cgtsvx-f(3)

cgtsvx.f –

Synopsis

Functions/Subroutines

subroutine cgtsvx (FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, RWORK, INFO)
CGTSVX computes the solution to system of linear equations A * X = B for GT matrices

Function/Subroutine Documentation

subroutine cgtsvx (characterFACT, characterTRANS, integerN, integerNRHS, complex, dimension( * )DL, complex, dimension( * )D, complex, dimension( * )DU, complex, dimension( * )DLF, complex, dimension( * )DF, complex, dimension( * )DUF, complex, dimension( * )DU2, 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)

CGTSVX computes the solution to system of linear equations A * X = B for GT matrices

Purpose:

 CGTSVX uses the LU factorization to compute the solution to a complex
 system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
 where A is a tridiagonal matrix of order N 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 LU decomposition is used to factor the matrix A
 as A = L * U, where L is a product of permutation and unit lower
 bidiagonal matrices and U is upper triangular with nonzeros in
 only the main diagonal and first two superdiagonals.
 2. If some U(i,i)=0, so that U 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': DLF, DF, DUF, DU2, and IPIV contain the factored form
 of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV will not
 be modified.
 = 'N': The matrix will be copied to DLF, DF, and DUF
 and factored.

TRANS

 TRANS is CHARACTER*1
 Specifies the form of the system of equations:
 = 'N': A * X = B (No transpose)
 = 'T': A**T * X = B (Transpose)
 = 'C': A**H * X = B (Conjugate transpose)

 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 matrix B. NRHS >= 0.

 DL is COMPLEX array, dimension (N-1)
 The (n-1) subdiagonal elements of A.

 D is COMPLEX array, dimension (N)
 The n diagonal elements of A.

 DU is COMPLEX array, dimension (N-1)
 The (n-1) superdiagonal elements of A.

DLF

 DLF is COMPLEX array, dimension (N-1)
 If FACT = 'F', then DLF is an input argument and on entry
 contains the (n-1) multipliers that define the matrix L from
 the LU factorization of A as computed by CGTTRF.
 If FACT = 'N', then DLF is an output argument and on exit
 contains the (n-1) multipliers that define the matrix L from
 the LU factorization of A.

 DF is COMPLEX array, dimension (N)
 If FACT = 'F', then DF is an input argument and on entry
 contains the n diagonal elements of the upper triangular
 matrix U from the LU factorization of A.
 If FACT = 'N', then DF is an output argument and on exit
 contains the n diagonal elements of the upper triangular
 matrix U from the LU factorization of A.

DUF

 DUF is COMPLEX array, dimension (N-1)
 If FACT = 'F', then DUF is an input argument and on entry
 contains the (n-1) elements of the first superdiagonal of U.
 If FACT = 'N', then DUF is an output argument and on exit
 contains the (n-1) elements of the first superdiagonal of U.

DU2

 DU2 is COMPLEX array, dimension (N-2)
 If FACT = 'F', then DU2 is an input argument and on entry
 contains the (n-2) elements of the second superdiagonal of
 U.
 If FACT = 'N', then DU2 is an output argument and on exit
 contains the (n-2) elements of the second superdiagonal of
 U.

IPIV

 IPIV is INTEGER array, dimension (N)
 If FACT = 'F', then IPIV is an input argument and on entry
 contains the pivot indices from the LU factorization of A as
 computed by CGTTRF.
 If FACT = 'N', then IPIV is an output argument and on exit
 contains the pivot indices from the LU factorization of A;
 row i of the matrix was interchanged with row IPIV(i).
 IPIV(i) will always be either i or i+1; IPIV(i) = i indicates
 a row interchange was not required.

 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 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: U(i,i) is exactly zero. The factorization
 has not been completed unless i = N, but the
 factor U is exactly singular, so the solution
 and error bounds could not be 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 293 of file cgtsvx.f.

Author

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