bssn_rhs_c: 融合逆度规+Gamma约束+Christoffel三循环为一循环 (Modify 2)
逆度规计算结果保留在局部标量中直接复用，减少对gupxx..gupzz数组的重复读取，每步加速0.01秒 Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
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@@ -145,138 +145,109 @@ int f_compute_rhs_bssn(int *ex, double &T,
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gxx[i] * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i]
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+ gzz[i] * betazx[i] - gxz[i] * betayy[i];
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}
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// 1ms //
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// Fused: inverse metric + Gamma constraint + Christoffel (3 loops -> 1)
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for(int i=0;i<all;i+=1){
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double det = gxx[i] * gyy[i] * gzz[i] + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i] -
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gxz[i] * gyy[i] * gxz[i] - gxy[i] * gxy[i] * gzz[i] - gxx[i] * gyz[i] * gyz[i];
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gupxx[i] = (gyy[i] * gzz[i] - gyz[i] * gyz[i]) / det;
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gupxy[i] = -(gxy[i] * gzz[i] - gyz[i] * gxz[i]) / det;
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gupxz[i] = (gxy[i] * gyz[i] - gyy[i] * gxz[i]) / det;
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gupyy[i] = (gxx[i] * gzz[i] - gxz[i] * gxz[i]) / det;
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gupyz[i] = -(gxx[i] * gyz[i] - gxy[i] * gxz[i]) / det;
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gupzz[i] = (gxx[i] * gyy[i] - gxy[i] * gxy[i]) / det;
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}
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// 2.2ms //
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if(co==0){
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for (int i=0;i<all;i+=1) {
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double det = gxx[i] * gyy[i] * gzz[i] + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i] -
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gxz[i] * gyy[i] * gxz[i] - gxy[i] * gxy[i] * gzz[i] - gxx[i] * gyz[i] * gyz[i];
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double lg_xx = (gyy[i] * gzz[i] - gyz[i] * gyz[i]) / det;
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double lg_xy = -(gxy[i] * gzz[i] - gyz[i] * gxz[i]) / det;
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double lg_xz = (gxy[i] * gyz[i] - gyy[i] * gxz[i]) / det;
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double lg_yy = (gxx[i] * gzz[i] - gxz[i] * gxz[i]) / det;
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double lg_yz = -(gxx[i] * gyz[i] - gxy[i] * gxz[i]) / det;
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double lg_zz = (gxx[i] * gyy[i] - gxy[i] * gxy[i]) / det;
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gupxx[i] = lg_xx; gupxy[i] = lg_xy; gupxz[i] = lg_xz;
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gupyy[i] = lg_yy; gupyz[i] = lg_yz; gupzz[i] = lg_zz;
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if(co==0){
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Gmx_Res[i] = Gamx[i] - (
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gupxx[i] * (gupxx[i]*gxxx[i] + gupxy[i]*gxyx[i] + gupxz[i]*gxzx[i]) +
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gupxy[i] * (gupxx[i]*gxyx[i] + gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i]) +
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gupxz[i] * (gupxx[i]*gxzx[i] + gupxy[i]*gyzx[i] + gupxz[i]*gzzx[i]) +
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gupxx[i] * (gupxy[i]*gxxy[i] + gupyy[i]*gxyy[i] + gupyz[i]*gxzy[i]) +
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gupxy[i] * (gupxy[i]*gxyy[i] + gupyy[i]*gyyy[i] + gupyz[i]*gyzy[i]) +
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gupxz[i] * (gupxy[i]*gxzy[i] + gupyy[i]*gyzy[i] + gupyz[i]*gzzy[i]) +
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gupxx[i] * (gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i] + gupzz[i]*gxzz[i]) +
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gupxy[i] * (gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i] + gupzz[i]*gyzz[i]) +
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gupxz[i] * (gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i] + gupzz[i]*gzzz[i])
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lg_xx * (lg_xx*gxxx[i] + lg_xy*gxyx[i] + lg_xz*gxzx[i]) +
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lg_xy * (lg_xx*gxyx[i] + lg_xy*gyyx[i] + lg_xz*gyzx[i]) +
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lg_xz * (lg_xx*gxzx[i] + lg_xy*gyzx[i] + lg_xz*gzzx[i]) +
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lg_xx * (lg_xy*gxxy[i] + lg_yy*gxyy[i] + lg_yz*gxzy[i]) +
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lg_xy * (lg_xy*gxyy[i] + lg_yy*gyyy[i] + lg_yz*gyzy[i]) +
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lg_xz * (lg_xy*gxzy[i] + lg_yy*gyzy[i] + lg_yz*gzzy[i]) +
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lg_xx * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
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lg_xy * (lg_xz*gxyz[i] + lg_yz*gyyz[i] + lg_zz*gyzz[i]) +
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lg_xz * (lg_xz*gxzz[i] + lg_yz*gyzz[i] + lg_zz*gzzz[i])
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);
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Gmy_Res[i] = Gamy[i] - (
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gupxx[i] * (gupxy[i]*gxxx[i] + gupyy[i]*gxyx[i] + gupyz[i]*gxzx[i]) +
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gupxy[i] * (gupxy[i]*gxyx[i] + gupyy[i]*gyyx[i] + gupyz[i]*gyzx[i]) +
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gupxz[i] * (gupxy[i]*gxzx[i] + gupyy[i]*gyzx[i] + gupyz[i]*gzzx[i]) +
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gupxy[i] * (gupxy[i]*gxxy[i] + gupyy[i]*gxyy[i] + gupyz[i]*gxzy[i]) +
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gupyy[i] * (gupxy[i]*gxyy[i] + gupyy[i]*gyyy[i] + gupyz[i]*gyzy[i]) +
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gupyz[i] * (gupxy[i]*gxzy[i] + gupyy[i]*gyzy[i] + gupyz[i]*gzzy[i]) +
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gupxy[i] * (gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i] + gupzz[i]*gxzz[i]) +
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gupyy[i] * (gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i] + gupzz[i]*gyzz[i]) +
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gupyz[i] * (gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i] + gupzz[i]*gzzz[i])
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lg_xx * (lg_xy*gxxx[i] + lg_yy*gxyx[i] + lg_yz*gxzx[i]) +
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lg_xy * (lg_xy*gxyx[i] + lg_yy*gyyx[i] + lg_yz*gyzx[i]) +
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lg_xz * (lg_xy*gxzx[i] + lg_yy*gyzx[i] + lg_yz*gzzx[i]) +
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lg_xy * (lg_xy*gxxy[i] + lg_yy*gxyy[i] + lg_yz*gxzy[i]) +
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lg_yy * (lg_xy*gxyy[i] + lg_yy*gyyy[i] + lg_yz*gyzy[i]) +
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lg_yz * (lg_xy*gxzy[i] + lg_yy*gyzy[i] + lg_yz*gzzy[i]) +
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lg_xy * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
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lg_yy * (lg_xz*gxyz[i] + lg_yz*gyyz[i] + lg_zz*gyzz[i]) +
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lg_yz * (lg_xz*gxzz[i] + lg_yz*gyzz[i] + lg_zz*gzzz[i])
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);
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Gmz_Res[i] = Gamz[i] - (
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gupxx[i] * (gupxz[i]*gxxx[i] + gupyz[i]*gxyx[i] + gupzz[i]*gxzx[i]) +
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gupxy[i] * (gupxz[i]*gxyx[i] + gupyz[i]*gyyx[i] + gupzz[i]*gyzx[i]) +
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gupxz[i] * (gupxz[i]*gxzx[i] + gupyz[i]*gyzx[i] + gupzz[i]*gzzx[i]) +
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gupxy[i] * (gupxz[i]*gxxy[i] + gupyz[i]*gxyy[i] + gupzz[i]*gxzy[i]) +
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gupyy[i] * (gupxz[i]*gxyy[i] + gupyz[i]*gyyy[i] + gupzz[i]*gyzy[i]) +
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gupyz[i] * (gupxz[i]*gxzy[i] + gupyz[i]*gyzy[i] + gupzz[i]*gzzy[i]) +
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gupxz[i] * (gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i] + gupzz[i]*gxzz[i]) +
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gupyz[i] * (gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i] + gupzz[i]*gyzz[i]) +
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gupzz[i] * (gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i] + gupzz[i]*gzzz[i])
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lg_xx * (lg_xz*gxxx[i] + lg_yz*gxyx[i] + lg_zz*gxzx[i]) +
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lg_xy * (lg_xz*gxyx[i] + lg_yz*gyyx[i] + lg_zz*gyzx[i]) +
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lg_xz * (lg_xz*gxzx[i] + lg_yz*gyzx[i] + lg_zz*gzzx[i]) +
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lg_xy * (lg_xz*gxxy[i] + lg_yz*gxyy[i] + lg_zz*gxzy[i]) +
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lg_yy * (lg_xz*gxyy[i] + lg_yz*gyyy[i] + lg_zz*gyzy[i]) +
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lg_yz * (lg_xz*gxzy[i] + lg_yz*gyzy[i] + lg_zz*gzzy[i]) +
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lg_xz * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
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lg_yz * (lg_xz*gxyz[i] + lg_yz*gyyz[i] + lg_zz*gyzz[i]) +
