NAME

SYNOPSIS

  SUBROUTINE DGELSS( M, N, NRHS, A, LDA, B, LDB, SING, RCOND, IRANK, 
 *      WORK, LDWORK, INFO)
  INTEGER M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO
  DOUBLE PRECISION RCOND
  DOUBLE PRECISION A(LDA,*), B(LDB,*), SING(*), WORK(*)
 
  SUBROUTINE DGELSS_64( M, N, NRHS, A, LDA, B, LDB, SING, RCOND, 
 *      IRANK, WORK, LDWORK, INFO)
  INTEGER*8 M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO
  DOUBLE PRECISION RCOND
  DOUBLE PRECISION A(LDA,*), B(LDB,*), SING(*), WORK(*)
 

F95 INTERFACE

  SUBROUTINE GELSS( [M], [N], [NRHS], A, [LDA], B, [LDB], SING, RCOND, 
 *       IRANK, [WORK], [LDWORK], [INFO])
  INTEGER :: M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO
  REAL(8) :: RCOND
  REAL(8), DIMENSION(:) :: SING, WORK
  REAL(8), DIMENSION(:,:) :: A, B
 
  SUBROUTINE GELSS_64( [M], [N], [NRHS], A, [LDA], B, [LDB], SING, 
 *       RCOND, IRANK, [WORK], [LDWORK], [INFO])
  INTEGER(8) :: M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO
  REAL(8) :: RCOND
  REAL(8), DIMENSION(:) :: SING, WORK
  REAL(8), DIMENSION(:,:) :: A, B
 

C INTERFACE

void dgelss(int m, int n, int nrhs, double *a, int lda, double *b, int ldb, double *sing, double rcond, int *irank, int *info);

void dgelss_64(long m, long n, long nrhs, double *a, long lda, double *b, long ldb, double *sing, double rcond, long *irank, long *info);

PURPOSE

Minimize 2-norm(| b - A*x |).

using the singular value decomposition (SVD) of A. A is an M-by-N matrix which may be rank-deficient.

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.

The effective rank of A is determined by treating as zero those singular values which are less than RCOND times the largest singular value.

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.

* 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, the first min(m,n) rows of A are overwritten with its right singular vectors, stored rowwise.

* LDA (input)

The leading dimension of the array A. LDA >= max(1,M).

* B (input/output)

On entry, the M-by-NRHS right hand side matrix B. On exit, B is overwritten by the N-by-NRHS solution matrix X. If m >= n and IRANK = n, the residual sum-of-squares for the solution in the i-th column is given by the sum of squares of elements n+1:m in that column.

* LDB (input)

The leading dimension of the array B. LDB >= max(1,max(M,N)).

* SING (output)

The singular values of A in decreasing order. The condition number of A in the 2-norm = SING(1)/SING(min(m,n)).

* RCOND (input)

RCOND is used to determine the effective rank of A. Singular values SING(i) <= RCOND*SING(1) are treated as zero. If RCOND < 0, machine precision is used instead.

* IRANK (output)

The effective rank of A, i.e., the number of singular values which are greater than RCOND*SING(1).

* WORK (workspace)

On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.

* LDWORK (input)

The dimension of the array WORK. LDWORK >= 1, and also: LDWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS ) For good performance, LDWORK should generally be larger.

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)