doubleGTsolve(3)

NAME
doubleGTsolve

SYNOPSIS

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

Detailed Description

This is the group of double solve driver functions for GT matrices

Function Documentation

  subroutine dgtsv (integer N, integer NRHS, double precision, dimension( * ) DL, double precision, dimension( * ) D, double precision, dimension( * ) DU, double precision, dimension( ldb, * ) B, integer LDB, integer INFO)

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

Purpose: @verbatim

DGTSV solves the equation

A*X = B,

where A is an n by n tridiagonal matrix, by Gaussian elimination with partial pivoting.

Note that the equation A**T*X = B may be solved by interchanging the order of the arguments DU and DL.

Parameters:
    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 DOUBLE PRECISION array, dimension (N-1)
              On entry, DL must contain the (n-1) sub-diagonal elements of
              A.
              On exit, DL is overwritten by the (n-2) elements of the
              second super-diagonal of the upper triangular matrix U from
              the LU factorization of A, in DL(1), ..., DL(n-2).

    D

              D is DOUBLE PRECISION array, dimension (N)
              On entry, D must contain the diagonal elements of A.
              On exit, D is overwritten by the n diagonal elements of U.

    DU

              DU is DOUBLE PRECISION array, dimension (N-1)
              On entry, DU must contain the (n-1) super-diagonal elements
              of A.
              On exit, DU is overwritten by the (n-1) elements of the first
              super-diagonal of U.

    B

              B is DOUBLE PRECISION array, dimension (LDB,NRHS)
              On entry, the N by NRHS matrix of right hand side matrix B.
              On exit, if INFO = 0, the N by NRHS solution matrix X.

    LDB

              LDB is INTEGER
              The leading dimension of the array B.  LDB >= max(1,N).

    INFO

              INFO is INTEGER
              = 0: successful exit
              < 0: if INFO = -i, the i-th argument had an illegal value
              > 0: if INFO = i, U(i,i) is exactly zero, and the solution
                   has not been computed.  The factorization has not been
                   completed unless i = N.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

Definition at line 129 of file dgtsv.f.

  subroutine dgtsvx (character FACT, character TRANS, integer N, integer NRHS, double precision, dimension( * ) DL, double precision, dimension( * ) D, double precision, dimension( * ) DU, double precision, dimension( * ) DLF, double precision, dimension( * ) DF, double precision, dimension( * ) DUF, double precision, dimension( * ) DU2, integer, dimension( * ) IPIV, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( ldx, * ) X, integer LDX, double precision RCOND, double precision, dimension( * ) FERR, double precision, dimension( * ) BERR, double precision, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO)

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

Purpose: @verbatim

DGTSVX 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: @verbatim

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 DOUBLE PRECISION array, dimension (N-1)
              The (n-1) subdiagonal elements of A.

    D

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

    DU

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

    DLF

              DLF is DOUBLE PRECISION 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 DGTTRF.
              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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DGTTRF.
              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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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:
    December 2016

Definition at line 295 of file dgtsvx.f.

Author

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