cspsvx man page on YellowDog

Man page or keyword search:  
man Server   18644 pages
apropos Keyword Search (all sections)
Output format
YellowDog logo
[printable version]

CSPSVX(l)			       )			     CSPSVX(l)

NAME
       CSPSVX  -  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	 equa‐
       tions A * X = B, where A is an N-by-N symmetric matrix stored in packed
       format and X and B are N-by-NRHS matrices

SYNOPSIS
       SUBROUTINE CSPSVX( 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

	   REAL		  RCOND

	   INTEGER	  IPIV( * )

	   REAL		  BERR( * ), FERR( * ), RWORK( * )

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

PURPOSE
       CSPSVX 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 equa‐
       tions A * X = B, where A is an N-by-N symmetric matrix stored in packed
       format  and  X and B are N-by-NRHS matrices.  Error bounds on the solu‐
       tion 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  sup‐
	       plied  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 array, dimension (N*(N+1)/2)
	       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)*(2*n-j)/2)  =
	       A(i,j) for j<=i<=n.  See below for further details.

       AFP     (input or output) COMPLEX array, dimension (N*(N+1)/2)
	       If  FACT = 'F', then AFP is an input argument and on entry con‐
	       tains 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 CSPTRF, stored as a packed triangu‐
	       lar matrix in the same storage format as A.

	       If  FACT = 'N', then AFP is an output argument and on exit con‐
	       tains 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 CSPTRF, stored as a packed triangu‐
	       lar 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 con‐
	       tains details of the interchanges and the block structure of D,
	       as determined by CSPTRF.	 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 con‐
	       tains details of the interchanges and the block structure of D,
	       as determined by CSPTRF.

       B       (input) COMPLEX 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 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) REAL
	       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) REAL 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 estimate is as reliable as the estimate for RCOND,  and  is
	       almost always a slight overestimate of the true error.

       BERR    (output) REAL array, dimension (NRHS)
	       The componentwise relative backward error of each solution vec‐
	       tor X(j) (i.e., the smallest relative change in any element  of
	       A or B that makes X(j) an exact solution).

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

       RWORK   (workspace) REAL 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 com‐
	       pleted but the factor 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	preci‐
	       sion, meaning that the matrix is singular to working precision.
	       Nevertheless,  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			     CSPSVX(l)
[top]

List of man pages available for YellowDog

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Tweet
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
....................................................................
Vote for polarhome
Free Shell Accounts :: the biggest list on the net