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RedHat 9 (Linux i386) - man page for chesv (redhat section l)

CHESV(l)					)					 CHESV(l)

NAME
       CHESV - compute the solution to a complex system of linear equations A * X = B,

SYNOPSIS
       SUBROUTINE CHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO )

	   CHARACTER	 UPLO

	   INTEGER	 INFO, LDA, LDB, LWORK, N, NRHS

	   INTEGER	 IPIV( * )

	   COMPLEX	 A( LDA, * ), B( LDB, * ), WORK( * )

PURPOSE
       CHESV  computes the solution to a complex system of linear equations A * X = B, where A is
       an N-by-N Hermitian matrix and X and B are N-by-NRHS matrices.

       The diagonal pivoting method is used to factor A as
	  A = U * D * U**H,  if UPLO = 'U', or
	  A = L * D * L**H,  if UPLO = 'L',
       where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and
       D  is  Hermitian  and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.  The factored
       form of A is then used to solve the system of equations A * X = B.

ARGUMENTS
       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangle of A is stored;
	       = 'L':  Lower triangle of A is stored.

       N       (input) INTEGER
	       The number of linear equations, i.e., the order of the matrix A.  N >= 0.

       NRHS    (input) INTEGER
	       The number of right hand sides, i.e., the number of columns of the matrix B.  NRHS
	       >= 0.

       A       (input/output) COMPLEX array, dimension (LDA,N)
	       On  entry, the Hermitian matrix A.  If UPLO = 'U', the leading N-by-N upper trian-
	       gular part of A contains the upper triangular  part  of	the  matrix  A,  and  the
	       strictly lower triangular part of A is not referenced.  If UPLO = 'L', the leading
	       N-by-N lower triangular part of A contains the lower triangular part of the matrix
	       A, and the strictly upper triangular part of A is not referenced.

	       On  exit,  if  INFO  =  0, the block diagonal matrix D and the multipliers used to
	       obtain the factor U or L from the factorization A = U*D*U**H or A  =  L*D*L**H  as
	       computed by CHETRF.

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

       IPIV    (output) INTEGER array, dimension (N)
	       Details of the interchanges and the block structure of D, as determined by CHETRF.
	       If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and  D(k,k)
	       is  a 1-by-1 diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows
	       and columns k-1 and -IPIV(k) were interchanged  and  D(k-1:k,k-1:k)  is	a  2-by-2
	       diagonal  block.  If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns
	       k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

       B       (input/output) COMPLEX array, dimension (LDB,NRHS)
	       On entry, the N-by-NRHS right hand side matrix B.  On exit, if INFO = 0, the N-by-
	       NRHS solution matrix X.

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

       WORK    (workspace/output) COMPLEX array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The  length of WORK.  LWORK >= 1, and for best performance LWORK >= N*NB, where NB
	       is the optimal blocksize for CHETRF.

	       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) INTEGER
	       = 0: successful exit
	       < 0: if INFO = -i, the i-th argument had an illegal value
	       > 0: if INFO = i, D(i,i) is exactly zero.  The factorization has  been  completed,
	       but  the block diagonal matrix D is exactly singular, so the solution could not be
	       computed.

LAPACK version 3.0			   15 June 2000 				 CHESV(l)


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