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cgelss(3P)		    Sun Performance Library		    cgelss(3P)

NAME
       cgelss  -  compute  the minimum norm solution to a complex linear least
       squares problem

SYNOPSIS
       SUBROUTINE CGELSS(M, N, NRHS, A, LDA, B, LDB, SING, RCOND, IRANK,
	     WORK, LDWORK, WORK2, INFO)

       COMPLEX A(LDA,*), B(LDB,*), WORK(*)
       INTEGER M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO
       REAL RCOND
       REAL SING(*), WORK2(*)

       SUBROUTINE CGELSS_64(M, N, NRHS, A, LDA, B, LDB, SING, RCOND, IRANK,
	     WORK, LDWORK, WORK2, INFO)

       COMPLEX A(LDA,*), B(LDB,*), WORK(*)
       INTEGER*8 M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO
       REAL RCOND
       REAL SING(*), WORK2(*)

   F95 INTERFACE
       SUBROUTINE GELSS([M], [N], [NRHS], A, [LDA], B, [LDB], SING, RCOND,
	      IRANK, [WORK], [LDWORK], [WORK2], [INFO])

       COMPLEX, DIMENSION(:) :: WORK
       COMPLEX, DIMENSION(:,:) :: A, B
       INTEGER :: M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO
       REAL :: RCOND
       REAL, DIMENSION(:) :: SING, WORK2

       SUBROUTINE GELSS_64([M], [N], [NRHS], A, [LDA], B, [LDB], SING,
	      RCOND, IRANK, [WORK], [LDWORK], [WORK2], [INFO])

       COMPLEX, DIMENSION(:) :: WORK
       COMPLEX, DIMENSION(:,:) :: A, B
       INTEGER(8) :: M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO
       REAL :: RCOND
       REAL, DIMENSION(:) :: SING, WORK2

   C INTERFACE
       #include <sunperf.h>

       void cgelss(int m, int n, int nrhs, complex *a, int  lda,  complex  *b,
		 int ldb, float *sing, float rcond, int *irank, int *info);

       void cgelss_64(long m, long n, long nrhs, complex *a, long lda, complex
		 *b, long ldb, float *sing, float  rcond,  long	 *irank,  long
		 *info);

PURPOSE
       cgelss  computes	 the  minimum  norm solution to a complex linear least
       squares problem:

       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 singu‐
       lar 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,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 >=  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 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.

       WORK2 (workspace)
		 dimension(5*min(M,N))

       INFO (output)
		 = 0:  successful exit
		 < 0:  if INFO = -i, the i-th argument had an illegal value.
		 > 0:  the algorithm for computing the SVD failed to converge;
		 if INFO = i, i off-diagonal elements of an intermediate bidi‐
		 agonal form did not converge to zero.

				  6 Mar 2009			    cgelss(3P)
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