zposv()

subroutine zposv	(	character	UPLO,
		integer	N,
		integer	NRHS,
		complex*16, dimension( lda, * )	A,
		integer	LDA,
		complex*16, dimension( ldb, * )	B,
		integer	LDB,
		integer	INFO
	)

ZPOSV computes the solution to system of linear equations A * X = B for PO matrices

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Purpose:

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

 The Cholesky decomposition is used to factor A as
    A = U**H* U,  if UPLO = 'U', or
    A = L * L**H,  if UPLO = 'L',
 where U is an upper triangular matrix and  L is a lower triangular
 matrix.  The factored form of A is then used to solve the system of
 equations A * X = B.

Parameters

[in]	UPLO	UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
[in]	N	N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]	A	A is COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular 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 factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in,out]	B	B is COMPLEX*16 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.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

December 2016

Definition at line 132 of file zposv.f.

*
*  -- LAPACK driver routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), B( LDB, * )
*     ..
*
*  =====================================================================
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, zpotrf, zpotrs
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
         info = -1
      ELSE IF( n.LT.0 ) THEN
         info = -2
      ELSE IF( nrhs.LT.0 ) THEN
         info = -3
      ELSE IF( lda.LT.max( 1, n ) ) THEN
         info = -5
      ELSE IF( ldb.LT.max( 1, n ) ) THEN
         info = -7
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZPOSV ', -info )
         RETURN
      END IF
*
*     Compute the Cholesky factorization A = U**H *U or A = L*L**H.
*
      CALL zpotrf( uplo, n, a, lda, info )
      IF( info.EQ.0 ) THEN
*
*        Solve the system A*X = B, overwriting B with X.
*
         CALL zpotrs( uplo, n, nrhs, a, lda, b, ldb, info )
*
      END IF
      RETURN
*
*     End of ZPOSV
*

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