src/gromacs/ewald/calculate_spline_moduli.cpp

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  37 #include "gmxpre.h"
  38
  39 #include "calculate_spline_moduli.h"
  40
  41 #include <cmath>
  42
  43 #include <algorithm>
  44
  45 #include "gromacs/math/utilities.h"
  46 #include "gromacs/math/vec.h"
  47 #include "gromacs/utility/exceptions.h"
  48 #include "gromacs/utility/gmxassert.h"
  49 #include "gromacs/utility/smalloc.h"
  50
  51 #include "pme_internal.h"
  52
  53 static void make_dft_mod(real *mod,
  54                          const double *data, int splineOrder, int ndata)
  55 {
  56     for (int i = 0; i < ndata; i++)
  57     {
  58         /* We use double precision, since this is only called once per grid.
  59          * But for single precision bsp_mod, single precision also seems
  60          * to give full accuracy.
  61          */
  62         double sc = 0;
  63         double ss = 0;
  64         for (int j = 0; j < splineOrder; j++)
  65         {
  66             double arg  = (2.0*M_PI*i*(j + 1))/ndata;
  67             sc         += data[j]*cos(arg);
  68             ss         += data[j]*sin(arg);
  69         }
  70         mod[i] = sc*sc + ss*ss;
  71     }
  72     if (splineOrder % 2 == 0 && ndata % 2 == 0)
  73     {
  74         /* Note that pme_order = splineOrder + 1 */
  75         GMX_RELEASE_ASSERT(mod[ndata/2] < GMX_DOUBLE_EPS, "With even spline order and even grid size (ndata), dft_mod[ndata/2] should first come out as zero");
  76         /* This factor causes a division by zero. But since this occurs in
  77          * the tail of the distribution, the term with this factor can
  78          * be ignored (see Essmann et al. JCP 103, 8577).
  79          * Using the average of the neighbors probably originates from
  80          * Tom Darden's original PME code. It seems to give slighlty better
  81          * accuracy than using a large value.
  82          */
  83         mod[ndata/2] = (mod[ndata/2 - 1] + mod[ndata/2 + 1])*0.5;
  84     }
  85 }
  86
  87 void make_bspline_moduli(splinevec bsp_mod,
  88                          int nx, int ny, int nz, int pme_order)
  89 {
  90     /* We use double precision, since this is only called once per grid.
  91      * But for single precision bsp_mod, single precision also seems
  92      * to give full accuracy.
  93      */
  94     double *data;
  95
  96     /* In GROMACS we, confusingly, defined pme-order as the order
  97      * of the cardinal B-spline + 1. This probably happened because
  98      * the smooth PME paper only talks about "n" which is the number
  99      * of points we spread to and that was chosen to be pme-order.
 100      */
 101     const int splineOrder = pme_order - 1;
 102
 103     snew(data, splineOrder);
 104
 105     data[0]     = 1;
 106     for (int k = 1; k < splineOrder; k++)
 107     {
 108         data[k] = 0;
 109     }
 110
 111     for (int k = 2; k <= splineOrder; k++)
 112     {
 113         double div  = 1.0/k;
 114         for (int m = k - 1; m > 0; m--)
 115         {
 116             data[m] = div*((k - m)*data[m - 1] + (m + 1)*data[m]);
 117         }
 118         data[0]     = div*data[0];
 119     }
 120
 121     make_dft_mod(bsp_mod[XX], data, splineOrder, nx);
 122     make_dft_mod(bsp_mod[YY], data, splineOrder, ny);
 123     make_dft_mod(bsp_mod[ZZ], data, splineOrder, nz);
 124
 125     sfree(data);
 126 }
 127
 128 /* Return the P3M optimal influence function */
 129 static double do_p3m_influence(double z, int order)
 130 {
 131     double z2, z4;
 132
 133     z2 = z*z;
 134     z4 = z2*z2;
 135
 136     /* The formula and most constants can be found in:
 137      * Ballenegger et al., JCTC 8, 936 (2012)
 138      */
 139     switch (order)
 140     {
 141         case 2:
 142             return 1.0 - 2.0*z2/3.0;
 143         case 3:
 144             return 1.0 - z2 + 2.0*z4/15.0;
 145         case 4:
 146             return 1.0 - 4.0*z2/3.0 + 2.0*z4/5.0 + 4.0*z2*z4/315.0;
 147         case 5:
 148             return 1.0 - 5.0*z2/3.0 + 7.0*z4/9.0 - 17.0*z2*z4/189.0 + 2.0*z4*z4/2835.0;
 149         case 6:
 150             return 1.0 - 2.0*z2 + 19.0*z4/15.0 - 256.0*z2*z4/945.0 + 62.0*z4*z4/4725.0 + 4.0*z2*z4*z4/155925.0;
 151         case 7:
 152             return 1.0 - 7.0*z2/3.0 + 28.0*z4/15.0 - 16.0*z2*z4/27.0 + 26.0*z4*z4/405.0 - 2.0*z2*z4*z4/1485.0 + 4.0*z4*z4*z4/6081075.0;
 153         case 8:
 154             return 1.0 - 8.0*z2/3.0 + 116.0*z4/45.0 - 344.0*z2*z4/315.0 + 914.0*z4*z4/4725.0 - 248.0*z4*z4*z2/22275.0 + 21844.0*z4*z4*z4/212837625.0 - 8.0*z4*z4*z4*z2/638512875.0;
 155     }
 156
 157     return 0.0;
 158 }
 159
 160 /* Calculate the P3M B-spline moduli for one dimension */
 161 static void make_p3m_bspline_moduli_dim(real *bsp_mod, int n, int order)
 162 {
 163     double zarg, zai, sinzai, infl;
 164     int    maxk, i;
 165
 166     if (order > 8)
 167     {
 168         GMX_THROW(gmx::InconsistentInputError("The current P3M code only supports orders up to 8"));
 169     }
 170
 171     zarg = M_PI/n;
 172
 173     maxk = (n + 1)/2;
 174
 175     for (i = -maxk; i < 0; i++)
 176     {
 177         zai          = zarg*i;
 178         sinzai       = sin(zai);
 179         infl         = do_p3m_influence(sinzai, order);
 180         bsp_mod[n+i] = infl*infl*pow(sinzai/zai, -2.0*order);
 181     }
 182     bsp_mod[0] = 1.0;
 183     for (i = 1; i < maxk; i++)
 184     {
 185         zai        = zarg*i;
 186         sinzai     = sin(zai);
 187         infl       = do_p3m_influence(sinzai, order);
 188         bsp_mod[i] = infl*infl*pow(sinzai/zai, -2.0*order);
 189     }
 190 }
 191
 192 /* Calculate the P3M B-spline moduli */
 193 void make_p3m_bspline_moduli(splinevec bsp_mod,
 194                              int nx, int ny, int nz, int order)
 195 {
 196     make_p3m_bspline_moduli_dim(bsp_mod[XX], nx, order);
 197     make_p3m_bspline_moduli_dim(bsp_mod[YY], ny, order);
 198     make_p3m_bspline_moduli_dim(bsp_mod[ZZ], nz, order);
 199 }