From b25dce857ed20badf203d36422502584b1e1ec84 Mon Sep 17 00:00:00 2001 From: antonl Date: Wed, 22 Apr 2026 20:04:38 +0200 Subject: [PATCH] double integral test --- out/bspline0.dat | 300 --------------------------------- out/bspline1.dat | 300 --------------------------------- out/bspline2.dat | 300 --------------------------------- out/bspline3.dat | 300 --------------------------------- out/bspline9.dat | 300 --------------------------------- out/bsplines_grid.dat | 301 ---------------------------------- out/bsplines_knots.dat | 41 ----- out/dBspline0.dat | 300 --------------------------------- out/dBspline1.dat | 300 --------------------------------- out/dBspline2.dat | 300 --------------------------------- out/dBspline3.dat | 300 --------------------------------- out/dBspline9.dat | 300 --------------------------------- out/dBsplines_grid.dat | 301 ---------------------------------- out/dBsplines_knots.dat | 41 ----- out/eigvec_n1_l0.dat | 34 ---- out/eigvec_n2_l0.dat | 34 ---- out/eigvec_n2_l1.dat | 34 ---- out/eigvec_n2_l2.dat | 34 ---- out/eigvec_n3_l0.dat | 34 ---- out/eigvec_n3_l1.dat | 34 ---- out/eigvec_n3_l2.dat | 34 ---- out/eigvec_n4_l0.dat | 34 ---- out/eigvec_n4_l1.dat | 34 ---- out/eigvec_n4_l2.dat | 34 ---- out/eigvec_n5_l0.dat | 34 ---- out/eigvec_n5_l1.dat | 34 ---- out/eigvec_n5_l2.dat | 34 ---- out/eigvec_n6_l0.dat | 34 ---- out/eigvec_n6_l1.dat | 34 ---- out/grid.bin | Bin 2400 -> 800 bytes out/grid.dat | 300 --------------------------------- out/knotpoints.dat | 40 ----- src/hf/hf_base.c | 202 +++++++++++++++++++---- src/hf/hf_base.h | 19 ++- src/hf/hf_bsplines_and_grid.c | 13 +- src/hf/hf_bsplines_and_grid.h | 10 +- src/main.c | 4 +- 37 files changed, 208 insertions(+), 4574 deletions(-) delete mode 100644 out/bspline0.dat delete mode 100644 out/bspline1.dat delete mode 100644 out/bspline2.dat delete mode 100644 out/bspline3.dat delete mode 100644 out/bspline9.dat delete mode 100644 out/bsplines_grid.dat delete mode 100644 out/bsplines_knots.dat delete mode 100644 out/dBspline0.dat delete mode 100644 out/dBspline1.dat delete mode 100644 out/dBspline2.dat delete mode 100644 out/dBspline3.dat delete mode 100644 out/dBspline9.dat delete mode 100644 out/dBsplines_grid.dat delete mode 100644 out/dBsplines_knots.dat delete mode 100644 out/eigvec_n1_l0.dat delete mode 100644 out/eigvec_n2_l0.dat delete mode 100644 out/eigvec_n2_l1.dat delete mode 100644 out/eigvec_n2_l2.dat delete mode 100644 out/eigvec_n3_l0.dat delete mode 100644 out/eigvec_n3_l1.dat delete mode 100644 out/eigvec_n3_l2.dat delete mode 100644 out/eigvec_n4_l0.dat delete mode 100644 out/eigvec_n4_l1.dat delete mode 100644 out/eigvec_n4_l2.dat delete mode 100644 out/eigvec_n5_l0.dat delete mode 100644 out/eigvec_n5_l1.dat delete mode 100644 out/eigvec_n5_l2.dat delete mode 100644 out/eigvec_n6_l0.dat delete mode 100644 out/eigvec_n6_l1.dat delete mode 100644 out/grid.dat delete mode 100644 out/knotpoints.dat diff --git a/out/bspline0.dat 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--3.647821e-01 --4.769945e-01 --4.732031e-01 --4.077962e-01 --3.223604e-01 --2.403128e-01 --1.716945e-01 --1.187758e-01 --8.011225e-02 --5.294166e-02 --3.440233e-02 --2.204206e-02 --1.395428e-02 --8.743348e-03 --5.429335e-03 --3.344953e-03 --2.046453e-03 --1.244260e-03 --7.523093e-04 --4.525787e-04 --2.710226e-04 --1.616214e-04 --9.600751e-05 --5.681871e-05 --3.349503e-05 --1.964742e-05 --1.142544e-05 --6.511164e-06 --3.501003e-06 --1.380734e-06 --4.297736e-07 diff --git a/out/eigvec_n2_l1.dat b/out/eigvec_n2_l1.dat deleted file mode 100644 index 898a089..0000000 --- a/out/eigvec_n2_l1.dat +++ /dev/null @@ -1,34 +0,0 @@ - 4.568581e-02 - 1.715259e-01 - 3.800945e-01 - 4.748557e-01 - 4.684619e-01 - 4.044180e-01 - 3.207165e-01 - 2.398656e-01 - 1.718813e-01 - 1.192131e-01 - 8.058830e-02 - 5.336048e-02 - 3.473366e-02 - 2.228763e-02 - 1.412832e-02 - 8.862720e-03 - 5.509171e-03 - 3.397288e-03 - 2.080203e-03 - 1.265731e-03 - 7.658122e-04 - 4.609880e-04 - 2.762165e-04 - 1.648084e-04 - 9.795509e-05 - 5.801055e-05 - 3.423528e-05 - 2.012991e-05 - 1.177990e-05 - 6.835745e-06 - 3.888415e-06 - 2.087721e-06 - 8.226129e-07 - 2.559301e-07 diff --git a/out/eigvec_n2_l2.dat b/out/eigvec_n2_l2.dat deleted file mode 100644 index e63ac94..0000000 --- a/out/eigvec_n2_l2.dat +++ /dev/null @@ -1,34 +0,0 @@ - 2.548436e-03 - 1.768047e-02 - 6.801789e-02 - 1.434030e-01 - 2.235356e-01 - 2.907379e-01 - 3.357788e-01 - 3.567533e-01 - 3.563788e-01 - 3.395486e-01 - 3.116223e-01 - 2.774422e-01 - 2.408901e-01 - 2.047894e-01 - 1.709988e-01 - 1.405887e-01 - 1.140369e-01 - 9.140819e-02 - 7.250238e-02 - 5.696782e-02 - 4.438296e-02 - 3.431126e-02 - 2.633551e-02 - 2.007697e-02 - 1.520409e-02 - 1.143438e-02 - 8.531931e-03 - 6.302777e-03 - 4.589046e-03 - 3.262862e-03 - 2.220364e-03 - 1.376048e-03 - 5.929916e-04 - 1.933374e-04 diff --git a/out/eigvec_n3_l0.dat b/out/eigvec_n3_l0.dat deleted file mode 100644 index 134eb72..0000000 --- a/out/eigvec_n3_l0.dat +++ /dev/null @@ -1,34 +0,0 @@ --5.527878e-02 --4.227569e-02 - 7.307560e-02 - 1.868932e-01 - 1.897137e-01 - 1.051407e-01 --1.865757e-02 --1.423168e-01 --2.427050e-01 --3.106362e-01 --3.461726e-01 --3.543255e-01 --3.419763e-01 --3.159970e-01 --2.822895e-01 --2.454316e-01 --2.086779e-01 --1.741361e-01 --1.430082e-01 --1.158313e-01 --9.268768e-02 --7.337228e-02 --5.751818e-02 --4.468484e-02 --3.441642e-02 --2.627765e-02 --1.987318e-02 --1.485589e-02 --1.092782e-02 --7.836567e-03 --5.369044e-03 --3.343767e-03 --1.445016e-03 --4.717849e-04 diff --git a/out/eigvec_n3_l1.dat b/out/eigvec_n3_l1.dat deleted file mode 100644 index ed21f9a..0000000 --- a/out/eigvec_n3_l1.dat +++ /dev/null @@ -1,34 +0,0 @@ - 2.639616e-02 - 9.528065e-02 - 1.931190e-01 - 1.950762e-01 - 1.146697e-01 --6.535372e-03 --1.302783e-01 --2.326975e-01 --3.035693e-01 --3.421425e-01 --3.529422e-01 --3.426365e-01 --3.180668e-01 --2.852058e-01 --2.487455e-01 --2.120617e-01 --1.773712e-01 --1.459643e-01 --1.184448e-01 --9.494176e-02 --7.528080e-02 --5.911345e-02 --4.600886e-02 --3.551519e-02 --2.719772e-02 --2.066010e-02 --1.555394e-02 --1.158077e-02 --8.489411e-03 --6.070464e-03 --4.149590e-03 --2.580067e-03 --1.113932e-03 --3.635198e-04 diff --git a/out/eigvec_n3_l2.dat b/out/eigvec_n3_l2.dat deleted file mode 100644 index f3c86a0..0000000 --- a/out/eigvec_n3_l2.dat +++ /dev/null @@ -1,34 +0,0 @@ - 2.052795e-03 - 1.409798e-02 - 5.320203e-02 - 1.082929e-01 - 1.595481e-01 - 1.904361e-01 - 1.933109e-01 - 1.684463e-01 - 1.212309e-01 - 5.940421e-02 --9.021441e-03 --7.704423e-02 --1.392939e-01 --1.921809e-01 --2.337545e-01 --2.634124e-01 --2.815605e-01 --2.892837e-01 --2.880615e-01 --2.795418e-01 --2.653746e-01 --2.470983e-01 --2.260709e-01 --2.034357e-01 --1.801115e-01 --1.568004e-01 --1.340053e-01 --1.120532e-01 --9.111955e-02 --7.125225e-02 --5.239235e-02 --3.439146e-02 --1.532991e-02 --5.084455e-03 diff --git a/out/eigvec_n4_l0.dat b/out/eigvec_n4_l0.dat deleted file mode 100644 index cf62cc3..0000000 --- a/out/eigvec_n4_l0.dat +++ /dev/null @@ -1,34 +0,0 @@ - 3.823086e-02 - 2.775873e-02 --5.382039e-02 --1.274489e-01 --1.159661e-01 --4.181822e-02 - 5.304292e-02 - 1.345192e-01 - 1.834605e-01 - 1.941481e-01 - 1.700828e-01 - 1.197272e-01 - 5.320353e-02 --1.986814e-02 --9.154813e-02 --1.560321e-01 --2.096379e-01 --2.505293e-01 --2.783254e-01 --2.936910e-01 --2.979636e-01 --2.928442e-01 --2.801591e-01 --2.616894e-01 --2.390595e-01 --2.136720e-01 --1.866782e-01 --1.589737e-01 --1.312095e-01 --1.038133e-01 --7.701350e-02 --5.086481e-02 --2.275063e-02 --7.558317e-03 diff --git a/out/eigvec_n4_l1.dat b/out/eigvec_n4_l1.dat deleted file mode 100644 index 24ac9ae..0000000 --- a/out/eigvec_n4_l1.dat +++ /dev/null @@ -1,34 +0,0 @@ --1.861078e-02 --6.623201e-02 --1.298685e-01 --1.200704e-01 --5.062013e-02 - 4.198582e-02 - 1.244960e-01 - 1.768737e-01 - 1.921407e-01 - 1.727260e-01 - 1.263726e-01 - 6.282282e-02 --8.421685e-03 --7.936593e-02 --1.440522e-01 --1.986030e-01 --2.409828e-01 --2.706297e-01 --2.880570e-01 --2.944844e-01 --2.915274e-01 --2.809563e-01 --2.645212e-01 --2.438354e-01 --2.203071e-01 --1.951057e-01 --1.691547e-01 --1.431415e-01 --1.175368e-01 --9.261920e-02 --6.849989e-02 --4.514624e-02 --2.016905e-02 --6.696793e-03 diff --git a/out/eigvec_n4_l2.dat b/out/eigvec_n4_l2.dat deleted file mode 100644 index c0ae6d6..0000000 --- a/out/eigvec_n4_l2.dat +++ /dev/null @@ -1,34 +0,0 @@ - 2.397900e-03 - 1.635451e-02 - 6.091003e-02 - 1.209947e-01 - 1.712237e-01 - 1.915618e-01 - 1.745845e-01 - 1.240843e-01 - 5.092879e-02 --3.120188e-02 --1.091345e-01 --1.722975e-01 --2.137082e-01 --2.301147e-01 --2.215832e-01 --1.907836e-01 --1.421659e-01 --8.116327e-02 --1.350138e-02 - 5.534645e-02 - 1.205474e-01 - 1.781503e-01 - 2.252008e-01 - 2.597544e-01 - 2.808161e-01 - 2.882286e-01 - 2.825319e-01 - 2.648112e-01 - 2.365449e-01 - 1.994640e-01 - 1.554264e-01 - 1.063124e-01 - 4.851276e-02 - 1.627974e-02 diff --git a/out/eigvec_n5_l0.dat b/out/eigvec_n5_l0.dat deleted file mode 100644 index e5d1850..0000000 --- a/out/eigvec_n5_l0.dat +++ /dev/null @@ -1,34 +0,0 @@ --4.265229e-02 --2.969724e-02 - 6.272303e-02 - 1.401480e-01 - 1.159669e-01 - 2.176849e-02 --8.736706e-02 --1.679777e-01 --1.981453e-01 --1.755624e-01 --1.112793e-01 --2.297322e-02 - 7.052835e-02 - 1.529467e-01 - 2.125500e-01 - 2.427945e-01 - 2.420202e-01 - 2.125826e-01 - 1.597258e-01 - 9.042216e-02 - 1.232214e-02 --6.710515e-02 --1.412078e-01 --2.045658e-01 --2.532070e-01 --2.846589e-01 --2.978749e-01 --2.930723e-01 --2.715162e-01 --2.352789e-01 --1.869949e-01 --1.296314e-01 --5.959242e-02 --2.007025e-02 diff --git a/out/eigvec_n5_l1.dat b/out/eigvec_n5_l1.dat deleted file mode 100644 index f456503..0000000 --- a/out/eigvec_n5_l1.dat +++ /dev/null @@ -1,34 +0,0 @@ - 2.084811e-02 - 7.341177e-02 - 1.403775e-01 - 1.208297e-01 - 3.452322e-02 --7.119267e-02 --1.543339e-01 --1.915535e-01 --1.781200e-01 --1.226955e-01 --4.110699e-02 - 4.894970e-02 - 1.316126e-01 - 1.949582e-01 - 2.317963e-01 - 2.395314e-01 - 2.194502e-01 - 1.757292e-01 - 1.143787e-01 - 4.226664e-02 --3.369646e-02 --1.071752e-01 --1.728280e-01 --2.265435e-01 --2.655257e-01 --2.882593e-01 --2.943913e-01 --2.845580e-01 --2.601841e-01 --2.232741e-01 --1.762115e-01 --1.215776e-01 --5.574432e-02 --1.875028e-02 diff --git a/out/eigvec_n5_l2.dat b/out/eigvec_n5_l2.dat deleted file mode 100644 index 216059c..0000000 --- a/out/eigvec_n5_l2.dat +++ /dev/null @@ -1,34 +0,0 @@ - 3.194588e-03 - 2.158517e-02 - 7.896538e-02 - 1.516771e-01 - 2.027176e-01 - 2.056758e-01 - 1.554588e-01 - 