 0.;
return 0;
}
/* Determine the block size. */
nb = ilaenv_(&c__1, "ZUNGQR", " ", m, n, k, &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, "ZUNGQR", " ", 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 = *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, "ZUNGQR", " ", 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 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 <= *n; ++j) {
i__2 = kk;
for (i = 1; i <= kk; ++i) {
i__3 = i + j * a_dim1;
A(i,j).r = 0., A(i,j).i = 0.;
/* 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;
zung2r_(&i__1, &i__2, &i__3, &A(kk+1,kk+1), lda, &
TAU(kk + 1), &WORK(1), &iinfo);
}
if (kk > 0) {
/* Use blocked code */
i__1 = -nb;
for (i = ki + 1; -nb < 0 ? i >= 1 : i <= 1; i += -nb) {
/* 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 reflec
tor
H = H(i) H(i+1) . . . H(i+ib-1) */
i__2 = *m - i + 1;
zlarft_("Forward", "Columnwise", &i__2, &ib, &A(i,i), 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;
zlarfb_("Left", "No transpose", "Forward", "Columnwise", &
i__2, &i__3, &ib, &A(i,i), lda, &WORK(1), &
ldwork, &A(i,i+ib), lda, &WORK(ib + 1),
&ldwork);
}
/* Apply H to rows i:m of current block */
i__2 = *m - i + 1;
zung2r_(&i__2, &ib, &ib, &A(i,i), 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+ib-1; ++j) {
i__3 = i - 1;
for (l = 1; l <= i-1; ++l) {
i__4 = l + j * a_dim1;
A(l,j).r = 0., A(l,j).i = 0.;
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
WORK(1).r = (doublereal) iws, WORK(1).i = 0.;
return 0;
/* End of ZUNGQR */
} /* zungqr_ */
/* Subroutine */ int zunmql_(char *side, char *trans, integer *m, integer *n,
integer *k, doublecomplex *a, integer *lda, doublecomplex *tau,
doublecomplex *c__, integer *ldc, doublecomplex *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
=======
ZUNMQL overwrites the general complex M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'C': Q**H * C C * Q**H
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(k) . . . H(2) H(1)
as returned by ZGEQLF. 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**H from the Left;
= 'R': apply Q or Q**H from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'C': Transpose, apply Q**H.
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) COMPLEX*16 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
ZGEQLF 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) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQLF.
C (input/output) COMPLEX*16 array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace/output) COMPLEX*16 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 doublecomplex t[4160] /* was [65][64] */;
extern logical lsame_(char *, char *);
static integer nbmin, iinfo, i1, i2, i3, ib, nb, mi, ni;
extern /* Subroutine */ int zunm2l_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *);
static integer nq, nw;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static logical notran;
static integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer lwkopt;
static logical lquery;
static integer iws;
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
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, "C")) {
*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
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, "ZUNMQL", ch__1, m, n, k, &c_n1, (
ftnlen)6, (ftnlen)2);
nb = min(i__1,i__2);
lwkopt = max(1,nw) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNMQL", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || *k == 0) {
work[1].r = 1., work[1].i = 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, "ZUNMQL", 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 */
zunm2l_(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;
zlarft_("Backward", "Columnwise", &i__4, &ib, &a_ref(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' */
zlarfb_(side, trans, "Backward", "Columnwise", &mi, &ni, &ib, &
a_ref(1, i__), lda, t, &c__65, &c__[c_offset], ldc, &work[
1], &ldwork);
/* L10: */
}
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
return 0;
/* End of ZUNMQL */
} /* zunmql_ */
/*< SUBROUTINE ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) >*/
/* Subroutine */ int zungqr_(integer *m, integer *n, integer *k,
doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
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, ki=0, kk, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int zung2r_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen);
integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, ftnlen, ftnlen);
integer lwkopt;
logical lquery;
/* -- 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 */
/* .. Scalar Arguments .. */
/*< INTEGER INFO, K, LDA, LWORK, M, N >*/
/* .. */
/* .. Array Arguments .. */
/*< COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* ZUNGQR generates an M-by-N complex 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 ZGEQRF. */
/* 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) COMPLEX*16 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 ZGEQRF 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) COMPLEX*16 array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by ZGEQRF. */
/* WORK (workspace/output) COMPLEX*16 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 */
/* ===================================================================== */
/* .. Parameters .. */
/*< COMPLEX*16 ZERO >*/
/*< PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) >*/
/* .. */
/* .. Local Scalars .. */
/*< LOGICAL LQUERY >*/
/*< >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNG2R >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC MAX, MIN >*/
/* .. */
/* .. External Functions .. */
/*< INTEGER ILAENV >*/
/*< EXTERNAL ILAENV >*/
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/*< INFO = 0 >*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
/*< NB = ILAENV( 1, 'ZUNGQR', ' ', M, N, K, -1 ) >*/
nb = ilaenv_(&c__1, "ZUNGQR", " ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1);
/*< LWKOPT = MAX( 1, N )*NB >*/
lwkopt = max(1,*n) * nb;
/*< WORK( 1 ) = LWKOPT >*/
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
/*< LQUERY = ( LWORK.EQ.-1 ) >*/
lquery = *lwork == -1;
/*< IF( M.LT.0 ) THEN >*/
if (*m < 0) {
/*< INFO = -1 >*/
*info = -1;
/*< ELSE IF( N.LT.0 .OR. N.GT.M ) THEN >*/
} else if (*n < 0 || *n > *m) {
/*< INFO = -2 >*/
*info = -2;
/*< ELSE IF( K.LT.0 .OR. K.GT.N ) THEN >*/
} else if (*k < 0 || *k > *n) {
/*< INFO = -3 >*/
*info = -3;
/*< ELSE IF( LDA.LT.MAX( 1, M ) ) THEN >*/
} else if (*lda < max(1,*m)) {
/*< INFO = -5 >*/
*info = -5;
/*< ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN >*/
} else if (*lwork < max(1,*n) && ! lquery) {
/*< INFO = -8 >*/
*info = -8;
/*< END IF >*/
}
/*< IF( INFO.NE.0 ) THEN >*/
if (*info != 0) {
/*< CALL XERBLA( 'ZUNGQR', -INFO ) >*/
i__1 = -(*info);
xerbla_("ZUNGQR", &i__1, (ftnlen)6);
/*< RETURN >*/
return 0;
/*< ELSE IF( LQUERY ) THEN >*/
} else if (lquery) {
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/* Quick return if possible */
/*< IF( N.LE.0 ) THEN >*/
if (*n <= 0) {
/*< WORK( 1 ) = 1 >*/
work[1].r = 1., work[1].i = 0.;
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/*< NBMIN = 2 >*/
nbmin = 2;
/*< NX = 0 >*/
nx = 0;
/*< IWS = N >*/
iws = *n;
/*< IF( NB.GT.1 .AND. NB.LT.K ) THEN >*/
if (nb > 1 && nb < *k) {
/* Determine when to cross over from blocked to unblocked code. */
/*< NX = MAX( 0, ILAENV( 3, 'ZUNGQR', ' ', M, N, K, -1 ) ) >*/
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "ZUNGQR", " ", m, n, k, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
/*< IF( NX.LT.K ) THEN >*/
if (nx < *k) {
/* Determine if workspace is large enough for blocked code. */
/*< LDWORK = N >*/
ldwork = *n;
/*< IWS = LDWORK*NB >*/
iws = ldwork * nb;
/*< IF( LWORK.LT.IWS ) THEN >*/
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduce NB and */
/* determine the minimum value of NB. */
/*< NB = LWORK / LDWORK >*/
nb = *lwork / ldwork;
/*< NBMIN = MAX( 2, ILAENV( 2, 'ZUNGQR', ' ', M, N, K, -1 ) ) >*/
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "ZUNGQR", " ", m, n, k, &c_n1,
(ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
/*< END IF >*/
}
/*< END IF >*/
}
/*< END IF >*/
}
/*< IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN >*/
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 >*/
ki = (*k - nx - 1) / nb * nb;
/*< KK = MIN( K, KI+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. */
/*< DO 20 J = KK + 1, N >*/
i__1 = *n;
for (j = kk + 1; j <= i__1; ++j) {
/*< DO 10 I = 1, KK >*/
i__2 = kk;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< A( I, J ) = ZERO >*/
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/*< 10 CONTINUE >*/
/* L10: */
}
/*< 20 CONTINUE >*/
/* L20: */
}
/*< ELSE >*/
} else {
/*< KK = 0 >*/
kk = 0;
/*< END IF >*/
}
/* Use unblocked code for the last or only block. */
/*< >*/
if (kk < *n) {
i__1 = *m - kk;
