/* Subroutine */ int cungrq_(integer *m, integer *n, integer *k, complex *a,
integer *lda, complex *tau, complex *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
=======
CUNGRQ 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 CGERQF.
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 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 CGERQF 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 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGERQF.
WORK (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,M).
For optimum performance LWORK >= M*NB, where NB is the
optimal blocksize.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
=====================================================================
Test the input arguments
Parameter adjustments
Function Body */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
/* Local variables */
static integer i, j, l, nbmin, iinfo;
extern /* Subroutine */ int cungr2_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *);
static integer ib, nb, ii, kk;
extern /* Subroutine */ int clarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, complex *, integer *, complex *,
integer *, complex *, integer *, complex *, integer *);
static integer nx;
extern /* Subroutine */ int clarft_(char *, char *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static integer ldwork, iws;
#define TAU(I) tau[(I)-1]
#define WORK(I) work[(I)-1]
#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < *m) {
*info = -2;
} else if (*k < 0 || *k > *m) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*lwork < max(1,*m)) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CUNGRQ", &i__1);
return 0;
}
/* Quick return if possible */
if (*m <= 0) {
WORK(1).r = 1.f, WORK(1).i = 0.f;
return 0;
}
/* Determine the block size. */
nb = ilaenv_(&c__1, "CUNGRQ", " ", m, n, k, &c_n1, 6L, 1L);
nbmin = 2;
nx = 0;
iws = *m;
if (nb > 1 && nb < *k) {
/* Determine when to cross over from blocked to unblocked code.
Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "CUNGRQ", " ", m, n, k, &c_n1, 6L, 1L)
;
nx = max(i__1,i__2);
if (nx < *k) {
/* Determine if workspace is large enough for blocked co
de. */
ldwork = *m;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduc
e NB and
determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "CUNGRQ", " ", m, n, k, &c_n1,
6L, 1L);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < *k && nx < *k) {
/* Use blocked code after the first block.
The last kk rows are handled by the block method.
Computing MIN */
i__1 = *k, i__2 = (*k - nx + nb - 1) / nb * nb;
kk = min(i__1,i__2);
/* Set A(1:m-kk,n-kk+1:n) to zero. */
i__1 = *n;
for (j = *n - kk + 1; j <= *n; ++j) {
i__2 = *m - kk;
for (i = 1; i <= *m-kk; ++i) {
i__3 = i + j * a_dim1;
A(i,j).r = 0.f, A(i,j).i = 0.f;
/* L10: */
}
/* L20: */
}
} else {
kk = 0;
}
/* Use unblocked code for the first or only block. */
i__1 = *m - kk;
i__2 = *n - kk;
i__3 = *k - kk;
cungr2_(&i__1, &i__2, &i__3, &A(1,1), lda, &TAU(1), &WORK(1), &iinfo)
;
if (kk > 0) {
/* Use blocked code */
i__1 = *k;
i__2 = nb;
for (i = *k - kk + 1; nb < 0 ? i >= *k : i <= *k; i += nb) {
/* Computing MIN */
i__3 = nb, i__4 = *k - i + 1;
ib = min(i__3,i__4);
ii = *m - *k + i;
if (ii > 1) {
/* Form the triangular factor of the block reflec
tor
H = H(i+ib-1) . . . H(i+1) H(i) */
i__3 = *n - *k + i + ib - 1;
clarft_("Backward", "Rowwise", &i__3, &ib, &A(ii,1),
lda, &TAU(i), &WORK(1), &ldwork);
/* Apply H' to A(1:m-k+i-1,1:n-k+i+ib-1) from the
right */
i__3 = ii - 1;
i__4 = *n - *k + i + ib - 1;
clarfb_("Right", "Conjugate transpose", "Backward", "Rowwise",
&i__3, &i__4, &ib, &A(ii,1), lda, &WORK(1), &
ldwork, &A(1,1), lda, &WORK(ib + 1), &ldwork);
}
/* Apply H' to columns 1:n-k+i+ib-1 of current block */
i__3 = *n - *k + i + ib - 1;
cungr2_(&ib, &i__3, &ib, &A(ii,1), lda, &TAU(i), &WORK(1),
&iinfo);
/* Set columns n-k+i+ib:n of current block to zero */
i__3 = *n;
for (l = *n - *k + i + ib; l <= *n; ++l) {
i__4 = ii + ib - 1;
for (j = ii; j <= ii+ib-1; ++j) {
i__5 = j + l * a_dim1;
A(j,l).r = 0.f, A(j,l).i = 0.f;
