/* Subroutine */ int zggqrf_(integer *n, integer *m, integer *p,
doublecomplex *a, integer *lda, doublecomplex *taua, doublecomplex *b,
integer *ldb, doublecomplex *taub, 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
=======
ZGGQRF computes a generalized QR factorization of an N-by-M matrix A
and an N-by-P matrix B:
A = Q*R, B = Q*T*Z,
where Q is an N-by-N unitary matrix, Z is a P-by-P unitary matrix,
and R and T assume one of the forms:
if N >= M, R = ( R11 ) M , or if N < M, R = ( R11 R12 ) N,
( 0 ) N-M N M-N
M
where R11 is upper triangular, and
if N <= P, T = ( 0 T12 ) N, or if N > P, T = ( T11 ) N-P,
P-N N ( T21 ) P
P
where T12 or T21 is upper triangular.
In particular, if B is square and nonsingular, the GQR factorization
of A and B implicitly gives the QR factorization of inv(B)*A:
inv(B)*A = Z'*(inv(T)*R)
where inv(B) denotes the inverse of the matrix B, and Z' denotes the
conjugate transpose of matrix Z.
Arguments
=========
N (input) INTEGER
The number of rows of the matrices A and B. N >= 0.
M (input) INTEGER
The number of columns of the matrix A. M >= 0.
P (input) INTEGER
The number of columns of the matrix B. P >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,M)
On entry, the N-by-M matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(N,M)-by-M upper trapezoidal matrix R (R is
upper triangular if N >= M); the elements below the diagonal,
with the array TAUA, represent the unitary matrix Q as a
product of min(N,M) elementary reflectors (see Further
Details).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TAUA (output) COMPLEX*16 array, dimension (min(N,M))
The scalar factors of the elementary reflectors which
represent the unitary matrix Q (see Further Details).
B (input/output) COMPLEX*16 array, dimension (LDB,P)
On entry, the N-by-P matrix B.
On exit, if N <= P, the upper triangle of the subarray
B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;
if N > P, the elements on and above the (N-P)-th subdiagonal
contain the N-by-P upper trapezoidal matrix T; the remaining
elements, with the array TAUB, represent the unitary
matrix Z as a product of elementary reflectors (see Further
Details).
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
TAUB (output) COMPLEX*16 array, dimension (min(N,P))
The scalar factors of the elementary reflectors which
represent the unitary matrix Z (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,M,P).
For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3),
where NB1 is the optimal blocksize for the QR factorization
of an N-by-M matrix, NB2 is the optimal blocksize for the
RQ factorization of an N-by-P matrix, and NB3 is the optimal
blocksize for a call of ZUNMQR.
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(n,m).
Each H(i) has the form
H(i) = I - taua * v * v'
where taua is a complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
and taua in TAUA(i).
To form Q explicitly, use LAPACK subroutine ZUNGQR.
To use Q to update another matrix, use LAPACK subroutine ZUNMQR.
The matrix Z is represented as a product of elementary reflectors
Z = H(1) H(2) . . . H(k), where k = min(n,p).
Each H(i) has the form
H(i) = I - taub * v * v'
where taub is a complex scalar, and v is a complex vector with
v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in
B(n-k+i,1:p-k+i-1), and taub in TAUB(i).
To form Z explicitly, use LAPACK subroutine ZUNGRQ.
To use Z to update another matrix, use LAPACK subroutine ZUNMRQ.
