cpbsv-f(3)

cpbsv.f –

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine cpbsv (characterUPLO, integerN, integerKD, integerNRHS, complex, dimension( ldab, * )AB, integerLDAB, complex, dimension( ldb, * )B, integerLDB, integerINFO)

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

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:

UPLO

 UPLO is CHARACTER*1
 = 'U': Upper triangle of A is stored;
 = 'L': Lower triangle of A is stored.

 N is INTEGER
 The number of linear equations, i.e., the order of the
 matrix A. N >= 0.

 KD is INTEGER
 The number of superdiagonals of the matrix A if UPLO = 'U',
 or the number of subdiagonals if UPLO = 'L'. KD >= 0.

NRHS

 NRHS is INTEGER
 The number of right hand sides, i.e., the number of columns
 of the matrix B. NRHS >= 0.

 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.

LDAB

 LDAB is INTEGER
 The leading dimension of the array AB. LDAB >= KD+1.

 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.

LDB

 LDB is INTEGER
 The leading dimension of the array B. LDB >= max(1,N).

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 cpbsv.f.

Author

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