6.524489e-02 --4.152321e-02 --1.394939e-01 --2.078697e-01 --2.341729e-01 --2.154065e-01 --1.571554e-01 --7.134852e-02 - 2.660655e-02 - 1.207165e-01 - 1.968862e-01 - 2.447246e-01 - 2.585619e-01 - 2.376926e-01 - 1.859516e-01 - 1.107886e-01 - 2.202992e-02 --6.948257e-02 --1.532075e-01 --2.200396e-01 --2.631715e-01 --2.786282e-01 --2.654646e-01 --2.256441e-01 --1.636501e-01 --7.712821e-02 --2.629720e-02 diff --git a/out/eigvec_n6_l0.dat b/out/eigvec_n6_l0.dat deleted file mode 100644 index bca9db3..0000000 --- a/out/eigvec_n6_l0.dat +++ /dev/null @@ -1,34 +0,0 @@ - 4.988324e-02 - 3.271647e-02 --7.736861e-02 --1.599261e-01 --1.140839e-01 - 1.089863e-02 - 1.368012e-01 - 2.062558e-01 - 1.975734e-01 - 1.206691e-01 - 5.039143e-03 --1.134678e-01 --2.033792e-01 --2.443005e-01 --2.294736e-01 --1.649082e-01 --6.618082e-02 - 4.593300e-02 - 1.499632e-01 - 2.276058e-01 - 2.664477e-01 - 2.613455e-01 - 2.144906e-01 - 1.343666e-01 - 3.392228e-02 --7.167219e-02 --1.673265e-01 --2.400782e-01 --2.806583e-01 --2.844341e-01 --2.516865e-01 --1.872609e-01 --8.946300e-02 --3.070363e-02 diff --git a/out/eigvec_n6_l1.dat b/out/eigvec_n6_l1.dat deleted file mode 100644 index 47cc227..0000000 --- a/out/eigvec_n6_l1.dat +++ /dev/null @@ -1,34 +0,0 @@ --2.514150e-02 --8.725387e-02 --1.611241e-01 --1.246321e-01 --9.746867e-03 - 1.155657e-01 - 1.945386e-01 - 2.012221e-01 - 1.397666e-01 - 3.460141e-02 --8.154511e-02 --1.779212e-01 --2.326198e-01 --2.357321e-01 --1.893006e-01 --1.049840e-01 --4.440132e-04 - 1.046256e-01 - 1.921035e-01 - 2.481963e-01 - 2.650991e-01 - 2.415258e-01 - 1.822318e-01 - 9.676098e-02 --2.296465e-03 --1.012407e-01 --1.871232e-01 --2.493175e-01 --2.806489e-01 --2.780071e-01 --2.424328e-01 --1.787253e-01 --8.497085e-02 --2.909361e-02 diff --git a/out/grid.bin b/out/grid.bin index 98f183a4f29a96ab08ad9b4f0454f14bc7bf9637..55d27d106e9189d19244c9d05f81c96699a66f06 100644 GIT binary patch literal 800 zcmYkzIZ8!A6a>%?4Gj$&BO?((5CmxyMN#xS&-$Ea{kno)%3p#@cuQ~zy%d9c0y{a> zt*(^*zp)Z&f|H!$G-o--c`k4((@o@#J@akcD;vvQ+(%6JkvsOx z5B6*MY_UxIT?b%pf?3rHe*)zY{v$4F}Gkw^zXa2NjV;;tRz{(#sj(^3!!XZce NW%`bPGwj%Zmp`!LU`PM} literal 2400 zcmXZed5F|?7{~FvQ%hZsb-njK-F0VX=bqW$duA-l$e^&$?xG^?AfcqgqWe}VC@iup zD!S~Df|3pki*7YaDlD`tEG$e-Ow8~--{+rYcjxzgJ)htAd0>t@s#-PH`l$MIQ}pP{ zBlTVQeOol&+7bEZl{=%Y)~@jX-BH5Y6F#>uT59bNpFa?-vkr#m4n>En6`mhJqcxD~ zIfIyO4W{Z2;bLnj)pLh&mvuDNeundcHG--$lFzMUsP=g*e_ErcvZKTEW2ok>p_;db zCi@u6OP)8Dqz#SZT@N0|9Qzv2M$aG50vnvbcA*I@w$EDj>eaH$h9@%A*IdU6`>vx- zcoM4(Fo{mx$*k3#OhI=F8+4~IPj@O?bf@wE#{L@lTc?qfeKv8OUQ>8aO$;<|Gso*T zbB}H_U+Ok9R=0)Ibz8#wZ{bJtw1jzR4foy}?zc7EV=HmpHm=ca<89wl8~=I1ZIpG} zxkI;|Pj%ZFrQ5-&x*a@h-VVOk?O?ijJGsETojhyaPJTCUCq24dEYa=aP2Dd3)$O8R zcP6*!&g3KAnT*iwW}a?059)UFt!_7yb$d8Rw}+>6d-zqihfdvDT%kLQ*L7#{kM1m{ z`Ft;telO>HPA|9GM=#HKUN0ZpPcJ(?x0jLj6{FkpW1M1tF|N{y@sNGSctbD77W<8H zKsUw|-8eP)4Fjs=*Ia?H_mX~1YNobPS#CurEY=;bQ7%AP4JCwg8jM) zCh7K(*X`qM-9B#8?PIlWA0O)Wu|v0yVY*2=bd#K3l3bTbUn&C;TqWsYu^OLeo{tDEIz-7H_}X4$QqWt?t~q;8Hg zbaPy*o8vLv9PjAn_(?a%0Np%Ix_OS%&2x!vp1XDPyr`S!3*9__>E@}?Es)SHFkiR8 zQr!Y8bqlQ1EwEL$z~M1R;35sWMJl>QF48S>r*4twb&GtaTV$7RkPO}C$` zb^Cclx1YCk`}sk)pF_G4Gjteb%}QSFNOIoG1nZWFy|#MGfyeZ zdx_=dDuuZ(@v8YsVg5^OHfJg9L5aQQEroq3Q)}LG*o!h5^OnPYlv!xra@dnHH<-5^ z_NB}!^OnQjlzHF0<*+|xwwt#c_NdHY^H#z>RcJMDCG1s&6Usize1); + U32 index = mat_ij_to_index(i, j, mat->size1); mat->data[index] = val; return; } @@ -29,7 +29,7 @@ mat_F64_set(Mat_F64 *mat, U32 i, U32 j, F64 val) function inline F64 mat_F64_get(Mat_F64 *mat, U32 i, U32 j) { - U32 index = mat_get_col_major_idx(i, j, mat->size1); + U32 index = mat_ij_to_index(i, j, mat->size1); return mat->data[index]; } @@ -233,7 +233,11 @@ function void print_eigenvalues(S32 l, S32 n, F64 *wr, F64 *wi) { } function void -set_up_first_matrices(Problem *problem, Mat_F64 *H, Mat_F64 *H_l, Mat_F64 *B_inv) { +set_up_base_matrices(Problem *problem, + Mat_F64 *H, + Mat_F64 *H_l, + Mat_F64 *B_inv) { + // We work in units hbar = 1, bohr radius a0 = 1, electron mass m_e = 1, and // charge e = 1, and 1/(4piepsilon_0) = 1. Set up Hamiltonian: H = // -0.5*d^2/dr^2 + l(l+1)/(2r^2) - Z/r @@ -245,7 +249,7 @@ set_up_first_matrices(Problem *problem, Mat_F64 *H, Mat_F64 *H_l, Mat_F64 *B_inv U32 k = bspl_ctx->order; // Skipping first bspline - for (U32 i = 0; i < H->size1; i++) { +for (U32 i = 0; i < H->size1; i++) { for (U32 j = 0; j < H->size2; j++) { U32 bspl_index_i = i + 1; // The second Bspline has index 1 in our array etc. @@ -359,11 +363,31 @@ compute_wf_norm_F64(F64 *coeffs, U64 coeff_size, U64 n, U64 l) { scratch_release(scratch); } +function F64 naive_kernel(F64 r1, F64 r2, F64 k, F64 alpha, F64 beta) { + if(r1 < r2) { + return pow(r1, 2.0*k+1.0)*exp(-alpha*r1)*exp(-beta*r2); + } else { + return exp(-alpha*r1)*pow(r2, 2.0*k+1.0)*exp(-beta*r2); + } +} + +function F64 factorial(S32 k) { + if(k == 0) { + return 1.0; + } else if(k == 1) { + return 1.0; + } else { + F64 kf = (F64)k; + S32 next = k - 1; + return kf * factorial(next); + } +} + ///////////////////////////////////////////////////////////////////////////////////////// -//~ -// Main problem function, called from entry point. -function void -hf_main(void) { +//~ Testing HF integrals. +function void +hf_coulomb_integrals_test(void) +{ Problem problem = problem_create(); LOG(str8_pushf(problem.arena, "Created Problem-struct for %s \n", problem.atom.name.str).str); @@ -397,52 +421,172 @@ hf_main(void) { U32 k = problem.bspline_ctx.order; U32 mat_size1 = N - k - 2; U32 mat_size2 = mat_size1; - Mat_F64 H_base = mat_F64(problem.arena, mat_size1, mat_size2); - Mat_F64 H_l_base = mat_F64(problem.arena, mat_size1, mat_size2); - Mat_F64 H_l = mat_F64(problem.arena, mat_size1, mat_size2); - Mat_F64 H = mat_F64(problem.arena, mat_size1, mat_size2); + + LOG(" *** Running tests for coulomb operator integrals! *** \n "); + Mat_F64 test_mat = mat_F64(problem.arena, mat_size1, mat_size2); + Mat_F64 double_int_mat = mat_F64(problem.arena, mat_size1, mat_size2); + + // We want to compute integrals over two r-coordinates r1 and r2, of the form + // int1(int2( F(r1) (r^k_smaller / r^(k+1)_greater) G(r2) ) + // We will test with analytic functions + // F(r) = r^(k+1) exp(-alpha*r) + // G(r) = r^(k+1) exp(-beta*r) + // Because then whenever r1 < r2 the kernel will be + // r1^(2k+1)exp(-alpha*r1)*exp(-beta*r2) + // and whenever r2 > r1 we have + // exp(-alpha*r1)*r2^(2k+1)exp(-beta*r2) + // That is we cancel the denominator. + // In particular we can get an analytic result as a function of k, alpha and beta: + // (2k+1)! / ((alpha*beta)(alpha+beta)^(2k+1)) + // The reason is so that we can + // 1) Make sure that we are integrating over two r-coordinates properly. + // 2) Compare a "fast" method to just brute force double integral loop to make sur + // it is correct. + // 3) Expand the method to the general spline case to compute the Coulomb matrix + // element with confidence that it is correct. + { + BSplineCtx *bspl_ctx = &problem.bspline_ctx; + U32 bspl_order = bspl_ctx->order; + F64 *t1 = bspl_ctx->knotpoints; + F64 k_mpole = 1.0; + + F64 