1 | #include <math.h> |
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2 | #include "invertor.h" |
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3 | #include <memory.h> |
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4 | #include <stdio.h> |
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5 | #include <stdlib.h> |
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6 | |
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7 | double pi = 3.1416; |
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8 | |
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9 | /** |
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10 | * Deallocate memory |
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11 | */ |
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12 | void invertor_dealloc(Invertor_params *pars) { |
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13 | free(pars->x); |
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14 | free(pars->y); |
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15 | free(pars->err); |
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16 | } |
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17 | |
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18 | void invertor_init(Invertor_params *pars) { |
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19 | pars->d_max = 180; |
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20 | pars->q_min = -1.0; |
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21 | pars->q_max = -1.0; |
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22 | pars->has_bck = 0; |
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23 | } |
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24 | |
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25 | |
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26 | /** |
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27 | * P(r) of a sphere, for test purposes |
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28 | * |
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29 | * @param R: radius of the sphere |
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30 | * @param r: distance, in the same units as the radius |
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31 | * @return: P(r) |
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32 | */ |
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33 | double pr_sphere(double R, double r) { |
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34 | if (r <= 2.0*R) { |
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35 | return 12.0* pow(0.5*r/R, 2.0) * pow(1.0-0.5*r/R, 2.0) * ( 2.0 + 0.5*r/R ); |
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36 | } else { |
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37 | return 0.0; |
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38 | } |
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39 | } |
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40 | |
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41 | /** |
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42 | * Orthogonal functions: |
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43 | * B(r) = 2r sin(pi*nr/d) |
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44 | * |
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45 | */ |
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46 | double ortho(double d_max, int n, double r) { |
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47 | return 2.0*r*sin(pi*n*r/d_max); |
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48 | } |
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49 | |
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50 | /** |
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51 | * Fourier transform of the nth orthogonal function |
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52 | * |
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53 | */ |
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54 | double ortho_transformed(double d_max, int n, double q) { |
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55 | return 8.0*pow(pi, 2.0)/q * d_max * n * pow(-1.0, n+1) |
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56 | *sin(q*d_max) / ( pow(pi*n, 2.0) - pow(q*d_max, 2.0) ); |
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57 | } |
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58 | |
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59 | /** |
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60 | * Slit-smeared Fourier transform of the nth orthogonal function. |
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61 | * Smearing follows Lake, Acta Cryst. (1967) 23, 191. |
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62 | */ |
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63 | double ortho_transformed_smeared(double d_max, int n, double height, double width, double q, int npts) { |
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64 | double sum, value, y, z; |
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65 | int i, j; |
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66 | double fnpts; |
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67 | sum = 0.0; |
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68 | fnpts = (float)npts-1.0; |
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69 | |
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70 | for(i=0; i<npts; i++) { |
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71 | y = -width/2.0+width/fnpts*(float)i; |
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72 | for(j=0; j<npts; j++) { |
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73 | z = height/fnpts*(float)j; |
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74 | sum += ortho_transformed(d_max, n, sqrt((q-y)*(q-y)+z*z)); |
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75 | } |
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76 | } |
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77 | |
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78 | return sum/npts/npts/height/width; |
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79 | } |
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80 | |
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81 | /** |
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82 | * First derivative in of the orthogonal function dB(r)/dr |
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83 | * |
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84 | */ |
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85 | double ortho_derived(double d_max, int n, double r) { |
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86 | return 2.0*sin(pi*n*r/d_max) + 2.0*r*cos(pi*n*r/d_max); |
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87 | } |
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88 | |
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89 | /** |
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90 | * Scattering intensity calculated from the expansion. |
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91 | */ |
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92 | double iq(double *pars, double d_max, int n_c, double q) { |
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93 | double sum = 0.0; |
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94 | int i; |
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95 | for (i=0; i<n_c; i++) { |
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96 | sum += pars[i] * ortho_transformed(d_max, i+1, q); |
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97 | } |
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98 | return sum; |
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99 | } |
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100 | |
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101 | /** |
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102 | * P(r) calculated from the expansion. |
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103 | */ |
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104 | double pr(double *pars, double d_max, int n_c, double r) { |
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105 | double sum = 0.0; |
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106 | int i; |
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107 | for (i=0; i<n_c; i++) { |
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108 | sum += pars[i] * ortho(d_max, i+1, r); |
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109 | } |
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110 | return sum; |
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111 | } |
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112 | |
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113 | /** |
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114 | * P(r) calculated from the expansion, with errors |
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115 | */ |
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116 | void pr_err(double *pars, double *err, double d_max, int n_c, |
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117 | double r, double *pr_value, double *pr_value_err) { |
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118 | double sum = 0.0; |
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119 | double sum_err = 0.0; |
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120 | double func_value; |
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121 | int i; |
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122 | for (i=0; i<n_c; i++) { |
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123 | func_value = ortho(d_max, i+1, r); |
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124 | sum += pars[i] * func_value; |
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125 | //sum_err += err[i]*err[i]*func_value*func_value; |
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126 | sum_err += err[i*n_c+i]*func_value*func_value; |
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127 | } |
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128 | *pr_value = sum; |
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129 | if (sum_err>0) { |
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130 | *pr_value_err = sqrt(sum_err); |
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131 | } else { |
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132 | *pr_value_err = sum; |
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133 | } |
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134 | } |
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135 | |
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136 | /** |
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137 | * dP(r)/dr calculated from the expansion. |
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138 | */ |
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139 | double dprdr(double *pars, double d_max, int n_c, double r) { |
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140 | double sum = 0.0; |
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141 | int i; |
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142 | for (i=0; i<n_c; i++) { |
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143 | sum += pars[i] * 2.0*(sin(pi*(i+1)*r/d_max) + pi*(i+1)*r/d_max * cos(pi*(i+1)*r/d_max)); |