i__2 = *n - kk;
i__3 = *k - kk;
zung2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, &
tau[kk + 1], &work[1], &iinfo);
}
/*< IF( KK.GT.0 ) THEN >*/
if (kk > 0) {
/* Use blocked code */
/*< DO 50 I = KI + 1, 1, -NB >*/
i__1 = -nb;
for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
/*< IB = MIN( NB, K-I+1 ) >*/
/* Computing MIN */
i__2 = nb, i__3 = *k - i__ + 1;
ib = min(i__2,i__3);
/*< IF( I+IB.LE.N ) THEN >*/
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;
zlarft_("Forward", "Columnwise", &i__2, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7,
(ftnlen)10);
/* Apply H to A(i:m,i+ib:n) from the left */
/*< >*/
i__2 = *m - i__ + 1;
i__3 = *n - i__ - ib + 1;
zlarfb_("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, (ftnlen)4, (ftnlen)12, (ftnlen)
7, (ftnlen)10);
/*< END IF >*/
}
/* Apply H to rows i:m of current block */
/*< >*/
i__2 = *m - i__ + 1;
zung2r_(&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 */
/*< DO 40 J = I, I + IB - 1 >*/
i__2 = i__ + ib - 1;
for (j = i__; j <= i__2; ++j) {
/*< DO 30 L = 1, I - 1 >*/
i__3 = i__ - 1;
for (l = 1; l <= i__3; ++l) {
/*< A( L, J ) = ZERO >*/
i__4 = l + j * a_dim1;
a[i__4].r = 0., a[i__4].i = 0.;
/*< 30 CONTINUE >*/
/* L30: */
}
/*< 40 CONTINUE >*/
/* L40: */
}
/*< 50 CONTINUE >*/
/* L50: */
}
/*< END IF >*/
}
/*< WORK( 1 ) = IWS >*/
work[1].r = (doublereal) iws, work[1].i = 0.;
/*< RETURN >*/
return 0;
/* End of ZUNGQR */
/*< END >*/
} /* zungqr_ */
/* Subroutine */ int zunmlq_(char *side, char *trans, integer *m, integer *n,
integer *k, doublecomplex *a, integer *lda, doublecomplex *tau,
doublecomplex *c__, integer *ldc, doublecomplex *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__;
#ifdef LAPACK_DISABLE_MEMORY_HOGS
doublecomplex t[1] /* was [65][64] */;
/** This function uses too much memory, so we stopped allocating the memory
* above and assert false here. */
assert(0 && "zunmlq_ was called. This function allocates too much"
" memory and has been disabled.");
#else
doublecomplex t[4160] /* was [65][64] */;
#endif
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 zunml2_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
logical notran;
integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
char transt[1];
integer 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 */
/* ======= */
/* ZUNMLQ overwrites the general complex M-by-N matrix C with */
/* SIDE = 'L' SIDE = 'R' */
/* TRANS = 'N': Q * C C * Q */
/* TRANS = 'C': Q**H * C C * Q**H */
/* where Q is a complex unitary matrix defined as the product of k */
/* elementary reflectors */
/* Q = H(k)' . . . H(2)' H(1)' */
/* as returned by ZGELQF. 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**H from the Left; */
/* = 'R': apply Q or Q**H from the Right. */
/* TRANS (input) CHARACTER*1 */
/* = 'N': No transpose, apply Q; */
/* = 'C': Conjugate transpose, apply Q**H. */
/* 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) COMPLEX*16 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 */
/* ZGELQF 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) COMPLEX*16 array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by ZGELQF. */
/* C (input/output) COMPLEX*16 array, dimension (LDC,N) */
/* On entry, the M-by-N matrix C. */
/* On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. */
/* LDC (input) INTEGER */
/* The leading dimension of the array C. LDC >= max(1,M). */
/* WORK (workspace/output) COMPLEX*16 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 = *n;
} else {
nq = *n;
nw = *m;
}
if (! left && ! lsame_(side, "R")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "C")) {
*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, "ZUNMLQ", ch__1, m, n, k, &c_n1);
nb = min(i__1,i__2);
lwkopt = max(1,nw) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNMLQ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || *k == 0) {
work[1].r = 1., work[1].i = 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, "ZUNMLQ", ch__1, m, n, k, &c_n1);
nbmin = max(i__1,i__2);
}
} else {
iws = nw;
}
if (nb < nbmin || nb >= *k) {
/* Use unblocked code */
zunml2_(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 = 'C';
} 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;
zlarft_("Forward", "Rowwise", &i__4, &ib, &a[i__ + i__ * a_dim1],
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' */
zlarfb_(side, transt, "Forward", "Rowwise", &mi, &ni, &ib, &a[i__