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
WORK(1).r = (real) iws, WORK(1).i = 0.f;
return 0;
/* End of CUNGRQ */
} /* cungrq_ */
/* Subroutine */ int cunmql_(char *side, char *trans, integer *m, integer *n,
integer *k, complex *a, integer *lda, complex *tau, complex *c__,
integer *ldc, complex *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__;
complex t[4160] /* was [65][64] */;
integer i1, i2, i3, ib, nb, mi, ni, nq, nw, iws;
logical left;
extern logical lsame_(char *, char *);
integer nbmin, iinfo;
extern /* Subroutine */ int cunm2l_(char *, char *, integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *), clarfb_(char *, char *,
char *, char *, integer *, integer *, integer *, complex *,
integer *, complex *, integer *, complex *, integer *, complex *,
integer *), clarft_(char *, char *
, integer *, integer *, complex *, integer *, complex *, complex *
, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
logical notran;
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CUNMQL 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 CGEQLF. 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 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 */
/* CGEQLF 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 array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by CGEQLF. */
/* C (input/output) COMPLEX 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 array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. */
/* If SIDE = 'L', LWORK >= max(1,N); */
/* if SIDE = 'R', LWORK >= max(1,M). */
/* For optimum performance LWORK >= N*NB if SIDE = 'L', and */
/* LWORK >= M*NB if SIDE = 'R', where NB is the optimal */
/* blocksize. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
left = lsame_(side, "L");
notran = lsame_(trans, "N");
lquery = *lwork == -1;
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = *m;
nw = max(1,*n);
} else {
nq = *n;
nw = max(1,*m);
}
if (! left && ! lsame_(side, "R")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "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;
}
if (*info == 0) {
if (*m == 0 || *n == 0) {
lwkopt = 1;
} else {
/* Determine the block size. NB may be at most NBMAX, where */
/* NBMAX is used to define the local array T. */
/* Computing MIN */
/* Writing concatenation */
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
i__1 = 64, i__2 = ilaenv_(&c__1, "CUNMQL", ch__1, m, n, k, &c_n1);
nb = min(i__1,i__2);
lwkopt = nw * nb;
}
work[1].r = (real) lwkopt, work[1].i = 0.f;
if (*lwork < nw && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CUNMQL", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
return 0;
}
nbmin = 2;
ldwork = nw;
if (nb > 1 && nb < *k) {
iws = nw * nb;
if (*lwork < iws) {
nb = *lwork / ldwork;
/* Computing MAX */
/* Writing concatenation */
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
i__1 = 2, i__2 = ilaenv_(&c__2, "CUNMQL", ch__1, m, n, k, &c_n1);
nbmin = max(i__1,i__2);
}
} else {
iws = nw;
}
if (nb < nbmin || nb >= *k) {
/* Use unblocked code */
cunm2l_(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;
clarft_("Backward", "Columnwise", &i__4, &ib, &a[i__ * a_dim1 + 1]
, lda, &tau[i__], t, &c__65);
if (left) {
/* H or H' is applied to C(1:m-k+i+ib-1,1:n) */
mi = *m - *k + i__ + ib - 1;
} else {
/* H or H' is applied to C(1:m,1:n-k+i+ib-1) */
ni = *n - *k + i__ + ib - 1;
}
/* Apply H or H' */
clarfb_(side, trans, "Backward", "Columnwise", &mi, &ni, &ib, &a[
i__ * a_dim1 + 1], lda, t, &c__65, &c__[c_offset], ldc, &
work[1], &ldwork);
/* L10: */
}
}
work[1].r = (real) lwkopt, work[1].i = 0.f;
return 0;
/* End of CUNMQL */
} /* cunmql_ */
/* Subroutine */ int cgerqf_(integer *m, integer *n, complex *a, integer *lda,
complex *tau, complex *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
=======
CGERQF 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 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 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) COMPLEX 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(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).
