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Optimized polynomials
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org/qmckl_ao.org
309
org/qmckl_ao.org
@ -4530,153 +4530,176 @@ qmckl_ao_polynomial_transp_vgl_hpc (const qmckl_context context,
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int32_t m;
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double* const vgl1 = VGL;
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double* const vgl2 = VGL + ldv;
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double* const vgl3 = VGL + (ldv << 1);
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double* const vgl4 = VGL + 3*ldv;
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double* const vgl5 = VGL + (ldv << 2);
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switch (lmax) {
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case 0:
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{
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if (ldv < 1) return QMCKL_INVALID_ARG_9;
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L[0] = 0;
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L[ldl] = 0;
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L[ldl << 1] = 0;
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m=1;
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L[0] = 0; L[1] = 0; L[2] = 0;
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vgl1[0] = 1.0;
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vgl2[0] = 0.0;
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vgl3[0] = 0.0;
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vgl4[0] = 0.0;
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vgl5[0] = 0.0;
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VGL[0 ] = 1.0;
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VGL[ldv ] = 0.0;
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VGL[ldv<<1 ] = 0.0;
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VGL[ldv<<2-1] = 0.0;
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VGL[ldv<<2 ] = 0.0;
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m=1;
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break;
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}
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case 1:
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{
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if (ldv < 4) return QMCKL_INVALID_ARG_9;
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const double Y[3] = { X[0]-R[0],
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X[1]-R[1],
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X[2]-R[2] };
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int32_t* const l[4] = {L, L+ldl, L+(ldl<<1), L+3*ldl};
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for (int32_t i=0 ; i<4 ; ++i) {
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l[i][0] = 0;
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l[i][1] = 0;
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l[i][2] = 0;
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}
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l[1][0] = 1;
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l[2][1] = 1;
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l[3][2] = 1;
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if (ldl == 3) {
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for (int32_t k=0 ; k<4 ; ++k) {
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vgl2[k] = 0.0;
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vgl3[k] = 0.0;
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vgl4[k] = 0.0;
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vgl5[k] = 0.0;
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const int32_t ltmp[12] = {0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1};
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for (int i=0 ; i<12 ; ++i)
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L[i] = ltmp[i];
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} else {
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int32_t* const l[4] = {L, L+ldl, L+(ldl<<1), L+3*ldl};
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l[0][0] = 0; l[0][1] = 0; l[0][2] = 0;
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l[1][0] = 1; l[1][1] = 0; l[1][2] = 0;
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l[2][0] = 0; l[2][1] = 1; l[2][2] = 0;
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l[3][0] = 0; l[3][1] = 0; l[3][2] = 1;
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}
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if (ldv == 4) {
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const double tmp[20] = {1.0, X[0]-R[0], X[1]-R[1], X[2]-R[2], 0.0,
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1.0, 0.0, 0.0, 0.0, 0.0,
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1.0, 0.0, 0.0, 0.0, 0.0,
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1.0, 0.0, 0.0, 0.0, 0.0};
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for (int i=0 ; i<20 ; ++i)
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VGL[i] = tmp[i];
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} else {
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double* const vgl1 = VGL;
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double* const vgl2 = VGL + ldv;
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double* const vgl3 = VGL + (ldv << 1);
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double* const vgl4 = VGL + 3*ldv;
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double* const vgl5 = VGL + (ldv << 2);
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for (int32_t k=0 ; k<4 ; ++k) {
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vgl2[k] = 0.0;
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vgl3[k] = 0.0;
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vgl4[k] = 0.0;
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vgl5[k] = 0.0;
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}
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vgl1[0] = 1.0;
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vgl1[1] = X[0]-R[0];
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vgl1[2] = X[1]-R[1];
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vgl1[3] = X[2]-R[2];
