ctzrzf - N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations
SUBROUTINE CTZRZF(M, N, A, LDA, TAU, WORK, LWORK, INFO) COMPLEX A(LDA,*), TAU(*), WORK(*) INTEGER M, N, LDA, LWORK, INFO SUBROUTINE CTZRZF_64(M, N, A, LDA, TAU, WORK, LWORK, INFO) COMPLEX A(LDA,*), TAU(*), WORK(*) INTEGER*8 M, N, LDA, LWORK, INFO F95 INTERFACE SUBROUTINE TZRZF(M, N, A, LDA, TAU, WORK, LWORK, INFO) COMPLEX, DIMENSION(:) :: TAU, WORK COMPLEX, DIMENSION(:,:) :: A INTEGER :: M, N, LDA, LWORK, INFO SUBROUTINE TZRZF_64(M, N, A, LDA, TAU, WORK, LWORK, INFO) COMPLEX, DIMENSION(:) :: TAU, WORK COMPLEX, DIMENSION(:,:) :: A INTEGER(8) :: M, N, LDA, LWORK, INFO C INTERFACE #include <sunperf.h> void ctzrzf(int m, int n, complex *a, int lda, complex *tau, int *info); void ctzrzf_64(long m, long n, complex *a, long lda, complex *tau, long *info);
Oracle Solaris Studio Performance Library ctzrzf(3P) NAME ctzrzf - reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations SYNOPSIS SUBROUTINE CTZRZF(M, N, A, LDA, TAU, WORK, LWORK, INFO) COMPLEX A(LDA,*), TAU(*), WORK(*) INTEGER M, N, LDA, LWORK, INFO SUBROUTINE CTZRZF_64(M, N, A, LDA, TAU, WORK, LWORK, INFO) COMPLEX A(LDA,*), TAU(*), WORK(*) INTEGER*8 M, N, LDA, LWORK, INFO F95 INTERFACE SUBROUTINE TZRZF(M, N, A, LDA, TAU, WORK, LWORK, INFO) COMPLEX, DIMENSION(:) :: TAU, WORK COMPLEX, DIMENSION(:,:) :: A INTEGER :: M, N, LDA, LWORK, INFO SUBROUTINE TZRZF_64(M, N, A, LDA, TAU, WORK, LWORK, INFO) COMPLEX, DIMENSION(:) :: TAU, WORK COMPLEX, DIMENSION(:,:) :: A INTEGER(8) :: M, N, LDA, LWORK, INFO C INTERFACE #include <sunperf.h> void ctzrzf(int m, int n, complex *a, int lda, complex *tau, int *info); void ctzrzf_64(long m, long n, complex *a, long lda, complex *tau, long *info); PURPOSE ctzrzf reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an N-by-N unitary matrix and R is an M-by-M upper triangular 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 contains the upper triangular matrix R, and elements M+1 to N of the first M rows of A, with the array TAU, represent the unitary 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)**H 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 CTZRZF, and tau(k) is the kth element of the array TAU. 7 Nov 2015 ctzrzf(3P)