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1 /*
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2 * Copyright 1996-2006 Catherine Loader.
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3 */
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4
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5 #include "mex.h"
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6 /*
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7 * Copyright 1996-2006 Catherine Loader.
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8 */
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9 /*
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10 * Integration for hazard rate estimation. The functions in this
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11 * file are used to evaluate
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12 * sum int_0^{Ti} W_i(t,x) A()A()' exp( P() ) dt
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13 * for hazard rate models.
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14 *
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15 * These routines assume the weight function is supported on [-1,1].
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16 * hasint_sph multiplies by exp(base(lf,i)), which allows estimating
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17 * the baseline in a proportional hazards model, when the covariate
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18 * effect base(lf,i) is known.
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19 *
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20 * TODO:
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21 * hazint_sph, should be able to reduce mint in some cases with
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22 * small integration range. onedint could be used for beta-family
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23 * (RECT,EPAN,BISQ,TRWT) kernels.
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24 * hazint_prod, restrict terms from the sum based on x values.
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25 * I should count obs >= max, and only do that integration once.
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26 */
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27
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28 #include "locf.h"
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29
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30 static double ilim[2*MXDIM], *ff, tmax;
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31 static lfdata *haz_lfd;
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32 static smpar *haz_sp;
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33
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34 /*
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35 * hrao returns 0 if integration region is empty.
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36 * 1 otherwise.
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37 */
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38 int haz_sph_int(dfx,cf,h,r1)
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39 double *dfx, *cf, h, *r1;
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40 { double s, t0, t1, wt, th;
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41 int j, dim, p;
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42 s = 0; p = npar(haz_sp);
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43 dim = haz_lfd->d;
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44 for (j=1; j<dim; j++) s += SQR(dfx[j]/(h*haz_lfd->sca[j]));
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45 if (s>1) return(0);
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46
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47 setzero(r1,p*p);
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48 t1 = sqrt(1-s)*h*haz_lfd->sca[0];
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49 t0 = -t1;
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50 if (t0<ilim[0]) t0 = ilim[0];
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51 if (t1>ilim[dim]) t1 = ilim[dim];
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52 if (t1>dfx[0]) t1 = dfx[0];
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53 if (t1<t0) return(0);
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54
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55 /* Numerical integration by Simpson's rule.
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56 */
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57 for (j=0; j<=de_mint; j++)
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58 { dfx[0] = t0+(t1-t0)*j/de_mint;
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59 wt = weight(haz_lfd, haz_sp, dfx, NULL, h, 0, 0.0);
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60 fitfun(haz_lfd, haz_sp, dfx,NULL,ff,NULL);
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61 th = innerprod(cf,ff,p);
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62 if (link(haz_sp)==LLOG) th = exp(th);
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63 wt *= 2+2*(j&1)-(j==0)-(j==de_mint);
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64 addouter(r1,ff,ff,p,wt*th);
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65 }
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66 multmatscal(r1,(t1-t0)/(3*de_mint),p*p);
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67
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68 return(1);
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69 }
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70
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71 int hazint_sph(t,resp,r1,cf,h)
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72 double *t, *resp, *r1, *cf, h;
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73 { int i, j, n, p, st;
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74 double dfx[MXDIM], eb, sb;
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75 p = npar(haz_sp);
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76 setzero(resp,p*p);
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77 sb = 0.0;
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78
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79 n = haz_lfd->n;
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80 for (i=0; i<=n; i++)
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81 {
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82 if (i==n)
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83 { dfx[0] = tmax-t[0];
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84 for (j=1; j<haz_lfd->d; j++) dfx[j] = 0.0;
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85 eb = exp(sb/n);
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86 }
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87 else
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88 { eb = exp(base(haz_lfd,i)); sb += base(haz_lfd,i);
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89 for (j=0; j<haz_lfd->d; j++) dfx[j] = datum(haz_lfd,j,i)-t[j];
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90 }
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91
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92 st = haz_sph_int(dfx,cf,h,r1);
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93 if (st)
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94 for (j=0; j<p*p; j++) resp[j] += eb*r1[j];
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95 }
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96 return(LF_OK);
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97 }
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98
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99 int hazint_prod(t,resp,x,cf,h)
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100 double *t, *resp, *x, *cf, h;
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101 { int d, p, i, j, k, st;
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102 double dfx[MXDIM], t_prev,
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103 hj, hs, ncf[MXDEG], ef, il1;
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104 double prod_wk[MXDIM][2*MXDEG+1], eb, sb;
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105
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106 p = npar(haz_sp);
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107 d = haz_lfd->d;
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108 setzero(resp,p*p);
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109 hj = hs = h*haz_lfd->sca[0];
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110
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111 ncf[0] = cf[0];
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112 for (i=1; i<=deg(haz_sp); i++)
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113 { ncf[i] = hj*cf[(i-1)*d+1]; hj *= hs;
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114 }
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115
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116 /* for i=0..n....
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117 * First we compute prod_wk[j], j=0..d.
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118 * For j=0, this is int_0^T_i (u-t)^k W((u-t)/h) exp(b0*(u-t)) du
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119 * For remaining j, (x(i,j)-x(j))^k Wj exp(bj*(x..-x.))
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120 *
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121 * Second, we add to the integration (exp(a) incl. in integral)
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122 * with the right factorial denominators.
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123 */
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124 t_prev = ilim[0]; sb = 0.0;
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125 for (i=0; i<=haz_lfd->n; i++)
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126 { if (i==haz_lfd->n)
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127 { dfx[0] = tmax-t[0];
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128 for (j=1; j<d; j++) dfx[j] = 0.0;
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129 eb = exp(sb/haz_lfd->n);
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130 }
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131 else
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132 { eb = exp(base(haz_lfd,i)); sb += base(haz_lfd,i);
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133 for (j=0; j<d; j++) dfx[j] = datum(haz_lfd,j,i)-t[j];
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134 }
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135
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136 if (dfx[0]>ilim[0]) /* else it doesn't contribute */
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137 {
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138 /* time integral */
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139 il1 = (dfx[0]>ilim[d]) ? ilim[d] : dfx[0];
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140 if (il1 != t_prev) /* don't repeat! */
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141 { st = onedint(haz_sp,ncf,ilim[0]/hs,il1/hs,prod_wk[0]);
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142 if (st>0) return(st);
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143 hj = eb;
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144 for (j=0; j<=2*deg(haz_sp); j++)
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145 { hj *= hs;
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146 prod_wk[0][j] *= hj;
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147 }
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148 t_prev = il1;
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149 }
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150
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151 /* covariate terms */
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152 for (j=1; j<d; j++)
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153 {
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154 ef = 0.0;
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155 for (k=deg(haz_sp); k>0; k--) ef = (ef+dfx[j])*cf[1+(k-1)*d+j];
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156 ef = exp(ef);
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157 prod_wk[j][0] = ef * W(dfx[j]/(h*haz_lfd->sca[j]),ker(haz_sp));
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158 for (k=1; k<=2*deg(haz_sp); k++)
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159 prod_wk[j][k] = prod_wk[j][k-1] * dfx[j];
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160 }
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161
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162 /* add to the integration. */
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163 prodintresp(resp,prod_wk,d,deg(haz_sp),p);
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164 } /* if dfx0 > ilim0 */
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165 } /* n loop */
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166
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167 /* symmetrize */
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168 for (k=0; k<p; k++)
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169 for (j=k; j<p; j++)
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170 resp[j*p+k] = resp[k*p+j];
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171 return(LF_OK);
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172 }
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173
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174 int hazint(t,resp,resp1,cf,h)
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175 double *t, *resp, *resp1, *cf, h;
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176 { if (haz_lfd->d==1) return(hazint_prod(t,resp,resp1,cf,h));
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177 if (kt(haz_sp)==KPROD) return(hazint_prod(t,resp,resp1,cf,h));
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178
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179 return(hazint_sph(t,resp,resp1,cf,h));
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180 }
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181
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182 void haz_init(lfd,des,sp,il)
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183 lfdata *lfd;
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184 design *des;
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185 smpar *sp;
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186 double *il;
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187 { int i;
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188
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189 haz_lfd = lfd;
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190 haz_sp = sp;
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191
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192 tmax = datum(lfd,0,0);
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193 for (i=1; i<lfd->n; i++) tmax = MAX(tmax,datum(lfd,0,i));
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194 ff = des->xtwx.wk;
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195 for (i=0; i<2*lfd->d; i++) ilim[i] = il[i];
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196 }
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197 /*
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198 * Copyright 1996-2006 Catherine Loader.
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199 */
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200 /*
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201 *
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202 * Routines for one-dimensional numerical integration
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203 * in density estimation. The entry point is
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204 *
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205 * onedint(cf,mi,l0,l1,resp)
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206 *
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207 * which evaluates int W(u)u^j exp( P(u) ), j=0..2*deg.
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208 * P(u) = cf[0] + cf[1]u + cf[2]u^2/2 + ... + cf[deg]u^deg/deg!
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209 * l0 and l1 are the integration limits.
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210 * The results are returned through the vector resp.
