zgtsvx.f(3)

NAME
zgtsvx.f -

SYNOPSIS

  Functions/Subroutines
subroutine ZGTSVX (FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, RWORK, INFO)
ZGTSVX

Function/Subroutine Documentation

  subroutine ZGTSVX (CHARACTERFACT, CHARACTERTRANS, INTEGERN, INTEGERNRHS, COMPLEX*16, dimension( * )DL, COMPLEX*16, dimension( * )D, COMPLEX*16, dimension( * )DU, COMPLEX*16, dimension( * )DLF, COMPLEX*16, dimension( * )DF, COMPLEX*16, dimension( * )DUF, COMPLEX*16, dimension( * )DU2, INTEGER, dimension( * )IPIV, COMPLEX*16, dimension( ldb, * )B, INTEGERLDB, COMPLEX*16, dimension( ldx, * )X, INTEGERLDX, DOUBLE PRECISIONRCOND, DOUBLE PRECISION, dimension( * )FERR, DOUBLE PRECISION, dimension( * )BERR, COMPLEX*16, dimension( * )WORK, DOUBLE PRECISION, dimension( * )RWORK, INTEGERINFO)

ZGTSVX

Purpose:

     ZGTSVX 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

              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 COMPLEX*16 array, dimension (N-1)
              The (n-1) subdiagonal elements of A.

    D

              D is COMPLEX*16 array, dimension (N)
              The n diagonal elements of A.

    DU

              DU is COMPLEX*16 array, dimension (N-1)
              The (n-1) superdiagonal elements of A.

    DLF

              DLF is COMPLEX*16 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 ZGTTRF.
              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 COMPLEX*16 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*16 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*16 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 ZGTTRF.
              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 COMPLEX*16 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*16 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 DOUBLE PRECISION
              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 DOUBLE PRECISION 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 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 solution).

    WORK

              WORK is COMPLEX*16 array, dimension (2*N)

    RWORK

              RWORK is DOUBLE PRECISION 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:
    April 2012

Definition at line 293 of file zgtsvx.f'.

Author

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