complex16PTsolve(3)

NAME
complex16PTsolve - complex16

SYNOPSIS

  Functions
subroutine zptsv (n, nrhs, d, e, b, ldb, info)
ZPTSV computes the solution to system of linear equations A * X = B for PT matrices
subroutine zptsvx (fact, n, nrhs, d, e, df, ef, b, ldb, x, ldx, rcond, ferr, berr, work, rwork, info)
ZPTSVX computes the solution to system of linear equations A * X = B for PT matrices

Detailed Description

This is the group of complex16 solve driver functions for PT matrices

Function Documentation

  subroutine zptsv (integer n, integer nrhs, double precision, dimension( * ) d, complex*16, dimension( * ) e, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZPTSV computes the solution to system of linear equations A * X = B for PT matrices

Purpose:

     ZPTSV computes the solution to a complex system of linear equations
     A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal
     matrix, and X and B are N-by-NRHS matrices.
     A is factored as A = L*D*L**H, and the factored form of A is then
     used to solve the system of equations.

Parameters
    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.

    D

              D is DOUBLE PRECISION array, dimension (N)
              On entry, the n diagonal elements of the tridiagonal matrix
              A.  On exit, the n diagonal elements of the diagonal matrix
              D from the factorization A = L*D*L**H.

    E

              E is COMPLEX*16 array, dimension (N-1)
              On entry, the (n-1) subdiagonal elements of the tridiagonal
              matrix A.  On exit, the (n-1) subdiagonal elements of the
              unit bidiagonal factor L from the L*D*L**H factorization of
              A.  E can also be regarded as the superdiagonal of the unit
              bidiagonal factor U from the U**H*D*U factorization of A.

    B

              B is COMPLEX*16 array, dimension (LDB,NRHS)
              On entry, the N-by-NRHS right hand side matrix B.
              On exit, if INFO = 0, the N-by-NRHS solution matrix 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
              > 0:  if INFO = i, the leading minor of order i is not
                    positive definite, and the solution has not been
                    computed.  The factorization has not been completed
                    unless i = N.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 114 of file zptsv.f.

  subroutine zptsvx (character fact, integer n, integer nrhs, double precision, dimension( * ) d, complex*16, dimension( * ) e, double precision, dimension( * ) df, complex*16, dimension( * ) ef, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx, double precision rcond, double precision, dimension( * ) ferr, double precision, dimension( * ) berr, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)

ZPTSVX computes the solution to system of linear equations A * X = B for PT matrices

Purpose:

     ZPTSVX uses the factorization A = L*D*L**H to compute the solution
     to a complex system of linear equations A*X = B, where A is an
     N-by-N Hermitian positive definite tridiagonal matrix and X and B
     are N-by-NRHS matrices.
     Error bounds on the solution and a condition estimate are also
     provided.

Description:

     The following steps are performed:
     1. If FACT = 'N', the matrix A is factored as A = L*D*L**H, where L
        is a unit lower bidiagonal matrix and D is diagonal.  The
        factorization can also be regarded as having the form
        A = U**H*D*U.
     2. If the leading i-by-i principal minor is not positive definite,
        then the routine returns with INFO = i. Otherwise, the factored
        form of A is used to estimate the condition number of the matrix
        A.  If the reciprocal of the condition number is less than machine
        precision, INFO = N+1 is returned as a warning, but the routine
        still goes on to solve for X and compute error bounds as
        described below.
     3. The system of equations is solved for X using the factored form
        of A.
     4. Iterative refinement is applied to improve the computed solution
        matrix and calculate error bounds and backward error estimates
        for it.

Parameters
    FACT

              FACT is CHARACTER*1
              Specifies whether or not the factored form of the matrix
              A is supplied on entry.
              = 'F':  On entry, DF and EF contain the factored form of A.
                      D, E, DF, and EF will not be modified.
              = 'N':  The matrix A will be copied to DF and EF and
                      factored.

    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 matrices B and X.  NRHS >= 0.

    D

              D is DOUBLE PRECISION array, dimension (N)
              The n diagonal elements of the tridiagonal matrix A.

    E

              E is COMPLEX*16 array, dimension (N-1)
              The (n-1) subdiagonal elements of the tridiagonal matrix A.

    DF

              DF is DOUBLE PRECISION array, dimension (N)
              If FACT = 'F', then DF is an input argument and on entry
              contains the n diagonal elements of the diagonal matrix D
              from the L*D*L**H factorization of A.
              If FACT = 'N', then DF is an output argument and on exit
              contains the n diagonal elements of the diagonal matrix D
              from the L*D*L**H factorization of A.

    EF

              EF is COMPLEX*16 array, dimension (N-1)
              If FACT = 'F', then EF is an input argument and on entry
              contains the (n-1) subdiagonal elements of the unit
              bidiagonal factor L from the L*D*L**H factorization of A.
              If FACT = 'N', then EF is an output argument and on exit
              contains the (n-1) subdiagonal elements of the unit
              bidiagonal factor L from the L*D*L**H factorization of A.

    B

              B is COMPLEX*16 array, dimension (LDB,NRHS)
              The N-by-NRHS 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)
              If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.

    LDX

              LDX is INTEGER
              The leading dimension of the array X.  LDX >= max(1,N).

    RCOND

              RCOND is DOUBLE PRECISION
              The reciprocal condition number of the matrix A.  If RCOND
              is less than the machine precision (in particular, if
              RCOND = 0), the matrix is singular to working precision.
              This condition is indicated by a return code of INFO > 0.

    FERR

              FERR is DOUBLE PRECISION array, dimension (NRHS)
              The 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).

    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 (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
              > 0:  if INFO = i, and i is
                    <= N:  the leading minor of order i of A is
                           not positive definite, so the factorization
                           could not be completed, and the solution has not
                           been computed. RCOND = 0 is returned.
                    = N+1: U is nonsingular, but RCOND is less than machine
                           precision, meaning that the matrix is singular
                           to working precision.  Nevertheless, the
                           solution and error bounds are computed because
                           there are a number of situations where the
                           computed solution can be more accurate than the
                           value of RCOND would suggest.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 232 of file zptsvx.f.

Author

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