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chesv(3P)		    Sun Performance Library		     chesv(3P)

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

SYNOPSIS
       SUBROUTINE CHESV(UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK, LDWORK,
	     INFO)

       CHARACTER * 1 UPLO
       COMPLEX A(LDA,*), B(LDB,*), WORK(*)
       INTEGER N, NRHS, LDA, LDB, LDWORK, INFO
       INTEGER IPIVOT(*)

       SUBROUTINE CHESV_64(UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK,
	     LDWORK, INFO)

       CHARACTER * 1 UPLO
       COMPLEX A(LDA,*), B(LDB,*), WORK(*)
       INTEGER*8 N, NRHS, LDA, LDB, LDWORK, INFO
       INTEGER*8 IPIVOT(*)

   F95 INTERFACE
       SUBROUTINE HESV(UPLO, [N], [NRHS], A, [LDA], IPIVOT, B, [LDB], [WORK],
	      [LDWORK], [INFO])

       CHARACTER(LEN=1) :: UPLO
       COMPLEX, DIMENSION(:) :: WORK
       COMPLEX, DIMENSION(:,:) :: A, B
       INTEGER :: N, NRHS, LDA, LDB, LDWORK, INFO
       INTEGER, DIMENSION(:) :: IPIVOT

       SUBROUTINE HESV_64(UPLO, [N], [NRHS], A, [LDA], IPIVOT, B, [LDB],
	      [WORK], [LDWORK], [INFO])

       CHARACTER(LEN=1) :: UPLO
       COMPLEX, DIMENSION(:) :: WORK
       COMPLEX, DIMENSION(:,:) :: A, B
       INTEGER(8) :: N, NRHS, LDA, LDB, LDWORK, INFO
       INTEGER(8), DIMENSION(:) :: IPIVOT

   C INTERFACE
       #include <sunperf.h>

       void chesv(char uplo, int  n,  int  nrhs,  complex  *a,	int  lda,  int
		 *ipivot, complex *b, int ldb, int *info);

       void  chesv_64(char uplo, long n, long nrhs, complex *a, long lda, long
		 *ipivot, complex *b, long ldb, long *info);

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) tri‐
       angular 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)
		 = 'U':	 Upper triangle of A is stored;
		 = 'L':	 Lower triangle of A is stored.

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

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

       A (input/output)
		 On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
		 N-by-N upper triangular part of A contains the upper triangu‐
		 lar 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 factor‐
		 ization A = U*D*U**H or A = L*D*L**H as computed by CHETRF.

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

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

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

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

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

		 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
		 >  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.

				  6 Mar 2009			     chesv(3P)
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