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211 *
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212 */
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213
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214 #include "locf.h"
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215
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216 static int debug;
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217
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218 int exbctay(b,c,n,z) /* n-term taylor series of e^(bx+cx^2) */
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219 double b, c, *z;
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220 int n;
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221 { double ec[20];
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222 int i, j;
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223 z[0] = 1;
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224 for (i=1; i<=n; i++) z[i] = z[i-1]*b/i;
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225 if (c==0.0) return(n);
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226 if (n>=40)
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227 { WARN(("exbctay limit to n<40"));
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228 n = 39;
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229 }
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230 ec[0] = 1;
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231 for (i=1; 2*i<=n; i++) ec[i] = ec[i-1]*c/i;
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232 for (i=n; i>1; i--)
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233 for (j=1; 2*j<=i; j++)
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234 z[i] += ec[j]*z[i-2*j];
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235 return(n);
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236 }
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237
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238 double explinjtay(l0,l1,j,cf)
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239 /* int_l0^l1 x^j e^(a+bx+cx^2); exbctay aroud l1 */
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240 double l0, l1, *cf;
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241 int j;
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242 { double tc[40], f, s;
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243 int k, n;
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244 if ((l0!=0.0) | (l1!=1.0)) WARN(("explinjtay: invalid l0, l1"));
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245 n = exbctay(cf[1]+2*cf[2]*l1,cf[2],20,tc);
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246 s = tc[0]/(j+1);
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247 f = 1/(j+1);
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248 for (k=1; k<=n; k++)
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249 { f *= -k/(j+k+1.0);
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250 s += tc[k]*f;
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251 }
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252 return(f);
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253 }
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254
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255 void explint1(l0,l1,cf,I,p) /* int x^j exp(a+bx); j=0..p-1 */
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256 double l0, l1, *cf, *I;
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257 int p;
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258 { double y0, y1, f;
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259 int j, k, k1;
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260 y0 = mut_exp(cf[0]+l0*cf[1]);
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261 y1 = mut_exp(cf[0]+l1*cf[1]);
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262 if (p<2*fabs(cf[1])) k = p; else k = (int)fabs(cf[1]);
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263
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264 if (k>0)
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265 { I[0] = (y1-y0)/cf[1];
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266 for (j=1; j<k; j++) /* forward steps for small j */
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267 { y1 *= l1; y0 *= l0;
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268 I[j] = (y1-y0-j*I[j-1])/cf[1];
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269 }
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270 if (k==p) return;
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271 y1 *= l1; y0 *= l0;
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272 }
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273
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274 f = 1; k1 = k;
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275 while ((k<50) && (f>1.0e-8)) /* initially Ik = diff(x^{k+1}e^{a+bx}) */
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276 { y1 *= l1; y0 *= l0;
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277 I[k] = y1-y0;
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278 if (k>=p) f *= fabs(cf[1])/(k+1);
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279 k++;
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280 }
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281 if (k==50) WARN(("explint1: want k>50"));
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282 I[k] = 0.0;
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283 for (j=k-1; j>=k1; j--) /* now do back step recursion */
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284 I[j] = (I[j]-cf[1]*I[j+1])/(j+1);
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285 }
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286
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287 void explintyl(l0,l1,cf,I,p) /* small c, use taylor series and explint1 */
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288 double l0, l1, *cf, *I;
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289 int p;
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290 { int i;
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291 double c;
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292 explint1(l0,l1,cf,I,p+8);
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293 c = cf[2];
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294 for (i=0; i<p; i++)
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295 I[i] = (((I[i+8]*c/4+I[i+6])*c/3+I[i+4])*c/2+I[i+2])*c+I[i];
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296 }
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297
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298 void solvetrid(X,y,m)
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299 double *X, *y;
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300 int m;
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301 { int i;
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302 double s;
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303 for (i=1; i<m; i++)
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304 { s = X[3*i]/X[3*i-2];
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305 X[3*i] = 0; X[3*i+1] -= s*X[3*i-1];
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306 y[i] -= s*y[i-1];
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307 }
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308 for (i=m-2; i>=0; i--)
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309 { s = X[3*i+2]/X[3*i+4];
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310 X[3*i+2] = 0;
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311 y[i] -= s*y[i+1];
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312 }
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313 for (i=0; i<m; i++) y[i] /= X[3*i+1];
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314 }
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315
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316 void initi0i1(I,cf,y0,y1,l0,l1)
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317 double *I, *cf, y0, y1, l0, l1;
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318 { double a0, a1, c, d, bi;
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319 d = -cf[1]/(2*cf[2]); c = sqrt(2*fabs(cf[2]));
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320 a0 = c*(l0-d); a1 = c*(l1-d);
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321 if (cf[2]<0)
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322 { bi = mut_exp(cf[0]+cf[1]*d+cf[2]*d*d)/c;
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323 if (a0>0)
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324 { if (a0>6) I[0] = (y0*ptail(-a0)-y1*ptail(-a1))/c;
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325 else I[0] = S2PI*(mut_pnorm(-a0)-mut_pnorm(-a1))*bi;
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326 }
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327 else
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328 { if (a1< -6) I[0] = (y1*ptail(a1)-y0*ptail(a0))/c;
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329 else I[0] = S2PI*(mut_pnorm(a1)-mut_pnorm(a0))*bi;
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330 }
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331 }
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332 else
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333 I[0] = (y1*mut_daws(a1)-y0*mut_daws(a0))/c;
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334 I[1] = (y1-y0)/(2*cf[2])+d*I[0];
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335 }
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336
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337 void explinsid(l0,l1,cf,I,p) /* large b; don't use fwd recursion */
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338 double l0, l1, *cf, *I;
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339 int p;
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340 { int k, k0, k1, k2;
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341 double y0, y1, Z[150];
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342 if (debug) mut_printf("side: %8.5f %8.5f %8.5f limt %8.5f %8.5f p %2d\n",cf[0],cf[1],cf[2],l0,l1,p);
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343
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344 k0 = 2;
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345 k1 = (int)(fabs(cf[1])+fabs(2*cf[2]));
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346 if (k1<2) k1 = 2;
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347 if (k1>p+20) k1 = p+20;
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348 k2 = p+20;
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349
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350 if (k2>50) { mut_printf("onedint: k2 warning\n"); k2 = 50; }
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351 if (debug) mut_printf("k0 %2d k1 %2d k2 %2d p %2d\n",k0,k1,k2,p);
|
|
|
352
|
|
|
353 y0 = mut_exp(cf[0]+l0*(cf[1]+l0*cf[2]));
|
|
|
354 y1 = mut_exp(cf[0]+l1*(cf[1]+l1*cf[2]));
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|
|
355 initi0i1(I,cf,y0,y1,l0,l1);
|
|
|
356 if (debug) mut_printf("i0 %8.5f i1 %8.5f\n",I[0],I[1]);
|
|
|
357
|
|
|
358 y1 *= l1; y0 *= l0; /* should be x^(k1)*exp(..) */
|
|
|
359 if (k0<k1) /* center steps; initially x^k*exp(...) */
|
|
|
360 for (k=k0; k<k1; k++)
|
|
|
361 { y1 *= l1; y0 *= l0;
|
|
|
362 I[k] = y1-y0;
|
|
|
363 Z[3*k] = k; Z[3*k+1] = cf[1]; Z[3*k+2] = 2*cf[2];
|
|
|
364 }
|
|
|
365
|
|
|
366 y1 *= l1; y0 *= l0; /* should be x^(k1)*exp(..) */
|
|
|
367 if (debug) mut_printf("k1 %2d y0 %8.5f y1 %8.5f\n",k1,y0,y1);
|
|
|
368 for (k=k1; k<k2; k++)
|
|
|
369 { y1 *= l1; y0 *= l0;
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|
|
