CSPSV(1) LAPACK driver routine (version 3.2) CSPSV(1)NAME
CSPSV - computes the solution to a complex system of linear equations
A * X = B,
SYNOPSIS
SUBROUTINE CSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
CHARACTER UPLO
INTEGER INFO, LDB, N, NRHS
INTEGER IPIV( * )
COMPLEX AP( * ), B( LDB, * )
PURPOSE
CSPSV computes the solution to a complex system of linear equations
A * X = B, where A is an N-by-N symmetric matrix stored in packed
format and X and B are N-by-NRHS 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) tri‐
angular matrices, D is symmetric and block diagonal with 1-by-1 and
2-by-2 diagonal blocks. The factored form of A is then used to solve
the system of equations A * X = B.
ARGUMENTS
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The number of linear equations, i.e., the order of the matrix
A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrix B. NRHS >= 0.
AP (input/output) 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 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, the block diagonal matrix D and the multi‐
pliers 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 (output) 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 1-by-1 diagonal
block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows
and columns k-1 and -IPIV(k) were interchanged and
D(k-1:k,k-1:k) is a 2-by-2 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 2-by-2 diagonal
block.
B (input/output) 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 (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th 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.
FURTHER DETAILS
The packed storage scheme is illustrated by the following example when
N = 4, UPLO = 'U':
Two-dimensional 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 ]
LAPACK driver routine (version 3November 2008 CSPSV(1)
