chpsv.f man page

chpsv.f —

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine chpsv (character UPLO, integer N, integer NRHS, complex, dimension( * ) AP, integer, dimension( * ) IPIV, complex, dimension( ldb, * ) B, integer LDB, integer INFO)

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

Purpose:

 CHPSV 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 format 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.
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 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 CHPTRF, stored as
          a packed triangular matrix in the same storage format as A.

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D, as
          determined by CHPTRF.  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

          B is COMPLEX 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, 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.
Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

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 164 of file chpsv.f.

Author

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Referenced By

The man page chpsv(3) is an alias of chpsv.f(3).

Sat Jun 24 2017 Version 3.7.1 LAPACK