370 I[k] = y1-y0;
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|
|
371 }
|
|
|
372 I[k2] = I[k2+1] = 0.0;
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|
373 for (k=k2-1; k>=k1; k--)
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|
374 I[k] = (I[k]-cf[1]*I[k+1]-2*cf[2]*I[k+2])/(k+1);
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|
375
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|
|
376 if (k0<k1)
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|
377 { I[k0] -= k0*I[k0-1];
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|
|
378 I[k1-1] -= 2*cf[2]*I[k1];
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|
|
379 Z[3*k0] = Z[3*k1-1] = 0;
|
|
|
380 solvetrid(&Z[3*k0],&I[k0],k1-k0);
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|
|
381 }
|
|
|
382 if (debug)
|
|
|
383 { mut_printf("explinsid:\n");
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|
|
384 for (k=0; k<p; k++) mut_printf(" %8.5f\n",I[k]);
|
|
|
385 }
|
|
|
386 }
|
|
|
387
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|
|
388 void explinbkr(l0,l1,cf,I,p) /* small b,c; use back recursion */
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|
|
389 double l0, l1, *cf, *I;
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|
|
390 int p;
|
|
|
391 { int k, km;
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|
|
392 double y0, y1;
|
|
|
393 y0 = mut_exp(cf[0]+l0*(cf[1]+cf[2]*l0));
|
|
|
394 y1 = mut_exp(cf[0]+l1*(cf[1]+cf[2]*l1));
|
|
|
395 km = p+10;
|
|
|
396 for (k=0; k<=km; k++)
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|
|
397 { y1 *= l1; y0 *= l0;
|
|
|
398 I[k] = y1-y0;
|
|
|
399 }
|
|
|
400 I[km+1] = I[km+2] = 0;
|
|
|
401 for (k=km; k>=0; k--)
|
|
|
402 I[k] = (I[k]-cf[1]*I[k+1]-2*cf[2]*I[k+2])/(k+1);
|
|
|
403 }
|
|
|
404
|
|
|
405 void explinfbk0(l0,l1,cf,I,p) /* fwd and bac recur; b=0; c<0 */
|
|
|
406 double l0, l1, *cf, *I;
|
|
|
407 int p;
|
|
|
408 { double y0, y1, f1, f2, f, ml2;
|
|
|
409 int k, ks;
|
|
|
410
|
|
|
411 y0 = mut_exp(cf[0]+l0*l0*cf[2]);
|
|
|
412 y1 = mut_exp(cf[0]+l1*l1*cf[2]);
|
|
|
413 initi0i1(I,cf,y0,y1,l0,l1);
|
|
|
414
|
|
|
415 ml2 = MAX(l0*l0,l1*l1);
|
|
|
416 ks = 1+(int)(2*fabs(cf[2])*ml2);
|
|
|
417 if (ks<2) ks = 2;
|
|
|
418 if (ks>p-3) ks = p;
|
|
|
419
|
|
|
420 /* forward recursion for k < ks */
|
|
|
421 for (k=2; k<ks; k++)
|
|
|
422 { y1 *= l1; y0 *= l0;
|
|
|
423 I[k] = (y1-y0-(k-1)*I[k-2])/(2*cf[2]);
|
|
|
424 }
|
|
|
425 if (ks==p) return;
|
|
|
426
|
|
|
427 y1 *= l1*l1; y0 *= l0*l0;
|
|
|
428 for (k=ks; k<p; k++) /* set I[k] = x^{k+1}e^(a+cx^2) | {l0,l1} */
|
|
|
429 { y1 *= l1; y0 *= l0;
|
|
|
430 I[k] = y1-y0;
|
|
|
431 }
|
|
|
432
|
|
|
433 /* initialize I[p-2] and I[p-1] */
|
|
|
434 f1 = 1.0/p; f2 = 1.0/(p-1);
|
|
|
435 I[p-1] *= f1; I[p-2] *= f2;
|
|
|
436 k = p; f = 1.0;
|
|
|
437 while (f>1.0e-8)
|
|
|
438 { y1 *= l1; y0 *= l0;
|
|
|
439 if ((k-p)%2==0) /* add to I[p-2] */
|
|
|
440 { f2 *= -2*cf[2]/(k+1);
|
|
|
441 I[p-2] += (y1-y0)*f2;
|
|
|
442 }
|
|
|
443 else /* add to I[p-1] */
|
|
|
444 { f1 *= -2*cf[2]/(k+1);
|
|
|
445 I[p-1] += (y1-y0)*f1;
|
|
|
446 f *= 2*fabs(cf[2])*ml2/(k+1);
|
|
|
447 }
|
|
|
448 k++;
|
|
|
449 }
|
|
|
450
|
|
|
451 /* use back recursion for I[ks..(p-3)] */
|
|
|
452 for (k=p-3; k>=ks; k--)
|
|
|
453 I[k] = (I[k]-2*cf[2]*I[k+2])/(k+1);
|
|
|
454 }
|
|
|
455
|
|
|
456 void explinfbk(l0,l1,cf,I,p) /* fwd and bac recur; b not too large */
|
|
|
457 double l0, l1, *cf, *I;
|
|
|
458 int p;
|
|
|
459 { double y0, y1;
|
|
|
460 int k, ks, km;
|
|
|
461
|
|
|
462 y0 = mut_exp(cf[0]+l0*(cf[1]+l0*cf[2]));
|
|
|
463 y1 = mut_exp(cf[0]+l1*(cf[1]+l1*cf[2]));
|
|
|
464 initi0i1(I,cf,y0,y1,l0,l1);
|
|
|
465
|
|
|
466 ks = (int)(3*fabs(cf[2]));
|
|
|
467 if (ks<3) ks = 3;
|
|
|
468 if (ks>0.75*p) ks = p; /* stretch the forward recurs as far as poss. */
|
|
|
469 /* forward recursion for k < ks */
|
|
|
470 for (k=2; k<ks; k++)
|
|
|
471 { y1 *= l1; y0 *= l0;
|
|
|
472 I[k] = (y1-y0-cf[1]*I[k-1]-(k-1)*I[k-2])/(2*cf[2]);
|
|
|
473 }
|
|
|
474 if (ks==p) return;
|
|
|
475
|
|
|
476 km = p+15;
|
|
|
477 y1 *= l1*l1; y0 *= l0*l0;
|
|
|
478 for (k=ks; k<=km; k++)
|
|
|
479 { y1 *= l1; y0 *= l0;
|
|
|
480 I[k] = y1-y0;
|
|
|
481 }
|
|
|
482 I[km+1] = I[km+2] = 0.0;
|
|
|
483 for (k=km; k>=ks; k--)
|
|
|
484 I[k] = (I[k]-cf[1]*I[k+1]-2*cf[2]*I[k+2])/(k+1);
|
|
|
485 }
|
|
|
486
|
|
|
487 void recent(I,resp,wt,p,s,x)
|
|
|
488 double *I, *resp, *wt, x;
|
|
|
489 int p, s;
|
|
|
490 { int i, j;
|
|
|
491
|
|
|
492 /* first, use W taylor series I -> resp */
|
|
|
493 for (i=0; i<=p; i++)
|
|
|
494 { resp[i] = 0.0;
|
|
|
495 for (j=0; j<s; j++) resp[i] += wt[j]*I[i+j];
|
|
|
496 }
|
|
|
497
|
|
|
498 /* now, recenter x -> 0 */
|
|
|
499 if (x==0) return;
|
|
|
500 for (j=0; j<=p; j++) for (i=p; i>j; i--) resp[i] += x*resp[i-1];
|
|
|
501 }
|
|
|
502
|
|
|
503 void recurint(l0,l2,cf,resp,p,ker)
|
|
|
504 double l0, l2, *cf, *resp;
|
|
|
505 int p, ker;
|
|
|
506 { int i, s;
|
|
|
507 double l1, d0, d1, d2, dl, z0, z1, z2, wt[20], ncf[3], I[50], r1[5], r2[5];
|
|
|
508 if (debug) mut_printf("\nrecurint: %8.5f %8.5f %8.5f %8.5f %8.5f\n",cf[0],cf[1],cf[2],l0,l2);
|
|
|
509
|
|
|
510 if (cf[2]==0) /* go straight to explint1 */
|
|
|
511 { s = wtaylor(wt,0.0,ker);
|
|
|
512 if (debug) mut_printf("case 1\n");
|
|
|
513 explint1(l0,l2,cf,I,p+s);
|
|
|
514 recent(I,resp,wt,p,s,0.0);
|
|
|
515 return;
|
|
|
516 }
|
|
|
517
|
|
|
518 dl = l2-l0;
|
|
|
519 d0 = cf[1]+2*l0*cf[2];
|
|
|
520 d2 = cf[1]+2*l2*cf[2];
|
|
|
521 z0 = cf[0]+l0*(cf[1]+l0*cf[2]);
|
|
|
522 z2 = cf[0]+l2*(cf[1]+l2*cf[2]);
|
|
|
523
|
|
|
524 if ((fabs(cf[1]*dl)<1) && (fabs(cf[2]*dl*dl)<1))
|
|
|
525 { ncf[0] = z0; ncf[1] = d0; ncf[2] = cf[2];
|
|
|
526 if (debug) mut_printf("case 2\n");
|
|
|
527 s = wtaylor(wt,l0,ker);
|
|
|
528 explinbkr(0.0,dl,ncf,I,p+s);
|
|
|
529 recent(I,resp,wt,p,s,l0);
|
|
|
530 return;
|
|
|
531 }
|
|
|
532
|
|
|
533 if (fabs(cf[2]*dl*dl)<0.001) /* small c, use explint1+tay.ser */
|
|
|
534 { ncf[0] = z0; ncf[1] = d0; ncf[2] = cf[2];
|
|
|
535 if (debug) mut_printf("case small c\n");
|
|
|
536 s = wtaylor(wt,l0,ker);
|
|
|
537 explintyl(0.0,l2-l0,ncf,I,p+s);
|
|
|
538 recent(I,resp,wt,p,s,l0);
|
|
|
539 return;
|
|
|
540 }
|
|
|
541
|
|
|
542 if (d0*d2<=0) /* max/min in [l0,l2] */
|
|
|
543 { l1 = -cf[1]/(2*cf[2]);
|
|
|
544 z1 = cf[0]+l1*(cf[1]+l1*cf[2]);
|
|
|
545 d1 = 0.0;
|
|
|
546 if (cf[2]<0) /* peak, integrate around l1 */
|
|
|
547 { s = wtaylor(wt,l1,ker);
|
|
|
548 ncf[0] = z1; ncf[1] = 0.0; ncf[2] = cf[2];
|
|
|
549 if (debug) mut_printf("case peak p %2d s %2d\n",p,s);
|
|
|
550 explinfbk0(l0-l1,l2-l1,ncf,I,p+s);
|
|
|
551 recent(I,resp,wt,p,s,l1);
|
|
|
552 return;
|
|
|
553 }
|
|
|
554 }
|
|
|
555
|
|
|
556 if ((d0-2*cf[2]*dl)*(d2+2*cf[2]*dl)<0) /* max/min is close to [l0,l2] */
|
|
|
557 { l1 = -cf[1]/(2*cf[2]);
|
|
|
558 z1 = cf[0]+l1*(cf[1]+l1*cf[2]);
|
|
|
559 if (l1<l0) { l1 = l0; z1 = z0; }
|
|
|
560 if (l1>l2) { l1 = l2; z1 = z2; }
|
|
|
561
|
|
|
562 if ((z1>=z0) & (z1>=z2)) /* peak; integrate around l1 */
|
|
|
563 { s = wtaylor(wt,l1,ker);
|
|
|
564 if (debug) mut_printf("case 4\n");
|
|
|
565 d1 = cf[1]+2*l1*cf[2];
|
|
|
566 ncf[0] = z1; ncf[1] = d1; ncf[2] = cf[2];
|
|
|
567 explinfbk(l0-l1,l2-l1,ncf,I,p+s);
|
|
|
568 recent(I,resp,wt,p,s,l1);
|
|
|
569 return;
|
|
|
570 }
|
|
|
571
|
|
|
572 /* trough; integrate [l0,l1] and [l1,l2] */
|
|
|
573 for (i=0; i<=p; i++) r1[i] = r2[i] = 0.0;
|
|
|
574 if (l0<l1)
|
|
|
575 { s = wtaylor(wt,l0,ker);
|
|
|
576 if (debug) mut_printf("case 5\n");
|
|
|
577 ncf[0] = z0; ncf[1] = d0; ncf[2] = cf[2];
|
|
|
578 explinfbk(0.0,l1-l0,ncf,I,p+s);
|
|
|
579 recent(I,r1,wt,p,s,l0);
|
|
|
580 }
|
|
|
581 if (l1<l2)
|
|
|
582 { s = wtaylor(wt,l2,ker);
|
|
|
583 if (debug) mut_printf("case 6\n");
|
|
|
584 ncf[0] = z2; ncf[1] = d2; ncf[2] = cf[2];
|
|
|
585 explinfbk(l1-l2,0.0,ncf,I,p+s);
|
|
|
586 recent(I,r2,wt,p,s,l2);
|
|
|
587 }
|
|
|
588 for (i=0; i<=p; i++) resp[i] = r1[i]+r2[i];
|
|
|
589 return;
|
|
|
590 }
|
|
|
591
|
|
|
592 /* Now, quadratic is monotone on [l0,l2]; big b; moderate c */
|
|
|
593 if (z2>z0+3) /* steep increase, expand around l2 */
|
|
|
594 { s = wtaylor(wt,l2,ker);
|
|
|
595 if (debug) mut_printf("case 7\n");
|
|
|
596
|
|
|
597
|
|
|
598 ncf[0] = z2; ncf[1] = d2; ncf[2] = cf[2];
|
|
|
599 explinsid(l0-l2,0.0,ncf,I,p+s);
|
|
|
600 recent(I,resp,wt,p,s,l2);
|
|
|
601 if (debug) mut_printf("7 resp: %8.5f %8.5f %8.5f %8.5f\n",resp[0],resp[1],resp[2],resp[3]);
|
|
|
602 return;
|
|
|
603 }
|
|
|
604
|
|
|
605 /* bias towards expansion around l0, because it's often 0 */
|
|
|
606 if (debug) mut_printf("case 8\n");
|
|
|
607 s = wtaylor(wt,l0,ker);
|
|
|
608 ncf[0] = z0; ncf[1] = d0; ncf[2] = cf[2];
|
|
|
609 explinsid(0.0,l2-l0,ncf,I,p+s);
|
|
|
610 recent(I,resp,wt,p,s,l0);
|
|
|
611 return;
|
|
|
612 }
|
|
|
613
|
|
|
614 int onedexpl(cf,deg,resp)
|
|
|
615 double *cf, *resp;
|
|
|
616 int deg;
|
|
|
617 { int i;
|
|
|
618 double f0, fr, fl;
|
|
|
619 if (deg>=2) LERR(("onedexpl only valid for deg=0,1"));
|
|
|
620 if (fabs(cf[1])>=EFACT) return(LF_BADP);
|
|
|
621
|
|
|
622 f0 = exp(cf[0]); fl = fr = 1.0;
|
|
|
623 for (i=0; i<=2*deg; i++)
|
|
|
624 { f0 *= i+1;
|
|
|
625 fl /=-(EFACT+cf[1]);
|
|
|
626 fr /= EFACT-cf[1];
|
|
|
627 resp[i] = f0*(fr-fl);
|
|
|
628 }
|
|
|
629 return(LF_OK);
|
|
|
630 }
|
|
|
631
|
|
|
632 int onedgaus(cf,deg,resp)
|
|
|
633 double *cf, *resp;
|
|
|
634 int deg;
|
|
|
635 { int i;
|
|
|
636 double f0, mu, s2;
|
|
|
637 if (deg==3)
|
|
|
638 { LERR(("onedgaus only valid for deg=0,1,2"));
|
|
|
639 return(LF_ERR);
|
|
|
640 }
|
|
|
641 if (2*cf[2]>=GFACT*GFACT) return(LF_BADP);
|
|
|
642
|
|
|
643 s2 = 1/(GFACT*GFACT-2*cf[2]);
|
|
|
644 mu = cf[1]*s2;
|
|
|
645 resp[0] = 1.0;
|
|
|
646 if (deg>=1)
|
|
|
647 { resp[1] = mu;
|
|
|
648 resp[2] = s2+mu*mu;
|
|
|
649 if (deg==2)
|
|
|
650 { resp[3] = mu*(3*s2+mu*mu);
|
|
|
651 resp[4] = 3*s2*s2 + mu*mu*(6*s2+mu*mu);
|
|
|
652 }
|
|
|
653 }
|
|
|
654 f0 = S2PI * exp(cf[0]+mu*mu/(2*s2))*sqrt(s2);
|
|
|
655 for (i=0; i<=2*deg; i++) resp[i] *= f0;
|
|
|
656 return(LF_OK);
|
|
|
657 }
|
|
|
658
|
|
|
659 int onedint(sp,cf,l0,l1,resp) /* int W(u)u^j exp(..), j=0..2*deg */
|
|
|
660 smpar *sp;
|
|
|
661 double *cf, l0, l1, *resp;
|
|
|
662 { double u, uj, y, ncf[4], rr[5];
|
|
|
663 int i, j;
|
|
|
664
|
|
|
665 if (debug) mut_printf("onedint: %f %f %f %f %f\n",cf[0],cf[1],cf[2],l0,l1);
|
|
|
666
|
|
|
667 if (deg(sp)<=2)
|
|
|
668 { for (i=0; i<3; i++) ncf[i] = (i>deg(sp)) ? 0.0 : cf[i];
|
|
|
669 ncf[2] /= 2;
|
|
|
670
|
|
|
671 if (ker(sp)==WEXPL) return(onedexpl(ncf,deg(sp),resp));
|
|
|
672 if (ker(sp)==WGAUS) return(onedgaus(ncf,deg(sp),resp));
|
|
|
673
|
|
|
674 if (l1>0)
|
|
|
675 recurint(MAX(l0,0.0),l1,ncf,resp,2*deg(sp),ker(sp));
|
|
|
676 else for (i=0; i<=2*deg(sp); i++) resp[i] = 0;
|
|
|
677
|
|
|
678 if (l0<0)
|
|
|
679 { ncf[1] = -ncf[1];
|
|
|
680 l0 = -l0; l1 = -l1;
|
|
|
681 recurint(MAX(l1,0.0),l0,ncf,rr,2*deg(sp),ker(sp));
|
|
|
682 }
|
|
|
683 else for (i=0; i<=2*deg(sp); i++) rr[i] = 0.0;
|
|
|
684
|
|
|
685 for (i=0; i<=2*deg(sp); i++)
|
|
|
686 resp[i] += (i%2==0) ? rr[i] : -rr[i];
|
|
|
687
|
|
|
688 return(LF_OK);
|
|
|
689 }
|
|
|
690
|
|
|
691 /* For degree >= 3, we use Simpson's rule. */
|
|
|
692 for (j=0; j<=2*deg(sp); j++) resp[j] = 0.0;
|
|
|
693 for (i=0; i<=de_mint; i++)
|
|
|
694 { u = l0+(l1-l0)*i/de_mint;
|
|
|
695 y = cf[0]; uj = 1;
|
|
|
696 for (j=1; j<=deg(sp); j++)
|
|
|
697 { uj *= u;
|
|
|
698 y += cf[j]*uj/fact[j];
|
|
|
699 }
|
|
|
700 y = (4-2*(i%2==0)-(i==0)-(i==de_mint)) *
|
|
|
701 W(fabs(u),ker(sp))*exp(MIN(y,300.0));
|
|
|
702 for (j=0; j<=2*deg(sp); j++)
|
|
|
703 { resp[j] += y;
|
|
|
704 y *= u;
|
|
|
705 }
|
|
|
706 }
|
|
|
707 for (j=0; j<=2*deg(sp); j++) resp[j] = resp[j]*(l1-l0)/(3*de_mint);
|
|
|
708 return(LF_OK);
|
|
|
709 }
|
|
|
710 /*
|
|
|
711 * Copyright 1996-2006 Catherine Loader.
