12 August 2022 05:02:45 PM

asa007_test():
  C version 
  Test asa007().

test01():
  syminv() computes the inverse of a symmetric positive
  definite matrix.
  A compressed storage format is used

  Here we look at the matrix A which is
  N+1 on the diagonal and
  N   on the off diagonals.

  Matrix order N = 1
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.110223e-16

  Matrix order N = 2
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.845925e-16

  Matrix order N = 3
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.140185e-16

  Matrix order N = 4
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.200890e-15

  Matrix order N = 5
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.270708e-15

  Matrix order N = 6
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.661630e-15

  Matrix order N = 7
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.873072e-15

  Matrix order N = 8
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.825037e-15

  Matrix order N = 9
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.735368e-15

  Matrix order N = 10
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 6.782363e-15

  Matrix order N = 11
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.694391e-14

  Matrix order N = 12
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 9.820925e-15

  Matrix order N = 13
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 2.330807e-14

  Matrix order N = 14
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 2.117705e-14

  Matrix order N = 15
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.548433e-14

test02():
  syminv() computes the inverse of a symmetric positive
  definite matrix.
  A compressed storage format is used

  Here we look at the Hilbert matrix
  A(I,J) = 1/(I+J-1)

  For this matrix, we expect errors to grow quickly.

  Matrix order N = 1
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 0.000000e+00

  Matrix order N = 2
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 6.280370e-16

  Matrix order N = 3
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.004859e-14

  Matrix order N = 4
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.457650e-13

  Matrix order N = 5
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 6.382683e-12

  Matrix order N = 6
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.498653e-10

  Matrix order N = 7
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.659510e-09

  Matrix order N = 8
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.572310e-07

  Matrix order N = 9
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 4.406828e-06

  Matrix order N = 10
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.478913e-04

  Matrix order N = 11
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.675044e-03

  Matrix order N = 12
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.431460e-01

  Matrix order N = 13
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.708889e+00

  Matrix order N = 14
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.747525e+00

  Matrix order N = 15
  Matrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.883206e+00

asa007_test():
  Normal end of execution.

12 August 2022 05:02:45 PM