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vgl2[1] = 1.0;
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vgl3[2] = 1.0;
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vgl4[3] = 1.0;
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}
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vgl1[0] = 1.0;
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vgl1[1] = Y[0];
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vgl1[2] = Y[1];
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vgl1[3] = Y[2];
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vgl2[1] = 1.0;
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vgl3[2] = 1.0;
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vgl4[3] = 1.0;
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m=4;
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break;
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}
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case 2:
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{
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if (ldv < 10) return QMCKL_INVALID_ARG_9;
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if (ldl == 3) {
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const int32_t ltmp[30] = {0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1,
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2, 0, 0, 1, 1, 0, 1, 0, 1, 0, 2, 0,
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0, 1, 1, 0, 0, 2};
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for (int i=0 ; i<30 ; ++i)
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L[i] = ltmp[i];
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} else {
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int32_t* l[10];
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for (int32_t i=0 ; i<10 ; ++i) {
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l[i] = L + i*ldl;
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}
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l[0][0] = 0; l[0][1] = 0; l[0][2] = 0;
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l[1][0] = 1; l[1][1] = 0; l[1][2] = 0;
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l[2][0] = 0; l[2][1] = 1; l[2][2] = 0;
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l[3][0] = 0; l[3][1] = 0; l[3][2] = 1;
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l[4][0] = 2; l[4][1] = 0; l[4][2] = 0;
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l[5][0] = 1; l[5][1] = 1; l[5][2] = 0;
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l[6][0] = 1; l[6][1] = 0; l[6][2] = 1;
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l[7][0] = 0; l[7][1] = 2; l[7][2] = 0;
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l[8][0] = 0; l[8][1] = 1; l[8][2] = 1;
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l[9][0] = 0; l[9][1] = 0; l[9][2] = 2;
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}
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const double Y[3] = { X[0]-R[0],
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X[1]-R[1],
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X[2]-R[2] };
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double pows[3][5] = { {1.0, 1.0, 1.0, Y[0], Y[0]*Y[0]},
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{1.0, 1.0, 1.0, Y[1], Y[1]*Y[1]},
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{1.0, 1.0, 1.0, Y[2], Y[2]*Y[2]} };
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if (ldv == 50) {
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const double tmp[50] = {
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1.0, Y[0], Y[1], Y[2], Y[0] * Y[0],
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Y[0] * Y[1], Y[0] * Y[2], Y[1] * Y[1], Y[1] * Y[2], Y[2] * Y[2],
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0.0, 1.0, 0.0, 0.0, Y[0] + Y[0],
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Y[1], Y[2], 0.0, 0.0, 0.0,
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0.0, 0.0, 1.0, 0.0, 0.0,
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Y[0], 0.0, Y[1] + Y[1], Y[2], 0.0,
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0.0, 0.0, 0.0, 1.0, 0.0,
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0.0, Y[0], 0.0, Y[1], Y[2] + Y[2],
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0.0, 0.0, 0.0, 0.0, 2.0,
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0.0, 0.0, 2.0, 0., 2.0 };
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for (int i=0 ; i<50 ; ++i)
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VGL[i] = tmp[i];
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} else {
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double* const vgl1 = VGL;
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double* const vgl2 = VGL + ldv;
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double* const vgl3 = VGL + (ldv << 1);
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double* const vgl4 = VGL + 3*ldv;
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double* const vgl5 = VGL + (ldv << 2);
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int32_t* l[10];
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for (int32_t i=0 ; i<10 ; ++i) {
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l[i] = L + i*ldl;
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}
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for (int32_t i=0 ; i<4 ; ++i) {
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l[i][0] = 0;
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l[i][1] = 0;
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l[i][2] = 0;
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}
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l[1][0] = 1;
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l[2][1] = 1;
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l[3][2] = 1;
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for (int32_t k=0 ; k<4 ; ++k) {
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vgl2[k] = 0.0;
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vgl3[k] = 0.0;
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vgl4[k] = 0.0;
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vgl5[k] = 0.0;
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}