|
|
|
712 */
|
|
|
713 #include "locf.h"
|
|
|
714
|
|
|
715 extern int lf_status;
|
|
|
716 static double u[MXDIM], ilim[2*MXDIM], *ff, hh, *cff;
|
|
|
717 static lfdata *den_lfd;
|
|
|
718 static design *den_des;
|
|
|
719 static smpar *den_sp;
|
|
|
720 int fact[] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800};
|
|
|
721 int de_mint = 20;
|
|
|
722 int de_itype = IDEFA;
|
|
|
723 int de_renorm= 0;
|
|
|
724
|
|
|
725 int multint(), prodint(), gausint(), mlinint();
|
|
|
726
|
|
|
727 #define NITYPE 7
|
|
|
728 static char *itype[NITYPE] = { "default", "multi", "product", "mlinear",
|
|
|
729 "hazard", "sphere", "monte" };
|
|
|
730 static int ivals[NITYPE] =
|
|
|
731 { IDEFA, IMULT, IPROD, IMLIN, IHAZD, ISPHR, IMONT };
|
|
|
732 int deitype(char *z)
|
|
|
733 { return(pmatch(z, itype, ivals, NITYPE, IDEFA));
|
|
|
734 }
|
|
|
735
|
|
|
736 void prresp(coef,resp,p)
|
|
|
737 double *coef, *resp;
|
|
|
738 int p;
|
|
|
739 { int i, j;
|
|
|
740 mut_printf("Coefficients:\n");
|
|
|
741 for (i=0; i<p; i++) mut_printf("%8.5f ",coef[i]);
|
|
|
742 mut_printf("\n");
|
|
|
743 mut_printf("Response matrix:\n");
|
|
|
744 for (i=0; i<p; i++)
|
|
|
745 { for (j=0; j<p; j++) mut_printf("%9.6f, ",resp[i+j*p]);
|
|
|
746 mut_printf("\n");
|
|
|
747 }
|
|
|
748 }
|
|
|
749
|
|
|
750 int mif(u,d,resp,M)
|
|
|
751 double *u, *resp, *M;
|
|
|
752 int d;
|
|
|
753 { double wt;
|
|
|
754 int i, j, p;
|
|
|
755
|
|
|
756 p = den_des->p;
|
|
|
757 wt = weight(den_lfd, den_sp, u, NULL, hh, 0, 0.0);
|
|
|
758 if (wt==0)
|
|
|
759 { setzero(resp,p*p);
|
|
|
760 return(p*p);
|
|
|
761 }
|
|
|
762
|
|
|
763 fitfun(den_lfd, den_sp, u,NULL,ff,NULL);
|
|
|
764 if (link(den_sp)==LLOG)
|
|
|
765 wt *= mut_exp(innerprod(ff,cff,p));
|
|
|
766 for (i=0; i<p; i++)
|
|
|
767 for (j=0; j<p; j++)
|
|
|
768 resp[i*p+j] = wt*ff[i]*ff[j];
|
|
|
769 return(p*p);
|
|
|
770 }
|
|
|
771
|
|
|
772 int multint(t,resp1,resp2,cf,h)
|
|
|
773 double *t, *resp1, *resp2, *cf, h;
|
|
|
774 { int d, i, mg[MXDIM];
|
|
|
775
|
|
|
776 if (ker(den_sp)==WGAUS) return(gausint(t,resp1,resp2,cf,h,den_lfd->sca));
|
|
|
777
|
|
|
778 d = den_lfd->d;
|
|
|
779 for (i=0; i<d; i++) mg[i] = de_mint;
|
|
|
780
|
|
|
781 hh = h;
|
|
|
782 cff= cf;
|
|
|
783 simpsonm(mif,ilim,&ilim[d],d,resp1,mg,resp2);
|
|
|
784 return(LF_OK);
|
|
|
785 }
|
|
|
786
|
|
|
787 int mlinint(t,resp1,resp2,cf,h)
|
|
|
788 double *t, *resp1, *resp2, *cf, h;
|
|
|
789 {
|
|
|
790 double hd, nb, wt, wu, g[4], w0, w1, v, *sca;
|
|
|
791 int d, p, i, j, jmax, k, l, z, jj[2];
|
|
|
792
|
|
|
793 d = den_lfd->d; p = den_des->p; sca = den_lfd->sca;
|
|
|
794 hd = 1;
|
|
|
795 for (i=0; i<d; i++) hd *= h*sca[i];
|
|
|
796
|
|
|
797 if (link(den_sp)==LIDENT)
|
|
|
798 { setzero(resp1,p*p);
|
|
|
799 resp1[0] = wint(d,NULL,0,ker(den_sp))*hd;
|
|
|
800 if (deg(den_sp)==0) return(LF_OK);
|
|
|
801 jj[0] = 2; w0 = wint(d,jj,1,ker(den_sp))*hd*h*h;
|
|
|
802 for (i=0; i<d; i++) resp1[(i+1)*p+i+1] = w0*sca[i]*sca[i];
|
|
|
803 if (deg(den_sp)==1) return(LF_OK);
|
|
|
804 for (i=0; i<d; i++)
|
|
|
805 { j = p-(d-i)*(d-i+1)/2;
|
|
|
806 resp1[j] = resp1[p*j] = w0*sca[i]*sca[i]/2;
|
|
|
807 }
|
|
|
808 if (d>1)
|
|
|
809 { jj[1] = 2;
|
|
|
810 w0 = wint(d,jj,2,ker(den_sp)) * hd*h*h*h*h;
|
|
|
811 }
|
|
|
812 jj[0] = 4;
|
|
|
813 w1 = wint(d,jj,1,ker(den_sp)) * hd*h*h*h*h/4;
|
|
|
814 z = d+1;
|
|
|
815 for (i=0; i<d; i++)
|
|
|
816 { k = p-(d-i)*(d-i+1)/2;
|
|
|
817 for (j=i; j<d; j++)
|
|
|
818 { l = p-(d-j)*(d-j+1)/2;
|
|
|
819 if (i==j) resp1[z*p+z] = w1*SQR(sca[i])*SQR(sca[i]);
|
|
|
820 else
|
|
|
821 { resp1[z*p+z] = w0*SQR(sca[i])*SQR(sca[j]);
|
|
|
822 resp1[k*p+l] = resp1[k+p*l] = w0/4*SQR(sca[i])*SQR(sca[j]);
|
|
|
823 }
|
|
|
824 z++;
|
|
|
825 } }
|
|
|
826 return(LF_OK);
|
|
|
827 }
|
|
|
828 switch(deg(den_sp))
|
|
|
829 { case 0:
|
|
|
830 resp1[0] = mut_exp(cf[0])*wint(d,NULL,0,ker(den_sp))*hd;
|
|
|
831 return(LF_OK);
|
|
|
832 case 1:
|
|
|
833 nb = 0.0;
|
|
|
834 for (i=1; i<=d; i++)
|
|
|
835 { v = h*cf[i]*sca[i-1];
|
|
|
836 nb += v*v;
|
|
|
837 }
|
|
|
838 if (ker(den_sp)==WGAUS)
|
|
|
839 { w0 = 1/(GFACT*GFACT);
|
|
|
840 g[0] = mut_exp(cf[0]+w0*nb/2+d*log(S2PI/2.5));
|
|
|
841 g[1] = g[3] = g[0]*w0;
|
|
|
842 g[2] = g[0]*w0*w0;
|
|
|
843 }
|
|
|
844 else
|
|
|
845 { wt = wu = mut_exp(cf[0]);
|
|
|
846 w0 = wint(d,NULL,0,ker(den_sp)); g[0] = wt*w0;
|
|
|
847 g[1] = g[2] = g[3] = 0.0;
|
|
|
848 j = 0; jmax = (d+2)*de_mint;
|
|
|
849 while ((j<jmax) && (wt*w0/g[0]>1.0e-8))
|
|
|
850 { j++;
|
|
|
851 jj[0] = 2*j; w0 = wint(d,jj,1,ker(den_sp));
|
|
|
852 if (d==1) g[3] += wt * w0;
|
|
|
853 else
|
|
|
854 { jj[0] = 2; jj[1] = 2*j-2; w1 = wint(d,jj,2,ker(den_sp));
|
|
|
855 g[3] += wt*w1;
|
|
|
856 g[2] += wu*(w0-w1);
|
|
|
857 }
|
|
|
858 wt /= (2*j-1.0); g[1] += wt*w0;
|
|
|
859 wt *= nb/(2*j); g[0] += wt*w0;
|
|
|
860 wu /= (2*j-1.0)*(2*j);
|
|
|
861 if (j>1) wu *= nb;
|
|
|
862 }
|
|
|
863 if (j==jmax) WARN(("mlinint: series not converged"));
|
|
|
864 }
|
|
|
865 g[0] *= hd; g[1] *= hd;
|
|
|
866 g[2] *= hd; g[3] *= hd;
|
|
|
867 resp1[0] = g[0];
|
|
|
868 for (i=1; i<=d; i++)
|
|
|
869 { resp1[i] = resp1[(d+1)*i] = cf[i]*SQR(h*sca[i-1])*g[1];
|
|
|
870 for (j=1; j<=d; j++)
|
|
|
871 { resp1[(d+1)*i+j] = (i==j) ? g[3]*SQR(h*sca[i-1]) : 0;
|
|
|
872 resp1[(d+1)*i+j] += g[2]*SQR(h*h*sca[i-1]*sca[j-1])*cf[i]*cf[j];
|
|
|
873 }
|
|
|
874 }
|
|
|
875 return(LF_OK);
|
|
|
876 }
|
|
|
877 LERR(("mlinint: deg=0,1 only"));
|
|
|
878 return(LF_ERR);
|
|
|
879 }
|
|
|
880
|
|
|
881 void prodintresp(resp,prod_wk,dim,deg,p)
|
|
|
882 double *resp, prod_wk[MXDIM][2*MXDEG+1];
|
|
|
883 int dim, deg, p;
|
|
|
884 { double prod;
|
|
|
885 int i, j, k, j1, k1;
|
|
|
886
|
|
|
887 prod = 1.0;
|
|
|
888 for (i=0; i<dim; i++) prod *= prod_wk[i][0];
|
|
|
889 resp[0] += prod;
|
|
|
890 if (deg==0) return;
|
|
|
891
|
|
|
892 for (j1=1; j1<=deg; j1++)
|
|
|
893 { for (j=0; j<dim; j++)
|
|
|
894 { prod = 1.0;
|
|
|
895 for (i=0; i<dim; i++) prod *= prod_wk[i][j1*(j==i)];
|
|
|
896 prod /= fact[j1];
|
|
|
897 resp[1 + (j1-1)*dim +j] += prod;
|
|
|
898 }
|
|
|
899 }
|
|
|
900
|
|
|
901 for (k1=1; k1<=deg; k1++)
|
|
|
902 for (j1=k1; j1<=deg; j1++)
|
|
|
903 { for (k=0; k<dim; k++)
|
|
|
904 for (j=0; j<dim; j++)
|
|
|
905 { prod = 1.0;
|
|
|
906 for (i=0; i<dim; i++) prod *= prod_wk[i][k1*(k==i) + j1*(j==i)];
|
|
|
907 prod /= fact[k1]*fact[j1];
|
|
|
908 resp[ (1+(k1-1)*dim+k)*p + 1+(j1-1)*dim+j] += prod;
|
|
|
909 }
|
|
|
910 }
|
|
|
911 }
|
|
|
912
|
|
|
913 int prodint(t,resp,resp2,coef,h)
|
|
|
914 double *t, *resp, *resp2, *coef, h;
|
|
|
915 { int dim, p, i, j, k, st;
|
|
|
916 double cf[MXDEG+1], hj, hs, prod_wk[MXDIM][2*MXDEG+1];
|
|
|
917
|
|
|
918 dim = den_lfd->d;
|
|
|
919 p = den_des->p;
|
|
|
920 for (i=0; i<p*p; i++) resp[i] = 0.0;
|
|
|
921 cf[0] = coef[0];
|
|
|
922
|
|
|
923 /* compute the one dimensional terms
|
|
|
924 */
|
|
|
925 for (i=0; i<dim; i++)
|
|
|
926 { hj = 1; hs = h*den_lfd->sca[i];
|
|
|
927 for (j=0; j<deg(den_sp); j++)
|
|
|
928 { hj *= hs;
|
|
|
929 cf[j+1] = hj*coef[ j*dim+i+1 ];
|
|
|
930 }
|
|
|
931 st = onedint(den_sp,cf,ilim[i]/hs,ilim[i+dim]/hs,prod_wk[i]);
|
|
|
932 if (st==LF_BADP) return(st);
|
|
|
933 hj = 1;
|
|
|
934 for (j=0; j<=2*deg(den_sp); j++)
|
|
|
935 { hj *= hs;
|
|
|
936 prod_wk[i][j] *= hj;
|
|
|
937 }
|
|
|
938 cf[0] = 0.0; /* so we only include it once, when d>=2 */
|
|
|
939 }
|
|
|
940
|
|
|
941 /* transfer to the resp array
|
|
|
942 */
|
|
|
943 prodintresp(resp,prod_wk,dim,deg(den_sp),p);
|
|
|
944
|
|
|
945 /* Symmetrize.
|
|
|
946 */
|
|
|
947 for (k=0; k<p; k++)
|
|
|
948 for (j=k; j<p; j++)
|
|
|
949 resp[j*p+k] = resp[k*p+j];
|
|
|
950
|
|
|
951 return(st);
|
|
|
952 }
|
|
|
953
|
|
|
954 int gausint(t,resp,C,cf,h,sca)
|
|
|
955 double *t, *resp, *C, *cf, h, *sca;
|
|
|
956 { double nb, det, z, *P;
|
|
|
957 int d, p, i, j, k, l, m1, m2, f;
|
|
|
958 d = den_lfd->d; p = den_des->p;
|
|
|
959 m1 = d+1; nb = 0;
|
|
|
960 P = &C[d*d];
|
|
|
961 resp[0] = 1;
|
|
|
962 for (i=0; i<d; i++)
|
|
|
963 { C[i*d+i] = SQR(GFACT/(h*sca[i]))-cf[m1++];
|
|
|
964 for (j=i+1; j<d; j++) C[i*d+j] = C[j*d+i] = -cf[m1++];
|
|
|
965 }
|
|
|
966 eig_dec(C,P,d);
|
|
|
967 det = 1;
|
|
|
968 for (i=1; i<=d; i++)
|
|
|
969 { det *= C[(i-1)*(d+1)];
|
|
|
970 if (det <= 0) return(LF_BADP);
|
|
|
971 resp[i] = cf[i];
|
|
|
972 for (j=1; j<=d; j++) resp[j+i*p] = 0;
|
|
|
973 resp[i+i*p] = 1;
|
|
|
974 svdsolve(&resp[i*p+1],u,P,C,P,d,0.0);
|
|
|
975 }
|
|
|
976 svdsolve(&resp[1],u,P,C,P,d,0.0);
|
|
|
977 det = sqrt(det);
|
|
|
978 for (i=1; i<=d; i++)
|
|
|
979 { nb += cf[i]*resp[i];
|
|
|
980 resp[i*p] = resp[i];
|
|
|
981 for (j=1; j<=d; j++)
|
|
|
982 resp[i+p*j] += resp[i]*resp[j];
|
|
|
983 }
|
|
|
984 m1 = d;
|
|
|
985 for (i=1; i<=d; i++)
|
|
|
986 for (j=i; j<=d; j++)
|
|
|
987 { m1++; f = 1+(i==j);
|
|
|
988 resp[m1] = resp[m1*p] = resp[i*p+j]/f;
|
|
|
989 m2 = d;
|
|
|
990 for (k=1; k<=d; k++)
|
|
|
991 { resp[m1+k*p] = resp[k+m1*p] =
|
|
|
992 ( resp[i]*resp[j*p+k] + resp[j]*resp[i*p+k]
|
|
|
993 + resp[k]*resp[i*p+j] - 2*resp[i]*resp[j]*resp[k] )/f;
|
|
|
994 for (l=k; l<=d; l++)
|
|
|
995 { m2++; f = (1+(i==j))*(1+(k==l));
|
|
|
996 resp[m1+m2*p] = resp[m2+m1*p] = ( resp[i+j*p]*resp[k+l*p]
|
|
|
997 + resp[i+k*p]*resp[j+l*p] + resp[i+l*p]*resp[j+k*p]
|
|
|
998 - 2*resp[i]*resp[j]*resp[k]*resp[l] )/f;
|
|
|
999 } } }
|
|
|
1000 z = mut_exp(d*0.918938533+cf[0]+nb/2)/det;
|
|
|
1001 multmatscal(resp,z,p*p);
|
|
|
1002 return(LF_OK);
|
|
|
1003 }
|
|
|
1004
|
|
|
1005 int likeden(coef, lk0, f1, A)
|
|
|
1006 double *coef, *lk0, *f1, *A;
|
|
|
1007 { double lk, r;
|
|
|
1008 int i, j, p, rstat;
|
|
|
1009
|
|
|
1010 lf_status = LF_OK;
|
|
|
1011 p = den_des->p;
|
|
|
1012 if ((link(den_sp)==LIDENT) && (coef[0] != 0.0)) return(NR_BREAK);
|
|
|
1013 lf_status = (den_des->itype)(den_des->xev,A,den_des->xtwx.Q,coef,den_des->h);
|
|
|
1014 if (lf_error) lf_status = LF_ERR;
|
|
|
1015 if (lf_status==LF_BADP)
|
|
|
1016 { *lk0 = -1.0e300;
|
|
|
1017 return(NR_REDUCE);
|
|
|
1018 }
|
|
|
1019 if (lf_status!=LF_OK) return(NR_BREAK);
|
|
|
1020 if (lf_debug>2) prresp(coef,A,p);
|
|
|
1021
|
|
|
1022 den_des->xtwx.p = p;
|
|
|
1023 rstat = NR_OK;
|
|
|
1024 switch(link(den_sp))
|
|
|
1025 { case LLOG:
|
|
|
1026 r = den_des->ss[0]/A[0];
|
|
|
1027 coef[0] += log(r);
|
|
|
1028 multmatscal(A,r,p*p);
|
|
|
1029 A[0] = den_des->ss[0];
|
|
|
1030 lk = -A[0];
|
|
|
1031 if (fabs(coef[0]) > 700)
|
|
|
1032 { lf_status = LF_OOB;
|
|
|
1033 rstat = NR_REDUCE;
|
|
|
1034 }
|
|
|
1035 for (i=0; i<p; i++)
|
|
|
1036 { lk += coef[i]*den_des->ss[i];
|
|
|
1037 f1[i] = den_des->ss[i]-A[i];
|
|
|
1038 }
|
|
|
1039 break;
|
|
|
1040 case LIDENT:
|
|
|
1041 lk = 0.0;
|
|
|
1042 for (i=0; i<p; i++)
|
|
|
1043 { f1[i] = den_des->ss[i];
|
|
|
1044 for (j=0; j<p; j++)
|
|
|
1045 den_des->res[i] -= A[i*p+j]*coef[j];
|
|
|
1046 }
|
|
|
1047 break;
|
|
|
1048 }
|
|
|
1049 *lk0 = den_des->llk = lk;
|
|
|
1050
|
|
|
1051 return(rstat);
|
|
|
1052 }
|
|
|
1053
|
|
|
1054 int inre(x,bound,d)
|
|
|
1055 double *x, *bound;
|
|
|
1056 int d;
|
|
|
1057 { int i, z;
|
|
|
1058 z = 1;
|
|
|
1059 for (i=0; i<d; i++)
|
|
|
1060 if (bound[i]<bound[i+d])
|
|
|
1061 z &= (x[i]>=bound[i]) & (x[i]<=bound[i+d]);
|
|
|
1062 return(z);
|
|
|
1063 }
|
|
|
1064
|
|
|
1065 int setintlimits(lfd, x, h, ang, lset)
|
|
|
1066 lfdata *lfd;
|
|
|
1067 int *ang, *lset;
|
|
|
1068 double *x, h;
|
|
|
1069 { int d, i;
|
|
|
1070 d = lfd->d;
|
|
|
1071 *ang = *lset = 0;
|
|
|
1072 for (i=0; i<d; i++)
|
|
|
1073 { if (lfd->sty[i]==STANGL)
|
|
|
1074 { ilim[i+d] = ((h<2) ? 2*asin(h/2) : PI)*lfd->sca[i];
|
|
|
1075 ilim[i] = -ilim[i+d];
|
|
|
1076 *ang = 1;
|
|
|
1077 }
|
|
|
1078 else
|
|
|
1079 { ilim[i+d] = h*lfd->sca[i];
|
|
|
1080 ilim[i] = -ilim[i+d];
|
|
|
1081
|
|
|
1082 if (lfd->sty[i]==STLEFT) { ilim[i+d] = 0; *lset = 1; }
|
|
|
1083 if (lfd->sty[i]==STRIGH) { ilim[i] = 0; *lset = 1; }
|
|
|
1084
|
|
|
1085 if (lfd->xl[i]<lfd->xl[i+d]) /* user limits for this variable */
|
|
|
1086 { if (lfd->xl[i]-x[i]> ilim[i])
|
|
|
1087 { ilim[i] = lfd->xl[i]-x[i]; *lset=1; }
|
|
|
1088 if (lfd->xl[i+d]-x[i]< ilim[i+d])
|
|
|
1089 { ilim[i+d] = lfd->xl[i+d]-x[i]; *lset=1; }
|
|
|
1090 }
|
|
|
1091 }
|
|
|
1092 if (ilim[i]==ilim[i+d]) return(LF_DEMP); /* empty integration */
|
|
|
1093 }
|
|
|
1094 return(LF_OK);
|
|
|
1095 }
|
|
|
1096
|
|
|
1097 int selectintmeth(itype,lset,ang)
|
|
|
1098 int itype, lset, ang;
|
|
|
1099 {
|
|
|
1100 if (itype==IDEFA) /* select the default method */
|
|
|
1101 { if (fam(den_sp)==THAZ)
|
|
|
1102 { if (ang) return(IDEFA);
|
|
|
1103 return( IHAZD );
|
|
|
1104 }
|
|
|
1105
|
|
|
1106 if (ubas(den_sp)) return(IMULT);
|
|
|
1107
|
|
|
1108 if (ang) return(IMULT);
|
|
|
1109
|
|
|
1110 if (iscompact(ker(den_sp)))
|
|
|
1111 { if (kt(den_sp)==KPROD) return(IPROD);
|
|
|
1112 if (lset)
|
|
|
1113 return( (den_lfd->d==1) ? IPROD : IMULT );
|
|
|
1114 if (deg(den_sp)<=1) return(IMLIN);
|
|
|
1115 if (den_lfd->d==1) return(IPROD);
|
|
|
1116 return(IMULT);
|
|
|
1117 }
|
|
|
1118
|
|
|
1119 if (ker(den_sp)==WGAUS)
|
|
|
1120 { if (lset) WARN(("Integration for Gaussian weights ignores limits"));
|
|
|
1121 if ((den_lfd->d==1)|(kt(den_sp)==KPROD)) return(IPROD);
|
|
|
1122 if (deg(den_sp)<=1) return(IMLIN);
|
|
|
1123 if (deg(den_sp)==2) return(IMULT);
|
|
|
1124 }
|
|
|
1125
|
|
|
1126 return(IDEFA);
|
|
|
1127 }
|
|
|
1128
|
|
|
1129 /* user provided an integration method, check it is valid */
|
|
|
1130
|
|
|
1131 if (fam(den_sp)==THAZ)
|
|
|
1132 { if (ang) return(INVLD);
|
|
|
1133 if (!iscompact(ker(den_sp))) return(INVLD);
|
|
|
1134 return( ((kt(den_sp)==KPROD) | (kt(den_sp)==KSPH)) ? IHAZD : INVLD );
|
|
|
1135 }
|
|
|
1136
|
|
|
1137 if ((ang) && (itype != IMULT)) return(INVLD);
|
|
|
1138
|
|
|
1139 switch(itype)
|
|
|
1140 { case IMULT:
|
|
|
1141 if (ker(den_sp)==WGAUS) return(deg(den_sp)==2);
|
|
|
1142 return( iscompact(ker(den_sp)) ? IMULT : INVLD );
|
|
|
1143 case IPROD: return( ((den_lfd->d==1) | (kt(den_sp)==KPROD)) ? IPROD : INVLD );
|
|
|
1144 case IMLIN: return( ((kt(den_sp)==KSPH) && (!lset) &&
|
|
|
1145 (deg(den_sp)<=1)) ? IMLIN : INVLD );
|
|
|
1146 }
|
|
|
1147
|
|
|
1148 return(INVLD);
|
|
|
1149 }
|
|
|
1150
|
|
|
1151 extern double lf_tol;
|
|
|
1152
|
|
|
1153 int densinit(lfd,des,sp)
|
|
|
1154 lfdata *lfd;
|
|
|
1155 design *des;
|
|
|
1156 smpar *sp;
|
|
|
1157 { int p, i, ii, j, nnz, rnz, ang, lset, status;
|
|
|
1158 double w, *cf;
|
|
|
1159
|
|
|
1160 den_lfd = lfd;
|
|
|
1161 den_des = des;
|
|
|
1162 den_sp = sp;
|
|
|
1163 cf = des->cf;
|
|
|
1164
|
|
|
1165 lf_tol = (link(sp)==LLOG) ? 1.0e-6 : 0.0;
|
|
|
1166
|
|
|
1167 p = des->p;
|
|
|
1168 ff = des->xtwx.wk;
|
|
|
1169 cf[0] = NOSLN;
|
|
|
1170 for (i=1; i<p; i++) cf[i] = 0.0;
|
|
|
1171
|
|
|
1172 if (!inre(des->xev,lfd->xl,lfd->d)) return(LF_XOOR);
|
|
|
1173
|
|
|
1174 status = setintlimits(lfd,des->xev,des->h,&ang,&lset);
|
|
|
1175 if (status != LF_OK) return(status);
|
|
|
1176
|
|
|
1177 switch(selectintmeth(de_itype,lset,ang))
|
|
|
1178 { case IMULT: des->itype = multint; break;
|
|
|
1179 case IPROD: des->itype = prodint; break;
|
|
|
1180 case IMLIN: des->itype = mlinint; break;
|
|
|
1181 case IHAZD: des->itype = hazint; break;
|
|
|
1182 case INVLD: LERR(("Invalid integration method %d",de_itype));
|
|
|
1183 break;
|
|
|
1184 case IDEFA: LERR(("No integration type available for this model"));
|
|
|
1185 break;
|
|
|
1186 default: LERR(("densinit: unknown integral type"));
|
|
|
1187 }
|
|
|
1188
|
|
|
1189 switch(deg(den_sp))
|
|
|
1190 { case 0: rnz = 1; break;
|
|
|
1191 case 1: rnz = 1; break;
|
|
|
1192 case 2: rnz = lfd->d+1; break;
|
|
|
1193 case 3: rnz = lfd->d+2; break;
|
|
|
1194 default: LERR(("densinit: invalid degree %d",deg(den_sp)));
|
|
|
1195 }
|
|
|
1196 if (lf_error) return(LF_ERR);
|
|
|
1197
|
|
|
1198 setzero(des->ss,p);
|
|
|
1199 nnz = 0;
|
|
|
1200 for (i=0; i<des->n; i++)
|
|
|
1201 { ii = des->ind[i];
|
|
|
1202 if (!cens(lfd,ii))
|
|
|
1203 { w = wght(des,ii)*prwt(lfd,ii);
|
|
|
1204 for (j=0; j<p; j++) des->ss[j] += d_xij(des,ii,j)*w;
|
|
|
1205 if (wght(des,ii)>0.00001) nnz++;
|
|
|
1206 } }
|
|
|
1207
|
|
|
1208 if (fam(den_sp)==THAZ) haz_init(lfd,des,sp,ilim);
|
|
|
1209 /* this should really only be done once. Not sure how to enforce that,
|
|
|
1210 * esp. when locfit() has been called directly.
