12 August 2022 05:16:21 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
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.11022e-16

  Matrix order N = 2
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.84593e-16

  Matrix order N = 3
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.14018e-16

  Matrix order N = 4
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.20089e-15

  Matrix order N = 5
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.27071e-15

  Matrix order N = 6
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.66163e-15

  Matrix order N = 7
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.87307e-15

  Matrix order N = 8
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.82504e-15

  Matrix order N = 9
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.73537e-15

  Matrix order N = 10
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 6.78236e-15

  Matrix order N = 11
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.69439e-14

  Matrix order N = 12
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 9.82093e-15

  Matrix order N = 13
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 2.33081e-14

  Matrix order N = 14
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 2.1177e-14

  Matrix order N = 15
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.54843e-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
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 0

  Matrix order N = 2
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 6.28037e-16

  Matrix order N = 3
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.00486e-14

  Matrix order N = 4
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.45765e-13

  Matrix order N = 5
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 6.38268e-12

  Matrix order N = 6
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.49865e-10

  Matrix order N = 7
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 3.65951e-09

  Matrix order N = 8
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 1.57231e-07

  Matrix order N = 9
  Maxtrix nullity NULLTY = 0
  RMS ( C * A - I ) = 4.40683e-06

  Matrix order N = 10
  Maxtrix nullity NULLTY = 1
  RMS ( C * A - I ) = 1

  Matrix order N = 11
  Maxtrix nullity NULLTY = 1
  RMS ( C * A - I ) = 3.29587

  Matrix order N = 12
  Maxtrix nullity NULLTY = 1
  RMS ( C * A - I ) = 3.443

  Matrix order N = 13
  Maxtrix nullity NULLTY = 1
  RMS ( C * A - I ) = 3.5882

  Matrix order N = 14
  Maxtrix nullity NULLTY = 1
  RMS ( C * A - I ) = 3.73148

  Matrix order N = 15
  Maxtrix nullity NULLTY = 1
  RMS ( C * A - I ) = 3.87289

asa007_test():
  Normal end of execution.

12 August 2022 05:16:21 PM