Warning: X does not support locale en_US.UTF-8
01-Jul-2023 09:16:23

spd_test():
  Demonstrate some tests for determining if a matrix
  is symmetric positive definite (SPD)

  dif2 matrix of order n = 10
  Deviation from symmetry = 0
  All eigenvalues are real and positive.
  Minimum eigenvalue is 0.0810141
  Out of 100 real vectors x, x'Ax was positive 100 times

  combinatorial matrix of order n = 5
  Deviation from symmetry = 0
  At least one eigenvalue is negative or complex
  Out of 100 real vectors x, x'Ax was positive 97 times

  Chebyshev T matrix of order n = 5
  Deviation from symmetry = 12.2474
  All eigenvalues are real and positive.
  Minimum eigenvalue is 1
  Out of 100 real vectors x, x'Ax was positive 100 times

  Random matrix of order n = 5
  Deviation from symmetry = 5.82226
  At least one eigenvalue is negative or complex
  Out of 100 real vectors x, x'Ax was positive 59 times

  Random matrix of shape 5 x 4
  Matrix is not symmetric!

  Random complex matrix of order 5
  Matrix is complex.  These tests are inadequate.

spd_test():
  Normal end of execution.