+ i__ * a_dim1], lda, t, &c__65, &c__[ic + jc * c_dim1],
ldc, &work[1], &ldwork);
/* L10: */
}
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
return 0;
/* End of ZUNMLQ */
} /* zunmlq_ */
/* Subroutine */ int zgeqrf_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
real r__1;
/* Local variables */
integer i__, j, k, ib, nb, nt, nx, iws;
extern doublereal sceil_(real *);
integer nbmin, iinfo;
extern /* Subroutine */ int zgeqr2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *), xerbla_(
char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
integer lbwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
integer llwork, lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* March 2008 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGEQRF computes a QR factorization of a real M-by-N matrix A: */
/* A = Q * R. */
/* This is the left-looking Level 3 BLAS version of the algorithm. */
/* 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) COMPLEX*16 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) COMPLEX*16 array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). */
/* WORK (workspace/output) COMPLEX*16 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. The dimension can be divided into three parts. */
/* 1) The part for the triangular factor T. If the very last T is not bigger */
/* than any of the rest, then this part is NB x ceiling(K/NB), otherwise, */
/* NB x (K-NT), where K = min(M,N) and NT is the dimension of the very last T */
/* 2) The part for the very last T when T is bigger than any of the rest T. */
/* The size of this part is NT x NT, where NT = K - ceiling ((K-NX)/NB) x NB, */
/* where K = min(M,N), NX is calculated by */
/* NX = MAX( 0, ILAENV( 3, 'ZGEQRF', ' ', M, N, -1, -1 ) ) */
/* 3) The part for dlarfb is of size max((N-M)*K, (N-M)*NB, K*NB, NB*NB) */
/* So LWORK = part1 + part2 + part3 */
/* 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(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). */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nbmin = 2;
nx = 0;
iws = *n;
k = min(*m,*n);
nb = ilaenv_(&c__1, "ZGEQRF", " ", m, n, &c_n1, &c_n1);
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, "ZGEQRF", " ", m, n, &c_n1, &c_n1);
nx = max(i__1,i__2);
}
/* Get NT, the size of the very last T, which is the left-over from in-between K-NX and K to K, eg.: */
/* NB=3 2NB=6 K=10 */
/* | | | */
/* 1--2--3--4--5--6--7--8--9--10 */
/* | \________/ */
/* K-NX=5 NT=4 */
/* So here 4 x 4 is the last T stored in the workspace */
r__1 = (real) (k - nx) / (real) nb;
nt = k - sceil_(&r__1) * nb;
/* optimal workspace = space for dlarfb + space for normal T's + space for the last T */
/* Computing MAX */
/* Computing MAX */
i__3 = (*n - *m) * k, i__4 = (*n - *m) * nb;
/* Computing MAX */
i__5 = k * nb, i__6 = nb * nb;
i__1 = max(i__3,i__4), i__2 = max(i__5,i__6);
llwork = max(i__1,i__2);
r__1 = (real) llwork / (real) nb;
llwork = sceil_(&r__1);
if (nt > nb) {
lbwork = k - nt;
/* Optimal workspace for dlarfb = MAX(1,N)*NT */
lwkopt = (lbwork + llwork) * nb;
i__1 = lwkopt + nt * nt;
work[1].r = (doublereal) i__1, work[1].i = 0.;
} else {
r__1 = (real) k / (real) nb;
lbwork = sceil_(&r__1) * nb;
lwkopt = (lbwork + llwork - nb) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
}
/* Test the input arguments */
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,*n) && ! lquery) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEQRF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (k == 0) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
if (nb > 1 && nb < k) {
if (nx < k) {
/* Determine if workspace is large enough for blocked code. */
if (nt <= nb) {
iws = (lbwork + llwork - nb) * nb;
} else {
iws = (lbwork + llwork) * nb + nt * nt;
}
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduce NB and */
/* determine the minimum value of NB. */
if (nt <= nb) {
nb = *lwork / (llwork + (lbwork - nb));
} else {
nb = (*lwork - nt * nt) / (lbwork + llwork);
}
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "ZGEQRF", " ", 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);
/* Update the current column using old T's */
i__3 = i__ - nb;
i__4 = nb;
for (j = 1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
/* Apply H' to A(J:M,I:I+IB-1) from the left */
i__5 = *m - j + 1;
zlarfb_("Left", "Transpose", "Forward", "Columnwise", &i__5, &
ib, &nb, &a[j + j * a_dim1], lda, &work[j], &lbwork, &
