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

ZPTSVX(l)					)					ZPTSVX(l)

NAME
       ZPTSVX - use the factorization A = L*D*L**H to compute the solution to a complex system of
       linear equations A*X = B, where A is an N-by-N  Hermitian  positive  definite  tridiagonal
       matrix and X and B are N-by-NRHS matrices

SYNOPSIS
       SUBROUTINE ZPTSVX( FACT,  N,  NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND, FERR, BERR, WORK,
			  RWORK, INFO )

	   CHARACTER	  FACT

	   INTEGER	  INFO, LDB, LDX, N, NRHS

	   DOUBLE	  PRECISION RCOND

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

	   COMPLEX*16	  B( LDB, * ), E( * ), EF( * ), WORK( * ), X( LDX, * )

PURPOSE
       ZPTSVX uses the factorization A = L*D*L**H to compute the solution to a complex system  of
       linear  equations  A*X  =  B, where A is an N-by-N Hermitian positive definite tridiagonal
       matrix 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 matrix A is factored as A = L*D*L**H, where L
	  is a unit lower bidiagonal matrix and D is diagonal.	The
	  factorization can also be regarded as having the form
	  A = U**H*D*U.

       2. If the leading i-by-i principal minor is not positive definite,
	  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 the matrix A is supplied on entry.
	       = 'F':  On entry, DF and EF contain the factored form of A.  D, E, DF, and EF will
	       not be modified.  = 'N':  The matrix A will be copied to DF and EF and factored.

       N       (input) INTEGER
	       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.

       D       (input) DOUBLE PRECISION array, dimension (N)
	       The n diagonal elements of the tridiagonal matrix A.

       E       (input) COMPLEX*16 array, dimension (N-1)
	       The (n-1) subdiagonal elements of the tridiagonal matrix A.

       DF      (input or output) DOUBLE PRECISION array, dimension (N)
	       If FACT = 'F', then DF is an input argument and on entry contains the  n  diagonal
	       elements of the diagonal matrix D from the L*D*L**H factorization of A.	If FACT =
	       'N', then DF is an output argument and on exit contains the n diagonal elements of
	       the diagonal matrix D from the L*D*L**H factorization of A.

       EF      (input or output) COMPLEX*16 array, dimension (N-1)
	       If FACT = 'F', then EF is an input argument and on entry contains the (n-1) subdi-
	       agonal elements of the unit bidiagonal factor L from the L*D*L**H factorization of
	       A.   If	FACT  = 'N', then EF is an output argument and on exit contains the (n-1)
	       subdiagonal elements of the unit bidiagonal factor L from the L*D*L**H  factoriza-
	       tion of A.

       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  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  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).

       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 (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:  the leading minor of order i of A is not positive definite, so the  factor-
	       ization	could not be completed, and the solution has not been computed. RCOND = 0
	       is returned.  = N+1: U is nonsingular, but RCOND is less than  machine  precision,
	       meaning that the matrix is singular to working precision.  Nevertheless, the solu-
	       tion 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.

LAPACK version 3.0			   15 June 2000 				ZPTSVX(l)


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