=====================================================================
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 cgerq2_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *);
static integer ib, nb, ki, kk;
extern /* Subroutine */ int clarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, complex *, integer *, complex *,
integer *, complex *, integer *, complex *, integer *);
static integer mu, nu, nx;
extern /* Subroutine */ int clarft_(char *, char *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static integer ldwork, 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, "CGERQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)
1);
lwkopt = *m * nb;
work[1].r = (real) lwkopt, work[1].i = 0.f;
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_("CGERQF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
k = min(*m,*n);
if (k == 0) {
work[1].r = 1.f, work[1].i = 0.f;
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, "CGERQF", " ", 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, "CGERQF", " ", 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.
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;
cgerq2_(&ib, &i__3, &a_ref(*m - k + i__, 1), 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;
clarft_("Backward", "Rowwise", &i__3, &ib, &a_ref(*m - k +
i__, 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 = *m - k + i__ - 1;
i__4 = *n - k + i__ + ib - 1;
clarfb_("Right", "No transpose", "Backward", "Rowwise", &i__3,
&i__4, &ib, &a_ref(*m - k + i__, 1), 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) {
cgerq2_(&mu, &nu, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
}
work[1].r = (real) iws, work[1].i = 0.f;
return 0;
/* End of CGERQF */
} /* cgerqf_ */
/* Subroutine */
int cungqr_(integer *m, integer *n, integer *k, complex *a, integer *lda, complex *tau, complex *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 cung2r_(integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *), clarfb_( char *, char *, char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *), clarft_( char *, char *, integer *, integer *, complex *, integer *, complex *, complex *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK computational routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "CUNGQR", " ", m, n, k, &c_n1);
lwkopt = max(1,*n) * nb;
work[1].r = (real) lwkopt;
work[1].i = 0.f; // , expr subst
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_("CUNGQR", &i__1);
return 0;
}
else if (lquery)
{
return 0;
}
/* Quick return if possible */
if (*n <= 0)
{
work[1].r = 1.f;
work[1].i = 0.f; // , expr subst
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, "CUNGQR", " ", m, n, k, &c_n1); // , expr subst
nx = max(i__1,i__2);
if (nx < *k)
{
/* Determine if workspace is large enough for blocked code. */
ldwork = *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, "CUNGQR", " ", m, n, k, &c_n1); // , expr subst
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < *k && nx < *k)
{
/* Use blocked code after the last block. */
/* The first kk columns are handled by the block method. */
ki = (*k - nx - 1) / nb * nb;
/* Computing MIN */
i__1 = *k;
i__2 = ki + nb; // , expr subst
kk = min(i__1,i__2);
/* Set A(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.f;
a[i__3].i = 0.f; // , expr subst
/* 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;
cung2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, & tau[kk + 1], &work[1], &iinfo);
}
if (kk > 0)
{
/* Use blocked code */
i__1 = -nb;
for (i__ = ki + 1;
i__1 < 0 ? i__ >= 1 : i__ <= 1;
i__ += i__1)
{
/* Computing MIN */
i__2 = nb;
i__3 = *k - i__ + 1; // , expr subst
ib = min(i__2,i__3);
if (i__ + ib <= *n)
{
/* Form the triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
i__2 = *m - i__ + 1;
clarft_("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;
clarfb_("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;
cung2r_(&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.f;
a[i__4].i = 0.f; // , expr subst
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
work[1].r = (real) iws;
work[1].i = 0.f; // , expr subst
return 0;
/* End of CUNGQR */
}
/* Subroutine */ int cgerqf_(integer *m, integer *n, complex *a, integer *lda,
