zspsv(l) [redhat man page]

ZSPSV(l)								 )								  ZSPSV(l)

NAME

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

SYNOPSIS

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

	   CHARACTER	 UPLO

	   INTEGER	 INFO, LDB, N, NRHS

	   INTEGER	 IPIV( * )

	   COMPLEX*16	 AP( * ), B( LDB, * )

PURPOSE

       ZSPSV  computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed for-
       mat and X and B are N-by-NRHS matrices.

       The diagonal pivoting method is used to factor A as
	  A = U * D * U**T,  if UPLO = 'U', or
	  A = L * D * L**T,  if UPLO = 'L',
       where U (or L) is a product of permutation and unit upper (lower) triangular matrices, D is symmetric 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*16 array, dimension (N*(N+1)/2)
	       On  entry,  the	upper  or  lower triangle of the symmetric 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**T or A
	       = L*D*L**T as computed by ZSPTRF, 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 ZSPTRF.  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*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, D(i,i) is exactly zero.  The factorization has been completed, but the block diagonal matrix D is exactly singu-
	       lar, 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 symmetric matrix A:

	  a11 a12 a13 a14
	      a22 a23 a24
		  a33 a34     (aij = 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 							  ZSPSV(l)