|
|
|
1211 */
|
|
|
1212 if (fam(den_sp)==TDEN)
|
|
|
1213 des->smwt = (lfd->w==NULL) ? lfd->n : vecsum(lfd->w,lfd->n);
|
|
|
1214
|
|
|
1215 if (lf_debug>2)
|
|
|
1216 { mut_printf(" LHS: ");
|
|
|
1217 for (i=0; i<p; i++) mut_printf(" %8.5f",des->ss[i]);
|
|
|
1218 mut_printf("\n");
|
|
|
1219 }
|
|
|
1220
|
|
|
1221 switch(link(den_sp))
|
|
|
1222 { case LIDENT:
|
|
|
1223 cf[0] = 0.0;
|
|
|
1224 return(LF_OK);
|
|
|
1225 case LLOG:
|
|
|
1226 if (nnz<rnz) { cf[0] = -1000; return(LF_DNOP); }
|
|
|
1227 cf[0] = 0.0;
|
|
|
1228 return(LF_OK);
|
|
|
1229 default:
|
|
|
1230 LERR(("unknown link in densinit"));
|
|
|
1231 return(LF_ERR);
|
|
|
1232 }
|
|
|
1233 }
|
|
|
1234 /*
|
|
|
1235 * Copyright 1996-2006 Catherine Loader.
|
|
|
1236 */
|
|
|
1237 #include "locf.h"
|
|
|
1238
|
|
|
1239 int bino_vallink(link)
|
|
|
1240 int link;
|
|
|
1241 { return((link==LLOGIT) | (link==LIDENT) | (link==LASIN));
|
|
|
1242 }
|
|
|
1243
|
|
|
1244 int bino_fam(y,p,th,link,res,cens,w)
|
|
|
1245 double y, p, th, *res, w;
|
|
|
1246 int link, cens;
|
|
|
1247 { double wp;
|
|
|
1248 if (link==LINIT)
|
|
|
1249 { if (y<0) y = 0;
|
|
|
1250 if (y>w) y = w;
|
|
|
1251 res[ZDLL] = y;
|
|
|
1252 return(LF_OK);
|
|
|
1253 }
|
|
|
1254 wp = w*p;
|
|
|
1255 if (link==LIDENT)
|
|
|
1256 { if ((p<=0) && (y>0)) return(LF_BADP);
|
|
|
1257 if ((p>=1) && (y<w)) return(LF_BADP);
|
|
|
1258 res[ZLIK] = res[ZDLL] = res[ZDDLL] = 0.0;
|
|
|
1259 if (y>0)
|
|
|
1260 { res[ZLIK] += y*log(wp/y);
|
|
|
1261 res[ZDLL] += y/p;
|
|
|
1262 res[ZDDLL]+= y/(p*p);
|
|
|
1263 }
|
|
|
1264 if (y<w)
|
|
|
1265 { res[ZLIK] += (w-y)*log((w-wp)/(w-y));
|
|
|
1266 res[ZDLL] -= (w-y)/(1-p);
|
|
|
1267 res[ZDDLL]+= (w-y)/SQR(1-p);
|
|
|
1268 }
|
|
|
1269 return(LF_OK);
|
|
|
1270 }
|
|
|
1271 if (link==LLOGIT)
|
|
|
1272 { if ((y<0) | (y>w)) /* goon observation; delete it */
|
|
|
1273 { res[ZLIK] = res[ZDLL] = res[ZDDLL] = 0.0;
|
|
|
1274 return(LF_OK);
|
|
|
1275 }
|
|
|
1276 res[ZLIK] = (th<0) ? th*y-w*log(1+exp(th)) : th*(y-w)-w*log(1+exp(-th));
|
|
|
1277 if (y>0) res[ZLIK] -= y*log(y/w);
|
|
|
1278 if (y<w) res[ZLIK] -= (w-y)*log(1-y/w);
|
|
|
1279 res[ZDLL] = (y-wp);
|
|
|
1280 res[ZDDLL]= wp*(1-p);
|
|
|
1281 return(LF_OK);
|
|
|
1282 }
|
|
|
1283 if (link==LASIN)
|
|
|
1284 { if ((p<=0) && (y>0)) return(LF_BADP);
|
|
|
1285 if ((p>=1) && (y<w)) return(LF_BADP);
|
|
|
1286 if ((th<0) | (th>PI/2)) return(LF_BADP);
|
|
|
1287 res[ZDLL] = res[ZDDLL] = res[ZLIK] = 0;
|
|
|
1288 if (y>0)
|
|
|
1289 { res[ZDLL] += 2*y*sqrt((1-p)/p);
|
|
|
1290 res[ZLIK] += y*log(wp/y);
|
|
|
1291 }
|
|
|
1292 if (y<w)
|
|
|
1293 { res[ZDLL] -= 2*(w-y)*sqrt(p/(1-p));
|
|
|
1294 res[ZLIK] += (w-y)*log((w-wp)/(w-y));
|
|
|
1295 }
|
|
|
1296 res[ZDDLL] = 4*w;
|
|
|
1297 return(LF_OK);
|
|
|
1298 }
|
|
|
1299 LERR(("link %d invalid for binomial family",link));
|
|
|
1300 return(LF_LNK);
|
|
|
1301 }
|
|
|
1302
|
|
|
1303 int bino_check(sp,des,lfd)
|
|
|
1304 smpar *sp;
|
|
|
1305 design *des;
|
|
|
1306 lfdata *lfd;
|
|
|
1307 { int i, ii;
|
|
|
1308 double t0, t1;
|
|
|
1309
|
|
|
1310 if (fabs(des->cf[0])>700) return(LF_OOB);
|
|
|
1311
|
|
|
1312 /* check for separation.
|
|
|
1313 * this won't detect separation if there's boundary points with
|
|
|
1314 * both 0 and 1 responses.
|
|
|
1315 */
|
|
|
1316 t0 = -1e100; t1 = 1e100;
|
|
|
1317 for (i=0; i<des->n; i++)
|
|
|
1318 { ii = des->ind[i];
|
|
|
1319 if ((resp(lfd,ii)<prwt(lfd,ii)) && (fitv(des,ii) > t0)) t0 = fitv(des,ii);
|
|
|
1320 if ((resp(lfd,ii)>0) && (fitv(des,ii) < t1)) t1 = fitv(des,ii);
|
|
|
1321 if (t1 <= t0) return(LF_OK);
|
|
|
1322 }
|
|
|
1323 mut_printf("separated %8.5f %8.5f\n",t0,t1);
|
|
|
1324 return(LF_NSLN);
|
|
|
1325 }
|
|
|
1326
|
|
|
1327 void setfbino(fam)
|
|
|
1328 family *fam;
|
|
|
1329 { fam->deflink = LLOGIT;
|
|
|
1330 fam->canlink = LLOGIT;
|
|
|
1331 fam->vallink = bino_vallink;
|
|
|
1332 fam->family = bino_fam;
|
|
|
1333 fam->pcheck = bino_check;
|
|
|
1334 }
|
|
|
1335
|
|
|
1336 int rbin_vallink(link)
|
|
|
1337 int link;
|
|
|
1338 { return(link==LLOGIT);
|
|
|
1339 }
|
|
|
1340
|
|
|
1341 int rbin_fam(y,p,th,link,res,cens,w)
|
|
|
1342 double y, p, th, *res, w;
|
|
|
1343 int link, cens;
|
|
|
1344 { double s2y;
|
|
|
1345 if (link==LINIT)
|
|
|
1346 { res[ZDLL] = y;
|
|
|
1347 return(LF_OK);
|
|
|
1348 }
|
|
|
1349 if ((y<0) | (y>w)) /* goon observation; delete it */
|
|
|
1350 { res[ZLIK] = res[ZDLL] = res[ZDDLL] = 0.0;
|
|
|
1351 return(LF_OK);
|
|
|
1352 }
|
|
|
1353 res[ZLIK] = (th<0) ? th*y-w*log(1+exp(th)) : th*(y-w)-w*log(1+exp(-th));
|
|
|
1354 if (y>0) res[ZLIK] -= y*log(y/w);
|
|
|
1355 if (y<w) res[ZLIK] -= (w-y)*log(1-y/w);
|
|
|
1356 res[ZDLL] = (y-w*p);
|
|
|
1357 res[ZDDLL]= w*p*(1-p);
|
|
|
1358 if (-res[ZLIK]>HUBERC*HUBERC/2.0)
|
|
|
1359 { s2y = sqrt(-2*res[ZLIK]);
|
|
|
1360 res[ZLIK] = HUBERC*(HUBERC/2.0-s2y);
|
|
|
1361 res[ZDLL] *= HUBERC/s2y;
|
|
|
1362 res[ZDDLL] = HUBERC/s2y*(res[ZDDLL]-1/(s2y*s2y)*w*p*(1-p));
|
|
|
1363 }
|
|
|
1364 return(LF_OK);
|
|
|
1365 }
|
|
|
1366
|
|
|
1367 void setfrbino(fam)
|
|
|
1368 family *fam;
|
|
|
1369 { fam->deflink = LLOGIT;
|
|
|
1370 fam->canlink = LLOGIT;
|
|
|
1371 fam->vallink = rbin_vallink;
|
|
|
1372 fam->family = rbin_fam;
|
|
|
1373 fam->pcheck = bino_check;
|
|
|
1374 }
|
|
|
1375 /*
|
|
|
1376 * Copyright 1996-2006 Catherine Loader.
