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- /* dggqrf.f -- translated by f2c (version 20061008).
- You must link the resulting object file with libf2c:
- on Microsoft Windows system, link with libf2c.lib;
- on Linux or Unix systems, link with .../path/to/libf2c.a -lm
- or, if you install libf2c.a in a standard place, with -lf2c -lm
- -- in that order, at the end of the command line, as in
- cc *.o -lf2c -lm
- Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
- http://www.netlib.org/f2c/libf2c.zip
- */
- #include "f2c.h"
- #include "blaswrap.h"
- /* Table of constant values */
- static integer c__1 = 1;
- static integer c_n1 = -1;
- /* 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)
- {
- /* System generated locals */
- integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
- /* 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 dormqr_(char *, char *, integer *, integer *,
- integer *, doublereal *, integer *, doublereal *, doublereal *,
- integer *, doublereal *, integer *, integer *);
- integer lwkopt;
- logical lquery;
- /* -- LAPACK routine (version 3.2) -- */
- /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
- /* November 2006 */
- /* .. Scalar Arguments .. */
- /* .. */
- /* .. Array Arguments .. */
- /* .. */
- /* Purpose */
- /* ======= */
- /* 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 (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 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. */
- /* ===================================================================== */
- /* .. 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, "DGEQRF", " ", n, m, &c_n1, &c_n1);
- nb2 = ilaenv_(&c__1, "DGERQF", " ", n, p, &c_n1, &c_n1);
- nb3 = ilaenv_(&c__1, "DORMQR", " ", n, m, 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 (*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_ */
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