
cspsv.f(3) LAPACK cspsv.f(3)
NAME
cspsv.f 
SYNOPSIS
Functions/Subroutines
subroutine cspsv (UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
CSPSV computes the solution to system of linear equations A * X = B for OTHER
matrices
Function/Subroutine Documentation
subroutine cspsv (characterUPLO, integerN, integerNRHS, complex, dimension( * )AP, integer,
dimension( * )IPIV, complex, dimension( ldb, * )B, integerLDB, integerINFO)
CSPSV computes the solution to system of linear equations A * X = B for OTHER matrices
Purpose:
CSPSV computes the solution to a complex system of linear equations
A * X = B,
where A is an NbyN symmetric matrix stored in packed format and X
and B are NbyNRHS matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, D is symmetric and block diagonal with 1by1
and 2by2 diagonal blocks. 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
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
AP is COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The jth column of A
is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j1)*(2nj)/2) = A(i,j) for j<=i<=n.
See below for further details.
On exit, the block diagonal matrix D and the multipliers used
to obtain the factor U or L from the factorization
A = U*D*U**T or A = L*D*L**T as computed by CSPTRF, stored as
a packed triangular matrix in the same storage format as A.
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D, as
determined by CSPTRF. If IPIV(k) > 0, then rows and columns
k and IPIV(k) were interchanged, and D(k,k) is a 1by1
diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k1) < 0,
then rows and columns k1 and IPIV(k) were interchanged and
D(k1:k,k1:k) is a 2by2 diagonal block. If UPLO = 'L' and
IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2by2
diagonal block.
B
B is COMPLEX array, dimension (LDB,NRHS)
On entry, the NbyNRHS right hand side matrix B.
On exit, if INFO = 0, the NbyNRHS 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 ith argument had an illegal value
> 0: if INFO = i, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be
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':
Twodimensional storage of the symmetric matrix A:
a11 a12 a13 a14
a22 a23 a24
a33 a34 (aij = aji)
a44
Packed storage of the upper triangle of A:
AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
Definition at line 163 of file cspsv.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 cspsv.f(3) 