|
|
|
1377 */
|
|
|
1378 #include "locf.h"
|
|
|
1379
|
|
|
1380 int circ_vallink(link)
|
|
|
1381 int link;
|
|
|
1382 { return(link==LIDENT);
|
|
|
1383 }
|
|
|
1384
|
|
|
1385 int circ_fam(y,mean,th,link,res,cens,w)
|
|
|
1386 double y, mean, th, *res, w;
|
|
|
1387 int link, cens;
|
|
|
1388 { if (link==LINIT)
|
|
|
1389 { res[ZDLL] = w*sin(y);
|
|
|
1390 res[ZLIK] = w*cos(y);
|
|
|
1391 return(LF_OK);
|
|
|
1392 }
|
|
|
1393 res[ZDLL] = w*sin(y-mean);
|
|
|
1394 res[ZDDLL]= w*cos(y-mean);
|
|
|
1395 res[ZLIK] = res[ZDDLL]-w;
|
|
|
1396 return(LF_OK);
|
|
|
1397 }
|
|
|
1398
|
|
|
1399 extern double lf_tol;
|
|
|
1400 int circ_init(lfd,des,sp)
|
|
|
1401 lfdata *lfd;
|
|
|
1402 design *des;
|
|
|
1403 smpar *sp;
|
|
|
1404 { int i, ii;
|
|
|
1405 double s0, s1;
|
|
|
1406 s0 = s1 = 0.0;
|
|
|
1407 for (i=0; i<des->n; i++)
|
|
|
1408 { ii = des->ind[i];
|
|
|
1409 s0 += wght(des,ii)*prwt(lfd,ii)*sin(resp(lfd,ii)-base(lfd,ii));
|
|
|
1410 s1 += wght(des,ii)*prwt(lfd,ii)*cos(resp(lfd,ii)-base(lfd,ii));
|
|
|
1411 }
|
|
|
1412 des->cf[0] = atan2(s0,s1);
|
|
|
1413 for (i=1; i<des->p; i++) des->cf[i] = 0.0;
|
|
|
1414 lf_tol = 1.0e-6;
|
|
|
1415 return(LF_OK);
|
|
|
1416 }
|
|
|
1417
|
|
|
1418
|
|
|
1419 void setfcirc(fam)
|
|
|
1420 family *fam;
|
|
|
1421 { fam->deflink = LIDENT;
|
|
|
1422 fam->canlink = LIDENT;
|
|
|
1423 fam->vallink = circ_vallink;
|
|
|
1424 fam->family = circ_fam;
|
|
|
1425 fam->initial = circ_init;
|
|
|
1426 }
|
|
|
1427 /*
|
|
|
1428 * Copyright 1996-2006 Catherine Loader.
|
|
|
1429 */
|
|
|
1430 #include "locf.h"
|
|
|
1431
|
|
|
1432 int dens_vallink(link)
|
|
|
1433 int link;
|
|
|
1434 { return((link==LIDENT) | (link==LLOG));
|
|
|
1435 }
|
|
|
1436
|
|
|
1437 int dens_fam(y,mean,th,link,res,cens,w)
|
|
|
1438 double y, mean, th, *res, w;
|
|
|
1439 int link, cens;
|
|
|
1440 { if (cens)
|
|
|
1441 res[ZLIK] = res[ZDLL] = res[ZDDLL] = 0.0;
|
|
|
1442 else
|
|
|
1443 { res[ZLIK] = w*th;
|
|
|
1444 res[ZDLL] = res[ZDDLL] = w;
|
|
|
1445 }
|
|
|
1446 return(LF_OK);
|
|
|
1447 }
|
|
|
1448
|
|
|
1449 void setfdensity(fam)
|
|
|
1450 family *fam;
|
|
|
1451 { fam->deflink = LLOG;
|
|
|
1452 fam->canlink = LLOG;
|
|
|
1453 fam->vallink = dens_vallink;
|
|
|
1454 fam->family = dens_fam;
|
|
|
1455 fam->initial = densinit;
|
|
|
1456 fam->like = likeden;
|
|
|
1457 }
|
|
|
1458 /*
|
|
|
1459 * Copyright 1996-2006 Catherine Loader.
|
|
|
1460 */
|
|
|
1461 #include "locf.h"
|
|
|
1462
|
|
|
1463 int gamma_vallink(link)
|
|
|
1464 int link;
|
|
|
1465 { return((link==LIDENT) | (link==LLOG) | (link==LINVER));
|
|
|
1466 }
|
|
|
1467
|
|
|
1468 int gamma_fam(y,mean,th,link,res,cens,w)
|
|
|
1469 double y, mean, th, *res, w;
|
|
|
1470 int link, cens;
|
|
|
1471 { double lb, pt, dg;
|
|
|
1472 if (link==LINIT)
|
|
|
1473 { res[ZDLL] = MAX(y,0.0);
|
|
|
1474 return(LF_OK);
|
|
|
1475 }
|
|
|
1476 res[ZLIK] = res[ZDLL] = res[ZDDLL] = 0.0;
|
|
|
1477 if (w==0.0) return(LF_OK);
|
|
|
1478 if ((mean<=0) & (y>0)) return(LF_BADP);
|
|
|
1479 if (link==LIDENT) lb = 1/th;
|
|
|
1480 if (link==LINVER) lb = th;
|
|
|
1481 if (link==LLOG) lb = mut_exp(-th);
|
|
|
1482 if (cens)
|
|
|
1483 { if (y<=0) return(LF_OK);
|
|
|
1484 pt = 1-igamma(lb*y,w);
|
|
|
1485 dg = dgamma(lb*y,w,1.0,0);
|
|
|
1486 res[ZLIK] = log(pt);
|
|
|
1487 res[ZDLL] = -y*dg/pt;
|
|
|
1488 /*
|
|
|
1489 * res[ZDLL] = -y*dg/pt * dlb/dth.
|
|
|
1490 * res[ZDDLL] = y*dg/pt * (d2lb/dth2 + ((w-1)/lb-y)*(dlb/dth)^2)
|
|
|
1491 * + res[ZDLL]^2.
|
|
|
1492 */
|
|
|
1493 if (link==LLOG) /* lambda = exp(-theta) */
|
|
|
1494 { res[ZDLL] *= -lb;
|
|
|
1495 res[ZDDLL] = dg*y*lb*(w-lb*y)/pt + SQR(res[ZDLL]);
|
|
|
1496 return(LF_OK);
|
|
|
1497 }
|
|
|
1498 if (link==LINVER) /* lambda = theta */
|
|
|
1499 { res[ZDLL] *= 1.0;
|
|
|
1500 res[ZDDLL] = dg*y*((w-1)*mean-y)/pt + SQR(res[ZDLL]);
|
|
|
1501 return(LF_OK);
|
|
|
1502 }
|
|
|
1503 if (link==LIDENT) /* lambda = 1/theta */
|
|
|
1504 { res[ZDLL] *= -lb*lb;
|
|
|
1505 res[ZDDLL] = dg*y*lb*lb*lb*(1+w-lb*y)/pt + SQR(res[ZDLL]);
|
|
|
1506 return(LF_OK);
|
|
|
1507 }
|
|
|
1508 }
|
|
|
1509 else
|
|
|
1510 { if (y<0) WARN(("Negative Gamma observation"));
|
|
|
1511 if (link==LLOG)
|
|
|
1512 { res[ZLIK] = -lb*y+w*(1-th);
|
|
|
1513 if (y>0) res[ZLIK] += w*log(y/w);
|
|
|
1514 res[ZDLL] = lb*y-w;
|
|
|
1515 res[ZDDLL]= lb*y;
|
|
|
1516 return(LF_OK);
|
|
|
1517 }
|
|
|
1518 if (link==LINVER)
|
|
|
1519 { res[ZLIK] = -lb*y+w-w*log(mean);
|
|
|
1520 if (y>0) res[ZLIK] += w*log(y/w);
|
|
|
1521 res[ZDLL] = -y+w*mean;
|
|
|
1522 res[ZDDLL]= w*mean*mean;
|
|
|
1523 return(LF_OK);
|
|
|
1524 }
|
|
|
1525 if (link==LIDENT)
|
|
|
1526 { res[ZLIK] = -lb*y+w-w*log(mean);
|
|
|
1527 if (y>0) res[ZLIK] += w*log(y/w);
|
|
|
1528 res[ZDLL] = lb*lb*(y-w*mean);
|
|
|
1529 res[ZDDLL]= lb*lb*lb*(2*y-w*mean);
|
|
|
1530 return(LF_OK);
|
|
|
1531 }
|
|
|
1532 }
|
|
|
1533 LERR(("link %d invalid for Gamma family",link));
|
|
|
1534 return(LF_LNK);
|
|
|
1535 }
|
|
|
1536
|
|
|
1537 void setfgamma(fam)
|
|
|
1538 family *fam;
|
|
|
1539 { fam->deflink = LLOG;
|
|
|
1540 fam->canlink = LINVER;
|
|
|
1541 fam->vallink = gamma_vallink;
|
|
|
1542 fam->family = gamma_fam;
|
|
|
1543 }
|
|
|
1544 /*
|
|
|
1545 * Copyright 1996-2006 Catherine Loader.
|
|
|
1546 */
|
|
|
1547 #include "locf.h"
|
|
|
1548
|
|
|
1549 int gaus_vallink(link)
|
|
|
1550 int link;
|
|
|
1551 { return((link==LIDENT) | (link==LLOG) | (link==LLOGIT));
|
|
|
1552 }
|
|
|
1553
|
|
|
1554 int gaus_fam(y,mean,th,link,res,cens,w)
|
|
|
1555 double y, mean, th, *res, w;
|
|
|
1556 int link, cens;
|
|
|
1557 { double z, pz, dp;
|
|
|
1558 if (link==LINIT)
|
|
|
1559 { res[ZDLL] = w*y;
|
|
|
1560 return(LF_OK);
|
|
|
1561 }
|
|
|
1562 z = y-mean;
|
|
|
1563 if (cens)
|
|
|
1564 { if (link!=LIDENT)
|
|
|
1565 { LERR(("Link invalid for censored Gaussian family"));
|
|
|
1566 return(LF_LNK);
|
|
|
1567 }
|
|
|
1568 pz = mut_pnorm(-z);
|
|
|
1569 dp = ((z>6) ? ptail(-z) : exp(-z*z/2)/pz)/2.5066283;
|
|
|
1570 res[ZLIK] = w*log(pz);
|
|
|
1571 res[ZDLL] = w*dp;
|
|
|
1572 res[ZDDLL]= w*dp*(dp-z);
|
|
|
1573 return(LF_OK);
|
|
|
1574 }
|
|
|
1575 res[ZLIK] = -w*z*z/2;
|
|
|
1576 switch(link)
|
|
|
1577 { case LIDENT:
|
|
|
1578 res[ZDLL] = w*z;
|
|
|
1579 res[ZDDLL]= w;
|
|
|
1580 break;
|
|
|
1581 case LLOG:
|
|
|
1582 res[ZDLL] = w*z*mean;
|
|
|
1583 res[ZDDLL]= w*mean*mean;
|
|
|
1584 break;
|
|
|
1585 case LLOGIT:
|
|
|
1586 res[ZDLL] = w*z*mean*(1-mean);
|
|
|
1587 res[ZDDLL]= w*mean*mean*(1-mean)*(1-mean);
|
|
|
1588 break;
|
|
|
1589 default:
|
|
|
1590 LERR(("Invalid link for Gaussian family"));
|
|
|
1591 return(LF_LNK);
|
|
|
1592 }
|
|
|
1593 return(LF_OK);
|
|
|
1594 }
|
|
|
1595
|
|
|
1596 int gaus_check(sp,des,lfd)
|
|
|
1597 smpar *sp;
|
|
|
1598 design *des;
|
|
|
1599 lfdata *lfd;
|
|
|
1600 { int i, ii;
|
|
|
1601 if (fami(sp)->robust) return(LF_OK);
|
|
|
1602 if (link(sp)==LIDENT)
|
|
|
1603 { for (i=0; i<des->n; i++)
|
|
|
1604 { ii = des->ind[i];
|
|
|
1605 if (cens(lfd,ii)) return(LF_OK);
|
|
|
1606 }
|
|
|
1607 return(LF_DONE);
|
|
|
1608 }
|
|
|
1609 return(LF_OK);
|
|
|
1610 }
|
|
|
1611
|
|
|
1612 void setfgauss(fam)
|
|
|
1613 family *fam;
|
|
|
1614 { fam->deflink = LIDENT;
|
|
|
1615 fam->canlink = LIDENT;
|
|
|
1616 fam->vallink = gaus_vallink;
|
|
|
1617 fam->family = gaus_fam;
|
|
|
1618 fam->pcheck = gaus_check;
|
|
|
1619 }
|
|
|
1620 /*
|
|
|
1621 * Copyright 1996-2006 Catherine Loader.
