zppsv.f man page

zppsv.f —

Synopsis

Functions/Subroutines

subroutine zppsv (UPLO, N, NRHS, AP, B, LDB, INFO)
ZPPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Function/Subroutine Documentation

subroutine zppsv (characterUPLO, integerN, integerNRHS, complex*16, dimension( * )AP, complex*16, dimension( ldb, * )B, integerLDB, integerINFO)

ZPPSV computes the solution to system of linear equations A * X = B for OTHER matrices

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 = 'U', or
   A = L * L**H,  if UPLO = 'L',
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.

Parameters:

UPLO

UPLO is CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N

N is INTEGER
The number of linear equations, i.e., the order of the
matrix A.  N >= 0.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B.  NRHS >= 0.

AP

AP is 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, 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

B is 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

LDB is INTEGER
The leading dimension of the array B.  LDB >= max(1,N).

INFO

INFO is 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.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

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 ]

Definition at line 145 of file zppsv.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

zppsv(3) is an alias of zppsv.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK