NAME

DTPCON - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm

SYNOPSIS

SUBROUTINE DTPCON(
NORM, UPLO, DIAG, N, AP, RCOND, WORK, IWORK, INFO )

CHARACTER DIAG, NORM, UPLO

INTEGER INFO, N

DOUBLE PRECISION RCOND

INTEGER IWORK( ∗ )

DOUBLE PRECISION AP( ∗ ), WORK( ∗ )

PURPOSE

DTPCON estimates the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm. 
 
The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as
   RCOND = 1 / ( norm(A) ∗ norm(inv(A)) ).
 

ARGUMENTS

NORM    (input) CHARACTER∗1
Specifies whether the 1-norm condition number or the infinity-norm condition number is required:
= ’1’ or ’O’:  1-norm;
= ’I’:         Infinity-norm.

UPLO    (input) CHARACTER∗1
= ’U’:  A is upper triangular;
= ’L’:  A is lower triangular.

DIAG    (input) CHARACTER∗1
= ’N’:  A is non-unit triangular;
= ’U’:  A is unit triangular.

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

AP      (input) DOUBLE PRECISION array, dimension (N∗(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in a linear array.  The j-th column of A is stored in the array AP as follows: if UPLO = ’U’, AP(i + (j-1)∗j/2) = A(i,j) for 1<=i<=j; if UPLO = ’L’, AP(i + (j-1)∗(2n-j)/2) = A(i,j) for j<=i<=n. If DIAG = ’U’, the diagonal elements of A are not referenced and are assumed to be 1.

RCOND   (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) ∗ norm(inv(A))).

WORK    (workspace) DOUBLE PRECISION array, dimension (3∗N)

IWORK   (workspace) INTEGER array, dimension (N)

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

  —  LAPACK version 2.0  —  08 October 1994