dgtcon (3p)

Name

dgtcon - estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF

Synopsis

SUBROUTINE DGTCON(NORM, N, LOW, D, UP1, UP2, IPIVOT, ANORM, RCOND,
WORK, IWORK2, INFO)

CHARACTER*1 NORM
INTEGER N, INFO
INTEGER IPIVOT(*), IWORK2(*)
DOUBLE PRECISION ANORM, RCOND
DOUBLE PRECISION LOW(*), D(*), UP1(*), UP2(*), WORK(*)

SUBROUTINE DGTCON_64(NORM, N, LOW, D, UP1, UP2, IPIVOT, ANORM,
RCOND, WORK, IWORK2, INFO)

CHARACTER*1 NORM
INTEGER*8 N, INFO
INTEGER*8 IPIVOT(*), IWORK2(*)
DOUBLE PRECISION ANORM, RCOND
DOUBLE PRECISION LOW(*), D(*), UP1(*), UP2(*), WORK(*)




F95 INTERFACE
SUBROUTINE GTCON(NORM, N, LOW, D, UP1, UP2, IPIVOT, ANORM,
RCOND, WORK, IWORK2, INFO)

CHARACTER(LEN=1) :: NORM
INTEGER :: N, INFO
INTEGER, DIMENSION(:) :: IPIVOT, IWORK2
REAL(8) :: ANORM, RCOND
REAL(8), DIMENSION(:) :: LOW, D, UP1, UP2, WORK

SUBROUTINE GTCON_64(NORM, N, LOW, D, UP1, UP2, IPIVOT, ANORM,
RCOND, WORK, IWORK2, INFO)

CHARACTER(LEN=1) :: NORM
INTEGER(8) :: N, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT, IWORK2
REAL(8) :: ANORM, RCOND
REAL(8), DIMENSION(:) :: LOW, D, UP1, UP2, WORK




C INTERFACE
#include <sunperf.h>

void dgtcon(char norm, int n, double *low, double *d, double *up1, dou-
ble  *up2,  int  *ipivot,  double  anorm,  double *rcond, int
*info);

void dgtcon_64(char norm, long n, double *low, double *d, double  *up1,
double  *up2, long *ipivot, double anorm, double *rcond, long
*info);

Description

Oracle Solaris Studio Performance Library                           dgtcon(3P)



NAME
       dgtcon  -  estimate  the  reciprocal  of the condition number of a real
       tridiagonal matrix A using the LU factorization as computed by DGTTRF


SYNOPSIS
       SUBROUTINE DGTCON(NORM, N, LOW, D, UP1, UP2, IPIVOT, ANORM, RCOND,
             WORK, IWORK2, INFO)

       CHARACTER*1 NORM
       INTEGER N, INFO
       INTEGER IPIVOT(*), IWORK2(*)
       DOUBLE PRECISION ANORM, RCOND
       DOUBLE PRECISION LOW(*), D(*), UP1(*), UP2(*), WORK(*)

       SUBROUTINE DGTCON_64(NORM, N, LOW, D, UP1, UP2, IPIVOT, ANORM,
             RCOND, WORK, IWORK2, INFO)

       CHARACTER*1 NORM
       INTEGER*8 N, INFO
       INTEGER*8 IPIVOT(*), IWORK2(*)
       DOUBLE PRECISION ANORM, RCOND
       DOUBLE PRECISION LOW(*), D(*), UP1(*), UP2(*), WORK(*)




   F95 INTERFACE
       SUBROUTINE GTCON(NORM, N, LOW, D, UP1, UP2, IPIVOT, ANORM,
              RCOND, WORK, IWORK2, INFO)

       CHARACTER(LEN=1) :: NORM
       INTEGER :: N, INFO
       INTEGER, DIMENSION(:) :: IPIVOT, IWORK2
       REAL(8) :: ANORM, RCOND
       REAL(8), DIMENSION(:) :: LOW, D, UP1, UP2, WORK

       SUBROUTINE GTCON_64(NORM, N, LOW, D, UP1, UP2, IPIVOT, ANORM,
              RCOND, WORK, IWORK2, INFO)

       CHARACTER(LEN=1) :: NORM
       INTEGER(8) :: N, INFO
       INTEGER(8), DIMENSION(:) :: IPIVOT, IWORK2
       REAL(8) :: ANORM, RCOND
       REAL(8), DIMENSION(:) :: LOW, D, UP1, UP2, WORK




   C INTERFACE
       #include <sunperf.h>

       void dgtcon(char norm, int n, double *low, double *d, double *up1, dou-
                 ble  *up2,  int  *ipivot,  double  anorm,  double *rcond, int
                 *info);

       void dgtcon_64(char norm, long n, double *low, double *d, double  *up1,
                 double  *up2, long *ipivot, double anorm, double *rcond, long
                 *info);



PURPOSE
       dgtcon estimates the reciprocal of  the  condition  number  of  a  real
       tridiagonal  matrix A using the LU factorization as computed by DGTTRF.

       An estimate is obtained for norm(inv(A)), and  the  reciprocal  of  the
       condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).


ARGUMENTS
       NORM (input)
                 Specifies  whether  the 1-norm condition number or the infin-
                 ity-norm condition number is required:
                 = '1' or 'O':  1-norm;
                 = 'I':         Infinity-norm.


       N (input) The order of the matrix A.  N >= 0.


       LOW (input)
                 The (n-1) multipliers that define the matrix L  from  the  LU
                 factorization of A as computed by DGTTRF.


       D (input) The n diagonal elements of the upper triangular matrix U from
                 the LU factorization of A.


       UP1 (input)
                 The (n-1) elements of the first superdiagonal of U.


       UP2 (input)
                 The (n-2) elements of the second superdiagonal of U.


       IPIVOT (input)
                 The pivot indices; for 1 <= i <= n, row i of the  matrix  was
                 interchanged  with  row  IPIVOT(i).  IPIVOT(i) will always be
                 either i or i+1; IPIVOT(i) = i indicates  a  row  interchange
                 was not required.


       ANORM (input)
                 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 (output)
                 The reciprocal of the condition number of the matrix A,  com-
                 puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is an esti-
                 mate of the 1-norm of inv(A) computed in this routine.


       WORK (workspace) DOUBLE PRECISION array, dimension (2*N)

       IWORK2 (workspace) INTEGER array, dimension (N)


       INFO (output)
                 = 0:  successful exit
                 < 0:  if INFO = -i, the i-th argument had an illegal value




                                  7 Nov 2015                        dgtcon(3P)