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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