IN R:
> mat
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] -1.776357e-15+0i -29.8653+5.39586i -0.7587359-0.0934662i -3.838166+1.757318i -0.7875201-0.193701i -1.758288+1.004135i
[2,] -1.776357e-15+0i -29.8653+5.39586i -0.7587359-0.0934662i -3.838166+1.757318i -0.7875201-0.193701i -1.758288+1.004135i
[3,] -1.776357e-15+0i -29.8653+5.39586i -0.7587359-0.0934662i -3.838166+1.757318i -0.7875201-0.193701i -1.758288+1.004135i
[4,] -1.776357e-15+0i -29.8653+5.39586i -0.7587359-0.0934662i -3.838166+1.757318i -0.7875201-0.193701i -1.758288+1.004135i
[5,] -1.776357e-15+0i -29.8653+5.39586i -0.7587359-0.0934662i -3.838166+1.757318i -0.7875201-0.193701i -1.758288+1.004135i
[6,] -1.776357e-15+0i -29.8653+5.39586i -0.7587359-0.0934662i -3.838166+1.757318i -0.7875201-0.193701i -1.758288+1.004135i
[7,] -1.776357e-15+0i -29.8653+5.39586i -0.7587359-0.0934662i -3.838166+1.757318i -0.7875201-0.193701i -1.758288+1.004135i
[8,] -1.776357e-15+0i -29.8653+5.39586i -0.7587359-0.0934662i -3.838166+1.757318i -0.7875201-0.193701i -1.758288+1.004135i
[,7] [,8] [,9] [,10] [,11] [,12]
[1,] -0.845844-0.3095869i -1.188386+0.662107i -0.957763-0.4558102i -0.957763+0.4558102i -1.188386-0.662107i -0.845844+0.3095869i
[2,] -0.845844-0.3095869i -1.188386+0.662107i -0.957763-0.4558102i -0.957763+0.4558102i -1.188386-0.662107i -0.845844+0.3095869i
[3,] -0.845844-0.3095869i -1.188386+0.662107i -0.957763-0.4558102i -0.957763+0.4558102i -1.188386-0.662107i -0.845844+0.3095869i
[4,] -0.845844-0.3095869i -1.188386+0.662107i -0.957763-0.4558102i -0.957763+0.4558102i -1.188386-0.662107i -0.845844+0.3095869i
[5,] -0.845844-0.3095869i -1.188386+0.662107i -0.957763-0.4558102i -0.957763+0.4558102i -1.188386-0.662107i -0.845844+0.3095869i
[6,] -0.845844-0.3095869i -1.188386+0.662107i -0.957763-0.4558102i -0.957763+0.4558102i -1.188386-0.662107i -0.845844+0.3095869i
[7,] -0.845844-0.3095869i -1.188386+0.662107i -0.957763-0.4558102i -0.957763+0.4558102i -1.188386-0.662107i -0.845844+0.3095869i
[8,] -0.845844-0.3095869i -1.188386+0.662107i -0.957763-0.4558102i -0.957763+0.4558102i -1.188386-0.662107i -0.845844+0.3095869i
[,13] [,14] [,15] [,16] [,17]
[1,] -1.758288-1.004135i -0.7875201+0.193701i -3.838166-1.757318i -0.7587359+0.0934662i -29.8653-5.39586i
[2,] -1.758288-1.004135i -0.7875201+0.193701i -3.838166-1.757318i -0.7587359+0.0934662i -29.8653-5.39586i
[3,] -1.758288-1.004135i -0.7875201+0.193701i -3.838166-1.757318i -0.7587359+0.0934662i -29.8653-5.39586i
[4,] -1.758288-1.004135i -0.7875201+0.193701i -3.838166-1.757318i -0.7587359+0.0934662i -29.8653-5.39586i
[5,] -1.758288-1.004135i -0.7875201+0.193701i -3.838166-1.757318i -0.7587359+0.0934662i -29.8653-5.39586i
[6,] -1.758288-1.004135i -0.7875201+0.193701i -3.838166-1.757318i -0.7587359+0.0934662i -29.8653-5.39586i
[7,] -1.758288-1.004135i -0.7875201+0.193701i -3.838166-1.757318i -0.7587359+0.0934662i -29.8653-5.39586i
[8,] -1.758288-1.004135i -0.7875201+0.193701i -3.838166-1.757318i -0.7587359+0.0934662i -29.8653-5.39586i
> psift
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 0 1.278370e+00 2.252991e+00 1.293244e+00 3.396188e-01 4.538799e-02 3.236891e-03 1.263402e-04 2.739938e-06 2.739938e-06
[2,] 0 2.285394e+00 1.825314e+00 2.801436e-01 1.160548e-02 1.443551e-04 5.653120e-07 7.148575e-10 2.963366e-13 2.963366e-13
[3,] 0 3.166847e+00 5.337773e-01 6.128173e-03 6.731508e-06 7.869581e-10 1.026712e-14 1.533177e-20 2.660366e-27 2.660366e-27
[4,] 0 2.659601e+00 2.106092e-02 1.479089e-06 1.294018e-12 1.568781e-20 2.763509e-30 7.254780e-42 2.881454e-55 2.881454e-55
[5,] 0 8.346908e-01 1.620588e-05 5.073802e-14 3.598162e-26 6.429271e-42 3.035125e-61 3.882522e-84 1.366258e-110 1.366258e-110
[6,] 0 3.784090e-02 5.429692e-12 4.766657e-29 3.596251e-53 2.593769e-84 1.875242e-122 1.393853e-167 1.081358e-219 1.081358e-219
[7,] 0 3.825796e-05 4.499615e-25 6.109615e-59 1.345271e-106 5.343311e-168 4.014358e-243 0.000000e+00 0.000000e+00 0.000000e+00
[8,] 0 2.192201e-11 3.847415e-51 4.724971e-118 5.703525e-212 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
[,11] [,12] [,13] [,14] [,15] [,16] [,17]
[1,] 1.263402e-04 3.236891e-03 4.538799e-02 3.396188e-01 1.293244e+00 2.252991e+00 1.278370e+00
[2,] 7.148575e-10 5.653120e-07 1.443551e-04 1.160548e-02 2.801436e-01 1.825314e+00 2.285394e+00
[3,] 1.533177e-20 1.026712e-14 7.869581e-10 6.731508e-06 6.128173e-03 5.337773e-01 3.166847e+00
[4,] 7.254780e-42 2.763509e-30 1.568781e-20 1.294018e-12 1.479089e-06 2.106092e-02 2.659601e+00
[5,] 3.882522e-84 3.035125e-61 6.429271e-42 3.598162e-26 5.073802e-14 1.620588e-05 8.346908e-01
[6,] 1.393853e-167 1.875242e-122 2.593769e-84 3.596251e-53 4.766657e-29 5.429692e-12 3.784090e-02
[7,] 0.000000e+00 4.014358e-243 5.343311e-168 1.345271e-106 6.109615e-59 4.499615e-25 3.825796e-05
[8,] 0.000000e+00 0.000000e+00 0.000000e+00 5.703525e-212 4.724971e-118 3.847415e-51 2.192201e-11
mvfft(mat*psift,inverse = TRUE)
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0+0i -306.501035+ 55.376527i -3.5153444-0.4330438i -6.062448+2.775713i -0.2766015-0.0680338i -0.08005897+0.04572064i
[2,] 0+0i -40.359639-197.384866i -2.5054897-1.7254107i -6.082868+1.836915i -0.2723284-0.0738420i -0.08008712+0.04549871i
[3,] 0+0i 33.287767+ 4.359385i -1.1358049-1.5296414i -5.432462+1.186639i -0.2652033-0.0749228i -0.07995010+0.04532187i
[4,] 0+0i -23.587552- 5.085224i -0.6692802-0.6769304i -4.540723+1.187742i -0.2594057-0.0706523i -0.07972817+0.04529371i
[5,] 0+0i -8.873233+ 1.603156i -0.7135227-0.0878965i -3.911962+1.791106i -0.2583224-0.0635378i -0.07955133+0.04543073i
