
Routine: Get_LegendreRoots():
 Read in quadrature of order: 4

Routine: Get_GaussLegendreWeights():
 Read in quadrature of order: 4

Routine: Get_GaussLegendreWeights():
 Read in quadrature of order: 7

Routine: Get_LegendreRoots():
 Read in quadrature of order: 7

*W->H0[0][] = 

7.0710678118654752440084436210484900e-01
0.0000000000000000000000000000000000e+00
2.0427571856496672372556444220945700e-34
0.0000000000000000000000000000000000e+00

*W->H0[1][] = 

-6.1237243569579452454932101867647290e-01
3.5355339059327376220042218105242450e-01
-1.9789210235981151360914055339041150e-34
-1.7661338167596081322106092399359300e-34

*W->H0[2][] = 

1.7022976547080560310463703517454750e-35
-6.8465319688145764182121222850100280e-01
1.7677669529663688110021109052621220e-01
2.8939060130036952527788295979673080e-34

*W->H0[3][] = 

2.3385358667337133659898429576978440e-01
4.0504629365049126443537296475549970e-01
-5.2291251658379721748635751611574190e-01
8.8388347648318440550105545263105910e-02

*W->G0[0][] = 

5.2430767765008125756228206833760630e-33
-1.5339299776947408740195227193950080e-01
-5.9408852578600458549196387747468250e-01
3.5146751167740366604477625486653580e-01

*W->G0[1][] = 

-1.5430334996209191026109446276399570e-01
-2.6726124191242438468455348087975580e-01
-1.7251638983558855444903171615678490e-01
6.1237243569579452454932101867647100e-01

*W->G0[2][] = 

-8.1369827895045078284016502813433710e-33
8.7866877919350916511194063716634320e-02
3.4030695486488630490614957067107590e-01
6.1357199107789634960780908775804370e-01

*W->G0[3][] = 

-2.1564548729448569306128964519598330e-01
-3.7350894041699801249025536865410170e-01
-4.4362213114101424200064658044649920e-01
-3.4232659844072882091060611425049780e-01

Checking the orthogonality conditions on the filters:
(see: Alpert, Beylkin, Gines, Vozovoi).
OBS: These filters should really be computed using extended precision.

The matrix identity: Id = (H0^T)H0+(G0^T)G0, has righthand side equal:

1e+00   -6e-34   -4e-33   6e-34   
-6e-34   1e+00   -5e-33   1e-33   
-4e-33   -5e-33   1e+00   -2e-33   
6e-34   1e-33   -2e-33   1e+00   

The matrix identity: Id = (H1^T)H1+(G1^T)G1, has righthand side equal:

1e+00   5e-34   -2e-33   1e-32   
5e-34   1e+00   -3e-33   1e-32   
-2e-33   -3e-33   1e+00   4e-33   
1e-32   1e-32   4e-33   1e+00   

The matrix identity: 0 = (H0^T)H1+(G0^T)G1, has righthand side equal:

-2e-34   2e-33   -7e-33   7e-33   
-3e-34   2e-33   -5e-33   -7e-33   
2e-34   6e-34   3e-33   -4e-33   
-4e-34   5e-34   -1e-33   2e-34   
The size of double is: 8 bytes.
The size of long double is: 16 bytes.
