dggqrf - M matrix A and an N-by-P matrix B.
SUBROUTINE DGGQRF(N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO) INTEGER N, M, P, LDA, LDB, LWORK, INFO DOUBLE PRECISION A(LDA,*), TAUA(*), B(LDB,*), TAUB(*), WORK(*) SUBROUTINE DGGQRF_64(N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO) INTEGER*8 N, M, P, LDA, LDB, LWORK, INFO DOUBLE PRECISION A(LDA,*), TAUA(*), B(LDB,*), TAUB(*), WORK(*) F95 INTERFACE SUBROUTINE GGQRF(N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO) INTEGER :: N, M, P, LDA, LDB, LWORK, INFO REAL(8), DIMENSION(:) :: TAUA, TAUB, WORK REAL(8), DIMENSION(:,:) :: A, B SUBROUTINE GGQRF_64(N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO) INTEGER(8) :: N, M, P, LDA, LDB, LWORK, INFO REAL(8), DIMENSION(:) :: TAUA, TAUB, WORK REAL(8), DIMENSION(:,:) :: A, B C INTERFACE #include <sunperf.h> void dggqrf(int n, int m, int p, double *a, int lda, double *taua, dou- ble *b, int ldb, double *taub, int *info); void dggqrf_64(long n, long m, long p, double *a, long lda, double *taua, double *b, long ldb, double *taub, long *info);
Oracle Solaris Studio Performance Library dggqrf(3P) NAME dggqrf - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B. SYNOPSIS SUBROUTINE DGGQRF(N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO) INTEGER N, M, P, LDA, LDB, LWORK, INFO DOUBLE PRECISION A(LDA,*), TAUA(*), B(LDB,*), TAUB(*), WORK(*) SUBROUTINE DGGQRF_64(N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO) INTEGER*8 N, M, P, LDA, LDB, LWORK, INFO DOUBLE PRECISION A(LDA,*), TAUA(*), B(LDB,*), TAUB(*), WORK(*) F95 INTERFACE SUBROUTINE GGQRF(N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO) INTEGER :: N, M, P, LDA, LDB, LWORK, INFO REAL(8), DIMENSION(:) :: TAUA, TAUB, WORK REAL(8), DIMENSION(:,:) :: A, B SUBROUTINE GGQRF_64(N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO) INTEGER(8) :: N, M, P, LDA, LDB, LWORK, INFO REAL(8), DIMENSION(:) :: TAUA, TAUB, WORK REAL(8), DIMENSION(:,:) :: A, B C INTERFACE #include <sunperf.h> void dggqrf(int n, int m, int p, double *a, int lda, double *taua, dou- ble *b, int ldb, double *taub, int *info); void dggqrf_64(long n, long m, long p, double *a, long lda, double *taua, double *b, long ldb, double *taub, long *info); 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) The number of rows of the matrices A and B. N >= 0. M (input) The number of columns of the matrix A. M >= 0. P (input) The number of columns of the matrix B. P >= 0. A (input/output) 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, repre- sent the orthogonal matrix Q as a product of min(N,M) elemen- tary reflectors (see Further Details). LDA (input) The leading dimension of the array A. LDA >= max(1,N). TAUA (output) The scalar factors of the elementary reflectors which repre- sent the orthogonal matrix Q (see Further Details). B (input/output) 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 ele- mentary reflectors (see Further Details). LDB (input) The leading dimension of the array B. LDB >= max(1,N). TAUB (output) The scalar factors of the elementary reflectors which repre- sent the orthogonal matrix Z (see Further Details). WORK (workspace) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) 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) = 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. 7 Nov 2015 dggqrf(3P)