complex *tau, complex *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;
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* CGERQF 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 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 array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). */
/* WORK (workspace/output) COMPLEX 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). */
/* ===================================================================== */
/* 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, "CGERQF", " ", m, n, &c_n1, &c_n1);
lwkopt = *m * nb;
}
work[1].r = (real) lwkopt, work[1].i = 0.f;
if (*lwork < max(1,*m) && ! lquery) {
*info = -7;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGERQF", &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, "CGERQF", " ", 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, "CGERQF", " ", 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;
cgerq2_(&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;
clarft_("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;
clarfb_("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);
}
}
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) {
cgerq2_(&mu, &nu, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
}
work[1].r = (real) iws, work[1].i = 0.f;
return 0;
/* End of CGERQF */
} /* cgerqf_ */
/* Subroutine */ int cungql_(integer *m, integer *n, integer *k, complex *a,
integer *lda, complex *tau, complex *work, integer *lwork, integer *
info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
/* Local variables */
integer i__, j, l, ib, nb, kk, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int cung2l_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *), clarfb_(
char *, char *, char *, char *, integer *, integer *, integer *,
complex *, integer *, complex *, integer *, complex *, integer *,
complex *, integer *), clarft_(
char *, char *, integer *, integer *, complex *, integer *,
complex *, complex *, integer *), xerbla_(char *,
integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CUNGQL generates an M-by-N complex matrix Q with orthonormal columns, */
/* which is defined as the last N columns of a product of K elementary */
/* reflectors of order M */
/* Q = H(k) . . . H(2) H(1) */
/* as returned by CGEQLF. */
/* 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 array, dimension (LDA,N) */
/* On entry, the (n-k+i)-th column must contain the vector which */
/* defines the elementary reflector H(i), for i = 1,2,...,k, as */
/* returned by CGEQLF in the last k columns of its array */
/* argument A. */
/* On exit, the M-by-N matrix Q. */
/* LDA (input) INTEGER */
/* The first dimension of the array A. LDA >= max(1,M). */
/* TAU (input) COMPLEX array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by CGEQLF. */
/* WORK (workspace/output) COMPLEX 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;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0 || *n > *m) {
*info = -2;
} else if (*k < 0 || *k > *n) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
}
if (*info == 0) {
if (*n == 0) {
lwkopt = 1;
} else {
nb = ilaenv_(&c__1, "CUNGQL", " ", m, n, k, &c_n1);
lwkopt = *n * nb;
}
work[1].r = (real) lwkopt, work[1].i = 0.f;
if (*lwork < max(1,*n) && ! lquery) {
*info = -8;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CUNGQL", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n <= 0) {
return 0;
}
nbmin = 2;
nx = 0;
iws = *n;
if (nb > 1 && nb < *k) {
/* Determine when to cross over from blocked to unblocked code. */
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "CUNGQL", " ", 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, "CUNGQL", " ", m, n, k, &c_n1);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < *k && nx < *k) {
/* Use blocked code after the first block. */
/* The last kk columns are handled by the block method. */
/* Computing MIN */
i__1 = *k, i__2 = (*k - nx + nb - 1) / nb * nb;
kk = min(i__1,i__2);
/* Set A(m-kk+1:m,1:n-kk) to zero. */
i__1 = *n - kk;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = *m - kk + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L10: */
}
/* L20: */
}
} else {
kk = 0;
}
/* Use unblocked code for the first or only block. */
