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

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

Routine: Get_GaussLegendreWeights():
 Read in quadrature of order: 13

Routine: Get_LegendreRoots():
 Read in quadrature of order: 13

*W->H0[0][] = 

7.0710678118654752440084436210484930e-01
8.5114882735402801552318517587273760e-36
1.1064934755602364201801407286345590e-34
-8.5114882735402801552318517587273760e-36
-1.8725274201788616341510073869200230e-34
0.0000000000000000000000000000000000e+00
1.2597002644839614629743140602916520e-33

*W->H0[1][] = 

-6.1237243569579452454932101867647300e-01
3.5355339059327376220042218105242460e-01
-1.0798950747054230446950411918885360e-34
-9.1498498940558011668742406406319290e-35
2.0055194244529285115765050706501380e-34
9.3626371008943081707550369346001140e-35
-1.0739104345130900352108937961206810e-33

*W->H0[2][] = 

6.8091906188322241241854814069819010e-35
-6.8465319688145764182121222850100300e-01
1.7677669529663688110021109052621230e-01
2.0427571856496672372556444220945700e-34
-1.3618381237664448248370962813963800e-34
-2.6385613647974868481218740452054860e-34
2.5960039234297854473457147864118500e-34

*W->H0[3][] = 

2.3385358667337133659898429576978440e-01
4.0504629365049126443537296475549980e-01
-5.2291251658379721748635751611574220e-01
8.8388347648318440550105545263105960e-02
3.7450548403577232683020147738400450e-34
1.0213785928248336186278222110472850e-34
-4.9898600003629892410046730935539240e-34

*W->H0[4][] = 

1.7022976547080560310463703517454750e-34
1.5309310892394863113733025466911810e-01
5.9292706128157112474979253958113490e-01
-3.5078038001005700489847644365467650e-01
4.4194173824159220275052772631552610e-02
1.9576423029142644357033259045072960e-34
1.0043556162777530583173585075298300e-33

*W->H0[5][] = 

-1.4657549249448217358017594104826460e-01
-2.5387620014487376126437136150831380e-01
-1.6387638252658617921741461151249010e-01
5.8170345215582140294374571666169380e-01
-2.1986323874172326037026391157239640e-01
2.2097086912079610137526386315776250e-02
-5.3888360131851898732811661447442700e-34

*W->H0[6][] = 

8.9370626872172941629934443466637440e-34
-6.8998131768186303552844083804370310e-02
-2.6722861525761046386001149036720770e-01
-4.2158554885100129579844705035923590e-01
4.7803307939932357781514601022088590e-01
-1.3212136347881064764197279627169240e-01
1.1048543456039805068763193157888240e-02

*W->G0[0][] = 

1.0698032684302814373475836906996830e-01
1.8529536150244933747464369543482540e-01
1.8180361513787886627215496034663440e-01
-5.6608668000612024995796086739924950e-02
-5.3490163421514071867379184535075380e-01
3.5481360408791037219666118223833870e-01
-7.7144610779686914946660235992487140e-02

*W->G0[1][] = 

1.5854859896419892261959684182087010e-30
-3.9528470752104741649986169304518100e-02
-1.5309310892394863113733025466907270e-01
-3.0190368221227997028580550327372310e-01
-2.0539595906443729254636366855075680e-01
5.2983881196706104144894324170036120e-01
-2.4685522072664373771798076304729890e-01

*W->G0[2][] = 

8.6476184935818028995097323370170610e-02
1.4978114595355919836697480443730160e-01
1.6578591881630839028916344723334760e-01
6.5624803952538099946677718370809340e-02
-2.2188551753199754130166157432464480e-01
-4.1132522686650828473741293760311860e-01
4.6890752482443832311412074156723950e-01

*W->G0[3][] = 

1.8307019668026846974681980673776360e-30
2.8670368513063214998374080535649430e-02
1.1103985978072333366784148992565860e-01
2.3684894889148662842071530432341850e-01
2.9085713319861236888398059393918780e-01
7.8427965725058565649920601687293610e-03
-5.8829529449725106734912242904012940e-01

*W->G0[4][] = 

9.5093166545435139055325131427058070e-02
1.6470619590930267798425495773855590e-01
1.9492068652291196908421773368243650e-01
1.4679485260262335799005314804731420e-01
-4.8164960478895518151945929702960570e-02
-3.7491678841511884046340144339142920e-01
-5.1127672963554556018535167654147370e-01

*W->G0[5][] = 

5.4041141346361946761598073186511850e-31
2.5831526896897778509243002902036880e-02
1.0004507347879405007907380968239750e-01
2.2798134150773089456277247322538460e-01
3.7781725485674243167661093943733280e-01
4.4916953279107836625935305984915800e-01
3.0471146378154635821166187291829370e-01

*W->G0[6][] = 

-1.4443854673828315092049969002011980e-01
-2.5017490152211835889586636235755500e-01
-3.1808085742538344432039777994945890e-01
-3.5319783240099521635137537321992980e-01
-3.3762012922157921089819280160972110e-01
-2.5272115980237209726180815600770400e-01
-1.1300684901301610714138444823712980e-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   -1e-32   -9e-33   2e-32   1e-31   -7e-31   -7e-30   
-1e-32   1e+00   9e-33   5e-32   8e-32   -8e-31   -5e-30   
-9e-33   9e-33   1e+00   5e-32   1e-32   -2e-31   -2e-31   
2e-32   5e-32   5e-32   1e+00   2e-32   2e-31   -1e-31   
1e-31   8e-32   1e-32   2e-32   1e+00   4e-32   2e-30   
-7e-31   -8e-31   -2e-31   2e-31   4e-32   1e+00   -6e-31   
-7e-30   -5e-30   -2e-31   -1e-31   2e-30   -6e-31   1e+00   

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

1e+00   -5e-32   2e-31   -4e-31   6e-31   -8e-31   1e-29   
-5e-32   1e+00   2e-31   -4e-31   4e-31   3e-31   1e-29   
2e-31   2e-31   1e+00   -2e-31   6e-31   -2e-30   8e-30   
-4e-31   -4e-31   -2e-31   1e+00   6e-32   4e-31   4e-30   
6e-31   4e-31   6e-31   6e-32   1e+00   2e-31   2e-30   
-8e-31   3e-31   -2e-30   4e-31   2e-31   1e+00   6e-31   
1e-29   1e-29   8e-30   4e-30   2e-30   6e-31   1e+00   

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

-3e-33   -3e-32   3e-32   -1e-31   7e-31   -3e-30   4e-30   
3e-32   6e-33   6e-32   -9e-32   4e-31   -2e-30   3e-30   
1e-31   1e-31   1e-31   4e-33   -5e-32   3e-31   -9e-31   
3e-31   2e-31   2e-31   6e-32   -2e-31   9e-31   -3e-30   
1e-31   6e-32   1e-31   -6e-32   -1e-31   -8e-32   2e-30   
-3e-31   2e-31   -3e-31   9e-32   2e-31   9e-32   -5e-31   
-6e-31   3e-30   -3e-30   3e-30   3e-30   8e-31   2e-31   
The size of double is: 8 bytes.
The size of long double is: 16 bytes.
