doubleGTcomputational(3)

NAME
doubleGTcomputational

SYNOPSIS

  Functions
subroutine dgtcon (NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
DGTCON
subroutine dgtrfs (TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
DGTRFS
subroutine dgttrf (N, DL, D, DU, DU2, IPIV, INFO)
DGTTRF
subroutine dgttrs (TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO)
DGTTRS
subroutine dgtts2 (ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB)
DGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Detailed Description

This is the group of double computational functions for GT matrices

Function Documentation

  subroutine dgtcon (character NORM, integer N, double precision, dimension( * ) DL, double precision, dimension( * ) D, double precision, dimension( * ) DU, double precision, dimension( * ) DU2, integer, dimension( * ) IPIV, double precision ANORM, double precision RCOND, double precision, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO)

DGTCON

Purpose:

     DGTCON estimates the reciprocal of the condition number of a real
     tridiagonal matrix A using the LU factorization as computed by
     DGTTRF.
     An estimate is obtained for norm(inv(A)), and the reciprocal of the
     condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters:
    NORM

              NORM is CHARACTER*1
              Specifies whether the 1-norm condition number or the
              infinity-norm condition number is required:
              = '1' or 'O':  1-norm;
              = 'I':         Infinity-norm.

    N

              N is INTEGER
              The order of the matrix A.  N >= 0.

    DL

              DL is DOUBLE PRECISION array, dimension (N-1)
              The (n-1) multipliers that define the matrix L from the
              LU factorization of A as computed by DGTTRF.

    D

              D is DOUBLE PRECISION array, dimension (N)
              The n diagonal elements of the upper triangular matrix U from
              the LU factorization of A.

    DU

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

    DU2

              DU2 is DOUBLE PRECISION array, dimension (N-2)
              The (n-2) elements of the second superdiagonal of U.

    IPIV

              IPIV is INTEGER array, dimension (N)
              The pivot indices; for 1 <= i <= n, 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.

    ANORM

              ANORM is DOUBLE PRECISION
              If NORM = '1' or 'O', the 1-norm of the original matrix A.
              If NORM = 'I', the infinity-norm of the original matrix A.

    RCOND

              RCOND is DOUBLE PRECISION
              The reciprocal of the condition number of the matrix A,
              computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
              estimate of the 1-norm of inv(A) computed in this routine.

    WORK

              WORK is DOUBLE PRECISION array, dimension (2*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

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

Definition at line 148 of file dgtcon.f.

  subroutine dgtrfs (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, dimension( * ) FERR, double precision, dimension( * ) BERR, double precision, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO)

DGTRFS

Purpose:

     DGTRFS improves the computed solution to a system of linear
     equations when the coefficient matrix is tridiagonal, and provides
     error bounds and backward error estimates for the solution.

Parameters:
    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 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)
              The (n-1) multipliers that define the matrix L from the
              LU factorization of A as computed by DGTTRF.

    DF

              DF is DOUBLE PRECISION array, dimension (N)
              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)
              The (n-1) elements of the first superdiagonal of U.

    DU2

              DU2 is DOUBLE PRECISION array, dimension (N-2)
              The (n-2) elements of the second superdiagonal of U.

    IPIV

              IPIV is INTEGER array, dimension (N)
              The pivot indices; for 1 <= i <= n, 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 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)
              On entry, the solution matrix X, as computed by DGTTRS.
              On exit, the improved solution matrix X.

    LDX

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

    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

Internal Parameters:

      ITMAX is the maximum number of steps of iterative refinement.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

Definition at line 211 of file dgtrfs.f.

  subroutine dgttrf (integer N, double precision, dimension( * ) DL, double precision, dimension( * ) D, double precision, dimension( * ) DU, double precision, dimension( * ) DU2, integer, dimension( * ) IPIV, integer INFO)

DGTTRF

Purpose:

     DGTTRF computes an LU factorization of a real tridiagonal matrix A
     using elimination with partial pivoting and row interchanges.
     The factorization has the form
        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.

