zppsv (l) - Linux Manuals

zppsv: computes the solution to a complex system of linear equations A * X = B,

NAME

ZPPSV - computes the solution to a complex system of linear equations A * X = B,

SYNOPSIS

SUBROUTINE ZPPSV(
UPLO, N, NRHS, AP, B, LDB, INFO )

    
CHARACTER UPLO

    
INTEGER INFO, LDB, N, NRHS

    
COMPLEX*16 AP( * ), B( LDB, * )

PURPOSE

ZPPSV computes the solution to a complex system of linear equations
A * X = B, where A is an N-by-N Hermitian positive definite matrix stored in packed format and X and B are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as

A = U**H* U,  if UPLO = aqUaq, or

A = L * L**H,  if UPLO = aqLaq,
where U is an upper triangular matrix and L is a lower triangular matrix. 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 j-th column of A is stored in the array AP as follows: if UPLO = aqUaq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = aqLaq, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. See below for further details. On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, in the same storage format as A.
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, the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed.

FURTHER DETAILS

The packed storage scheme is illustrated by the following example when N = 4, UPLO = aqUaq:
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 ]

Pages related to zppsv

  • zppsv (3)
  • zppsvx (l) - uses the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B,
  • zppcon (l) - estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF
  • zppequ (l) - computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
  • zpprfs (l) - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution
  • zpptrf (l) - computes the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format
  • zpptri (l) - computes the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF
  • zpptrs (l) - solves a system of linear equations A*X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF
  • zpbcon (l) - estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPBTRF