cptsvx.f man page

cptsvx.f —

Synopsis

Functions/Subroutines

subroutine cptsvx (FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, RWORK, INFO)
CPTSVX computes the solution to system of linear equations A * X = B for PT matrices

Function/Subroutine Documentation

subroutine cptsvx (characterFACT, integerN, integerNRHS, real, dimension( * )D, complex, dimension( * )E, real, dimension( * )DF, complex, dimension( * )EF, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldx, * )X, integerLDX, realRCOND, real, dimension( * )FERR, real, dimension( * )BERR, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)

CPTSVX computes the solution to system of linear equations A * X = B for PT matrices

Purpose:

CPTSVX 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.

Parameters:

FACT

FACT is 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

N is INTEGER
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.

D

D is REAL array, dimension (N)
The n diagonal elements of the tridiagonal matrix A.

E

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

DF

DF is REAL 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

EF is COMPLEX array, dimension (N-1)
If FACT = 'F', then EF is an input argument and on entry
contains the (n-1) subdiagonal 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 factorization of A.

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 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 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

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 (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:  the leading minor of order i of A is
             not positive definite, so the factorization
             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
             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:

September 2012

Definition at line 234 of file cptsvx.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

cptsvx(3) is an alias of cptsvx.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK