cppsv-f(3)

cppsv.f –

Synopsis

Functions/Subroutines

subroutine cppsv (UPLO, N, NRHS, AP, B, LDB, INFO)
CPPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Function/Subroutine Documentation

subroutine cppsv (characterUPLO, integerN, integerNRHS, complex, dimension( * )AP, complex, dimension( ldb, * )B, integerLDB, integerINFO)

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

Purpose:

 CPPSV computes the solution to a complex system of linear equations
 A * X = B,
 where A is an N-by-N Hermitian positive definite matrix stored in
 packed format 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 matrix and L is a lower triangular
 matrix. 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.

NRHS

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

 AP is COMPLEX array, dimension (N*(N+1)/2)
 On entry, the upper or lower triangle of the Hermitian 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, if INFO = 0, the factor U or L from the Cholesky
 factorization A = U**H*U or A = L*L**H, in the same storage
 format as A.

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

Definition at line 145 of file cppsv.f.

Author

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