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

NAME

       complex16GTcomputational

SYNOPSIS

   Functions
       subroutine zgtcon (NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, INFO)
           ZGTCON
       subroutine zgtrfs (TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX,
           FERR, BERR, WORK, RWORK, INFO)
           ZGTRFS
       subroutine zgttrf (N, DL, D, DU, DU2, IPIV, INFO)
           ZGTTRF
       subroutine zgttrs (TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO)
           ZGTTRS
       subroutine zgtts2 (ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB)
           ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU
           factorization computed by sgttrf.

Detailed Description

       This is the group of complex16 computational functions for GT matrices

Function Documentation

   subroutine zgtcon (character NORM, integer N, complex*16, dimension( * ) DL, complex*16,
       dimension( * ) D, complex*16, dimension( * ) DU, complex*16, dimension( * ) DU2, integer,
       dimension( * ) IPIV, double precision ANORM, double precision RCOND, complex*16,
       dimension( * ) WORK, integer INFO)
       ZGTCON

       Purpose:

            ZGTCON estimates the reciprocal of the condition number of a complex
            tridiagonal matrix A using the LU factorization as computed by
            ZGTTRF.

            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 COMPLEX*16 array, dimension (N-1)
                     The (n-1) multipliers that define the matrix L from the
                     LU factorization of A as computed by ZGTTRF.

           D

                     D is COMPLEX*16 array, dimension (N)
                     The n diagonal elements of the upper triangular matrix U from
                     the LU factorization of A.

           DU

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

           DU2

                     DU2 is COMPLEX*16 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 COMPLEX*16 array, dimension (2*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 zgtrfs (character TRANS, integer N, integer NRHS, 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, integer LDB,
       complex*16, dimension( ldx, * ) X, integer LDX, double precision, dimension( * ) FERR,
       double precision, dimension( * ) BERR, complex*16, dimension( * ) WORK, double precision,
       dimension( * ) RWORK, integer INFO)
       ZGTRFS

       Purpose:

            ZGTRFS 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)

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

           DF

                     DF is COMPLEX*16 array, dimension (N)
                     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)
                     The (n-1) elements of the first superdiagonal of U.

           DU2

                     DU2 is COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 array, dimension (LDX,NRHS)
                     On entry, the solution matrix X, as computed by ZGTTRS.
                     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 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

       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 zgttrf (integer N, complex*16, dimension( * ) DL, complex*16, dimension( * ) D,
       complex*16, dimension( * ) DU, complex*16, dimension( * ) DU2, integer, dimension( * )
       IPIV, integer INFO)
       ZGTTRF

       Purpose:

            ZGTTRF computes an LU factorization of a complex 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 zgttrs (character TRANS, integer N, integer NRHS, complex*16, dimension( * ) DL,
       complex*16, dimension( * ) D, complex*16, dimension( * ) DU, complex*16, dimension( * )
       DU2, integer, dimension( * ) IPIV, complex*16, dimension( ldb, * ) B, integer LDB, integer
       INFO)
       ZGTTRS

       Purpose:

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

       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)

           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 COMPLEX*16 array, dimension (N-1)
                     The (n-1) multipliers that define the matrix L from the
                     LU factorization of A.

           D

                     D is COMPLEX*16 array, dimension (N)
                     The n diagonal elements of the upper triangular matrix U from
                     the LU factorization of A.

           DU

                     DU is COMPLEX*16 array, dimension (N-1)
                     The (n-1) elements of the first super-diagonal of U.

           DU2

                     DU2 is COMPLEX*16 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 COMPLEX*16 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 = -k, the k-th argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

   subroutine zgtts2 (integer ITRANS, integer N, integer NRHS, complex*16, dimension( * ) DL,
       complex*16, dimension( * ) D, complex*16, dimension( * ) DU, complex*16, dimension( * )
       DU2, integer, dimension( * ) IPIV, complex*16, dimension( ldb, * ) B, integer LDB)
       ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU
       factorization computed by sgttrf.

       Purpose:

            ZGTTS2 solves one of the systems of equations
               A * X = B,  A**T * X = B,  or  A**H * X = B,
            with a tridiagonal matrix A using the LU factorization computed
            by ZGTTRF.

       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**H * X = B  (Conjugate 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 COMPLEX*16 array, dimension (N-1)
                     The (n-1) multipliers that define the matrix L from the
                     LU factorization of A.

           D

                     D is COMPLEX*16 array, dimension (N)
                     The n diagonal elements of the upper triangular matrix U from
                     the LU factorization of A.

           DU

                     DU is COMPLEX*16 array, dimension (N-1)
                     The (n-1) elements of the first super-diagonal of U.

           DU2

                     DU2 is COMPLEX*16 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 COMPLEX*16 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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