SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
$ LWORK, INFO )
*
* -- LAPACK driver routine (version 3.3.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* -- April 2011 --
* @precisions normal z -> c
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDA, LDB, LWORK, N, NRHS
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* ZHESV 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*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 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
* ZHETRF.
*
* 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 ZHETRF. 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*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.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,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 >= max(1,N*NB), where NB is the optimal blocksize for
* ZHETRF.
* for LWORK < N, TRS will be done with Level BLAS 2
* for LWORK >= N, TRS will be done with Level BLAS 3
*
* 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.
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL LQUERY
INTEGER LWKOPT, NB
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZHETRF, ZHETRS, ZHETRS2
* ..
* .. 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.1 .AND. .NOT.LQUERY ) THEN
INFO = -10
END IF
*
IF( INFO.EQ.0 ) THEN
IF( N.EQ.0 ) THEN
LWKOPT = 1
ELSE
NB = ILAENV( 1, 'ZHETRF', UPLO, N, -1, -1, -1 )
LWKOPT = N*NB
END IF
WORK( 1 ) = LWKOPT
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZHESV ', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Compute the factorization A = U*D*U**H or A = L*D*L**H.
*
CALL ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
IF( INFO.EQ.0 ) THEN
*
* Solve the system A*X = B, overwriting B with X.
*
IF ( LWORK.LT.N ) THEN
*
* Solve with TRS ( Use Level BLAS 2)
*
CALL ZHETRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
ELSE
*
* Solve with TRS2 ( Use Level BLAS 3)
*
CALL ZHETRS2( UPLO,N,NRHS,A,LDA,IPIV,B,LDB,WORK,INFO )
*
END IF
*
END IF
*
WORK( 1 ) = LWKOPT
*
RETURN
*
* End of ZHESV
*
END