alpha = 2.0; + F64 beta = 3.0; + // The set of r coordinates will be all knotpoints and the quadrature points in + // between them + F64 result = 0.0; + U32 phys_point_first_index = bspl_ctx->first_phys_index;; + U32 phys_point_last_index = bspl_ctx->num_phys_points + k-1; + for(S32 r1_i = phys_point_first_index; r1_i < phys_point_last_index-1; r1_i += 1) + { + F64 a1 = t1[r1_i]; + F64 b1 = t1[r1_i + 1]; + F64 c1 = (a1+b1); + F64 h1 = (b1-a1); + for(S32 r2_i = phys_point_first_index; r2_i < phys_point_last_index-1; r2_i += 1) + { + F64 a2 = t1[r2_i]; + F64 b2 = t1[r2_i + 1]; + F64 c2 = (a2+b2); + F64 h2 = (b2-a2); + for(S32 q1 = 0; q1 < g_gauss_legendre.order; q1 += 1) { + F64 w1 = 0.5 * h1 * g_gauss_legendre.weights[q1]; + F64 z1 = g_gauss_legendre.abscissae[q1]; + F64 r1 = (z1 * (0.5 * h1)) + (c1 * 0.5); + for(S32 q2 = 0; q2 < g_gauss_legendre.order; q2 += 1) { + F64 w2 = 0.5 * h2 * g_gauss_legendre.weights[q2]; + F64 z2 = g_gauss_legendre.abscissae[q2]; + F64 r2 = (z2 * (0.5 * h2)) + (c2 * 0.5); + F64 kernel = naive_kernel(r1, r2, k_mpole, alpha, beta); + result += w1 * w2 * kernel; + } + } + } + } + + ArenaTemp scratch = scratch_get(0,0); + // Analytic + S32 k_mpole_int = 1; + F64 fact = factorial(2*k_mpole_int + 1); + F64 reference = fact / ((alpha*beta)*pow((alpha+beta),2.0*k_mpole+1.0)); + LOG(str8_pushf(scratch.arena, "Reference: %.12f \n", reference).str); + LOG(str8_pushf(scratch.arena, "Computed: %.12f \n", result).str); + + scratch_release(scratch); + } + +} + +///////////////////////////////////////////////////////////////////////////////////////// +//~ +// Main problem function, called from entry point. +function void +hf_eigenvalues_main(void) +{ + + Problem problem = problem_create(); + LOG(str8_pushf(problem.arena, "Created Problem-struct for %s \n", problem.atom.name.str).str); + + set_up_gauss_legendre_points(problem.arena); + + //- Set up grid and write to file. + grid_assign(&problem.grid); + set_up_grid(problem.arena); + + write_array_binary_F64(str8_lit(grid_file_path_bin), + problem.grid.points, + problem.grid.num_steps); + + write_array_F64(str8_lit(grid_file_path), + problem.grid.points, + problem.grid.num_steps, + "%13.6e\n"); + + //- The BSpline context is the knotpoints and the BSpline order etc. + bspline_ctx_assign(&problem.bspline_ctx); + set_up_bspline_context(problem.arena); + write_array_F64(str8_lit(knotpoints_file_path), problem.bspline_ctx.knotpoints, + problem.bspline_ctx.num_knotpoints, "%13.6e\n"); + + //- Then we generate the BSplines and save them off for reference and + // debugging. + set_up_bsplines_at_points_and_write_matrix_F64(problem.arena); + + U32 N = problem.bspline_ctx.num_knotpoints; + U32 k = problem.bspline_ctx.order; + U32 mat_size1 = N - k - 2; + U32 mat_size2 = mat_size1; + problem.H_base = mat_F64(problem.arena, mat_size1, mat_size2); + problem.H_l_base = mat_F64(problem.arena, mat_size1, mat_size2); + problem.H_l = mat_F64(problem.arena, mat_size1, mat_size2); + problem.H = mat_F64(problem.arena, mat_size1, mat_size2); // This will be the inverse of B, but to start with we construct B. - Mat_F64 B_inv = mat_F64(problem.arena, mat_size1, mat_size2); + problem.B_inv = mat_F64(problem.arena, mat_size1, mat_size2); // A is the actual matrix for each eigenvalue problem. - Mat_F64 A = mat_F64(problem.arena, H.size1, H.size2); - set_up_first_matrices(&problem, &H_base, &H_l_base, &B_inv); + problem.A = mat_F64(problem.arena, problem.H.size1, problem.H.size2); + set_up_base_matrices(&problem, + &problem.H_base, + &problem.H_l_base, + &problem.B_inv); // Our