i__1 = *m - kk;
i__2 = *n - kk;
i__3 = *k - kk;
cung2l_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], &iinfo)
;
if (kk > 0) {
/* Use blocked code */
i__1 = *k;
i__2 = nb;
for (i__ = *k - kk + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
i__2) {
/* Computing MIN */
i__3 = nb, i__4 = *k - i__ + 1;
ib = min(i__3,i__4);
if (*n - *k + i__ > 1) {
/* Form the triangular factor of the block reflector */
/* H = H(i+ib-1) . . . H(i+1) H(i) */
i__3 = *m - *k + i__ + ib - 1;
clarft_("Backward", "Columnwise", &i__3, &ib, &a[(*n - *k +
i__) * a_dim1 + 1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left */
i__3 = *m - *k + i__ + ib - 1;
i__4 = *n - *k + i__ - 1;
clarfb_("Left", "No transpose", "Backward", "Columnwise", &
i__3, &i__4, &ib, &a[(*n - *k + i__) * a_dim1 + 1],
lda, &work[1], &ldwork, &a[a_offset], lda, &work[ib +
1], &ldwork);
}
/* Apply H to rows 1:m-k+i+ib-1 of current block */
i__3 = *m - *k + i__ + ib - 1;
cung2l_(&i__3, &ib, &ib, &a[(*n - *k + i__) * a_dim1 + 1], lda, &
tau[i__], &work[1], &iinfo);
/* Set rows m-k+i+ib:m of current block to zero */
i__3 = *n - *k + i__ + ib - 1;
for (j = *n - *k + i__; j <= i__3; ++j) {
i__4 = *m;
for (l = *m - *k + i__ + ib; l <= i__4; ++l) {
i__5 = l + j * a_dim1;
a[i__5].r = 0.f, a[i__5].i = 0.f;
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
work[1].r = (real) iws, work[1].i = 0.f;
return 0;
/* End of CUNGQL */
} /* cungql_ */
/* Subroutine */ int cungqr_(integer *m, integer *n, integer *k, complex *a,
integer *lda, complex *tau, complex *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
=======
CUNGQR 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 CGEQRF.
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 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 CGEQRF 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 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGEQRF.
WORK (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,N).
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
=====================================================================
Test the input arguments
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer i__, j, l, nbmin, iinfo;
extern /* Subroutine */ int cung2r_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *);
static integer ib, nb, ki, kk;
extern /* Subroutine */ int clarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, complex *, integer *, complex *,
integer *, complex *, integer *, complex *, integer *);
static integer nx;
extern /* Subroutine */ int clarft_(char *, char *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static integer ldwork, 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, "CUNGQR", " ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1);
lwkopt = max(1,*n) * nb;
work[1].r = (real) lwkopt, work[1].i = 0.f;
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_("CUNGQR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n <= 0) {
work[1].r = 1.f, work[1].i = 0.f;
return 0;
}
nbmin = 2;
nx = 0;
iws = *n;
if (nb > 1 && nb < *k) {
/* Determine when to cross over from blocked to unblocked code.
Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "CUNGQR", " ", m, n, k, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
if (nx < *k) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *n;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduce NB and
determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "CUNGQR", " ", 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 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 = a_subscr(i__, j);
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L10: */
}
/* L20: */
}
} else {
kk = 0;
}
/* Use unblocked code for the last or only block. */
if (kk < *n) {
i__1 = *m - kk;
i__2 = *n - kk;
i__3 = *k - kk;
cung2r_(&i__1, &i__2, &i__3, &a_ref(kk + 1, kk + 1), 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;
clarft_("Forward", "Columnwise", &i__2, &ib, &a_ref(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;
clarfb_("Left", "No transpose", "Forward", "Columnwise", &
i__2, &i__3, &ib, &a_ref(i__, i__), lda, &work[1], &
ldwork, &a_ref(i__, i__ + ib), lda, &work[ib + 1], &
ldwork);
}
/* Apply H to rows i:m of current block */
