March 10th, 2017, 12:25 pm
Comparing Genz trivariate and Goursat 3d (on rough meshes); how much effort/function evaluations needed to achieve a given accuracy.
The FDM approach seems to scale to 3d quite well. You turn the knob to determine the level of accuracy needed.
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***Trivariate, NX, NY, NZ: 5,5,5
** a,b, rho21, rho31, rho32: 6,0.34,5,0,0.8660254,-0.01
Goursat Classico NX: 0.599523504012804
Goursat Extrap 2*NX: 0.5672737978616413
Goursat Extrap 4*NX: 0.6535811570580227
Genz trivariate 0.6330715488562566
***Trivariate, NX, NY, NZ: 10,10,10
** a,b, rho21, rho31, rho32: 6,0.34,5,0,0.8660254,-0.01
Goursat Classico NX: 0.575336224399432
Goursat Extrap 2*NX: 0.6535811570580227
Goursat Extrap 4*NX: 0.6330657997160345
Genz trivariate 0.6330715488562566
***Trivariate, NX, NY, NZ: 15,15,15
** a,b, rho21, rho31, rho32: 6,0.34,5,0,0.8660254,-0.01
Goursat Classico NX: 0.6339577269600256
Goursat Extrap 2*NX: 0.6333295042229049
Goursat Extrap 4*NX: 0.6330708876660983
Genz trivariate 0.6330715488562566
***Trivariate, NX, NY, NZ: 20,20,20
** a,b, rho21, rho31, rho32: 6,0.34,5,0,0.8660254,-0.01
Goursat Classico NX: 0.634019923893375
Goursat Extrap 2*NX: 0.6330657997160345
Goursat Extrap 4*NX: 0.6330713519004104
Genz trivariate 0.6330715488562566
***Trivariate, NX, NY, NZ: 25,25,25
** a,b, rho21, rho31, rho32: 6,0.34,5,0,0.8660254,-0.01
Goursat Classico NX: 0.6336709039109505
Goursat Extrap 2*NX: 0.6330701496719837
Goursat Extrap 4*NX: 0.6330714779678041
Genz trivariate 0.6330715488562566
***Trivariate, NX, NY, NZ: 30,30,30
** a,b, rho21, rho31, rho32: 6,0.34,5,0,0.8660254,-0.01
Goursat Classico NX: 0.6334865599071851
Goursat Extrap 2*NX: 0.6330708876660983
Goursat Extrap 4*NX: 0.6330715231145035
Genz trivariate 0.6330715488562566
***Trivariate, NX, NY, NZ: 35,35,35
** a,b, rho21, rho31, rho32: 6,0.34,5,0,0.8660254,-0.01
Goursat Classico NX: 0.6333759285107489
Goursat Extrap 2*NX: 0.6330712006360999
Goursat Extrap 4*NX: 0.633071542435185
Genz trivariate 0.6330715488562566
***Trivariate, NX, NY, NZ: 40,40,40
** a,b, rho21, rho31, rho32: 6,0.34,5,0,0.8660254,-0.01
Goursat Classico NX: 0.6333043307603696
Goursat Extrap 2*NX: 0.6330713519004104
Goursat Extrap 4*NX: 0.6330715518026937
Genz trivariate 0.6330715488562566
***Trivariate, NX, NY, NZ: 45,45,45
** a,b, rho21, rho31, rho32: 6,0.34,5,0,0.8660254,-0.01
Goursat Classico NX: 0.6332553368798947
Goursat Extrap 2*NX: 0.6330714321801681
Goursat Extrap 4*NX: 0.633071556784604
Genz trivariate 0.6330715488562566
***Trivariate, NX, NY, NZ: 50,50,50
** a,b, rho21, rho31, rho32: 6,0.34,5,0,0.8660254,-0.01
Goursat Classico NX: 0.6332203382317254
Goursat Extrap 2*NX: 0.6330714779678041
Goursat Extrap 4*NX: 0.6330715596300344
Genz trivariate 0.6330715488562566
***Trivariate, NX, NY, NZ: 55,55,55
** a,b, rho21, rho31, rho32: 6,0.34,5,0,0.8660254,-0.01
Goursat Classico NX: 0.6331944680253506
Goursat Extrap 2*NX: 0.6330715056196582
Goursat Extrap 4*NX: 0.6330715613503234
Genz trivariate 0.6330715488562566
***Trivariate, NX, NY, NZ: 60,60,60
** a,b, rho21, rho31, rho32: 6,0.34,5,0,0.8660254,-0.01
Goursat Classico NX: 0.63317480572637
Goursat Extrap 2*NX: 0.6330715231145035
Goursat Extrap 4*NX: 0.6330715624395525
Genz trivariate 0.6330715488562566
***Trivariate, NX, NY, NZ: 65,65,65
** a,b, rho21, rho31, rho32: 6,0.34,5,0,0.8660254,-0.01
Goursat Classico NX: 0.6331595122602685
Goursat Extrap 2*NX: 0.6330715346191126
Goursat Extrap 4*NX: 0.6330715631563174
Genz trivariate 0.6330715488562566
***Trivariate, NX, NY, NZ: 70,70,70
** a,b, rho21, rho31, rho32: 6,0.34,5,0,0.8660254,-0.01
Goursat Classico NX: 0.6331473826047621
Goursat Extrap 2*NX: 0.633071542435185
Goursat Extrap 4*NX: 0.6330715636434827
Genz trivariate 0.6330715488562566
Last edited by
Cuchulainn on March 10th, 2017, 12:38 pm, edited 2 times in total.