• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

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

  SUBROUTINE SGTCON_64( NORM, N, LOW, DIAG, UP1, UP2, IPIVOT, ANORM, 
 *      RCOND, WORK, IWORK2, INFO)
  CHARACTER * 1 NORM
  INTEGER*8 N, INFO
  INTEGER*8 IPIVOT(*), IWORK2(*)
  REAL ANORM, RCOND
  REAL LOW(*), DIAG(*), UP1(*), UP2(*), WORK(*)

F95 INTERFACE

  SUBROUTINE GTCON( NORM, [N], LOW, DIAG, 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, DIAG, UP1, UP2, WORK

  SUBROUTINE GTCON_64( NORM, [N], LOW, DIAG, 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, DIAG, UP1, UP2, WORK

C INTERFACE

#include <sunperf.h>

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

void sgtcon_64(char norm, long n, float *low, float *diag, 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 infinity-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.

• DIAG (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, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.

• WORK (workspace)
  dimension(2*N)

• IWORK2 (workspace)
  
• INFO (output)
  

   = 0:  successful exit

   < 0:  if INFO  = -i, the i-th argument had an illegal value