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lg_zz * (lg_xz*gxzz[i] + lg_yz*gyzz[i] + lg_zz*gzzz[i])
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);
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}
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}
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// 5ms //
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for (int i=0;i<all;i+=1) {
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Gamxxx[i] = HALF * ( gupxx[i]*gxxx[i]
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+ gupxy[i]*(TWO*gxyx[i] - gxxy[i])
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+ gupxz[i]*(TWO*gxzx[i] - gxxz[i]) );
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Gamyxx[i] = HALF * ( gupxy[i]*gxxx[i]
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+ gupyy[i]*(TWO*gxyx[i] - gxxy[i])
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+ gupyz[i]*(TWO*gxzx[i] - gxxz[i]) );
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Gamzxx[i] = HALF * ( gupxz[i]*gxxx[i]
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+ gupyz[i]*(TWO*gxyx[i] - gxxy[i])
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+ gupzz[i]*(TWO*gxzx[i] - gxxz[i]) );
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Gamxyy[i] = HALF * ( gupxx[i]*(TWO*gxyy[i] - gyyx[i])
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+ gupxy[i]*gyyy[i]
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+ gupxz[i]*(TWO*gyzy[i] - gyyz[i]) );
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Gamyyy[i] = HALF * ( gupxy[i]*(TWO*gxyy[i] - gyyx[i])
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+ gupyy[i]*gyyy[i]
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+ gupyz[i]*(TWO*gyzy[i] - gyyz[i]) );
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Gamzyy[i] = HALF * ( gupxz[i]*(TWO*gxyy[i] - gyyx[i])
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+ gupyz[i]*gyyy[i]
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+ gupzz[i]*(TWO*gyzy[i] - gyyz[i]) );
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Gamxzz[i] = HALF * ( gupxx[i]*(TWO*gxzz[i] - gzzx[i])
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+ gupxy[i]*(TWO*gyzz[i] - gzzy[i])
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+ gupxz[i]*gzzz[i] );
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Gamyzz[i] = HALF * ( gupxy[i]*(TWO*gxzz[i] - gzzx[i])
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+ gupyy[i]*(TWO*gyzz[i] - gzzy[i])
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+ gupyz[i]*gzzz[i] );
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Gamzzz[i] = HALF * ( gupxz[i]*(TWO*gxzz[i] - gzzx[i])
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+ gupyz[i]*(TWO*gyzz[i] - gzzy[i])
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+ gupzz[i]*gzzz[i] );
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Gamxxy[i] = HALF * ( gupxx[i]*gxxy[i]
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+ gupxy[i]*gyyx[i]
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+ gupxz[i]*(gxzy[i] + gyzx[i] - gxyz[i]) );
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Gamyxy[i] = HALF * ( gupxy[i]*gxxy[i]
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+ gupyy[i]*gyyx[i]
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+ gupyz[i]*(gxzy[i] + gyzx[i] - gxyz[i]) );
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Gamzxy[i] = HALF * ( gupxz[i]*gxxy[i]
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+ gupyz[i]*gyyx[i]
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+ gupzz[i]*(gxzy[i] + gyzx[i] - gxyz[i]) );
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Gamxxz[i] = HALF * ( gupxx[i]*gxxz[i]
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+ gupxy[i]*(gxyz[i] + gyzx[i] - gxzy[i])
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+ gupxz[i]*gzzx[i] );
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Gamyxz[i] = HALF * ( gupxy[i]*gxxz[i]
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+ gupyy[i]*(gxyz[i] + gyzx[i] - gxzy[i])
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+ gupyz[i]*gzzx[i] );
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Gamzxz[i] = HALF * ( gupxz[i]*gxxz[i]
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+ gupyz[i]*(gxyz[i] + gyzx[i] - gxzy[i])
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+ gupzz[i]*gzzx[i] );
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Gamxyz[i] = HALF * ( gupxx[i]*(gxyz[i] + gxzy[i] - gyzx[i])
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+ gupxy[i]*gyyz[i]
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+ gupxz[i]*gzzy[i] );
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Gamyyz[i] = HALF * ( gupxy[i]*(gxyz[i] + gxzy[i] - gyzx[i])
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+ gupyy[i]*gyyz[i]
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+ gupyz[i]*gzzy[i] );
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Gamzyz[i] = HALF * ( gupxz[i]*(gxyz[i] + gxzy[i] - gyzx[i])
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+ gupyz[i]*gyyz[i]
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+ gupzz[i]*gzzy[i] );
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Gamxxx[i] = HALF * ( lg_xx*gxxx[i]
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+ lg_xy*(TWO*gxyx[i] - gxxy[i])
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+ lg_xz*(TWO*gxzx[i] - gxxz[i]) );
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Gamyxx[i] = HALF * ( lg_xy*gxxx[i]
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+ lg_yy*(TWO*gxyx[i] - gxxy[i])
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+ lg_yz*(TWO*gxzx[i] - gxxz[i]) );
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Gamzxx[i] = HALF * ( lg_xz*gxxx[i]
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+ lg_yz*(TWO*gxyx[i] - gxxy[i])
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+ lg_zz*(TWO*gxzx[i] - gxxz[i]) );
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Gamxyy[i] = HALF * ( lg_xx*(TWO*gxyy[i] - gyyx[i])
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+ lg_xy*gyyy[i]
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+ lg_xz*(TWO*gyzy[i] - gyyz[i]) );
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Gamyyy[i] = HALF * ( lg_xy*(TWO*gxyy[i] - gyyx[i])
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+ lg_yy*gyyy[i]
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+ lg_yz*(TWO*gyzy[i] - gyyz[i]) );
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Gamzyy[i] = HALF * ( lg_xz*(TWO*gxyy[i] - gyyx[i])
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+ lg_yz*gyyy[i]
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+ lg_zz*(TWO*gyzy[i] - gyyz[i]) );
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Gamxzz[i] = HALF * ( lg_xx*(TWO*gxzz[i] - gzzx[i])
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+ lg_xy*(TWO*gyzz[i] - gzzy[i])
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+ lg_xz*gzzz[i] );
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Gamyzz[i] = HALF * ( lg_xy*(TWO*gxzz[i] - gzzx[i])
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+ lg_yy*(TWO*gyzz[i] - gzzy[i])
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+ lg_yz*gzzz[i] );
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Gamzzz[i] = HALF * ( lg_xz*(TWO*gxzz[i] - gzzx[i])
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+ lg_yz*(TWO*gyzz[i] - gzzy[i])
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+ lg_zz*gzzz[i] );
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Gamxxy[i] = HALF * ( lg_xx*gxxy[i]
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+ lg_xy*gyyx[i]
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+ lg_xz*(gxzy[i] + gyzx[i] - gxyz[i]) );
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Gamyxy[i] = HALF * ( lg_xy*gxxy[i]
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+ lg_yy*gyyx[i]
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+ lg_yz*(gxzy[i] + gyzx[i] - gxyz[i]) );
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Gamzxy[i] = HALF * ( lg_xz*gxxy[i]
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+ lg_yz*gyyx[i]
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+ lg_zz*(gxzy[i] + gyzx[i] - gxyz[i]) );
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Gamxxz[i] = HALF * ( lg_xx*gxxz[i]
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+ lg_xy*(gxyz[i] + gyzx[i] - gxzy[i])
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+ lg_xz*gzzx[i] );
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Gamyxz[i] = HALF * ( lg_xy*gxxz[i]
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+ lg_yy*(gxyz[i] + gyzx[i] - gxzy[i])
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+ lg_yz*gzzx[i] );
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Gamzxz[i] = HALF * ( lg_xz*gxxz[i]
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+ lg_yz*(gxyz[i] + gyzx[i] - gxzy[i])
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+ lg_zz*gzzx[i] );
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Gamxyz[i] = HALF * ( lg_xx*(gxyz[i] + gxzy[i] - gyzx[i])
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+ lg_xy*gyyz[i]
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+ lg_xz*gzzy[i] );
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Gamyyz[i] = HALF * ( lg_xy*(gxyz[i] + gxzy[i] - gyzx[i])
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+ lg_yy*gyyz[i]
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+ lg_yz*gzzy[i] );
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Gamzyz[i] = HALF * ( lg_xz*(gxyz[i] + gxzy[i] - gyzx[i])
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+ lg_yz*gyyz[i]
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+ lg_zz*gzzy[i] );
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}
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// 1.8ms //
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for (int i=0;i<all;i+=1) {
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