sgtcon (3p)

Name

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

Synopsis

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

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

SUBROUTINE SGTCON_64(NORM, N, LOW, D, UP1, UP2, IPIVOT, ANORM,
RCOND, WORK, IWORK2, INFO)

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




C INTERFACE
#include <sunperf.h>

void sgtcon(char norm, int n, float *low, float *d, float  *up1,  float
*up2, int *ipivot, float anorm, float *rcond, int *info);

void  sgtcon_64(char  norm,  long  n, float *low, float *d, float *up1,
float *up2, long *ipivot, float  anorm,  float  *rcond,  long
*info);

Description

Oracle Solaris Studio Performance Library                           sgtcon(3P)



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


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

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

       SUBROUTINE SGTCON_64(NORM, N, LOW, D, UP1, UP2, IPIVOT, ANORM,
             RCOND, WORK, IWORK2, INFO)

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




   C INTERFACE
       #include <sunperf.h>

       void sgtcon(char norm, int n, float *low, float *d, float  *up1,  float
                 *up2, int *ipivot, float anorm, float *rcond, int *info);

       void  sgtcon_64(char  norm,  long  n, float *low, float *d, float *up1,
                 float *up2, long *ipivot, float  anorm,  float  *rcond,  long
                 *info);



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

       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 SGTTRF.


       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) REAL 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                        sgtcon(3P)