i__2 = *m - i__ + 1;
cung2r_(&i__2, &ib, &ib, &a_ref(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__2; ++j) {
i__3 = i__ - 1;
for (l = 1; l <= i__3; ++l) {
i__4 = a_subscr(l, j);
a[i__4].r = 0.f, a[i__4].i = 0.f;
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
work[1].r = (real) iws, work[1].i = 0.f;
return 0;
/* End of CUNGQR */
} /* cungqr_ */
/* Subroutine */
int cunmrq_(char *side, char *trans, integer *m, integer *n, integer *k, complex *a, integer *lda, complex *tau, complex *c__, integer *ldc, complex *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__4, i__5;
char ch__1[2];
/* Builtin functions */
/* Subroutine */
/* Local variables */
integer i__;
complex t[4160] /* was [65][64] */
;
integer i1, i2, i3, ib, nb, mi, ni, nq, nw, iws;
logical left;
extern logical lsame_(char *, char *);
integer nbmin, iinfo;
extern /* Subroutine */
int cunmr2_(char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, complex *, integer *), clarfb_(char *, char *, char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *), clarft_(char *, char * , integer *, integer *, complex *, integer *, complex *, complex * , integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
logical notran;
integer ldwork;
char transt[1];
integer lwkopt;
logical lquery;
/* -- LAPACK computational routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
left = lsame_(side, "L");
notran = lsame_(trans, "N");
lquery = *lwork == -1;
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left)
{
nq = *m;
nw = max(1,*n);
}
else
{
nq = *n;
nw = max(1,*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;
}
if (*info == 0)
{
if (*m == 0 || *n == 0)
{
lwkopt = 1;
}
else
{
/* Determine the block size. NB may be at most NBMAX, where */
/* NBMAX is used to define the local array T. */
/* Computing MIN */
i__1 = 64;
i__2 = ilaenv_(&c__1, "CUNMRQ", ch__1, m, n, k, &c_n1); // , expr subst
nb = min(i__1,i__2);
lwkopt = nw * nb;
}
work[1].r = (real) lwkopt;
work[1].i = 0.f; // , expr subst
if (*lwork < nw && ! lquery)
{
*info = -12;
}
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CUNMRQ", &i__1);
return 0;
}
else if (lquery)
{
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0)
{
return 0;
}
nbmin = 2;
ldwork = nw;
if (nb > 1 && nb < *k)
{
iws = nw * nb;
if (*lwork < iws)
{
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2;
i__2 = ilaenv_(&c__2, "CUNMRQ", ch__1, m, n, k, &c_n1); // , expr subst
nbmin = max(i__1,i__2);
}
}
else
{
iws = nw;
}
if (nb < nbmin || nb >= *k)
{
/* Use unblocked code */
cunmr2_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ c_offset], ldc, &work[1], &iinfo);
}
else
{
/* Use blocked code */
if (left && ! notran || ! left && notran)
{
i1 = 1;
i2 = *k;
i3 = nb;
}
else
{
i1 = (*k - 1) / nb * nb + 1;
i2 = 1;
i3 = -nb;
}
if (left)
{
ni = *n;
}
else
{
mi = *m;
}
if (notran)
{
*(unsigned char *)transt = '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; // , expr subst
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;
clarft_("Backward", "Rowwise", &i__4, &ib, &a[i__ + a_dim1], lda, &tau[i__], t, &c__65);
if (left)
{
/* H or H**H is applied to C(1:m-k+i+ib-1,1:n) */
mi = *m - *k + i__ + ib - 1;
}
else
{
/* H or H**H is applied to C(1:m,1:n-k+i+ib-1) */
ni = *n - *k + i__ + ib - 1;
}
/* Apply H or H**H */
clarfb_(side, transt, "Backward", "Rowwise", &mi, &ni, &ib, &a[ i__ + a_dim1], lda, t, &c__65, &c__[c_offset], ldc, &work[ 1], &ldwork);
/* L10: */
}
}
work[1].r = (real) lwkopt;
work[1].i = 0.f; // , expr subst
return 0;
/* End of CUNMRQ */
}
/* Subroutine */ int cunmrq_(char *side, char *trans, integer *m, integer *n,
integer *k, complex *a, integer *lda, complex *tau, complex *c__,
integer *ldc, complex *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
=======
CUNMRQ 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(1)' H(2)' . . . H(k)'
as returned by CGERQF. 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 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
CGERQF in the last k rows of its array argument A.
A is modified by the routine but restored on exit.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,K).
TAU (input) COMPLEX array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGERQF.