=====================================================================
Test the input parameters
Parameter adjustments
Function Body */
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
doublereal d__1;
/* Local variables */
static integer lopt;
extern /* Subroutine */ int xerbla_(char *, integer *), zgeqrf_(
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, integer *), zgerqf_(integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, integer *), zunmqr_(char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, integer *);
#define TAUA(I) taua[(I)-1]
#define TAUB(I) taub[(I)-1]
#define WORK(I) work[(I)-1]
#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
#define B(I,J) b[(I)-1 + ((J)-1)* ( *ldb)]
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*m < 0) {
*info = -2;
} else if (*p < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -8;
} else { /* if(complicated condition) */
/* Computing MAX */
i__1 = max(1,*n), i__1 = max(i__1,*m);
if (*lwork < max(i__1,*p)) {
*info = -11;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGGQRF", &i__1);
return 0;
}
/* QR factorization of N-by-M matrix A: A = Q*R */
zgeqrf_(n, m, &A(1,1), lda, &TAUA(1), &WORK(1), lwork, info);
lopt = (integer) WORK(1).r;
/* Update B := Q'*B. */
i__1 = min(*n,*m);
zunmqr_("Left", "Conjugate Transpose", n, p, &i__1, &A(1,1), lda, &
TAUA(1), &B(1,1), ldb, &WORK(1), lwork, info);
/* Computing MAX */
i__1 = lopt, i__2 = (integer) WORK(1).r;
lopt = max(i__1,i__2);
/* RQ factorization of N-by-P matrix B: B = T*Z. */
zgerqf_(n, p, &B(1,1), ldb, &TAUB(1), &WORK(1), lwork, info);
/* Computing MAX */
i__1 = lopt, i__2 = (integer) WORK(1).r;
d__1 = (doublereal) max(i__1,i__2);
WORK(1).r = d__1, WORK(1).i = 0.;
return 0;
/* End of ZGGQRF */
} /* zggqrf_ */
/* Subroutine */ int zggrqf_(integer *m, integer *p, integer *n,
doublecomplex *a, integer *lda, doublecomplex *taua, doublecomplex *b,
integer *ldb, doublecomplex *taub, doublecomplex *work, integer *
lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Local variables */
integer nb, nb1, nb2, nb3, lopt;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int zgeqrf_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *, integer *
), zgerqf_(integer *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, integer *, integer *);
integer lwkopt;
logical lquery;
extern /* Subroutine */ int zunmrq_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGGRQF computes a generalized RQ factorization of an M-by-N matrix A */
/* and a P-by-N matrix B: */
/* A = R*Q, B = Z*T*Q, */
/* where Q is an N-by-N unitary matrix, Z is a P-by-P unitary */
/* matrix, and R and T assume one of the forms: */
/* if M <= N, R = ( 0 R12 ) M, or if M > N, R = ( R11 ) M-N, */
/* N-M M ( R21 ) N */
/* N */
/* where R12 or R21 is upper triangular, and */
/* if P >= N, T = ( T11 ) N , or if P < N, T = ( T11 T12 ) P, */
/* ( 0 ) P-N P N-P */
/* N */
/* where T11 is upper triangular. */
/* In particular, if B is square and nonsingular, the GRQ factorization */
/* of A and B implicitly gives the RQ factorization of A*inv(B): */
/* A*inv(B) = (R*inv(T))*Z' */
/* where inv(B) denotes the inverse of the matrix B, and Z' denotes the */
/* conjugate transpose of the matrix Z. */
/* Arguments */
/* ========= */
/* M (input) INTEGER */
/* The number of rows of the matrix A. M >= 0. */
/* P (input) INTEGER */
/* The number of rows of the matrix B. P >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrices A and B. 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 TAUA, 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). */
/* TAUA (output) COMPLEX*16 array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors which */
/* represent the unitary matrix Q (see Further Details). */
/* B (input/output) COMPLEX*16 array, dimension (LDB,N) */
/* On entry, the P-by-N matrix B. */
/* On exit, the elements on and above the diagonal of the array */
/* contain the min(P,N)-by-N upper trapezoidal matrix T (T is */
/* upper triangular if P >= N); the elements below the diagonal, */
/* with the array TAUB, represent the unitary matrix Z as a */
/* product of elementary reflectors (see Further Details). */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,P). */
/* TAUB (output) COMPLEX*16 array, dimension (min(P,N)) */
/* The scalar factors of the elementary reflectors which */
/* represent the unitary matrix Z (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,M,P). */
/* For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3), */
/* where NB1 is the optimal blocksize for the RQ factorization */
/* of an M-by-N matrix, NB2 is the optimal blocksize for the */
/* QR factorization of a P-by-N matrix, and NB3 is the optimal */
/* blocksize for a call of ZUNMRQ. */
/* 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 - taua * v * v' */
/* where taua is a complex scalar, and v is a complex vector with */
/* v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in */
/* A(m-k+i,1:n-k+i-1), and taua in TAUA(i). */
/* To form Q explicitly, use LAPACK subroutine ZUNGRQ. */
/* To use Q to update another matrix, use LAPACK subroutine ZUNMRQ. */
/* The matrix Z is represented as a product of elementary reflectors */
/* Z = H(1) H(2) . . . H(k), where k = min(p,n). */
/* Each H(i) has the form */
/* H(i) = I - taub * v * v' */
/* where taub is a complex scalar, and v is a complex vector with */
/* v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i), */
/* and taub in TAUB(i). */
/* To form Z explicitly, use LAPACK subroutine ZUNGQR. */
/* To use Z to update another matrix, use LAPACK subroutine ZUNMQR. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--taua;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--taub;
--work;
/* Function Body */
*info = 0;
nb1 = ilaenv_(&c__1, "ZGERQF", " ", m, n, &c_n1, &c_n1);
nb2 = ilaenv_(&c__1, "ZGEQRF", " ", p, n, &c_n1, &c_n1);
nb3 = ilaenv_(&c__1, "ZUNMRQ", " ", m, n, p, &c_n1);
/* Computing MAX */
i__1 = max(nb1,nb2);
nb = max(i__1,nb3);
/* Computing MAX */
i__1 = max(*n,*m);
lwkopt = max(i__1,*p) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*p < 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*ldb < max(1,*p)) {
*info = -8;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = max(1,*m), i__1 = max(i__1,*p);
if (*lwork < max(i__1,*n) && ! lquery) {
*info = -11;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGGRQF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* RQ factorization of M-by-N matrix A: A = R*Q */
zgerqf_(m, n, &a[a_offset], lda, &taua[1], &work[1], lwork, info);
lopt = (integer) work[1].r;
/* Update B := B*Q' */
i__1 = min(*m,*n);
/* Computing MAX */
i__2 = 1, i__3 = *m - *n + 1;
zunmrq_("Right", "Conjugate Transpose", p, n, &i__1, &a[max(i__2, i__3)+
a_dim1], lda, &taua[1], &b[b_offset], ldb, &work[1], lwork, info);
/* Computing MAX */
i__1 = lopt, i__2 = (integer) work[1].r;
lopt = max(i__1,i__2);
/* QR factorization of P-by-N matrix B: B = Z*T */
zgeqrf_(p, n, &b[b_offset], ldb, &taub[1], &work[1], lwork, info);
/* Computing MAX */
i__2 = lopt, i__3 = (integer) work[1].r;
i__1 = max(i__2,i__3);
work[1].r = (doublereal) i__1, work[1].i = 0.;
return 0;
/* End of ZGGRQF */
} /* zggrqf_ */
/* Subroutine */ int zggrqf_(integer *m, integer *p, integer *n,
doublecomplex *a, integer *lda, doublecomplex *taua, doublecomplex *b,
integer *ldb, doublecomplex *taub, 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
=======
ZGGRQF computes a generalized RQ factorization of an M-by-N matrix A
and a P-by-N matrix B:
A = R*Q, B = Z*T*Q,
where Q is an N-by-N unitary matrix, Z is a P-by-P unitary
matrix, and R and T assume one of the forms:
if M <= N, R = ( 0 R12 ) M, or if M > N, R = ( R11 ) M-N,
N-M M ( R21 ) N
N
where R12 or R21 is upper triangular, and
if P >= N, T = ( T11 ) N , or if P < N, T = ( T11 T12 ) P,
( 0 ) P-N P N-P
N
where T11 is upper triangular.
In particular, if B is square and nonsingular, the GRQ factorization
of A and B implicitly gives the RQ factorization of A*inv(B):
A*inv(B) = (R*inv(T))*Z'
where inv(B) denotes the inverse of the matrix B, and Z' denotes the
conjugate transpose of the matrix Z.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
P (input) INTEGER
The number of rows of the matrix B. P >= 0.
N (input) INTEGER
The number of columns of the matrices A and B. 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 TAUA, 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).
TAUA (output) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors which
represent the unitary matrix Q (see Further Details).
B (input/output) COMPLEX*16 array, dimension (LDB,N)
On entry, the P-by-N matrix B.
On exit, the elements on and above the diagonal of the array
contain the min(P,N)-by-N upper trapezoidal matrix T (T is
upper triangular if P >= N); the elements below the diagonal,
with the array TAUB, represent the unitary matrix Z as a
product of elementary reflectors (see Further Details).
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,P).
TAUB (output) COMPLEX*16 array, dimension (min(P,N))
The scalar factors of the elementary reflectors which
represent the unitary matrix Z (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,M,P).
For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3),
where NB1 is the optimal blocksize for the RQ factorization
of an M-by-N matrix, NB2 is the optimal blocksize for the
QR factorization of a P-by-N matrix, and NB3 is the optimal
blocksize for a call of ZUNMRQ.
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 - taua * v * v'
where taua is a complex scalar, and v is a complex vector with
v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
A(m-k+i,1:n-k+i-1), and taua in TAUA(i).
To form Q explicitly, use LAPACK subroutine ZUNGRQ.
To use Q to update another matrix, use LAPACK subroutine ZUNMRQ.
The matrix Z is represented as a product of elementary reflectors
Z = H(1) H(2) . . . H(k), where k = min(p,n).
Each H(i) has the form
H(i) = I - taub * v * v'
where taub is a complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i),
and taub in TAUB(i).
To form Z explicitly, use LAPACK subroutine ZUNGQR.
To use Z to update another matrix, use LAPACK subroutine ZUNMQR.
=====================================================================
Test the input parameters
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Local variables */
static integer lopt, nb;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zgeqrf_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *, integer *
), zgerqf_(integer *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, integer *, integer *);
static integer nb1, nb2, nb3, lwkopt;
static logical lquery;
extern /* Subroutine */ int zunmrq_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
#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;
--taua;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--taub;
--work;
/* Function Body */
*info = 0;
nb1 = ilaenv_(&c__1, "ZGERQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
nb2 = ilaenv_(&c__1, "ZGEQRF", " ", p, n, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
nb3 = ilaenv_(&c__1, "ZUNMRQ", " ", m, n, p, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = max(nb1,nb2);
nb = max(i__1,nb3);
/* Computing MAX */
i__1 = max(*n,*m);
lwkopt = max(i__1,*p) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*p < 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*ldb < max(1,*p)) {
*info = -8;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = max(1,*m), i__1 = max(i__1,*p);
if (*lwork < max(i__1,*n) && ! lquery) {
*info = -11;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGGRQF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* RQ factorization of M-by-N matrix A: A = R*Q */
zgerqf_(m, n, &a[a_offset], lda, &taua[1], &work[1], lwork, info);
lopt = (integer) work[1].r;
/* Update B := B*Q'
Computing MAX */
i__1 = 1, i__2 = *m - *n + 1;
i__3 = min(*m,*n);
zunmrq_("Right", "Conjugate Transpose", p, n, &i__3, &a_ref(max(i__1,i__2)
, 1), lda, &taua[1], &b[b_offset], ldb, &work[1], lwork, info);
/* Computing MAX */
i__1 = lopt, i__2 = (integer) work[1].r;
lopt = max(i__1,i__2);
/* QR factorization of P-by-N matrix B: B = Z*T */
zgeqrf_(p, n, &b[b_offset], ldb, &taub[1], &work[1], lwork, info);
/* Computing MAX */
i__2 = lopt, i__3 = (integer) work[1].r;
i__1 = max(i__2,i__3);
work[1].r = (doublereal) i__1, work[1].i = 0.;
return 0;
/* End of ZGGRQF */
} /* zggrqf_ */
/* Subroutine */ int zrqt01_(integer *m, integer *n, doublecomplex *a,
doublecomplex *af, doublecomplex *q, doublecomplex *r__, integer *lda,
doublecomplex *tau, doublecomplex *work, integer *lwork, doublereal *
rwork, doublereal *result)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, q_dim1, q_offset, r_dim1,
r_offset, i__1, i__2;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
doublereal eps;
integer info;
doublereal resid, anorm;
integer minmn;
extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), zherk_(char *, char *, integer *,
integer *, doublereal *, doublecomplex *, integer *, doublereal *,
doublecomplex *, integer *);
extern doublereal dlamch_(char *), zlange_(char *, integer *,
integer *, doublecomplex *, integer *, doublereal *);
extern /* Subroutine */ int zgerqf_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *, integer *
), zlacpy_(char *, integer *, integer *, doublecomplex *, integer
*, doublecomplex *, integer *), zlaset_(char *, integer *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
integer *);
extern doublereal zlansy_(char *, char *, integer *, doublecomplex *,
integer *, doublereal *);
extern /* Subroutine */ int zungrq_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *);
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZRQT01 tests ZGERQF, which computes the RQ factorization of an m-by-n */
/* matrix A, and partially tests ZUNGRQ which forms the n-by-n */
/* orthogonal matrix Q. */
/* ZRQT01 compares R with A*Q', and checks that Q is orthogonal. */
/* 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) COMPLEX*16 array, dimension (LDA,N) */
/* The m-by-n matrix A. */
/* AF (output) COMPLEX*16 array, dimension (LDA,N) */
/* Details of the RQ factorization of A, as returned by ZGERQF. */
/* See ZGERQF for further details. */
/* Q (output) COMPLEX*16 array, dimension (LDA,N) */
/* The n-by-n orthogonal matrix Q. */
/* R (workspace) COMPLEX*16 array, dimension (LDA,max(M,N)) */
/* LDA (input) INTEGER */
/* The leading dimension of the arrays A, AF, Q and L. */
/* LDA >= max(M,N). */
/* TAU (output) COMPLEX*16 array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors, as returned */
/* by ZGERQF. */
/* WORK (workspace) COMPLEX*16 array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (max(M,N)) */
/* RESULT (output) DOUBLE PRECISION array, dimension (2) */
/* The test ratios: */
/* RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS ) */
/* RESULT(2) = norm( I - Q*Q' ) / ( N * EPS ) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
r_dim1 = *lda;
r_offset = 1 + r_dim1;
r__ -= r_offset;
q_dim1 = *lda;
q_offset = 1 + q_dim1;
q -= q_offset;
af_dim1 = *lda;
af_offset = 1 + af_dim1;
af -= af_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
--rwork;
--result;
/* Function Body */
minmn = min(*m,*n);
eps = dlamch_("Epsilon");
/* Copy the matrix A to the array AF. */
zlacpy_("Full", m, n, &a[a_offset], lda, &af[af_offset], lda);
/* Factorize the matrix A in the array AF. */
s_copy(srnamc_1.srnamt, "ZGERQF", (ftnlen)6, (ftnlen)6);
zgerqf_(m, n, &af[af_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy details of Q */
zlaset_("Full", n, n, &c_b1, &c_b1, &q[q_offset], lda);
if (*m <= *n) {
if (*m > 0 && *m < *n) {
i__1 = *n - *m;
zlacpy_("Full", m, &i__1, &af[af_offset], lda, &q[*n - *m + 1 +
q_dim1], lda);
}
if (*m > 1) {
i__1 = *m - 1;
i__2 = *m - 1;
zlacpy_("Lower", &i__1, &i__2, &af[(*n - *m + 1) * af_dim1 + 2],
lda, &q[*n - *m + 2 + (*n - *m + 1) * q_dim1], lda);
}
} else {
if (*n > 1) {
i__1 = *n - 1;
i__2 = *n - 1;
zlacpy_("Lower", &i__1, &i__2, &af[*m - *n + 2 + af_dim1], lda, &
q[q_dim1 + 2], lda);
}
}
/* Generate the n-by-n matrix Q */
s_copy(srnamc_1.srnamt, "ZUNGRQ", (ftnlen)6, (ftnlen)6);
zungrq_(n, n, &minmn, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy R */
zlaset_("Full", m, n, &c_b12, &c_b12, &r__[r_offset], lda);
if (*m <= *n) {
if (*m > 0) {
zlacpy_("Upper", m, m, &af[(*n - *m + 1) * af_dim1 + 1], lda, &
r__[(*n - *m + 1) * r_dim1 + 1], lda);
}
} else {
if (*m > *n && *n > 0) {
i__1 = *m - *n;
zlacpy_("Full", &i__1, n, &af[af_offset], lda, &r__[r_offset],
lda);
}
if (*n > 0) {
zlacpy_("Upper", n, n, &af[*m - *n + 1 + af_dim1], lda, &r__[*m -
*n + 1 + r_dim1], lda);
}
}
/* Compute R - A*Q' */
zgemm_("No transpose", "Conjugate transpose", m, n, n, &c_b19, &a[
a_offset], lda, &q[q_offset], lda, &c_b20, &r__[r_offset], lda);
/* Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) . */
anorm = zlange_("1", m, n, &a[a_offset], lda, &rwork[1]);
resid = zlange_("1", m, n, &r__[r_offset], lda, &rwork[1]);
if (anorm > 0.) {
result[1] = resid / (doublereal) max(1,*n) / anorm / eps;
} else {
result[1] = 0.;
}
/* Compute I - Q*Q' */
zlaset_("Full", n, n, &c_b12, &c_b20, &r__[r_offset], lda);
zherk_("Upper", "No transpose", n, n, &c_b28, &q[q_offset], lda, &c_b29, &
r__[r_offset], lda);
/* Compute norm( I - Q*Q' ) / ( N * EPS ) . */
resid = zlansy_("1", "Upper", n, &r__[r_offset], lda, &rwork[1]);
result[2] = resid / (doublereal) max(1,*n) / eps;
return 0;
/* End of ZRQT01 */
} /* zrqt01_ */
