#include "blaswrap.h" #include "f2c.h" /* 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_ */