dtzrzf - N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations
SUBROUTINE DTZRZF(M, N, A, LDA, TAU, WORK, LWORK, INFO) INTEGER M, N, LDA, LWORK, INFO DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*) SUBROUTINE DTZRZF_64(M, N, A, LDA, TAU, WORK, LWORK, INFO) INTEGER*8 M, N, LDA, LWORK, INFO DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*) F95 INTERFACE SUBROUTINE TZRZF(M, N, A, LDA, TAU, WORK, LWORK, INFO) INTEGER :: M, N, LDA, LWORK, INFO REAL(8), DIMENSION(:) :: TAU, WORK REAL(8), DIMENSION(:,:) :: A SUBROUTINE TZRZF_64(M, N, A, LDA, TAU, WORK, LWORK, INFO) INTEGER(8) :: M, N, LDA, LWORK, INFO REAL(8), DIMENSION(:) :: TAU, WORK REAL(8), DIMENSION(:,:) :: A C INTERFACE #include <sunperf.h> void dtzrzf(int m, int n, double *a, int lda, double *tau, int *info); void dtzrzf_64(long m, long n, double *a, long lda, double *tau, long *info);
Oracle Solaris Studio Performance Library dtzrzf(3P) NAME dtzrzf - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations SYNOPSIS SUBROUTINE DTZRZF(M, N, A, LDA, TAU, WORK, LWORK, INFO) INTEGER M, N, LDA, LWORK, INFO DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*) SUBROUTINE DTZRZF_64(M, N, A, LDA, TAU, WORK, LWORK, INFO) INTEGER*8 M, N, LDA, LWORK, INFO DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*) F95 INTERFACE SUBROUTINE TZRZF(M, N, A, LDA, TAU, WORK, LWORK, INFO) INTEGER :: M, N, LDA, LWORK, INFO REAL(8), DIMENSION(:) :: TAU, WORK REAL(8), DIMENSION(:,:) :: A SUBROUTINE TZRZF_64(M, N, A, LDA, TAU, WORK, LWORK, INFO) INTEGER(8) :: M, N, LDA, LWORK, INFO REAL(8), DIMENSION(:) :: TAU, WORK REAL(8), DIMENSION(:,:) :: A C INTERFACE #include <sunperf.h> void dtzrzf(int m, int n, double *a, int lda, double *tau, int *info); void dtzrzf_64(long m, long n, double *a, long lda, double *tau, long *info); PURPOSE dtzrzf reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an N-by-N orthogonal matrix and R is an M-by-M upper trian- gular matrix. ARGUMENTS M (input) The number of rows of the matrix A. M >= 0. N (input) The number of columns of the matrix A. N >= 0. A (input/output) On entry, the leading M-by-N upper trapezoidal part of the array A must contain the matrix to be factorized. On exit, the leading M-by-M upper triangular part of A con- tains the upper triangular matrix R, and elements M+1 to N of the first M rows of A, with the array TAU, represent the orthogonal matrix Z as a product of M elementary reflectors. LDA (input) The leading dimension of the array A. LDA >= max(1,M). TAU (output) The scalar factors of the elementary reflectors. WORK (workspace) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= M*NB, where NB is the optimal blocksize. 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 Based on contributions by A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA The N-by-N matrix Z can be computed by Z = Z(1)*Z(2)* ... *Z(M) where each N-by-N Z(k) is given by Z(k) = I - tau(k)*v(k)*v(k)**T with v(k) is the kth row vector of the M-by-N matrix V = ( I A(:,M+1:N) ) I is the M-by-M identity matrix, A(:,M+1:N) is the output stored in A on exit from DTZRZF, and tau(k) is the kth element of the array TAU. 7 Nov 2015 dtzrzf(3P)