complexGTcomputational(3)

NAME
complexGTcomputational - complex

SYNOPSIS

  Functions
subroutine cgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, info)
CGTCON
subroutine cgtrfs (trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CGTRFS
subroutine cgttrf (n, dl, d, du, du2, ipiv, info)
CGTTRF
subroutine cgttrs (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)
CGTTRS
subroutine cgtts2 (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)
CGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Detailed Description

This is the group of complex computational functions for GT matrices

Function Documentation

  subroutine cgtcon (character norm, integer n, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, integer info)

CGTCON

Purpose:

     CGTCON estimates the reciprocal of the condition number of a complex
     tridiagonal matrix A using the LU factorization as computed by
     CGTTRF.
     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 array, dimension (N-1)
              The (n-1) multipliers that define the matrix L from the
              LU factorization of A as computed by CGTTRF.

    D

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

    DU

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

    DU2

              DU2 is COMPLEX 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 REAL
              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 REAL
              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 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.

Definition at line 139 of file cgtcon.f.

  subroutine cgtrfs (character trans, integer n, integer nrhs, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) dlf, complex, dimension( * ) df, complex, dimension( * ) duf, complex, dimension( * ) du2, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real, dimension( * ) berr, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CGTRFS

Purpose:

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

    D

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

    DU

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

    DLF

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

    DF

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

    DUF

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

    DU2

              DU2 is COMPLEX 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 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 array, dimension (LDX,NRHS)
              On entry, the solution matrix X, as computed by CGTTRS.
              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 REAL 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 REAL 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 array, dimension (2*N)

    RWORK

              RWORK is REAL 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.

Definition at line 207 of file cgtrfs.f.

  subroutine cgttrf (integer n, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, integer info)

CGTTRF

Purpose:

     CGTTRF 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 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 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 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 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.

Definition at line 123 of file cgttrf.f.

  subroutine cgttrs (character trans, integer n, integer nrhs, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, integer info)

CGTTRS

Purpose:

     CGTTRS 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 CGTTRF.

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

    D

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

    DU

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

    DU2

              DU2 is COMPLEX 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 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.

Definition at line 136 of file cgttrs.f.

  subroutine cgtts2 (integer itrans, integer n, integer nrhs, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb)

CGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose:

     CGTTS2 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 CGTTRF.

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

    D

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

    DU

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

    DU2

              DU2 is COMPLEX 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 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.

Definition at line 127 of file cgtts2.f.

Author

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