problem is Hc = EBc, but we want to solve B^-1Hc = Ec, // so we invert the B matrix and compute the product A = B^-1H before calling // zgeev - mat_invert_F64(&B_inv); + mat_invert_F64(&problem.B_inv); // This arena is used to push results from f. ex eigenvalue computations. // For each angular momentum for (U32 ang_mom_idx = 0; ang_mom_idx < MAX_NUM_ANGULAR_MOMENTA; ang_mom_idx++) { ArenaTemp scratch = scratch_get(0, 0); - mat_F64_copy_to_dst(&H, &H_base); + mat_F64_copy_to_dst(&problem.H, &problem.H_base); F64 l = problem.angular_momentum_l[ang_mom_idx]; Eigensolution_F64 *eigsol = &problem.eigsols[ang_mom_idx]; eigsol->l = (U32)l; if (l > 1e-16) { F64 l_factor = l * (l + 1.0); - U64 mat_size = H_l.size1 * H_l.size2; - mat_F64_copy_to_dst(&H_l, &H_l_base); + U64 mat_size = problem.H_l.size1 * problem.H_l.size2; + mat_F64_copy_to_dst(&problem.H_l, &problem.H_l_base); // Multiply l(l+1) - cblas_dscal(mat_size, l_factor, H_l.data, 1); + cblas_dscal(mat_size, l_factor, problem.H_l.data, 1); // Add H = H_base + H_l - cblas_daxpy(mat_size, 1.0, H_l.data, 1, H.data, 1); + cblas_daxpy(mat_size, 1.0, problem.H_l.data, 1, problem.H.data, 1); } + //LOG("Matrix H: \n"); + //print_mat_F64(&problem.H); // Multiply to get A = B^-1 H { - S32 n = A.size1; + S32 n = problem.A.size1; cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, n, n, n, 1.0, - B_inv.data, n, H.data, n, 0.0, A.data, n); + problem.B_inv.data, n, problem.H.data, n, 0.0, problem.A.data, n); //LOG("Matrix A: \n"); - //print_mat_F64(&A); + //print_mat_F64(&problem.A); } // Solve generalised eigenvalue problem { - S32 size1 = A.size1; + S32 size1 = problem.A.size1; S32 lda = size1; S32 ldvl = size1; S32 ldvr = size1; @@ -462,7 +606,7 @@ hf_main(void) { F64 *vr = eigsol->right_eigvecs.data; lwork = -1; - F64 *a = A.data; + F64 *a = problem.A.data; dgeev("Vectors", "Vectors", &size1, a, &lda, wr, wi, vl, &ldvl, vr, &ldvr, &wkopt, &lwork, &info); lwork = (S32)wkopt; @@ -482,7 +626,7 @@ hf_main(void) { print_eigenvalues((U32)l, size1, wr, wi ); U32 i = 0; - F64 energy = -1000.0; + F64 energy = -1.0*(F64)(U32Max); // Just have an unreasonable energy bound U32 counter = 0; while (energy < 0.0) { energy = wr[i]; @@ -495,7 +639,7 @@ hf_main(void) { // compute_wf_norm_F64(eigensolution.right_eigenvectors.matrix[energy_index], // size1, n, ang_mom_idx); - U64 eigvec_idx = mat_get_col_major_idx(0, energy_index, size1); + U64 eigvec_idx = mat_ij_to_index(0, energy_index, size1); F64 *eigvecs = &eigsol->right_eigvecs.data[eigvec_idx]; write_array_F64( get_eigenvector_filename(scratch.arena, n, ang_mom_idx), diff --git a/src/hf/hf_base.h b/src/hf/hf_base.h index 8ab54af..947de7c 100644 --- a/src/hf/hf_base.h +++ b/src/hf/hf_base.h @@ -81,14 +81,25 @@ struct Problem { F64 angular_momentum_l[ANGMOM_NUM_MOMENTA]; Eigensolution_F64 eigsols[MAX_NUM_ANGULAR_MOMENTA]; U32 num_eigsols; + // Problem matrices. Since we can perform the "mass" integral once we call that + // "base", and similarly we can compute the integral for the l-dependent part once, + // and call that H_l_base. Then we can add whatever numerical factors we want on the + // base matrices, and finally combine them. + Mat_F64 H_base; Mat_F64 H; + Mat_F64 H_l_base; Mat_F64 H_l; + // Our problem is Hc = EBc, but we want to solve B^-1Hc = Ec, + // so we invert the B matrix and compute the product A = B^-1H before calling + // zgeev for Ac = Ec + Mat_F64 B_inv; + Mat_F64 A; }; //~ Base math and utility functions // Mat_F64 functions -function inline U32 mat_get_col_major_idx(U32 i, U32 j, U32 size1); +function inline U32 mat_ij_to_index(U32 i, U32 j, U32 size1); function Mat_F64 mat_F64(Arena* arena, U32 size1, U32 size2); function inline void mat_F64_set(Mat_F64 *mat, U32 i, U32 j, F64 val); function inline F64 mat_F64_get(Mat_F64 *mat, U32 i, U32 j); @@ -108,8 +119,10 @@ function void compute_wf_norm_F64(F64 *coeffs, U64 coeff_size, U64 n, U64 l); // Problem function Problem problem_create(); -function void set_up_first_matrices(Problem *problem, Mat_F64 *H, - Mat_F64 *H_l, Mat_F64 *B_inv); +function void set_up_base_matrices(Problem *problem, + Mat_F64 *H, + Mat_F64 *H_l, + Mat_F64 *B_inv); function void hf_main(); diff --git a/src/hf/hf_bsplines_and_grid.c b/src/hf/hf_bsplines_and_grid.c index ab8f2fe..57aa8a2 100644 --- a/src/hf/hf_bsplines_and_grid.c +++ b/src/hf/hf_bsplines_and_grid.c @@ -121,31 +121,36 @@ set_up_bspline_context(Arena* arena) { // Create knotpoint sequence. U32 k = 4; - U32 bspl_N = 40; + U32 bspl_N = BSPLINES_NUM; g_bspline_ctx->order = k; g_bspline_ctx->num_knotpoints = bspl_N; g_bspline_ctx->num_bsplines = bspl_N-k; - g_bspline_ctx->num_phys_points = bspl_N-(2*k)+2; // Remove k points at each end, and then add back the first and last points. + g_bspline_ctx->num_phys_points = bspl_N-(2*k)+2; // Remove k points at each end, + // and then add back + // the first and last points. g_bspline_ctx->arena = arena; g_bspline_ctx->knotpoints = PushArray(arena, F64, g_bspline_ctx->num_knotpoints); // Set up physical points; F64 delta = (g_grid->end-g_grid->start)/(g_bspline_ctx->num_phys_points-1); // Set ghost points including first physical + U32 first_phys_index = k-1; U32 phys_point_last_index = g_bspline_ctx->num_phys_points + k-1; - for(U32 i = 0; i < k; i++) + for(U32 i = 0; i <= first_phys_index; i++) { g_bspline_ctx->knotpoints[i] = g_grid->start; } + g_bspline_ctx->first_phys_index = first_phys_index; for(U32 i = k; i < phys_point_last_index; i++) { g_bspline_ctx->knotpoints[i] = g_bspline_ctx->knotpoints[i-1] + delta; } - // Set the last points + // Set the last points. including last physical point F64 last_physical = g_grid->end; for(U32 i = phys_point_last_index; i < g_bspline_ctx->num_knotpoints; i++) { g_bspline_ctx->knotpoints[i] = last_physical; } + g_bspline_ctx->last_phys_index = phys_point_last_index; } function void diff --git a/src/hf/hf_bsplines_and_grid.h b/src/hf/hf_bsplines_and_grid.h index 13863f0..d2ac8a6 100644 --- a/src/hf/hf_bsplines_and_grid.h +++ b/src/hf/hf_bsplines_and_grid.h @@ -3,8 +3,12 @@ // coordinates in Bohr radii #define GRID_START_POINT 0.0 -#define GRID_END_POINT 40.0 -#define GRID_NUM_STEPS 300 +#define GRID_END_POINT 300.0 + +#define GRID_NUM_STEPS 100 // Just for plotting/writing, + // else we stick to knotpts and quadrature + +#define BSPLINES_NUM 2000 typedef struct Grid Grid; struct Grid @@ -24,6 +28,8 @@ struct BSplineCtx U32 num_knotpoints; U32 num_bsplines; U32 num_phys_points; + U32 first_phys_index; + U32 last_phys_index; F64 *bsplines_grid; // In grid points F64 *dBsplines_grid; // First deriv in grid points F64 *bsplines; // In knotpoints diff --git a/src/main.c b/src/main.c index 77813d9..fe94dea 100644 --- a/src/main.c +++ b/src/main.c @@ -39,6 +39,6 @@ function void EntryPoint(void) { OS_InitGfxReceipt os_gfx_receipt = OS_gfx_init(os_receipt); // Main program - hf_main(); - + //hf_main(); + hf_coulomb_integrals_test(); }