chpsv man page on YellowDog

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CHPSV(l)			       )			      CHPSV(l)

NAME
       CHPSV  - compute the solution to a complex system of linear equations A
       * X = B,

SYNOPSIS
       SUBROUTINE CHPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )

	   CHARACTER	 UPLO

	   INTEGER	 INFO, LDB, N, NRHS

	   INTEGER	 IPIV( * )

	   COMPLEX	 AP( * ), B( LDB, * )

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)  tri‐
       angular	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 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  tri‐
	       angular 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 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       (input/output) 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     (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
	       singular, 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			      CHPSV(l)
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