/* Subroutine */ int dggqrf_(integer *n, integer *m, integer *p, doublereal *
a, integer *lda, doublereal *taua, doublereal *b, integer *ldb,
doublereal *taub, doublereal *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
=======
DGGQRF 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 orthogonal matrix, Z is a P-by-P orthogonal
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
transpose of the 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) DOUBLE PRECISION 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 orthogonal 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) DOUBLE PRECISION array, dimension (min(N,M))
The scalar factors of the elementary reflectors which
represent the orthogonal matrix Q (see Further Details).
B (input/output) DOUBLE PRECISION 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 orthogonal
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) DOUBLE PRECISION array, dimension (min(N,P))
The scalar factors of the elementary reflectors which
represent the orthogonal matrix Z (see Further Details).
WORK (workspace/output) DOUBLE PRECISION 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 DORMQR.
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(n,m).
Each H(i) has the form
H(i) = I - taua * v * v'
where taua is a real scalar, and v is a real 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 DORGQR.
To use Q to update another matrix, use LAPACK subroutine DORMQR.
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 real scalar, and v is a real 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 DORGRQ.
To use Z to update another matrix, use LAPACK subroutine DORMRQ.
=====================================================================
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;
/* Local variables */
static integer lopt, nb;
extern /* Subroutine */ int dgeqrf_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *),
dgerqf_(integer *, integer *, doublereal *, integer *, doublereal
*, doublereal *, integer *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static integer nb1, nb2, nb3;
extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *);
static integer lwkopt;
static logical lquery;
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, "DGEQRF", " ", n, m, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
nb2 = ilaenv_(&c__1, "DGERQF", " ", n, p, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
nb3 = ilaenv_(&c__1, "DORMQR", " ", n, m, 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] = (doublereal) lwkopt;
lquery = *lwork == -1;
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) && ! lquery) {
*info = -11;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGGQRF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* QR factorization of N-by-M matrix A: A = Q*R */
dgeqrf_(n, m, &a[a_offset], lda, &taua[1], &work[1], lwork, info);
lopt = (integer) work[1];
/* Update B := Q'*B. */
i__1 = min(*n,*m);
dormqr_("Left", "Transpose", n, p, &i__1, &a[a_offset], lda, &taua[1], &b[
b_offset], ldb, &work[1], lwork, info);
/* Computing MAX */
i__1 = lopt, i__2 = (integer) work[1];
lopt = max(i__1,i__2);
/* RQ factorization of N-by-P matrix B: B = T*Z. */
dgerqf_(n, p, &b[b_offset], ldb, &taub[1], &work[1], lwork, info);
/* Computing MAX */
i__1 = lopt, i__2 = (integer) work[1];
work[1] = (doublereal) max(i__1,i__2);
return 0;
/* End of DGGQRF */
} /* dggqrf_ */
/* Subroutine */ int dggrqf_(integer *m, integer *p, integer *n, doublereal *
a, integer *lda, doublereal *taua, doublereal *b, integer *ldb,
doublereal *taub, doublereal *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 dgeqrf_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *),
dgerqf_(integer *, integer *, doublereal *, integer *, doublereal
*, doublereal *, integer *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int dormrq_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *);
integer 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 */
/* ======= */
/* DGGRQF 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 orthogonal matrix, Z is a P-by-P orthogonal */
/* 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 */
/* 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) DOUBLE PRECISION 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 orthogonal */
/* 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) DOUBLE PRECISION array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors which */
/* represent the orthogonal matrix Q (see Further Details). */
