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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

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) triangular 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

= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
The number of linear equations, i.e., the order of the matrix A. N >= 0.
The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
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 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.
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.
On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X.
The leading dimension of the array B. LDB >= max(1,N).
= 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 ]

November 2008 LAPACK driver routine (version 3.2)