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

NAME

       complex16PTsolve

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.

       Date:
           December 2016

   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.

       Date:
           December 2016

Author

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