zspsv()

subroutine zspsv	(	character	uplo,
		integer	n,
		integer	nrhs,
		complex*16, dimension( * )	ap,
		integer, dimension( * )	ipiv,
		complex*16, dimension( ldb, * )	b,
		integer	ldb,
		integer	info )

ZSPSV computes the solution to system of linear equations A * X = B for OTHER matrices

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Purpose:

!>
!> ZSPSV computes the solution to a complex system of linear equations
!>    A * X = B,
!> where A is an N-by-N symmetric matrix stored in packed format and X
!> and B are N-by-NRHS matrices.
!>
!> The diagonal pivoting method is used to factor A as
!>    A = U * D * U**T,  if UPLO = 'U', or
!>    A = L * D * L**T,  if UPLO = 'L',
!> where U (or L) is a product of permutation and unit upper (lower)
!> triangular matrices, D is symmetric 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.
!> 

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]	AP	!> AP is COMPLEX*16 array, dimension (N*(N+1)/2) !> On entry, the upper or lower triangle of the symmetric matrix !> A, packed columnwise in a linear array. The j-th column of A !> is stored in the array AP as follows: !> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; !> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. !> See below for further details. !> !> On exit, the block diagonal matrix D and the multipliers used !> to obtain the factor U or L from the factorization !> A = U*D*U**T or A = L*D*L**T as computed by ZSPTRF, stored as !> a packed triangular matrix in the same storage format as A. !>
[out]	IPIV	!> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D, as !> determined by ZSPTRF. 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. !>
[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, 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.

Further Details:

!>
!>  The packed storage scheme is illustrated by the following example
!>  when N = 4, UPLO = 'U':
!>
!>  Two-dimensional storage of the symmetric matrix A:
!>
!>     a11 a12 a13 a14
!>         a22 a23 a24
!>             a33 a34     (aij = aji)
!>                 a44
!>
!>  Packed storage of the upper triangle of A:
!>
!>  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
!> 

Definition at line 159 of file zspsv.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, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      COMPLEX*16         AP( * ), B( LDB, * )
*     ..
*
*  =====================================================================
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, zsptrf, zsptrs
*     ..
*     .. 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( ldb.LT.max( 1, n ) ) THEN
         info = -7
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZSPSV ', -info )
         RETURN
      END IF
*
*     Compute the factorization A = U*D*U**T or A = L*D*L**T.
*
      CALL zsptrf( uplo, n, ap, ipiv, info )
      IF( info.EQ.0 ) THEN
*
*        Solve the system A*X = B, overwriting B with X.
*
         CALL zsptrs( uplo, n, nrhs, ap, ipiv, b, ldb, info )
*
      END IF
      RETURN
*
*     End of ZSPSV
*

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