cptsvx-f(3)

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

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

 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 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 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 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

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