/* B (input/output) DOUBLE PRECISION 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 orthogonal 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) DOUBLE PRECISION array, dimension (min(P,N)) */
/* The scalar factors of the elementary reflectors which */
/* represent the orthogonal matrix Z (see Further Details). */
/* WORK (workspace/output) DOUBLE PRECISION 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 DORMRQ. */
/* 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 INF0= -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 real scalar, and v is a real 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 DORGRQ. */
/* To use Q to update another matrix, use LAPACK subroutine DORMRQ. */
/* 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 real scalar, and v is a real 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 DORGQR. */
/* To use Z to update another matrix, use LAPACK subroutine DORMQR. */
/* ===================================================================== */
/* .. 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, "DGERQF", " ", m, n, &c_n1, &c_n1);
nb2 = ilaenv_(&c__1, "DGEQRF", " ", p, n, &c_n1, &c_n1);
nb3 = ilaenv_(&c__1, "DORMRQ", " ", 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] = (doublereal) lwkopt;
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_("DGGRQF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* RQ factorization of M-by-N matrix A: A = R*Q */
dgerqf_(m, n, &a[a_offset], lda, &taua[1], &work[1], lwork, info);
lopt = (integer) work[1];
/* Update B := B*Q' */
i__1 = min(*m,*n);
/* Computing MAX */
i__2 = 1, i__3 = *m - *n + 1;
dormrq_("Right", "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];
lopt = max(i__1,i__2);
/* QR factorization of P-by-N matrix B: B = Z*T */
dgeqrf_(p, n, &b[b_offset], ldb, &taub[1], &work[1], lwork, info);
/* Computing MAX */
i__1 = lopt, i__2 = (integer) work[1];
work[1] = (doublereal) max(i__1,i__2);
return 0;
/* End of DGGRQF */
} /* dggrqf_ */
/* Subroutine */ int drqt01_(integer *m, integer *n, doublereal *a,
doublereal *af, doublereal *q, doublereal *r__, integer *lda,
doublereal *tau, doublereal *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;
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
doublereal resid, anorm;
integer minmn;
extern /* Subroutine */ int dsyrk_(char *, char *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, doublereal *,
integer *);
extern doublereal dlamch_(char *), dlange_(char *, integer *,
integer *, doublereal *, integer *, doublereal *);
extern /* Subroutine */ int dgerqf_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *),
dlacpy_(char *, integer *, integer *, doublereal *, integer *,
doublereal *, integer *), dlaset_(char *, integer *,
integer *, doublereal *, doublereal *, doublereal *, integer *);
extern doublereal dlansy_(char *, char *, integer *, doublereal *,
integer *, doublereal *);
extern /* Subroutine */ int dorgrq_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, 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 */
/* ======= */
/* DRQT01 tests DGERQF, which computes the RQ factorization of an m-by-n */
/* matrix A, and partially tests DORGRQ which forms the n-by-n */
/* orthogonal matrix Q. */
/* DRQT01 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) DOUBLE PRECISION array, dimension (LDA,N) */
/* The m-by-n matrix A. */
/* AF (output) DOUBLE PRECISION array, dimension (LDA,N) */
/* Details of the RQ factorization of A, as returned by DGERQF. */
/* See DGERQF for further details. */
/* Q (output) DOUBLE PRECISION array, dimension (LDA,N) */
/* The n-by-n orthogonal matrix Q. */
/* R (workspace) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors, as returned */
/* by DGERQF. */
/* WORK (workspace) DOUBLE PRECISION 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. */
dlacpy_("Full", m, n, &a[a_offset], lda, &af[af_offset], lda);
/* Factorize the matrix A in the array AF. */
s_copy(srnamc_1.srnamt, "DGERQF", (ftnlen)6, (ftnlen)6);
dgerqf_(m, n, &af[af_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy details of Q */
dlaset_("Full", n, n, &c_b6, &c_b6, &q[q_offset], lda);
if (*m <= *n) {
if (*m > 0 && *m < *n) {
i__1 = *n - *m;
dlacpy_("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;
dlacpy_("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;
dlacpy_("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, "DORGRQ", (ftnlen)6, (ftnlen)6);