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vgl1[0] = 1.0;
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vgl1[1] = Y[0];
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vgl1[2] = Y[1];
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vgl1[3] = Y[2];
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vgl2[1] = 1.0;
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vgl3[2] = 1.0;
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vgl4[3] = 1.0;
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m=4;
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double da = 2.0;
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for (int32_t a=2 ; a>=0 ; --a) {
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double db = 2.0-da;
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for (int32_t b=2-a ; b>=0 ; --b) {
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const int32_t c = 2 - a - b;
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const double dc = 2.0 - da - db;
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double xy = pows[0][a+2] * pows[1][b+2];
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double yz = pows[1][b+2] * pows[2][c+2];
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double xz = pows[0][a+2] * pows[2][c+2];
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l[m][0] = a;
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l[m][1] = b;
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l[m][2] = c;
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vgl1[m] = xy * pows[2][c+2];
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xy *= dc;
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xz *= db;
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yz *= da;
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vgl2[m] = pows[0][a+1] * yz;
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vgl3[m] = pows[1][b+1] * xz;
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vgl4[m] = pows[2][c+1] * xy;
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vgl5[m] = (da-1.) * pows[0][a] * yz +
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(db-1.) * pows[1][b] * xz +
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(dc-1.) * pows[2][c] * xy;
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db -= 1.0;
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++m;
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}
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da -= 1.0;
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vgl1[0] = 1.0 ; vgl1[1] = Y[0] ; vgl1[2] = Y[1];
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vgl1[3] = Y[2] ; vgl1[4] = Y[0]*Y[0]; vgl1[5] = Y[0]*Y[1];
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vgl1[6] = Y[0]*Y[2]; vgl1[7] = Y[1]*Y[1]; vgl1[8] = Y[1]*Y[2];
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vgl1[9] = Y[2]*Y[2];
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vgl2[0] = 0.0 ; vgl2[1] = 1.0 ; vgl2[2] = 0.0 ;
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vgl2[3] = 0.0 ; vgl2[4] = Y[0]+Y[0]; vgl2[5] = Y[1];
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vgl2[6] = Y[2]; vgl2[7] = 0.0 ; vgl2[8] = 0.0 ;
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vgl2[9] = 0.0 ;
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vgl3[0] = 0.0; vgl3[1] = 0.0 ; vgl3[2] = 1.0 ;
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vgl3[3] = 0.0; vgl3[4] = 0.0 ; vgl3[5] = Y[0];
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vgl3[6] = 0.0; vgl3[7] = Y[1]+Y[1]; vgl3[8] = Y[2];
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vgl3[9] = 0.0;
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vgl4[0] = 0.0 ; vgl4[1] = 0.0; vgl4[2] = 0.0 ;
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vgl4[3] = 1.0 ; vgl4[4] = 0.0; vgl4[5] = 0.0 ;
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vgl4[6] = Y[0] ; vgl4[7] = 0.0; vgl4[8] = Y[1];
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vgl4[9] = Y[2]+Y[2];
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vgl5[0] = 0.0; vgl5[1] = 0.0; vgl5[2] = 0.0;
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vgl5[3] = 0.0; vgl5[4] = 2.0; vgl5[5] = 0.0;
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vgl5[6] = 0.0; vgl5[7] = 2.0; vgl5[8] = 0.0;
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vgl5[9] = 2.0;
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}
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m=10;
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break;
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}
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/*
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case 3:
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{
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if (ldv < 20) return QMCKL_INVALID_ARG_9;
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}
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,*/
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case 3:
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{
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if (ldv < 20) return QMCKL_INVALID_ARG_9;
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}
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,*/
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default:
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{
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const int32_t size_max = (lmax+1)*(lmax+2)*(lmax+3)/6;
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if (ldv < size_max) return QMCKL_INVALID_ARG_9;
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double* const vgl1 = VGL;
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double* const vgl2 = VGL + ldv;
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double* const vgl3 = VGL + (ldv << 1);
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double* const vgl4 = VGL + 3*ldv;
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double* const vgl5 = VGL + (ldv << 2);
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const double Y[3] = { X[0]-R[0],
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X[1]-R[1],
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X[2]-R[2] };
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double pows[3][size_max];
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for (int32_t i=0 ; i<=2 ; ++i) {
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@ -4949,36 +4972,38 @@ assert(0 == test_qmckl_ao_polynomial_vgl(context));
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double X[3] = { 1.1, 2.2, 3.3 };
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double R[3] = { 0.2, 1.1, 3.0 };
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int64_t n;
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int64_t ldl = 4;
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int64_t ldv = 24;
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int32_t L0[24][ldl];
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int32_t L1[24][ldl];
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double VGL0[5][ldv];
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double VGL1[5][ldv];
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memset(&L0[0][0], 0, sizeof(L0));
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memset(&L1[0][0], 0, sizeof(L1));
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memset(&VGL0[0][0], 0, sizeof(VGL0));
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memset(&VGL1[0][0], 0, sizeof(VGL1));
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for (int32_t lmax=0 ; lmax<=3 ; lmax++) {
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rc = qmckl_ao_polynomial_transp_vgl_doc (context, X, R, lmax, &n, &(L0[0][0]), ldl, &(VGL0[0][0]), ldv);
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assert (rc == QMCKL_SUCCESS);
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rc = qmckl_ao_polynomial_transp_vgl_hpc (context, X, R, lmax, &n, &(L1[0][0]), ldl, &(VGL1[0][0]), ldv);
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assert (rc == QMCKL_SUCCESS);
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printf("lmax=%d\n", lmax);
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for (int32_t l=0 ; l<n ; ++l) {
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for (int32_t k=0 ; k<3 ; ++k) {
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printf("L[%d][%d] = %d %d\n", l, k, L0[l][k], L1[l][k]);
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assert( L0[l][k] == L1[l][k] );
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}
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}
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int32_t ldv[4] = {1, 4, 10, 20};
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for (int32_t ldl=3 ; ldl<5 ; ++ldl) {
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int64_t n;
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int32_t L0[24][ldl];
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int32_t L1[24][ldl];
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printf("ldl=%d\n", ldl);
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for (int32_t lmax=0 ; lmax<=3 ; lmax++) {
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double VGL0[5][ldv[lmax]];
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double VGL1[5][ldv[lmax]];
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memset(&L0[0][0], 0, sizeof(L0));
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memset(&L1[0][0], 0, sizeof(L1));
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memset(&VGL0[0][0], 0, sizeof(VGL0));
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memset(&VGL1[0][0], 0, sizeof(VGL1));
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rc = qmckl_ao_polynomial_transp_vgl_doc (context, X, R, lmax, &n, &(L0[0][0]), ldl, &(VGL0[0][0]), ldv[lmax]);
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assert (rc == QMCKL_SUCCESS);
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rc = qmckl_ao_polynomial_transp_vgl_hpc (context, X, R, lmax, &n, &(L1[0][0]), ldl, &(VGL1[0][0]), ldv[lmax]);
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assert (rc == QMCKL_SUCCESS);
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printf("lmax=%d\n", lmax);
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for (int32_t l=0 ; l<n ; ++l) {
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for (int32_t k=0 ; k<3 ; ++k) {
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printf("L[%d][%d] = %d %d\n", l, k, L0[l][k], L1[l][k]);
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assert( L0[l][k] == L1[l][k] );
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}
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}
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for (int32_t k=0 ; k<5 ; ++k) {
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for (int32_t l=0 ; l<n ; ++l) {
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printf("VGL[%d][%d] = %e %e\n", k, l, VGL0[k][l], VGL1[k][l]);
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assert( VGL0[k][l] == VGL1[k][l] );
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}
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}
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for (int32_t k=0 ; k<5 ; ++k) {
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for (int32_t l=0 ; l<n ; ++l) {
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printf("VGL[%d][%d] = %e %e\n", k, l, VGL0[k][l], VGL1[k][l]);
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assert( VGL0[k][l] == VGL1[k][l] );
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}
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}
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}
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}
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#+end_src
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@ -5251,7 +5276,7 @@ qmckl_compute_ao_vgl_hpc (
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int64_t n_poly;
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const qmckl_exit_code rc =
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qmckl_ao_polynomial_transp_vgl(context, e_coord, n_coord,
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qmckl_ao_polynomial_transp_vgl_hpc(context, e_coord, n_coord,
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nucleus_max_ang_mom[inucl], &n_poly, powers, (int64_t) 3,
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&(poly_vgl[0][0]), size_max);
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