04-14-2009
@OP, if you want to avoid such "shell versions issue", use a dedicated tool like awk or scripting language such as Perl/Python, where the methods of file parsing works the same across different language versions.
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ZHPSV(l) ) ZHPSV(l)
NAME
ZHPSV - compute the solution to a complex system of linear equations A * X = B,
SYNOPSIS
SUBROUTINE ZHPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
CHARACTER UPLO
INTEGER INFO, LDB, N, NRHS
INTEGER IPIV( * )
COMPLEX*16 AP( * ), B( LDB, * )
PURPOSE
ZHPSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix stored in packed for-
mat and X and B are N-by-NRHS matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**H, if UPLO = 'U', or
A = L * D * L**H, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower) triangular matrices, D is Hermitian 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*16 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, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**H or A
= L*D*L**H as computed by ZHPTRF, 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 ZHPTRF. 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*16 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 singu-
lar, 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 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 ]
LAPACK version 3.0 15 June 2000 ZHPSV(l)