zhpsv (l)  Linux Manuals
zhpsv: computes the solution to a complex system of linear equations A * X = B,
NAME
ZHPSV  computes 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 equationsA
The diagonal pivoting method is used to factor A as
A
A
where U (or L) is a product of permutation and unit upper (lower) triangular matrices, D is Hermitian 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.
ARGUMENTS
 UPLO (input) CHARACTER*1

= aqUaq: Upper triangle of A is stored;
= aqLaq: 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 jth column of A is stored in the array AP as follows: if UPLO = aqUaq, AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = aqLaq, 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**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 1by1 diagonal block. If UPLO = aqUaq 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 = aqLaq 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 (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
 On entry, the NbyNRHS right hand side matrix B. On exit, if INFO = 0, the NbyNRHS 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 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.
FURTHER DETAILS
The packed storage scheme is illustrated by the following example when N = 4, UPLO = aqUaq:Twodimensional storage of the Hermitian matrix A:
a11 a12 a13 a14
Packed storage of the upper triangle of A:
AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]