24 January 2020 01:09:20 PM
ASA006_TEST:
C++ version
Test the ASA006 library.
TEST01:
CHOLESKY computes the Cholesky factorization
of a positive definite symmetric 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 ( A - U'*U ) = 4.44089e-16
Matrix order N = 2
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 4.44089e-16
Matrix order N = 3
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 0
Matrix order N = 4
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 8.88178e-16
Matrix order N = 5
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 8.88178e-16
Matrix order N = 6
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 8.88178e-16
Matrix order N = 7
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 2.80867e-15
Matrix order N = 8
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 3.76822e-15
Matrix order N = 9
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 7.32411e-15
Matrix order N = 10
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 5.61733e-15
Matrix order N = 11
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 5.61733e-15
Matrix order N = 12
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 1.05091e-14
Matrix order N = 13
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 8.51911e-15
Matrix order N = 14
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 1.36445e-14
Matrix order N = 15
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 1.74951e-14
TEST02:
CHOLESKY computes the Cholesky factorization
of a positive definite symmetric 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 ( A - U'*U ) = 0
Matrix order N = 2
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 0
Matrix order N = 3
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 0
Matrix order N = 4
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 0
Matrix order N = 5
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 1.38778e-17
Matrix order N = 6
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 1.38778e-17
Matrix order N = 7
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 2.4037e-17
Matrix order N = 8
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 3.10317e-17
Matrix order N = 9
Maxtrix nullity NULLTY = 0
RMS ( A - U'*U ) = 3.80059e-17
Matrix order N = 10
Maxtrix nullity NULLTY = 1
RMS ( A - U'*U ) = 2.22673e-11
Matrix order N = 11
Maxtrix nullity NULLTY = 1
RMS ( A - U'*U ) = 1.09934
Matrix order N = 12
Maxtrix nullity NULLTY = 1
RMS ( A - U'*U ) = 16.7193
Matrix order N = 13
Maxtrix nullity NULLTY = 1
RMS ( A - U'*U ) = 27.9614
Matrix order N = 14
Maxtrix nullity NULLTY = 1
RMS ( A - U'*U ) = 38.8361
Matrix order N = 15
Maxtrix nullity NULLTY = 1
RMS ( A - U'*U ) = 49.5867
TEST03:
SUBCHL computes the Cholesky factor
of a submatrix
of a positive definite symmetric matrix.
A compressed storage format is used.
Here we look at the Hilbert matrix
A(I,J) = 1/(I+J-1).
For this particular matrix, we expect the
errors to grow rapidly.
Matrix order N = 1
Maxtrix nullity NULLTY = 0
Matrix determinant DET = 1
RMS ( A - U'*U ) = 0
Matrix order N = 2
Maxtrix nullity NULLTY = 0
Matrix determinant DET = 0.0833333
RMS ( A - U'*U ) = 0
Matrix order N = 3
Maxtrix nullity NULLTY = 0
Matrix determinant DET = 0.000462963
RMS ( A - U'*U ) = 0
Matrix order N = 4
Maxtrix nullity NULLTY = 0
Matrix determinant DET = 1.65344e-07
RMS ( A - U'*U ) = 0
Matrix order N = 5
Maxtrix nullity NULLTY = 0
Matrix determinant DET = 3.7493e-12
RMS ( A - U'*U ) = 1.38778e-17
Matrix order N = 6
Maxtrix nullity NULLTY = 0
Matrix determinant DET = 5.3673e-18
RMS ( A - U'*U ) = 1.38778e-17
Matrix order N = 7
Maxtrix nullity NULLTY = 0
Matrix determinant DET = 4.8358e-25
RMS ( A - U'*U ) = 2.4037e-17
Matrix order N = 8
Maxtrix nullity NULLTY = 0
Matrix determinant DET = 2.73705e-33
RMS ( A - U'*U ) = 3.10317e-17
Matrix order N = 9
Maxtrix nullity NULLTY = 0
Matrix determinant DET = 9.72027e-43
RMS ( A - U'*U ) = 3.80059e-17
Matrix order N = 10
Maxtrix nullity NULLTY = 1
Matrix determinant DET = 0
RMS ( A - U'*U ) = 2.22673e-11
Matrix order N = 11
Maxtrix nullity NULLTY = 1
Matrix determinant DET = 0
RMS ( A - U'*U ) = 1.09934
Matrix order N = 12
Maxtrix nullity NULLTY = 1
Matrix determinant DET = 0
RMS ( A - U'*U ) = 16.7193
Matrix order N = 13
Maxtrix nullity NULLTY = 1
Matrix determinant DET = 0
RMS ( A - U'*U ) = 27.9614
Matrix order N = 14
Maxtrix nullity NULLTY = 1
Matrix determinant DET = 0
RMS ( A - U'*U ) = 38.8361
Matrix order N = 15
Maxtrix nullity NULLTY = 1
Matrix determinant DET = 0
RMS ( A - U'*U ) = 49.5867
ASA006_TEST:
Normal end of execution.
24 January 2020 01:09:20 PM