Home Man
Search
Today's Posts
Register

Linux & Unix Commands - Search Man Pages

RedHat 9 (Linux i386) - man page for zspsvx (redhat section l)

ZSPSVX(l)					)					ZSPSVX(l)

NAME
       ZSPSVX  -  use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute
       the solution to a complex system of linear equations A * X = B, where A is an N-by-N  sym-
       metric matrix stored in packed format and X and B are N-by-NRHS matrices

SYNOPSIS
       SUBROUTINE ZSPSVX( FACT,  UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR,
			  WORK, RWORK, INFO )

	   CHARACTER	  FACT, UPLO

	   INTEGER	  INFO, LDB, LDX, N, NRHS

	   DOUBLE	  PRECISION RCOND

	   INTEGER	  IPIV( * )

	   DOUBLE	  PRECISION BERR( * ), FERR( * ), RWORK( * )

	   COMPLEX*16	  AFP( * ), AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )

PURPOSE
       ZSPSVX uses the diagonal pivoting factorization A = U*D*U**T or A =  L*D*L**T  to  compute
       the  solution to a complex system of linear equations A * X = B, where A is an N-by-N sym-
       metric matrix stored in packed format and X and B are N-by-NRHS matrices.  Error bounds on
       the solution and a condition estimate are also provided.

DESCRIPTION
       The following steps are performed:

       1. If FACT = 'N', 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 and D is symmetric and block diagonal with
	  1-by-1 and 2-by-2 diagonal blocks.

       2. If some D(i,i)=0, so that D is exactly singular, then the routine
	  returns with INFO = i. Otherwise, the factored form of A is used
	  to estimate the condition number of the matrix A.  If the
	  reciprocal of the condition number is less than machine precision,
	  INFO = N+1 is returned as a warning, but the routine still goes on
	  to solve for X and compute error bounds as described below.

       3. The system of equations is solved for X using the factored form
	  of A.

       4. Iterative refinement is applied to improve the computed solution
	  matrix and calculate error bounds and backward error estimates
	  for it.

ARGUMENTS
       FACT    (input) CHARACTER*1
	       Specifies  whether  or  not  the factored form of A has been supplied on entry.	=
	       'F':  On entry, AFP and IPIV contain the factored form of A.   AP,  AFP	and  IPIV
	       will not be modified.  = 'N':  The matrix A will be copied to AFP and factored.

       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 matrices B and
	       X.  NRHS >= 0.

       AP      (input) COMPLEX*16 array, dimension (N*(N+1)/2)
	       The upper or lower triangle of the symmetric matrix A, packed columnwise in a lin-
	       ear  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)*(2*n-
	       j)/2) = A(i,j) for j<=i<=n.  See below for further details.

       AFP     (input or output) COMPLEX*16 array, dimension (N*(N+1)/2)
	       If FACT = 'F', then AFP is an input argument and on entry contains the block diag-
	       onal matrix D and the multipliers used to obtain the factor U or L from	the  fac-
	       torization  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.

	       If FACT = 'N', then AFP is an output argument and on exit contains the block diag-
	       onal  matrix  D and the multipliers used to obtain the factor U or L from the fac-
	       torization 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    (input or output) INTEGER array, dimension (N)
	       If FACT = 'F', then IPIV is an input argument and on entry contains 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.

	       If FACT = 'N', then IPIV is an output argument and on exit contains details of the
	       interchanges and the block structure of D, as determined by ZSPTRF.

       B       (input) COMPLEX*16 array, dimension (LDB,NRHS)
	       The N-by-NRHS right hand side matrix B.

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

       X       (output) COMPLEX*16 array, dimension (LDX,NRHS)
	       If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.

       LDX     (input) INTEGER
	       The leading dimension of the array X.  LDX >= max(1,N).

       RCOND   (output) DOUBLE PRECISION
	       The estimate of the reciprocal condition number of the matrix A.  If RCOND is less
	       than  the  machine precision (in particular, if RCOND = 0), the matrix is singular
	       to working precision.  This condition is indicated by a return code of INFO > 0.

       FERR    (output) DOUBLE PRECISION array, dimension (NRHS)
	       The estimated forward error bound for each solution vector X(j) (the  j-th  column
	       of  the	solution matrix X).  If XTRUE is the true solution corresponding to X(j),
	       FERR(j) is an estimated upper bound for the magnitude of the  largest  element  in
	       (X(j) - XTRUE) divided by the magnitude of the largest element in X(j).	The esti-
	       mate is as reliable as the estimate for RCOND, and is almost always a slight over-
	       estimate of the true error.

       BERR    (output) DOUBLE PRECISION array, dimension (NRHS)
	       The  componentwise relative backward error of each solution vector X(j) (i.e., the
	       smallest relative change in any element of A or B that makes X(j) an  exact  solu-
	       tion).

       WORK    (workspace) COMPLEX*16 array, dimension (2*N)

       RWORK   (workspace) DOUBLE PRECISION array, dimension (N)

       INFO    (output) INTEGER
	       = 0: successful exit
	       < 0: if INFO = -i, the i-th argument had an illegal value
	       > 0:  if INFO = i, and i is
	       <=  N:  D(i,i) is exactly zero.	The factorization has been completed but the fac-
	       tor D is exactly singular, so the solution and error bounds could not be computed.
	       RCOND  =  0  is returned.  = N+1: D is nonsingular, but RCOND is less than machine
	       precision, meaning that the matrix is singular to  working  precision.	Neverthe-
	       less,  the  solution  and  error bounds are computed because there are a number of
	       situations where the computed solution can be more  accurate  than  the	value  of
	       RCOND would suggest.

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 				ZSPSVX(l)


All times are GMT -4. The time now is 06:03 PM.

Unix & Linux Forums Content Copyrightę1993-2018. All Rights Reserved.
UNIX.COM Login
Username:
Password:  
Show Password