Parameters:
    N

              N is INTEGER
              The order of the matrix A.

    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-1) multipliers that
              define the matrix L from the LU factorization of A.

    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 the
              upper triangular matrix U from the LU factorization of A.

    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.

    DU2

              DU2 is DOUBLE PRECISION array, dimension (N-2)
              On exit, DU2 is overwritten by the (n-2) elements of the
              second super-diagonal of U.

    IPIV

              IPIV is INTEGER array, dimension (N)
              The pivot indices; for 1 <= i <= n, 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.

    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -k, the k-th argument had an illegal value
              > 0:  if INFO = k, U(k,k) is exactly zero. The factorization
                    has been completed, but the factor U is exactly
                    singular, and division by zero will occur if it is used
                    to solve a system of equations.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

Definition at line 126 of file dgttrf.f.

  subroutine dgttrs (character TRANS, integer N, integer NRHS, double precision, dimension( * ) DL, double precision, dimension( * ) D, double precision, dimension( * ) DU, double precision, dimension( * ) DU2, integer, dimension( * ) IPIV, double precision, dimension( ldb, * ) B, integer LDB, integer INFO)

DGTTRS

Purpose:

     DGTTRS solves one of the systems of equations
        A*X = B  or  A**T*X = B,
     with a tridiagonal matrix A using the LU factorization computed
     by DGTTRF.

Parameters:
    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**T* X = B  (Conjugate transpose = Transpose)

    N

              N is INTEGER
              The order of the matrix A.

    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) multipliers that define the matrix L from the
              LU factorization of A.

    D

              D is DOUBLE PRECISION array, dimension (N)
              The n diagonal elements of the upper triangular matrix U from
              the LU factorization of A.

    DU

              DU is DOUBLE PRECISION array, dimension (N-1)
              The (n-1) elements of the first super-diagonal of U.

    DU2

              DU2 is DOUBLE PRECISION array, dimension (N-2)
              The (n-2) elements of the second super-diagonal of U.

    IPIV

              IPIV is INTEGER array, dimension (N)
              The pivot indices; for 1 <= i <= n, 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)
              On entry, the matrix of right hand side vectors B.
              On exit, B is overwritten by the solution vectors 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

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

Definition at line 140 of file dgttrs.f.

  subroutine dgtts2 (integer ITRANS, integer N, integer NRHS, double precision, dimension( * ) DL, double precision, dimension( * ) D, double precision, dimension( * ) DU, double precision, dimension( * ) DU2, integer, dimension( * ) IPIV, double precision, dimension( ldb, * ) B, integer LDB)

DGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose:

     DGTTS2 solves one of the systems of equations
        A*X = B  or  A**T*X = B,
     with a tridiagonal matrix A using the LU factorization computed
     by DGTTRF.

Parameters:
    ITRANS

              ITRANS is INTEGER
              Specifies the form of the system of equations.
              = 0:  A * X = B  (No transpose)
              = 1:  A**T* X = B  (Transpose)
              = 2:  A**T* X = B  (Conjugate transpose = Transpose)

    N

              N is INTEGER
              The order of the matrix A.

    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) multipliers that define the matrix L from the
              LU factorization of A.

    D

              D is DOUBLE PRECISION array, dimension (N)
              The n diagonal elements of the upper triangular matrix U from
              the LU factorization of A.

    DU

              DU is DOUBLE PRECISION array, dimension (N-1)
              The (n-1) elements of the first super-diagonal of U.

    DU2

              DU2 is DOUBLE PRECISION array, dimension (N-2)
              The (n-2) elements of the second super-diagonal of U.

    IPIV

              IPIV is INTEGER array, dimension (N)
              The pivot indices; for 1 <= i <= n, 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)
              On entry, the matrix of right hand side vectors B.
              On exit, B is overwritten by the solution vectors X.

    LDB

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

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

Definition at line 130 of file dgtts2.f.

Author

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