dorgrq_(n, n, &minmn, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy R */
dlaset_("Full", m, n, &c_b13, &c_b13, &r__[r_offset], lda);
if (*m <= *n) {
if (*m > 0) {
dlacpy_("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;
dlacpy_("Full", &i__1, n, &af[af_offset], lda, &r__[r_offset],
lda);
}
if (*n > 0) {
dlacpy_("Upper", n, n, &af[*m - *n + 1 + af_dim1], lda, &r__[*m -
*n + 1 + r_dim1], lda);
}
}
/* Compute R - A*Q' */
dgemm_("No transpose", "Transpose", m, n, n, &c_b20, &a[a_offset], lda, &
q[q_offset], lda, &c_b21, &r__[r_offset], lda);
/* Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) . */
anorm = dlange_("1", m, n, &a[a_offset], lda, &rwork[1]);
resid = dlange_("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' */
dlaset_("Full", n, n, &c_b13, &c_b21, &r__[r_offset], lda);
dsyrk_("Upper", "No transpose", n, n, &c_b20, &q[q_offset], lda, &c_b21, &
r__[r_offset], lda);
/* Compute norm( I - Q*Q' ) / ( N * EPS ) . */
resid = dlansy_("1", "Upper", n, &r__[r_offset], lda, &rwork[1]);
result[2] = resid / (doublereal) max(1,*n) / eps;
return 0;
/* End of DRQT01 */
} /* drqt01_ */
/* Compute an RQ factorization of an m by n matrix A */
void dgerqf_driver(int m, int n, double *A, double *R, double *Q)
{
double *AT;
int lda = m;
double *tau;
int tau_dim = MIN(m, n);
double *work;
int block_size = 64; /* Just a guess... */
int lwork = n * block_size;
int info;
double *H;
double *v, *vvT;
double *Qtmp;
int i, j;
/* Transpose A */
AT = (double *) malloc(sizeof(double) * m * n);
matrix_transpose(m, n, A, AT);
/* Call the LAPACK routine */
tau = (double *) malloc(sizeof(double) * tau_dim);
work = (double *) malloc(sizeof(double) * lwork);
dgerqf_(&m, &n, AT, &lda, tau, work, &lwork, &info);
if (info < 0) {
printf("[dgeqrf_driver] An error occurred.\n");
free(AT);
free(work);
free(tau);
return;
}
/* Extract the R matrix */
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
if (j < i)
R[i * n + j] = 0.0;
else
R[i * n + j] = AT[(n - m + j) * m + i];
}
}
/* Now extract the Q matrix */
H = (double *) malloc(sizeof(double) * n * n);
v = (double *) malloc(sizeof(double) * n);
vvT = (double *) malloc(sizeof(double) * n * n);
Qtmp = (double *) malloc(sizeof(double) * n * n);
for (i = 0; i < tau_dim; i++) {
matrix_ident(m, H);
for (j = 0; j < n; j++) {
if (j > n - tau_dim + i)
v[j] = 0.0;
else if (j == n - tau_dim + i)
v[j] = 1.0;
else
v[j] = AT[j * m + (m-tau_dim+i)];
}
matrix_transpose_product2(n, 1, n, 1, v, v, vvT);
matrix_scale(n, n, vvT, tau[i], vvT);
matrix_diff(n, n, n, n, H, vvT, H);
if (i == 0) {
memcpy(Q, H, sizeof(double) * n * n);
} else {
matrix_product(n, n, n, n, Q, H, Qtmp);
memcpy(Q, Qtmp, sizeof(double) * n * n);
}
}
matrix_product(m, n, n, n, R, Q, H);
free(H);
free(v);
free(vvT);
free(Qtmp);
free(tau);
free(work);
free(AT);
}
/* Subroutine */
int dggrqf_(integer *m, integer *p, integer *n, doublereal * a, integer *lda, doublereal *taua, doublereal *b, integer *ldb, doublereal *taub, doublereal *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 dgeqrf_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *), dgerqf_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
extern /* Subroutine */
int dormrq_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *);
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 .. */
/* .. */
/* ===================================================================== */
/* .. 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, "DGERQF", " ", m, n, &c_n1, &c_n1);
nb2 = ilaenv_(&c__1, "DGEQRF", " ", p, n, &c_n1, &c_n1);
nb3 = ilaenv_(&c__1, "DORMRQ", " ", 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] = (doublereal) lwkopt;
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); // , expr subst
if (*lwork < max(i__1,*n) && ! lquery)
{
*info = -11;
}
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("DGGRQF", &i__1);
return 0;
}
else if (lquery)
{
return 0;
}
/* RQ factorization of M-by-N matrix A: A = R*Q */
dgerqf_(m, n, &a[a_offset], lda, &taua[1], &work[1], lwork, info);
lopt = (integer) work[1];
/* Update B := B*Q**T */
i__1 = min(*m,*n);
/* Computing MAX */
i__2 = 1;
i__3 = *m - *n + 1; // , expr subst
dormrq_("Right", "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]; // , expr subst
lopt = max(i__1,i__2);
/* QR factorization of P-by-N matrix B: B = Z*T */
dgeqrf_(p, n, &b[b_offset], ldb, &taub[1], &work[1], lwork, info);
/* Computing MAX */
i__1 = lopt;
i__2 = (integer) work[1]; // , expr subst
work[1] = (doublereal) max(i__1,i__2);
return 0;
/* End of DGGRQF */
}