a[j + i__ * a_dim1], lda, &work[lbwork * nb + nt * nt
+ 1], &ib);
/* L20: */
}
/* Compute the QR factorization of the current block */
/* A(I:M,I:I+IB-1) */
i__4 = *m - i__ + 1;
zgeqr2_(&i__4, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[
lbwork * nb + nt * nt + 1], &iinfo);
if (i__ + ib <= *n) {
/* Form the triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
i__4 = *m - i__ + 1;
zlarft_("Forward", "Columnwise", &i__4, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[i__], &lbwork);
}
/* L10: */
}
} else {
i__ = 1;
}
/* Use unblocked code to factor the last or only block. */
if (i__ <= k) {
if (i__ != 1) {
i__2 = i__ - nb;
i__1 = nb;
for (j = 1; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
/* Apply H' to A(J:M,I:K) from the left */
i__4 = *m - j + 1;
i__3 = k - i__ + 1;
i__5 = k - i__ + 1;
zlarfb_("Left", "Transpose", "Forward", "Columnwise", &i__4, &
i__3, &nb, &a[j + j * a_dim1], lda, &work[j], &lbwork,
&a[j + i__ * a_dim1], lda, &work[lbwork * nb + nt *
nt + 1], &i__5);
/* L30: */
}
i__1 = *m - i__ + 1;
i__2 = k - i__ + 1;
zgeqr2_(&i__1, &i__2, &a[i__ + i__ * a_dim1], lda, &tau[i__], &
work[lbwork * nb + nt * nt + 1], &iinfo);
} else {
/* Use unblocked code to factor the last or only block. */
i__1 = *m - i__ + 1;
i__2 = *n - i__ + 1;
zgeqr2_(&i__1, &i__2, &a[i__ + i__ * a_dim1], lda, &tau[i__], &
work[1], &iinfo);
}
}
/* Apply update to the column M+1:N when N > M */
if (*m < *n && i__ != 1) {
/* Form the last triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
if (nt <= nb) {
i__1 = *m - i__ + 1;
i__2 = k - i__ + 1;
zlarft_("Forward", "Columnwise", &i__1, &i__2, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[i__], &lbwork);
} else {
i__1 = *m - i__ + 1;
i__2 = k - i__ + 1;
zlarft_("Forward", "Columnwise", &i__1, &i__2, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[lbwork * nb + 1], &nt);
}
/* Apply H' to A(1:M,M+1:N) from the left */
i__1 = k - nx;
i__2 = nb;
for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Computing MIN */
i__4 = k - j + 1;
ib = min(i__4,nb);
i__4 = *m - j + 1;
i__3 = *n - *m;
i__5 = *n - *m;
zlarfb_("Left", "Transpose", "Forward", "Columnwise", &i__4, &
i__3, &ib, &a[j + j * a_dim1], lda, &work[j], &lbwork, &a[
j + (*m + 1) * a_dim1], lda, &work[lbwork * nb + nt * nt
+ 1], &i__5);
/* L40: */
}
if (nt <= nb) {
i__2 = *m - j + 1;
i__1 = *n - *m;
i__4 = k - j + 1;
i__3 = *n - *m;
zlarfb_("Left", "Transpose", "Forward", "Columnwise", &i__2, &
i__1, &i__4, &a[j + j * a_dim1], lda, &work[j], &lbwork, &
a[j + (*m + 1) * a_dim1], lda, &work[lbwork * nb + nt *
nt + 1], &i__3);
} else {
i__2 = *m - j + 1;
i__1 = *n - *m;
i__4 = k - j + 1;
i__3 = *n - *m;
zlarfb_("Left", "Transpose", "Forward", "Columnwise", &i__2, &
i__1, &i__4, &a[j + j * a_dim1], lda, &work[lbwork * nb +
1], &nt, &a[j + (*m + 1) * a_dim1], lda, &work[lbwork *
nb + nt * nt + 1], &i__3);
}
}
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZGEQRF */
} /* zgeqrf_ */
/*< SUBROUTINE ZGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) >*/
/* Subroutine */ int zgeqrf_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublecomplex *tau, doublecomplex *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;
extern /* Subroutine */ int zgeqr2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *), xerbla_(
char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen);
integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, ftnlen, ftnlen);
integer lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2006 */
/* .. Scalar Arguments .. */
/*< INTEGER INFO, LDA, LWORK, M, N >*/
/* .. */
/* .. Array Arguments .. */
/*< COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* ZGEQRF computes a QR factorization of a complex 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) COMPLEX*16 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 unitary 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) COMPLEX*16 array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). */
/* WORK (workspace/output) COMPLEX*16 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 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 complex scalar, and v is a complex vector with */
/* v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), */
/* and tau in TAU(i). */
/* ===================================================================== */
/* .. Local Scalars .. */
/*< LOGICAL LQUERY >*/
