• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

dgels - solve overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A

SYNOPSIS

  SUBROUTINE DGELS( TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK, LDWORK, 
 *      INFO)
  CHARACTER * 1 TRANSA
  INTEGER M, N, NRHS, LDA, LDB, LDWORK, INFO
  DOUBLE PRECISION A(LDA,*), B(LDB,*), WORK(*)

  SUBROUTINE DGELS_64( TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK, 
 *      LDWORK, INFO)
  CHARACTER * 1 TRANSA
  INTEGER*8 M, N, NRHS, LDA, LDB, LDWORK, INFO
  DOUBLE PRECISION A(LDA,*), B(LDB,*), WORK(*)

F95 INTERFACE

  SUBROUTINE GELS( [TRANSA], [M], [N], [NRHS], A, [LDA], B, [LDB], 
 *       [WORK], [LDWORK], [INFO])
  CHARACTER(LEN=1) :: TRANSA
  INTEGER :: M, N, NRHS, LDA, LDB, LDWORK, INFO
  REAL(8), DIMENSION(:) :: WORK
  REAL(8), DIMENSION(:,:) :: A, B

  SUBROUTINE GELS_64( [TRANSA], [M], [N], [NRHS], A, [LDA], B, [LDB], 
 *       [WORK], [LDWORK], [INFO])
  CHARACTER(LEN=1) :: TRANSA
  INTEGER(8) :: M, N, NRHS, LDA, LDB, LDWORK, INFO
  REAL(8), DIMENSION(:) :: WORK
  REAL(8), DIMENSION(:,:) :: A, B

C INTERFACE

#include <sunperf.h>

void dgels(char transa, int m, int n, int nrhs, double *a, int lda, double *b, int ldb, int *info);

void dgels_64(char transa, long m, long n, long nrhs, double *a, long lda, double *b, long ldb, long *info);

PURPOSE

dgels solves overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its 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 = 'T' and m >= n: find the minimum norm solution of an undetermined system A**T * X = B.

4. If TRANS = 'T' and m < n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize || B - A**T * 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;

   = 'T': the linear system involves A**T.

• 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. On exit, if M > = N, A is overwritten by details of its QR factorization as returned by SGEQRF; if M < N, A is overwritten by details of its LQ factorization as returned by SGELQF.

• 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 = 'T'. 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 minimum norm solution vectors; if TRANSA = 'T' and m > = n, rows 1 to M of B contain the minimum norm solution vectors; if TRANSA = 'T' 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 performance, 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 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 LDWORK is issued by XERBLA.

• INFO (output)
  

   = 0:  successful exit

   < 0:  if INFO  = -i, the i-th argument had an illegal value