Provided by: liblapack-doc_3.11.0-2build1_all bug

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.

   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.

   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.

   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.

   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.

Author

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