/*< >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL XERBLA, ZGEQR2, ZLARFB, ZLARFT >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC MAX, MIN >*/
/* .. */
/* .. External Functions .. */
/*< INTEGER ILAENV >*/
/*< EXTERNAL ILAENV >*/
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/*< INFO = 0 >*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
/*< NB = ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 ) >*/
nb = ilaenv_(&c__1, "ZGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)
1);
/*< LWKOPT = N*NB >*/
lwkopt = *n * nb;
/*< WORK( 1 ) = LWKOPT >*/
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
/*< LQUERY = ( LWORK.EQ.-1 ) >*/
lquery = *lwork == -1;
/*< IF( M.LT.0 ) THEN >*/
if (*m < 0) {
/*< INFO = -1 >*/
*info = -1;
/*< ELSE IF( N.LT.0 ) THEN >*/
} else if (*n < 0) {
/*< INFO = -2 >*/
*info = -2;
/*< ELSE IF( LDA.LT.MAX( 1, M ) ) THEN >*/
} else if (*lda < max(1,*m)) {
/*< INFO = -4 >*/
*info = -4;
/*< ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN >*/
} else if (*lwork < max(1,*n) && ! lquery) {
/*< INFO = -7 >*/
*info = -7;
/*< END IF >*/
}
/*< IF( INFO.NE.0 ) THEN >*/
if (*info != 0) {
/*< CALL XERBLA( 'ZGEQRF', -INFO ) >*/
i__1 = -(*info);
xerbla_("ZGEQRF", &i__1, (ftnlen)6);
/*< RETURN >*/
return 0;
/*< ELSE IF( LQUERY ) THEN >*/
} else if (lquery) {
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/* Quick return if possible */
/*< K = MIN( M, N ) >*/
k = min(*m,*n);
/*< IF( K.EQ.0 ) THEN >*/
if (k == 0) {
/*< WORK( 1 ) = 1 >*/
work[1].r = 1., work[1].i = 0.;
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/*< NBMIN = 2 >*/
nbmin = 2;
/*< NX = 0 >*/
nx = 0;
/*< IWS = N >*/
iws = *n;
/*< IF( NB.GT.1 .AND. NB.LT.K ) THEN >*/
if (nb > 1 && nb < k) {
/* Determine when to cross over from blocked to unblocked code. */
/*< NX = MAX( 0, ILAENV( 3, 'ZGEQRF', ' ', M, N, -1, -1 ) ) >*/
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "ZGEQRF", " ", m, n, &c_n1, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
/*< IF( NX.LT.K ) THEN >*/
if (nx < k) {
/* Determine if workspace is large enough for blocked code. */
/*< LDWORK = N >*/
ldwork = *n;
/*< IWS = LDWORK*NB >*/
iws = ldwork * nb;
/*< IF( LWORK.LT.IWS ) THEN >*/
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduce NB and */
/* determine the minimum value of NB. */
/*< NB = LWORK / LDWORK >*/
nb = *lwork / ldwork;
/*< >*/
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "ZGEQRF", " ", m, n, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
/*< END IF >*/
}
/*< END IF >*/
}
/*< END IF >*/
}
/*< IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN >*/
if (nb >= nbmin && nb < k && nx < k) {
/* Use blocked code initially */
/*< DO 10 I = 1, K - NX, NB >*/
i__1 = k - nx;
i__2 = nb;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/*< IB = MIN( K-I+1, 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;
zgeqr2_(&i__3, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[
1], &iinfo);
/*< IF( I+IB.LE.N ) THEN >*/
if (i__ + ib <= *n) {
/* Form the triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
/*< >*/
i__3 = *m - i__ + 1;
zlarft_("Forward", "Columnwise", &i__3, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7,
(ftnlen)10);
/* Apply H' to A(i:m,i+ib:n) from the left */
/*< >*/
i__3 = *m - i__ + 1;
i__4 = *n - i__ - ib + 1;
zlarfb_("Left", "Conjugate transpose", "Forward", "Columnwise"
, &i__3, &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &
work[1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda,
&work[ib + 1], &ldwork, (ftnlen)4, (ftnlen)19, (
ftnlen)7, (ftnlen)10);
/*< END IF >*/
}
/*< 10 CONTINUE >*/
/* L10: */
}
/*< ELSE >*/
} else {
/*< I = 1 >*/
i__ = 1;
/*< END IF >*/
}
/* Use unblocked code to factor the last or only block. */
/*< >*/
if (i__ <= k) {
i__2 = *m - i__ + 1;
i__1 = *n - i__ + 1;
zgeqr2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1]
, &iinfo);
}
/*< WORK( 1 ) = IWS >*/
work[1].r = (doublereal) iws, work[1].i = 0.;
/*< RETURN >*/
return 0;
/* End of ZGEQRF */
/*< END >*/
} /* zgeqrf_ */
/* Subroutine */ int zgeqrf_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublecomplex *tau, doublecomplex *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
=======
ZGEQRF computes a QR factorization of a complex 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) COMPLEX*16 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 unitary 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) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) COMPLEX*16 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 complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
