zhesv_aa()

subroutine zhesv_aa	(	character	uplo,
		integer	n,
		integer	nrhs,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		integer, dimension( * )	ipiv,
		complex*16, dimension( ldb, * )	b,
		integer	ldb,
		complex*16, dimension( * )	work,
		integer	lwork,
		integer	info
	)

ZHESV_AA computes the solution to system of linear equations A * X = B for HE matrices

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Purpose:

 ZHESV_AA 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.

 Aasen's algorithm is used to factor A as
    A = U**H * T * U,  if UPLO = 'U', or
    A = L * T * L**H,  if UPLO = 'L',
 where U (or L) is a product of permutation and unit upper (lower)
 triangular matrices, and T is Hermitian and tridiagonal. 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 tridiagonal matrix T and the multipliers used to obtain the factor U or L from the factorization A = U**H*T*U or A = L*T*L**H as computed by ZHETRF_AA.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	IPIV	IPIV is INTEGER array, dimension (N) On exit, it contains the details of the interchanges, i.e., the row and column k of A were interchanged with the row and column IPIV(k).
[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]	WORK	WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]	LWORK	LWORK is INTEGER The length of WORK. LWORK >= MAX(1,2*N,3*N-2), and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for ZHETRF. 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.
[out]	INFO	INFO is 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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 160 of file zhesv_aa.f.

*
*  -- LAPACK driver routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            LQUERY
      INTEGER            LWKOPT, LWKOPT_HETRF, LWKOPT_HETRS
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           lsame, ilaenv
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, zhetrf_aa, zhetrs_aa
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      lquery = ( lwork.EQ.-1 )
      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 = -8
      ELSE IF( lwork.LT.max(2*n, 3*n-2) .AND. .NOT.lquery ) THEN
         info = -10
      END IF
*
      IF( info.EQ.0 ) THEN
         CALL zhetrf_aa( uplo, n, a, lda, ipiv, work, -1, info )
         lwkopt_hetrf = int( work(1) )
         CALL zhetrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
     $                   -1, info )
         lwkopt_hetrs = int( work(1) )
         lwkopt = max( lwkopt_hetrf, lwkopt_hetrs )
         work( 1 ) = lwkopt
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZHESV_AA ', -info )
         RETURN
      ELSE IF( lquery ) THEN
         RETURN
      END IF
*
*     Compute the factorization A = U**H*T*U or A = L*T*L**H.
*
      CALL zhetrf_aa( uplo, n, a, lda, ipiv, work, lwork, info )
      IF( info.EQ.0 ) THEN
*
*        Solve the system A*X = B, overwriting B with X.
*
         CALL zhetrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
     $                      lwork, info )
*
      END IF
*
      work( 1 ) = lwkopt
*
      RETURN
*
*     End of ZHESV_AA
*

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