C (input/output) COMPLEX 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 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 complex t[4160] /* was [65][64] */;
extern logical lsame_(char *, char *);
static integer nbmin, iinfo, i1, i2, i3;
extern /* Subroutine */ int cunmr2_(char *, char *, integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *);
static integer ib, nb, mi, ni;
extern /* Subroutine */ int clarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, complex *, integer *, complex *,
integer *, complex *, integer *, complex *, integer *);
static integer nq, nw;
extern /* Subroutine */ int clarft_(char *, char *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static logical notran;
static integer ldwork;
static char transt[1];
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,*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, "CUNMRQ", 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 = (real) lwkopt, work[1].i = 0.f;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CUNMRQ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || *k == 0) {
work[1].r = 1.f, work[1].i = 0.f;
return 0;
}
nbmin = 2;
ldwork = nw;
if (nb > 1 && nb < *k) {
iws = nw * nb;
if (*lwork < iws) {
nb = *lwork / ldwork;
/* Computing MAX
Writing concatenation */
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
i__1 = 2, i__2 = ilaenv_(&c__2, "CUNMRQ", 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 */
cunmr2_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[
c_offset], ldc, &work[1], &iinfo);
} else {
/* Use blocked code */
if (left && ! notran || ! left && notran) {
i1 = 1;
i2 = *k;
i3 = nb;
} else {
i1 = (*k - 1) / nb * nb + 1;
i2 = 1;
i3 = -nb;
}
if (left) {
ni = *n;
} else {
mi = *m;
}
if (notran) {
*(unsigned char *)transt = '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+ib-1) . . . H(i+1) H(i) */
i__4 = nq - *k + i__ + ib - 1;
clarft_("Backward", "Rowwise", &i__4, &ib, &a_ref(i__, 1), lda, &
tau[i__], t, &c__65);
if (left) {
/* H or H' is applied to C(1:m-k+i+ib-1,1:n) */
mi = *m - *k + i__ + ib - 1;
} else {
/* H or H' is applied to C(1:m,1:n-k+i+ib-1) */
ni = *n - *k + i__ + ib - 1;
}
/* Apply H or H' */
clarfb_(side, transt, "Backward", "Rowwise", &mi, &ni, &ib, &
a_ref(i__, 1), lda, t, &c__65, &c__[c_offset], ldc, &work[
1], &ldwork);
/* L10: */
}
}
work[1].r = (real) lwkopt, work[1].i = 0.f;
return 0;
/* End of CUNMRQ */
} /* cunmrq_ */
/* Subroutine */ int cgelqf_(integer *m, integer *n, complex *a, integer *lda,
complex *tau, complex *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 cgelq2_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *), clarfb_(char *, char
*, char *, char *, integer *, integer *, integer *, complex *,
integer *, complex *, integer *, complex *, integer *, complex *,
integer *), clarft_(char *, char *
, integer *, integer *, complex *, integer *, complex *, complex *
, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGELQF 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 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 array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). */
/* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= max(1,M). */
/* For optimum performance LWORK >= M*NB, where NB is the */
/* optimal blocksize. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Further Details */
/* =============== */
/* The matrix Q is represented as a product of elementary reflectors */
/* Q = H(k)' . . . H(2)' H(1)', where k = min(m,n). */
/* Each H(i) has the form */
/* H(i) = I - tau * v * v' */
/* where tau is a 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). */
/* ===================================================================== */
/* .. 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, "CGELQF", " ", m, n, &c_n1, &c_n1);
lwkopt = *m * nb;
work[1].r = (real) lwkopt, work[1].i = 0.f;
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_("CGELQF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
k = min(*m,*n);
if (k == 0) {
work[1].r = 1.f, work[1].i = 0.f;
return 0;
}
nbmin = 2;
nx = 0;
iws = *m;
if (nb > 1 && nb < k) {
/* Determine when to cross over from blocked to unblocked code. */
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "CGELQF", " ", 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, "CGELQF", " ", m, n, &c_n1, &
c_n1);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < k && nx < k) {
/* Use blocked code initially */
i__1 = k - nx;
i__2 = nb;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__3 = k - i__ + 1;
ib = min(i__3,nb);
/* Compute the LQ factorization of the current block */
/* A(i:i+ib-1,i:n) */
i__3 = *n - i__ + 1;
cgelq2_(&ib, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[
1], &iinfo);
if (i__ + ib <= *m) {
/* Form the triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
i__3 = *n - i__ + 1;
clarft_("Forward", "Rowwise", &i__3, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H to A(i+ib:m,i:n) from the right */
i__3 = *m - i__ - ib + 1;
i__4 = *n - i__ + 1;
