DTPCON (3lapack)

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