sgtsvx.f man page

sgtsvx.f —

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine sgtsvx (characterFACT, characterTRANS, integerN, integerNRHS, real, dimension( * )DL, real, dimension( * )D, real, dimension( * )DU, real, dimension( * )DLF, real, dimension( * )DF, real, dimension( * )DUF, real, dimension( * )DU2, integer, dimension( * )IPIV, real, dimension( ldb, * )B, integerLDB, real, dimension( ldx, * )X, integerLDX, realRCOND, real, dimension( * )FERR, real, dimension( * )BERR, real, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)

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

Purpose:

SGTSVX uses the LU factorization to compute the solution to a real
system of linear equations A * X = B or A**T * 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 = Transpose)

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 matrix B.  NRHS >= 0.

DL

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

D

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

DU

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

DLF

DLF is REAL 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 SGTTRF.

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

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 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 REAL 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 REAL 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 SGTTRF.

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

B is REAL 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 REAL 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 REAL array, dimension (3*N)

IWORK

IWORK is INTEGER 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 292 of file sgtsvx.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK