Diagonal Matrices 2 testing
Form of the matrix
The matrix to invert is of the form
(1)
Am,n  A  f n  f m 
With the periodicity requirement that A(fn+M)=A(fn). In particular for M = 4 as below A(-3+4)=A(1)
0 1 2 3  0 1 2 1 
1 0 1 2   1 0 1 2 

 




2 1 0 1 2 1 0 1
3 2 1 0   1 2 1 0 
The specific test of interest is to generate a set of N values in the time domain. These are then transformed to N
frequency values. The frequency values are truncated to M values. This truncation leaves Time alone, but there are
now only M points. The original time spacing of Time/N goes to  Time/M with fewer points. A transform over
these fewer points is periodic in M, rather than N.
for\DiagMat.wpj for\diagmat2p.zip
Af linear
-0.108108E+00
0.229049E+01
0.000000E+00 The matrix of 16 values in time is truncated to 8 in frequency. Note
-0.810811E-01
0.276179E+01 -0.290837E-16
that the frequency does not go to zero at the ends
-0.540541E-01
0.317146E+01
0.641848E-16
-0.270270E-01
0.345038E+01 -0.691992E-16
0.000000E+00
0.354932E+01
0.000000E+00
0.270270E-01
0.345038E+01 -0.131378E-15
0.540541E-01
0.317146E+01
0.000000E+00
0.810811E-01
0.276179E+01 -0.912627E-16
Afinv(f)
-0.108108E+00 -0.199833E+01 -0.126535E-14 The inverse matrix is small indicating that more terms could have been
-0.810811E-01
0.106351E+01
0.728372E-15
used. Definitely not diagonal.
-0.540541E-01 -0.153619E-01 -0.374458E-15
-0.270270E-01 -0.186530E-01
0.279078E-15
0.000000E+00 -0.200229E-01 -0.256948E-15
0.270270E-01 -0.186530E-01
0.920926E-15
0.540541E-01 -0.153619E-01 -0.140141E-14
0.810811E-01
0.106351E+01
0.137022E-14
Afinv * AF
F -0.108E+00-0.811E-01-0.541E-01-0.270E-01 0.000E+00 0.270E-01 0.541E-01 0.811E-01
R 0.100E+01 0.749E-15-0.430E-15 0.312E-15-0.138E-14-0.104E-15-0.583E-15 0.319E-15
I 0.369E-15 0.109E-17 0.201E-15-0.484E-16-0.369E-15-0.109E-17-0.201E-15 0.484E-16
F -0.108E+00-0.811E-01-0.541E-01-0.270E-01 0.000E+00 0.270E-01 0.541E-01 0.811E-01
R 0.576E-15 0.100E+01 0.541E-15-0.430E-15 0.104E-15-0.139E-14 0.132E-15-0.749E-15
I 0.484E-16 0.369E-15 0.109E-17 0.201E-15-0.484E-16-0.369E-15-0.109E-17-0.201E-15
F -0.108E+00-0.811E-01-0.541E-01-0.270E-01 0.000E+00 0.270E-01 0.541E-01 0.811E-01
R -0.888E-15 0.444E-15 0.100E+01 0.444E-15-0.444E-15 0.000E+00-0.178E-14 0.000E+00
I -0.201E-15 0.484E-16 0.369E-15 0.109E-17 0.201E-15-0.484E-16-0.369E-15-0.109E-17
F -0.108E+00-0.811E-01-0.541E-01-0.270E-01 0.000E+00 0.270E-01 0.541E-01 0.811E-01
R -0.888E-15-0.888E-15 0.000E+00 0.100E+01 0.888E-15 0.000E+00 0.000E+00-0.178E-14
I -0.109E-17-0.201E-15 0.484E-16 0.369E-15 0.109E-17 0.201E-15-0.484E-16-0.369E-15
F -0.108E+00-0.811E-01-0.541E-01-0.270E-01 0.000E+00 0.270E-01 0.541E-01 0.811E-01
R -0.178E-14-0.444E-15-0.888E-15 0.444E-15 0.100E+01 0.444E-15-0.444E-15 0.000E+00
I -0.369E-15-0.109E-17-0.201E-15 0.484E-16 0.369E-15 0.109E-17 0.201E-15-0.484E-16
F -0.108E+00-0.811E-01-0.541E-01-0.270E-01 0.000E+00 0.270E-01 0.541E-01 0.811E-01
R 0.194E-15-0.154E-14 0.833E-16-0.687E-15 0.569E-15 0.100E+01 0.687E-15-0.576E-15
I -0.484E-16-0.369E-15-0.109E-17-0.201E-15 0.484E-16 0.369E-15 0.109E-17 0.201E-15
F -0.108E+00-0.811E-01-0.541E-01-0.270E-01 0.000E+00 0.270E-01 0.541E-01 0.811E-01
R -0.597E-15 0.298E-15-0.172E-14 0.298E-15-0.666E-15 0.756E-15 0.100E+01 0.805E-15
I 0.201E-15-0.484E-16-0.369E-15-0.109E-17-0.201E-15 0.484E-16 0.369E-15 0.109E-17
F -0.108E+00-0.811E-01-0.541E-01-0.270E-01 0.000E+00 0.270E-01 0.541E-01 0.811E-01
R 0.486E-15-0.527E-15 0.416E-16-0.173E-14 0.763E-16-0.680E-15 0.486E-15 0.100E+01
I 0.109E-17 0.201E-15-0.484E-16-0.369E-15-0.109E-17-0.201E-15 0.484E-16 0.369E-15