zpbsv.f File Reference

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Functions/Subroutines
subroutine	zpbsv (UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO)
	ZPBSV computes the solution to system of linear equations A * X = B for OTHER matrices

---

Function/Subroutine Documentation

subroutine zpbsv	(	character	UPLO,
		integer	N,
		integer	KD,
		integer	NRHS,
		complex*16, dimension( ldab, * )	AB,
		integer	LDAB,
		complex*16, dimension( ldb, * )	B,
		integer	LDB,
		integer	INFO
	)

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

Download ZPBSV + dependencies [TGZ] [ZIP] [TXT]

Purpose:

 ZPBSV 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*16 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*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, the leading minor of order i of A is not positive definite, 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.

Date:

November 2011

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 165 of file zpbsv.f.

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