zgels - solve overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A
SUBROUTINE ZGELS(TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK, LDWORK, INFO) CHARACTER*1 TRANSA DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER M, N, NRHS, LDA, LDB, LDWORK, INFO SUBROUTINE ZGELS_64(TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK, LDWORK, INFO) CHARACTER*1 TRANSA DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER*8 M, N, NRHS, LDA, LDB, LDWORK, INFO F95 INTERFACE SUBROUTINE GELS(TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK, LDWORK, INFO) CHARACTER(LEN=1) :: TRANSA COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER :: M, N, NRHS, LDA, LDB, LDWORK, INFO SUBROUTINE GELS_64(TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK, LDWORK, INFO) CHARACTER(LEN=1) :: TRANSA COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER(8) :: M, N, NRHS, LDA, LDB, LDWORK, INFO C INTERFACE #include <sunperf.h> void zgels (char transa, int m, int n, int nrhs, doublecomplex* a, int lda, doublecomplex* b, int ldb, int* info); void zgels_64 (char transa, long m, long n, long nrhs, doublecomplex* a, long lda, doublecomplex* b, long ldb, long* info);
Oracle Solaris Studio Performance Library zgels(3P) NAME zgels - solve overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A SYNOPSIS SUBROUTINE ZGELS(TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK, LDWORK, INFO) CHARACTER*1 TRANSA DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER M, N, NRHS, LDA, LDB, LDWORK, INFO SUBROUTINE ZGELS_64(TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK, LDWORK, INFO) CHARACTER*1 TRANSA DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER*8 M, N, NRHS, LDA, LDB, LDWORK, INFO F95 INTERFACE SUBROUTINE GELS(TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK, LDWORK, INFO) CHARACTER(LEN=1) :: TRANSA COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER :: M, N, NRHS, LDA, LDB, LDWORK, INFO SUBROUTINE GELS_64(TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK, LDWORK, INFO) CHARACTER(LEN=1) :: TRANSA COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER(8) :: M, N, NRHS, LDA, LDB, LDWORK, INFO C INTERFACE #include <sunperf.h> void zgels (char transa, int m, int n, int nrhs, doublecomplex* a, int lda, doublecomplex* b, int ldb, int* info); void zgels_64 (char transa, long m, long n, long nrhs, doublecomplex* a, long lda, doublecomplex* b, long ldb, long* info); PURPOSE zgels solves overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A. It is assumed that A has full rank. The following options are provided: 1. If TRANS = 'N' and m >= n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize || B - A*X ||. 2. If TRANS = 'N' and m < n: find the minimum norm solution of an underdetermined system A * X = B. 3. If TRANS = 'C' and m >= n: find the minimum norm solution of an undetermined system A**H * X = B. 4. If TRANS = 'C' and m < n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize || B - A**H * X ||. Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix X. ARGUMENTS TRANSA (input) = 'N': the linear system involves A; = 'C': the linear system involves A**H. M (input) The number of rows of the matrix A. M >= 0. N (input) The number of columns of the matrix A. N >= 0. NRHS (input) The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0. A (input/output) On entry, the M-by-N matrix A. if M >= N, A is overwritten by details of its QR factoriza- tion as returned by ZGEQRF; if M < N, A is overwritten by details of its LQ factoriza- tion as returned by ZGELQF. LDA (input) The leading dimension of the array A. LDA >= max(1,M). B (input/output) On entry, the matrix B of right hand side vectors, stored columnwise; B is M-by-NRHS if TRANSA = 'N', or N-by-NRHS if TRANSA = 'C'. On exit, B is overwritten by the solution vectors, stored columnwise: if TRANSA = 'N' and m >= n, rows 1 to n of B contain the least squares solution vectors; the residual sum of squares for the solution in each column is given by the sum of squares of elements N+1 to M in that column; if TRANSA = 'N' and m < n, rows 1 to N of B contain the mini- mum norm solution vectors; if TRANSA = 'C' and m >= n, rows 1 to M of B contain the min- imum norm solution vectors; if TRANSA = 'C' and m < n, rows 1 to M of B contain the least squares solution vectors; the residual sum of squares for the solution in each column is given by the sum of squares of elements M+1 to N in that column. LDB (input) The leading dimension of the array B. LDB >= MAX(1,M,N). WORK (workspace) On exit, if INFO = 0, WORK(1) returns the optimal LDWORK. LDWORK (input) The dimension of the array WORK. LDWORK >= max( 1, MN + max( MN, NRHS )). For optimal perfor- mance, LDWORK >= max( 1, MN + max( MN, NRHS )*NB ), where MN = min(M,N) and NB is the optimum block size. If LDWORK = -1, then a workspace query is assumed; the rou- tine 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 LDWORK is issued by XERBLA. INFO (output) = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value. 7 Nov 2015 zgels(3P)