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cspsvx.f(3)				      LAPACK				      cspsvx.f(3)

NAME
       cspsvx.f -

SYNOPSIS
   Functions/Subroutines
       subroutine cspsvx (FACT, UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR,
	   WORK, RWORK, INFO)
	    CSPSVX computes the solution to system of linear equations A * X = B for OTHER
	   matrices

Function/Subroutine Documentation
   subroutine cspsvx (characterFACT, characterUPLO, integerN, integerNRHS, complex, dimension( *
       )AP, complex, dimension( * )AFP, integer, dimension( * )IPIV, complex, dimension( ldb, *
       )B, integerLDB, complex, dimension( ldx, * )X, integerLDX, realRCOND, real, dimension( *
       )FERR, real, dimension( * )BERR, complex, dimension( * )WORK, real, dimension( * )RWORK,
       integerINFO)
	CSPSVX computes the solution to system of linear equations A * X = B for OTHER matrices

       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
	    equations 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 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.

       Parameters:
	   FACT

		     FACT is 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

		     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 matrices B and X.  NRHS >= 0.

	   AP

		     AP is 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

		     AFP is COMPLEX array, dimension (N*(N+1)/2)
		     If FACT = 'F', then AFP is an input argument and on entry
		     contains 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 triangular matrix in the same storage format as A.

		     If FACT = 'N', then AFP is an output argument and on exit
		     contains 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 triangular matrix in the same storage format as A.

	   IPIV

		     IPIV is 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 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
		     contains details of the interchanges and the block structure
		     of D, as determined by CSPTRF.

	   B

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

	   LDB

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

	   X

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

	   LDX

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

	   RCOND

		     RCOND is 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

		     FERR is 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

		     BERR is REAL 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 solution).

	   WORK

		     WORK is COMPLEX array, dimension (2*N)

	   RWORK

		     RWORK is REAL array, dimension (N)

	   INFO

		     INFO is 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 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
				  precision, 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.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   April 2012

       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 ]

       Definition at line 277 of file cspsvx.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      cspsvx.f(3)
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