chesv_aa_2stage()

subroutine chesv_aa_2stage	(	character	uplo,
		integer	n,
		integer	nrhs,
		complex, dimension( lda, * )	a,
		integer	lda,
		complex, dimension( * )	tb,
		integer	ltb,
		integer, dimension( * )	ipiv,
		integer, dimension( * )	ipiv2,
		complex, dimension( ldb, * )	b,
		integer	ldb,
		complex, dimension( * )	work,
		integer	lwork,
		integer	info )

CHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices

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Purpose:

!>
!> CHESV_AA_2STAGE 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 2-stage 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 band. The matrix T is
!> then LU-factored with partial pivoting. The factored form of A
!> is then used to solve the system of equations A * X = B.
!>
!> This is the blocked version of the algorithm, calling Level 3 BLAS.
!> 

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 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 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, L is stored below (or above) the subdiagonal blocks, !> when UPLO is 'L' (or 'U'). !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[out]	TB	!> TB is COMPLEX array, dimension (MAX(1,LTB)). !> On exit, details of the LU factorization of the band matrix. !>
[in]	LTB	!> LTB is INTEGER !> The size of the array TB. LTB >= MAX(1,4*N), internally !> used to select NB such that LTB >= (3*NB+1)*N. !> !> If LTB = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of LTB, !> returns this value as the first entry of TB, and !> no error message related to LTB is issued by XERBLA. !>
[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). !>
[out]	IPIV2	!> IPIV2 is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i.e., !> the row and column k of T were interchanged with the !> row and column IPIV(k). !>
[in,out]	B	!> B is COMPLEX array, dimension (LDB,NRHS) !> On entry, the right hand side matrix B. !> On exit, the solution matrix X. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !>
[out]	WORK	!> WORK is COMPLEX workspace of size (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>
[in]	LWORK	!> LWORK is INTEGER !> The size of WORK. LWORK >= MAX(1,N), internally used to !> select NB such that LWORK >= N*NB. !> !> 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, band LU factorization failed on i-th column !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 182 of file chesv_aa_2stage.f.

*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
      IMPLICIT NONE
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            N, NRHS, LDA, LDB, LTB, LWORK, INFO
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * ), IPIV2( * )
      COMPLEX            A( LDA, * ), B( LDB, * ), TB( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            UPPER, TQUERY, WQUERY
      INTEGER            LWKMIN, LWKOPT
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               SROUNDUP_LWORK
      EXTERNAL           lsame, sroundup_lwork
*     ..
*     .. External Subroutines ..
      EXTERNAL           chetrf_aa_2stage, chetrs_aa_2stage,
     $                   xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      upper = lsame( uplo, 'U' )
      wquery = ( lwork.EQ.-1 )
      tquery = ( ltb.EQ.-1 )
      lwkmin = max( 1, n )
      IF( .NOT.upper .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( ltb.LT.max( 1, 4*n ) .AND. .NOT.tquery ) THEN
         info = -7
      ELSE IF( ldb.LT.max( 1, n ) ) THEN
         info = -11
      ELSE IF( lwork.LT.lwkmin .AND. .NOT.wquery ) THEN
         info = -13
      END IF
*
      IF( info.EQ.0 ) THEN
         CALL chetrf_aa_2stage( uplo, n, a, lda, tb, -1, ipiv,
     $                          ipiv2, work, -1, info )
         lwkopt = max( lwkmin, int( work( 1 ) ) )
         work( 1 ) = sroundup_lwork( lwkopt )
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'CHESV_AA_2STAGE', -info )
         RETURN
      ELSE IF( wquery .OR. tquery ) THEN
         RETURN
      END IF
*
*     Compute the factorization A = U**H*T*U or A = L*T*L**H.
*
      CALL chetrf_aa_2stage( uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
     $                       work, lwork, info )
      IF( info.EQ.0 ) THEN
*
*        Solve the system A*X = B, overwriting B with X.
*
         CALL chetrs_aa_2stage( uplo, n, nrhs, a, lda, tb, ltb, ipiv,
     $                          ipiv2, b, ldb, info )
*
      END IF
*
      work( 1 ) = sroundup_lwork( lwkopt )
*
      RETURN
*
*     End of CHESV_AA_2STAGE
*

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