Provided by: liblapack-doc_3.8.0-2_all bug

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

   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

   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

   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

   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

Author

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