[6,] 0+0i -20.316861+ 13.017576i -0.8135559+0.4942647i -3.866038+2.661323i -0.2625823-0.0577376i -0.07952318+0.04565266i
[7,] 0+0i 29.657799- 15.731962i -1.4730782+1.2082616i -4.447864+3.337103i -0.2696993-0.0566437i -0.07966020+0.04582950i
[8,] 0+0i 31.261661+199.028627i -2.8493259+1.0657684i -5.365107+3.404581i -0.2755101-0.0609061i -0.07988213+0.04585766i
[,7] [,8] [,9] [,10]
[1,] -0.002738383-0.001002274i -1.501417e-04+8.36512e-05i -2.624212e-06-1.248892e-06i -2.624212e-06+1.248892e-06i
[2,] -0.002738119-0.001002561i -1.501418e-04+8.36505e-05i -2.624212e-06-1.248892e-06i -2.624212e-06+1.248892e-06i
[3,] -0.002737730-0.001002577i -1.501414e-04+8.36499e-05i -2.624211e-06-1.248892e-06i -2.624212e-06+1.248892e-06i
[4,] -0.002737443-0.001002313i -1.501406e-04+8.36498e-05i -2.624211e-06-1.248892e-06i -2.624211e-06+1.248892e-06i
[5,] -0.002737427-0.001001924i -1.501400e-04+8.36503e-05i -2.624211e-06-1.248892e-06i -2.624211e-06+1.248892e-06i
[6,] -0.002737690-0.001001637i -1.501400e-04+8.36510e-05i -2.624211e-06-1.248892e-06i -2.624211e-06+1.248892e-06i
[7,] -0.002738080-0.001001621i -1.501404e-04+8.36516e-05i -2.624212e-06-1.248892e-06i -2.624211e-06+1.248892e-06i
[8,] -0.002738367-0.001001885i -1.501412e-04+8.36517e-05i -2.624212e-06-1.248892e-06i -2.624212e-06+1.248892e-06i
[,11] [,12] [,13] [,14] [,15]
[1,] -1.501417e-04-8.36512e-05i -0.002738383+0.001002274i -0.08005897-0.04572064i -0.2766015+0.0680338i -6.062448-2.775713i
[2,] -1.501412e-04-8.36517e-05i -0.002738367+0.001001885i -0.07988213-0.04585766i -0.2755101+0.0609061i -5.365107-3.404581i
[3,] -1.501404e-04-8.36516e-05i -0.002738080+0.001001621i -0.07966020-0.04582950i -0.2696993+0.0566437i -4.447864-3.337103i
[4,] -1.501400e-04-8.36510e-05i -0.002737690+0.001001637i -0.07952318-0.04565266i -0.2625823+0.0577376i -3.866038-2.661323i
[5,] -1.501400e-04-8.36503e-05i -0.002737427+0.001001924i -0.07955133-0.04543073i -0.2583224+0.0635378i -3.911962-1.791106i
[6,] -1.501406e-04-8.36498e-05i -0.002737443+0.001002313i -0.07972817-0.04529371i -0.2594057+0.0706523i -4.540723-1.187742i
[7,] -1.501414e-04-8.36499e-05i -0.002737730+0.001002577i -0.07995010-0.04532187i -0.2652033+0.0749228i -5.432462-1.186639i
[8,] -1.501418e-04-8.36505e-05i -0.002738119+0.001002561i -0.08008712-0.04549871i -0.2723284+0.0738420i -6.082868-1.836915i
[,16] [,17]
[1,] -3.5153444+0.4330438i -306.501035- 55.376527i
[2,] -2.8493259-1.0657684i 31.261661-199.028627i
[3,] -1.4730782-1.2082616i 29.657799+ 15.731962i
[4,] -0.8135559-0.4942647i -20.316861- 13.017576i
[5,] -0.7135227+0.0878965i -8.873233- 1.603156i
[6,] -0.6692802+0.6769304i -23.587552+ 5.085224i
[7,] -1.1358049+1.5296414i 33.287767- 4.359385i
[8,] -2.5054897+1.7254107i -40.359639+197.384866i