cpbsv()

subroutine cpbsv	(	character	uplo,
		integer	n,
		integer	kd,
		integer	nrhs,
		complex, dimension( ldab, * )	ab,
		integer	ldab,
		complex, dimension( ldb, * )	b,
		integer	ldb,
		integer	info )

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

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Purpose:

!>
!> CPBSV computes the solution to a complex system of linear equations
!>    A * X = B,
!> where A is an N-by-N Hermitian positive definite band 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 band matrix, and L is a lower
!> triangular band matrix, with the same number of superdiagonals or
!> subdiagonals as A.  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]	KD	!> KD is INTEGER !> The number of superdiagonals of the matrix A if UPLO = 'U', !> or the number of subdiagonals if UPLO = 'L'. KD >= 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]	AB	!> AB is COMPLEX array, dimension (LDAB,N) !> On entry, the upper or lower triangle of the Hermitian band !> matrix A, stored in the first KD+1 rows of the array. The !> j-th column of A is stored in the j-th column of the array AB !> as follows: !> if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; !> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD). !> See below for further details. !> !> On exit, if INFO = 0, the triangular factor U or L from the !> Cholesky factorization A = U**H*U or A = L*L**H of the band !> matrix A, in the same storage format as A. !>
[in]	LDAB	!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KD+1. !>
[in,out]	B	!> B is COMPLEX 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 principal minor of order i !> of A is not positive, 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.

Further Details:

!>
!>  The band storage scheme is illustrated by the following example, when
!>  N = 6, KD = 2, and UPLO = 'U':
!>
!>  On entry:                       On exit:
!>
!>      *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
!>      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
!>     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
!>
!>  Similarly, if UPLO = 'L' the format of A is as follows:
!>
!>  On entry:                       On exit:
!>
!>     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
!>     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
!>     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
!>
!>  Array elements marked * are not used by the routine.
!> 

Definition at line 161 of file cpbsv.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, KD, LDAB, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      COMPLEX            AB( LDAB, * ), B( LDB, * )
*     ..
*
*  =====================================================================
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           cpbtrf, cpbtrs, xerbla
*     ..
*     .. 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( kd.LT.0 ) THEN
         info = -3
      ELSE IF( nrhs.LT.0 ) THEN
         info = -4
      ELSE IF( ldab.LT.kd+1 ) THEN
         info = -6
      ELSE IF( ldb.LT.max( 1, n ) ) THEN
         info = -8
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'CPBSV ', -info )
         RETURN
      END IF
*
*     Compute the Cholesky factorization A = U**H*U or A = L*L**H.
*
      CALL cpbtrf( uplo, n, kd, ab, ldab, info )
      IF( info.EQ.0 ) THEN
*
*        Solve the system A*X = B, overwriting B with X.
*
         CALL cpbtrs( uplo, n, kd, nrhs, ab, ldab, b, ldb, info )
*
      END IF
      RETURN
*
*     End of CPBSV
*

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