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144 | } |
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145 | return sum; |
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146 | } |
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147 | |
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148 | /** |
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149 | * regularization term calculated from the expansion. |
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150 | */ |
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151 | double reg_term(double *pars, double d_max, int n_c, int nslice) { |
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152 | double sum = 0.0; |
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153 | double r; |
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154 | double deriv; |
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155 | int i; |
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156 | for (i=0; i<nslice; i++) { |
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157 | r = d_max/(1.0*nslice)*i; |
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158 | deriv = dprdr(pars, d_max, n_c, r); |
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159 | sum += deriv*deriv; |
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160 | } |
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161 | return sum/(1.0*nslice)*d_max; |
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162 | } |
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163 | |
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164 | /** |
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165 | * regularization term calculated from the expansion. |
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166 | */ |
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167 | double int_p2(double *pars, double d_max, int n_c, int nslice) { |
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168 | double sum = 0.0; |
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169 | double r; |
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170 | double value; |
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171 | int i; |
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172 | for (i=0; i<nslice; i++) { |
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173 | r = d_max/(1.0*nslice)*i; |
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174 | value = pr(pars, d_max, n_c, r); |
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175 | sum += value*value; |
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176 | } |
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177 | return sum/(1.0*nslice)*d_max; |
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178 | } |
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179 | |
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180 | /** |
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181 | * Integral of P(r) |
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182 | */ |
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183 | double int_pr(double *pars, double d_max, int n_c, int nslice) { |
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184 | double sum = 0.0; |
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185 | double r; |
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186 | double value; |
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187 | int i; |
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188 | for (i=0; i<nslice; i++) { |
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189 | r = d_max/(1.0*nslice)*i; |
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190 | value = pr(pars, d_max, n_c, r); |
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191 | sum += value; |
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192 | } |
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193 | return sum/(1.0*nslice)*d_max; |
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194 | } |
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195 | |
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196 | /** |
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197 | * Get the number of P(r) peaks. |
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198 | */ |
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199 | int npeaks(double *pars, double d_max, int n_c, int nslice) { |
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200 | double r; |
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201 | double value; |
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202 | int i; |
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203 | double previous = 0.0; |
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204 | double slope = 0.0; |
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205 | int count = 0; |
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206 | for (i=0; i<nslice; i++) { |
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207 | r = d_max/(1.0*nslice)*i; |
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208 | value = pr(pars, d_max, n_c, r); |
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209 | if (previous<=value){ |
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210 | //if (slope<0) count += 1; |
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211 | slope = 1; |
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212 | } else { |
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213 | //printf("slope -1"); |
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214 | if (slope>0) count += 1; |
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215 | slope = -1; |
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216 | } |
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217 | previous = value; |
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218 | } |
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219 | return count; |
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220 | } |
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221 | |
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222 | /** |
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223 | * Get the fraction of the integral of P(r) over the whole range |
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224 | * of r that is above zero. |
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225 | * A valid P(r) is define as being positive for all r. |
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226 | */ |
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227 | double positive_integral(double *pars, double d_max, int n_c, int nslice) { |
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228 | double r; |
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229 | double value; |
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230 | int i; |
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231 | double sum_pos = 0.0; |
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232 | double sum = 0.0; |
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233 | |
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234 | for (i=0; i<nslice; i++) { |
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235 | r = d_max/(1.0*nslice)*i; |
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236 | value = pr(pars, d_max, n_c, r); |
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237 | if (value>0.0) sum_pos += value; |
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238 | sum += fabs(value); |
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239 | } |
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240 | return sum_pos/sum; |
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241 | } |
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242 | |
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243 | /** |
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244 | * Get the fraction of the integral of P(r) over the whole range |
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245 | * of r that is at least one sigma above zero. |
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246 | */ |
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247 | double positive_errors(double *pars, double *err, double d_max, int n_c, int nslice) { |
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248 | double r; |
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249 | double value; |
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250 | int i; |
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251 | double sum_pos = 0.0; |
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252 | double sum = 0.0; |
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253 | double pr_val; |
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254 | double pr_val_err; |
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255 | |
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256 | for (i=0; i<nslice; i++) { |
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257 | r = d_max/(1.0*nslice)*i; |
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258 | pr_err(pars, err, d_max, n_c, r, &pr_val, &pr_val_err); |
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259 | if (pr_val>pr_val_err) sum_pos += pr_val; |
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260 | sum += fabs(pr_val); |
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261 | |
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262 | |
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263 | } |
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264 | return sum_pos/sum; |
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265 | } |
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266 | |
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267 | /** |
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268 | * R_g radius of gyration calculation |
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269 | * |
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270 | * R_g**2 = integral[r**2 * p(r) dr] / (2.0 * integral[p(r) dr]) |
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271 | */ |
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272 | double rg(double *pars, double d_max, int n_c, int nslice) { |
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273 | double sum_r2 = 0.0; |
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274 | double sum = 0.0; |
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275 | double r; |
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276 | double value; |
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277 | int i; |
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278 | for (i=0; i<nslice; i++) { |
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279 | r = d_max/(1.0*nslice)*i; |
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280 | value = pr(pars, d_max, n_c, r); |
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281 | sum += value; |
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282 | sum_r2 += r*r*value; |
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283 | } |
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284 | return sqrt(sum_r2/(2.0*sum)); |
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285 | } |
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286 | |
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