zpbtrs()

subroutine zpbtrs	(	character	uplo,
		integer	n,
		integer	kd,
		integer	nrhs,
		complex*16, dimension( ldab, * )	ab,
		integer	ldab,
		complex*16, dimension( ldb, * )	b,
		integer	ldb,
		integer	info
	)

ZPBTRS

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Purpose:

 ZPBTRS solves a system of linear equations A*X = B with a Hermitian
 positive definite band matrix A using the Cholesky factorization
 A = U**H *U or A = L*L**H computed by ZPBTRF.

Parameters

[in]	UPLO	UPLO is CHARACTER*1 = 'U': Upper triangular factor stored in AB; = 'L': Lower triangular factor stored in AB.
[in]	N	N is INTEGER 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]	AB	AB is COMPLEX*16 array, dimension (LDAB,N) The triangular factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
[in]	LDAB	LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.
[in,out]	B	B is COMPLEX*16 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]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 120 of file zpbtrs.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..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, KD, LDAB, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      COMPLEX*16         AB( LDAB, * ), B( LDB, * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            J
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, ztbsv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      upper = lsame( uplo, 'U' )
      IF( .NOT.upper .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( 'ZPBTRS', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 .OR. nrhs.EQ.0 )
     $   RETURN
*
      IF( upper ) THEN
*
*        Solve A*X = B where A = U**H *U.
*
         DO 10 j = 1, nrhs
*
*           Solve U**H *X = B, overwriting B with X.
*
            CALL ztbsv( 'Upper', 'Conjugate transpose', 'Non-unit', n,
     $                  kd, ab, ldab, b( 1, j ), 1 )
*
*           Solve U*X = B, overwriting B with X.
*
            CALL ztbsv( 'Upper', 'No transpose', 'Non-unit', n, kd, ab,
     $                  ldab, b( 1, j ), 1 )
   10    CONTINUE
      ELSE
*
*        Solve A*X = B where A = L*L**H.
*
         DO 20 j = 1, nrhs
*
*           Solve L*X = B, overwriting B with X.
*
            CALL ztbsv( 'Lower', 'No transpose', 'Non-unit', n, kd, ab,
     $                  ldab, b( 1, j ), 1 )
*
*           Solve L**H *X = B, overwriting B with X.
*
            CALL ztbsv( 'Lower', 'Conjugate transpose', 'Non-unit', n,
     $                  kd, ab, ldab, b( 1, j ), 1 )
   20    CONTINUE
      END IF
*
      RETURN
*
*     End of ZPBTRS
*

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