=====================================================================
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 zgeqr2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *);
static integer ib, nb, nx;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer 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_("ZGEQRF", &i__1);
return 0;
}
/* Quick return if possible */
k = min(*m,*n);
if (k == 0) {
WORK(1).r = 1., WORK(1).i = 0.;
return 0;
}
/* Determine the block size. */
nb = ilaenv_(&c__1, "ZGEQRF", " ", 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, "ZGEQRF", " ", 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, "ZGEQRF", " ", 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;
zgeqr2_(&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;
zlarft_("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;
zlarfb_("Left", "Conjugate 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;
zgeqr2_(&i__2, &i__1, &A(i,i), lda, &TAU(i), &WORK(1), &
iinfo);
}
WORK(1).r = (doublereal) iws, WORK(1).i = 0.;
return 0;
/* End of ZGEQRF */
} /* zgeqrf_ */
int zgehrd_(int *n, int *ilo, int *ihi,
doublecomplex *a, int *lda, doublecomplex *tau, doublecomplex *
work, int *lwork, int *info)
{
/* System generated locals */
int a_dim1, a_offset, i__1, i__2, i__3, i__4;
doublecomplex z__1;
/* Local variables */
int i__, j;
doublecomplex t[4160] /* was [65][64] */;
int ib;
doublecomplex ei;
int nb, nh, nx, iws, nbmin, iinfo;
extern int zgemm_(char *, char *, int *, int *,
int *, doublecomplex *, doublecomplex *, int *,
doublecomplex *, int *, doublecomplex *, doublecomplex *,
int *), ztrmm_(char *, char *, char *, char *,
int *, int *, doublecomplex *, doublecomplex *, int *
, doublecomplex *, int *),
zaxpy_(int *, doublecomplex *, doublecomplex *, int *,
doublecomplex *, int *), zgehd2_(int *, int *,
int *, doublecomplex *, int *, doublecomplex *,
doublecomplex *, int *), zlahr2_(int *, int *,
int *, doublecomplex *, int *, doublecomplex *,
doublecomplex *, int *, doublecomplex *, int *), xerbla_(
char *, int *);
extern int ilaenv_(int *, char *, char *, int *, int *,
int *, int *);
extern int zlarfb_(char *, char *, char *, char *,
int *, int *, int *, doublecomplex *, int *,
doublecomplex *, int *, doublecomplex *, int *,
doublecomplex *, 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 */
/* ======= */
/* ZGEHRD reduces a complex general matrix A to upper Hessenberg form H by */
/* an unitary similarity transformation: Q' * A * Q = H . */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* ILO (input) INTEGER */
/* IHI (input) INTEGER */
/* It is assumed that A is already upper triangular in rows */
/* and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally */
/* set by a previous call to ZGEBAL; otherwise they should be */
/* set to 1 and N respectively. See Further Details. */
/* 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the N-by-N general matrix to be reduced. */
/* On exit, the upper triangle and the first subdiagonal of A */
/* are overwritten with the upper Hessenberg matrix H, and the */
/* elements below the first subdiagonal, with the array TAU, */
/* represent the unitary matrix Q as a product of elementary */
/* reflectors. See Further Details. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= MAX(1,N). */
/* TAU (output) COMPLEX*16 array, dimension (N-1) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to */
/* zero. */
/* WORK (workspace/output) COMPLEX*16 array, dimension (LWORK) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The length 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 had an illegal value. */
/* Further Details */
/* =============== */
/* The matrix Q is represented as a product of (ihi-ilo) elementary */
/* reflectors */
/* Q = H(ilo) H(ilo+1) . . . H(ihi-1). */
/* Each H(i) has the form */
/* H(i) = I - tau * v * v' */
/* where tau is a complex scalar, and v is a complex vector with */
/* v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on */
/* exit in A(i+2:ihi,i), and tau in TAU(i). */
/* The contents of A are illustrated by the following example, with */
/* n = 7, ilo = 2 and ihi = 6: */
/* on entry, on exit, */
/* ( a a a a a a a ) ( a a h h h h a ) */
/* ( a a a a a a ) ( a h h h h a ) */
/* ( a a a a a a ) ( h h h h h h ) */