clarfb_("Right", "No transpose", "Forward", "Rowwise", &i__3,
&i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], &
ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib +
1], &ldwork);
}
/* 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;
cgelq2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1]
, &iinfo);
}
work[1].r = (real) iws, work[1].i = 0.f;
return 0;
/* End of CGELQF */
} /* cgelqf_ */
/* Subroutine */ int cgeqrf_(integer *m, integer *n, complex *a, integer *lda,
complex *tau, complex *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 cgeqr2_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *), clarfb_(char *, char
*, char *, char *, integer *, integer *, integer *, complex *,
integer *, complex *, integer *, complex *, integer *, complex *,
integer *), clarft_(char *, char *
, integer *, integer *, complex *, integer *, complex *, complex *
, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
integer lbwork, 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 */
/* ======= */
/* CGEQRF 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 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 array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). */
/* WORK (workspace/output) COMPLEX 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, 'CGEQRF', ' ', 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, "CGEQRF", " ", 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, "CGEQRF", " ", 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 = (real) i__1, work[1].i = 0.f;
} else {
r__1 = (real) k / (real) nb;
lbwork = sceil_(&r__1) * nb;
lwkopt = (lbwork + llwork - nb) * nb;
work[1].r = (real) lwkopt, work[1].i = 0.f;
}
/* 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_("CGEQRF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (k == 0) {
work[1].r = 1.f, work[1].i = 0.f;
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, "CGEQRF", " ", 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;
clarfb_("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;
cgeqr2_(&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;
clarft_("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;
clarfb_("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;
cgeqr2_(&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;
cgeqr2_(&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;
clarft_("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;
clarft_("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;
clarfb_("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;
clarfb_("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;
clarfb_("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 = (real) iws, work[1].i = 0.f;
return 0;
/* End of CGEQRF */
} /* cgeqrf_ */
/* Subroutine */
int cgelqf_(integer *m, integer *n, complex *a, integer *lda, complex *tau, complex *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 cgelq2_(integer *, integer *, complex *, integer *, complex *, complex *, integer *), clarfb_(char *, char *, char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *), clarft_(char *, char * , integer *, integer *, complex *, integer *, complex *, complex * , integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK computational routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "CGELQF", " ", m, n, &c_n1, &c_n1);
lwkopt = *m * nb;
work[1].r = (real) lwkopt;
work[1].i = 0.f; // , expr subst
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_("CGELQF", &i__1);
return 0;
}
else if (lquery)
{
return 0;
}
/* Quick return if possible */
k = min(*m,*n);
if (k == 0)
{
work[1].r = 1.f;
work[1].i = 0.f; // , expr subst
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, "CGELQF", " ", m, n, &c_n1, &c_n1); // , expr subst
nx = max(i__1,i__2);
if (nx < k)
{
/* Determine if workspace is large enough for blocked code. */
ldwork = *m;
iws = ldwork * nb;
if (*lwork < iws)
{
/* Not enough workspace to use optimal NB: reduce NB and */
/* determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2;
i__2 = ilaenv_(&c__2, "CGELQF", " ", m, n, &c_n1, & c_n1); // , expr subst
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < k && nx < k)
{
/* Use blocked code initially */
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;
cgelq2_(&ib, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[ 1], &iinfo);
if (i__ + ib <= *m)
{
/* Form the triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
i__3 = *n - i__ + 1;
clarft_("Forward", "Rowwise", &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H to A(i+ib:m,i:n) from the right */
i__3 = *m - i__ - ib + 1;
i__4 = *n - i__ + 1;
clarfb_("Right", "No transpose", "Forward", "Rowwise", &i__3, &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], & ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib + 1], &ldwork);
}
/* 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;
cgelq2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1] , &iinfo);
}
work[1].r = (real) iws;
work[1].i = 0.f; // , expr subst
return 0;
/* End of CGELQF */
}