/* ( a a a a a a ) ( v2 h h h h h ) */
/* ( a a a a a a ) ( v2 v3 h h h h ) */
/* ( a a a a a a ) ( v2 v3 v4 h h h ) */
/* ( a ) ( a ) */
/* where a denotes an element of the original matrix A, h denotes a */
/* modified element of the upper Hessenberg matrix H, and vi denotes an */
/* element of the vector defining H(i). */
/* This file is a slight modification of LAPACK-3.0's ZGEHRD */
/* subroutine incorporating improvements proposed by Quintana-Orti and */
/* Van de Geijn (2005). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
/* Computing MIN */
i__1 = 64, i__2 = ilaenv_(&c__1, "ZGEHRD", " ", n, ilo, ihi, &c_n1);
nb = MIN(i__1,i__2);
lwkopt = *n * nb;
work[1].r = (double) lwkopt, work[1].i = 0.;
lquery = *lwork == -1;
if (*n < 0) {
*info = -1;
} else if (*ilo < 1 || *ilo > MAX(1,*n)) {
*info = -2;
} else if (*ihi < MIN(*ilo,*n) || *ihi > *n) {
*info = -3;
} else if (*lda < MAX(1,*n)) {
*info = -5;
} else if (*lwork < MAX(1,*n) && ! lquery) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEHRD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Set elements 1:ILO-1 and IHI:N-1 of TAU to zero */
i__1 = *ilo - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
tau[i__2].r = 0., tau[i__2].i = 0.;
/* L10: */
}
i__1 = *n - 1;
for (i__ = MAX(1,*ihi); i__ <= i__1; ++i__) {
i__2 = i__;
tau[i__2].r = 0., tau[i__2].i = 0.;
/* L20: */
}
/* Quick return if possible */
nh = *ihi - *ilo + 1;
if (nh <= 1) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
/* Determine the block size */
/* Computing MIN */
i__1 = 64, i__2 = ilaenv_(&c__1, "ZGEHRD", " ", n, ilo, ihi, &c_n1);
nb = MIN(i__1,i__2);
nbmin = 2;
iws = 1;
if (nb > 1 && nb < nh) {
/* Determine when to cross over from blocked to unblocked code */
/* (last block is always handled by unblocked code) */
/* Computing MAX */
i__1 = nb, i__2 = ilaenv_(&c__3, "ZGEHRD", " ", n, ilo, ihi, &c_n1);
nx = MAX(i__1,i__2);
if (nx < nh) {
/* Determine if workspace is large enough for blocked code */
iws = *n * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: determine the */
/* minimum value of NB, and reduce NB or force use of */
/* unblocked code */
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "ZGEHRD", " ", n, ilo, ihi, &
c_n1);
nbmin = MAX(i__1,i__2);
if (*lwork >= *n * nbmin) {
nb = *lwork / *n;
} else {
nb = 1;
}
}
}
}
ldwork = *n;
if (nb < nbmin || nb >= nh) {
/* Use unblocked code below */
i__ = *ilo;
} else {
/* Use blocked code */
i__1 = *ihi - 1 - nx;
i__2 = nb;
for (i__ = *ilo; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__3 = nb, i__4 = *ihi - i__;
ib = MIN(i__3,i__4);
/* Reduce columns i:i+ib-1 to Hessenberg form, returning the */
/* matrices V and T of the block reflector H = I - V*T*V' */
/* which performs the reduction, and also the matrix Y = A*V*T */
zlahr2_(ihi, &i__, &ib, &a[i__ * a_dim1 + 1], lda, &tau[i__], t, &
c__65, &work[1], &ldwork);
/* Apply the block reflector H to A(1:ihi,i+ib:ihi) from the */
/* right, computing A := A - Y * V'. V(i+ib,ib-1) must be set */
/* to 1 */
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
ei.r = a[i__3].r, ei.i = a[i__3].i;
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
a[i__3].r = 1., a[i__3].i = 0.;
i__3 = *ihi - i__ - ib + 1;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "Conjugate transpose", ihi, &i__3, &ib, &
z__1, &work[1], &ldwork, &a[i__ + ib + i__ * a_dim1], lda,
&c_b2, &a[(i__ + ib) * a_dim1 + 1], lda);
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
a[i__3].r = ei.r, a[i__3].i = ei.i;
/* Apply the block reflector H to A(1:i,i+1:i+ib-1) from the */
/* right */
i__3 = ib - 1;
ztrmm_("Right", "Lower", "Conjugate transpose", "Unit", &i__, &
i__3, &c_b2, &a[i__ + 1 + i__ * a_dim1], lda, &work[1], &
ldwork);
i__3 = ib - 2;
for (j = 0; j <= i__3; ++j) {
z__1.r = -1., z__1.i = -0.;
zaxpy_(&i__, &z__1, &work[ldwork * j + 1], &c__1, &a[(i__ + j
+ 1) * a_dim1 + 1], &c__1);
/* L30: */
}
/* Apply the block reflector H to A(i+1:ihi,i+ib:n) from the */
/* left */
i__3 = *ihi - i__;
i__4 = *n - i__ - ib + 1;
zlarfb_("Left", "Conjugate transpose", "Forward", "Columnwise", &
i__3, &i__4, &ib, &a[i__ + 1 + i__ * a_dim1], lda, t, &
c__65, &a[i__ + 1 + (i__ + ib) * a_dim1], lda, &work[1], &
ldwork);
/* L40: */
}
}
/* Use unblocked code to reduce the rest of the matrix */
zgehd2_(n, &i__, ihi, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
work[1].r = (double) iws, work[1].i = 0.;
return 0;
/* End of ZGEHRD */
} /* zgehrd_ */