|
|
|
1622 */
|
|
|
1623 #include "locf.h"
|
|
|
1624
|
|
|
1625 int geom_vallink(link)
|
|
|
1626 int link;
|
|
|
1627 { return((link==LIDENT) | (link==LLOG));
|
|
|
1628 }
|
|
|
1629
|
|
|
1630 int geom_fam(y,mean,th,link,res,cens,w)
|
|
|
1631 double y, mean, th, *res, w;
|
|
|
1632 int link, cens;
|
|
|
1633 { double p, pt, dp, p1;
|
|
|
1634 if (link==LINIT)
|
|
|
1635 { res[ZDLL] = MAX(y,0.0);
|
|
|
1636 return(LF_OK);
|
|
|
1637 }
|
|
|
1638 p = 1/(1+mean);
|
|
|
1639 if (cens) /* censored observation */
|
|
|
1640 { if (y<=0)
|
|
|
1641 { res[ZLIK] = res[ZDLL] = res[ZDDLL] = 0;
|
|
|
1642 return(LF_OK);
|
|
|
1643 }
|
|
|
1644 p1 = (link==LIDENT) ? -p*p : -p*(1-p);
|
|
|
1645 pt = 1-ibeta(p,w,y);
|
|
|
1646 dp = dbeta(p,w,y,0)/pt;
|
|
|
1647 res[ZLIK] = log(pt);
|
|
|
1648 res[ZDLL] = -dp*p1;
|
|
|
1649 res[ZDDLL] = dp*dp*p1*p1;
|
|
|
1650 if (link==LIDENT)
|
|
|
1651 res[ZDDLL] += dp*p*p*p*(1+w*(1-p)-p*y)/(1-p);
|
|
|
1652 else
|
|
|
1653 res[ZDDLL] += dp*p*(1-p)*(w*(1-p)-p*y);
|
|
|
1654 return(LF_OK);
|
|
|
1655 }
|
|
|
1656 else
|
|
|
1657 { res[ZLIK] = (y+w)*log((y/w+1)/(mean+1));
|
|
|
1658 if (y>0) res[ZLIK] += y*log(w*mean/y);
|
|
|
1659 if (link==LLOG)
|
|
|
1660 { res[ZDLL] = (y-w*mean)*p;
|
|
|
1661 res[ZDDLL]= (y+w)*p*(1-p);
|
|
|
1662 return(LF_OK);
|
|
|
1663 }
|
|
|
1664 if (link==LIDENT)
|
|
|
1665 { res[ZDLL] = (y-w*mean)/(mean*(1+mean));
|
|
|
1666 res[ZDDLL]= w/(mean*(1+mean));
|
|
|
1667 return(LF_OK);
|
|
|
1668 }
|
|
|
1669 }
|
|
|
1670 LERR(("link %d invalid for geometric family",link));
|
|
|
1671 return(LF_LNK);
|
|
|
1672 }
|
|
|
1673
|
|
|
1674 void setfgeom(fam)
|
|
|
1675 family *fam;
|
|
|
1676 { fam->deflink = LLOG;
|
|
|
1677 fam->canlink = LIDENT; /* this isn't correct. I haven't prog. canon */
|
|
|
1678 fam->vallink = geom_vallink;
|
|
|
1679 fam->family = geom_fam;
|
|
|
1680 }
|
|
|
1681 /*
|
|
|
1682 * Copyright 1996-2006 Catherine Loader.
|
|
|
1683 */
|
|
|
1684 #include "locf.h"
|
|
|
1685
|
|
|
1686 #define HUBERC 2.0
|
|
|
1687
|
|
|
1688 double links_rs;
|
|
|
1689 int inllmix=0;
|
|
|
1690
|
|
|
1691 /*
|
|
|
1692 * lffamily("name") converts family names into a numeric value.
|
|
|
1693 * typical usage is fam(&lf->sp) = lffamily("gaussian");
|
|
|
1694 * Note that family can be preceded by q and/or r for quasi, robust.
|
|
|
1695 *
|
|
|
1696 * link(&lf->sp) = lflink("log") does the same for the link function.
|
|
|
1697 */
|
|
|
1698 #define NFAMILY 18
|
|
|
1699 static char *famil[NFAMILY] =
|
|
|
1700 { "density", "ate", "hazard", "gaussian", "binomial",
|
|
|
1701 "poisson", "gamma", "geometric", "circular", "obust", "huber",
|
|
|
1702 "weibull", "cauchy","probab", "logistic", "nbinomial",
|
|
|
1703 "vonmises", "quant" };
|
|
|
1704 static int fvals[NFAMILY] =
|
|
|
1705 { TDEN, TRAT, THAZ, TGAUS, TLOGT,
|
|
|
1706 TPOIS, TGAMM, TGEOM, TCIRC, TROBT, TROBT,
|
|
|
1707 TWEIB, TCAUC, TPROB, TLOGT, TGEOM, TCIRC, TQUANT };
|
|
|
1708 int lffamily(z)
|
|
|
1709 char *z;
|
|
|
1710 { int quasi, robu, f;
|
|
|
1711 quasi = robu = 0;
|
|
|
1712 while ((z[0]=='q') | (z[0]=='r'))
|
|
|
1713 { quasi |= (z[0]=='q');
|
|
|
1714 robu |= (z[0]=='r');
|
|
|
1715 z++;
|
|
|
1716 }
|
|
|
1717 z[0] = tolower(z[0]);
|
|
|
1718 f = pmatch(z,famil,fvals,NFAMILY,-1);
|
|
|
1719 if ((z[0]=='o') | (z[0]=='a')) robu = 0;
|
|
|
1720 if (f==-1)
|
|
|
1721 { WARN(("unknown family %s",z));
|
|
|
1722 f = TGAUS;
|
|
|
1723 }
|
|
|
1724 if (quasi) f += 64;
|
|
|
1725 if (robu) f += 128;
|
|
|
1726 return(f);
|
|
|
1727 }
|
|
|
1728
|
|
|
1729 #define NLINKS 8
|
|
|
1730 static char *ltype[NLINKS] = { "default", "canonical", "identity", "log",
|
|
|
1731 "logi", "inverse", "sqrt", "arcsin" };
|
|
|
1732 static int lvals[NLINKS] = { LDEFAU, LCANON, LIDENT, LLOG,
|
|
|
1733 LLOGIT, LINVER, LSQRT, LASIN };
|
|
|
1734 int lflink(char *z)
|
|
|
1735 { int f;
|
|
|
1736 if (z==NULL) return(LDEFAU);
|
|
|
1737 z[0] = tolower(z[0]);
|
|
|
1738 f = pmatch(z, ltype, lvals, NLINKS, -1);
|
|
|
1739 if (f==-1)
|
|
|
1740 { WARN(("unknown link %s",z));
|
|
|
1741 f = LDEFAU;
|
|
|
1742 }
|
|
|
1743 return(f);
|
|
|
1744 }
|
|
|
1745
|
|
|
1746 int defaultlink(link,fam)
|
|
|
1747 int link;
|
|
|
1748 family *fam;
|
|
|
1749 { if (link==LDEFAU) return(fam->deflink);
|
|
|
1750 if (link==LCANON) return(fam->canlink);
|
|
|
1751 return(link);
|
|
|
1752 }
|
|
|
1753
|
|
|
1754 /*
|
|
|
1755 void robustify(res,rs)
|
|
|
1756 double *res, rs;
|
|
|
1757 { double sc, z;
|
|
|
1758 sc = rs*HUBERC;
|
|
|
1759 if (res[ZLIK] > -sc*sc/2) return;
|
|
|
1760 z = sqrt(-2*res[ZLIK]);
|
|
|
1761 res[ZDDLL]= -sc*res[ZDLL]*res[ZDLL]/(z*z*z)+sc*res[ZDDLL]/z;
|
|
|
1762 res[ZDLL]*= sc/z;
|
|
|
1763 res[ZLIK] = sc*sc/2-sc*z;
|
|
|
1764 }
|
|
|
1765 */
|
|
|
1766 void robustify(res,rs)
|
|
|
1767 double *res, rs;
|
|
|
1768 { double sc, z;
|
|
|
1769 sc = rs*HUBERC;
|
|
|
1770 if (res[ZLIK] > -sc*sc/2)
|
|
|
1771 { res[ZLIK] /= sc*sc;
|
|
|
1772 res[ZDLL] /= sc*sc;
|
|
|
1773 res[ZDDLL] /= sc*sc;
|
|
|
1774 return;
|
|
|
1775 }
|
|
|
1776 z = sqrt(-2*res[ZLIK]);
|
|
|
1777 res[ZDDLL]= (-sc*res[ZDLL]*res[ZDLL]/(z*z*z)+sc*res[ZDDLL]/z)/(sc*sc);
|
|
|
1778 res[ZDLL]*= 1.0/(z*sc);
|
|
|
1779 res[ZLIK] = 0.5-z/sc;
|
|
|
1780 }
|
|
|
1781
|
|
|
1782 double lf_link(y,lin)
|
|
|
1783 double y;
|
|
|
1784 int lin;
|
|
|
1785 { switch(lin)
|
|
|
1786 { case LIDENT: return(y);
|
|
|
1787 case LLOG: return(log(y));
|
|
|
1788 case LLOGIT: return(logit(y));
|
|
|
1789 case LINVER: return(1/y);
|
|
|
1790 case LSQRT: return(sqrt(fabs(y)));
|
|
|
1791 case LASIN: return(asin(sqrt(y)));
|
|
|
1792 }
|
|
|
1793 LERR(("link: unknown link %d",lin));
|
|
|
1794 return(0.0);
|
|
|
1795 }
|
|
|
1796
|
|
|
1797 double invlink(th,lin)
|
|
|
1798 double th;
|
|
|
1799 int lin;
|
|
|
1800 { switch(lin)
|
|
|
1801 { case LIDENT: return(th);
|
|
|
1802 case LLOG: return(mut_exp(th));
|
|
|
1803 case LLOGIT: return(expit(th));
|
|
|
1804 case LINVER: return(1/th);
|
|
|
1805 case LSQRT: return(th*fabs(th));
|
|
|
1806 case LASIN: return(sin(th)*sin(th));
|
|
|
1807 case LINIT: return(0.0);
|
|
|
1808 }
|
|
|
1809 LERR(("invlink: unknown link %d",lin));
|
|
|
1810 return(0.0);
|
|
|
1811 }
|
|
|
1812
|
|
|
1813 /* the link and various related functions */
|
|
|
1814 int links(th,y,fam,link,res,c,w,rs)
|
|
|
1815 double th, y, *res, w, rs;
|
|
|
1816 int link, c;
|
|
|
1817 family *fam;
|
|
|
1818 { double mean;
|
|
|
1819 int st;
|
|
|
1820
|
|
|
1821 mean = res[ZMEAN] = invlink(th,link);
|
|
|
1822 if (lf_error) return(LF_LNK);
|
|
|
1823 links_rs = rs;
|
|
|
1824 /* mut_printf("links: rs %8.5f\n",rs); */
|
|
|
1825
|
|
|
1826 st = fam->family(y,mean,th,link,res,c,w);
|
|
|
1827
|
|
|
1828 if (st!=LF_OK) return(st);
|
|
|
1829 if (link==LINIT) return(st);
|
|
|
1830 if (isrobust(fam)) robustify(res,rs);
|
|
|
1831 return(st);
|
|
|
1832 }
|
|
|
1833
|
|
|
1834 /*
|
|
|
1835 stdlinks is a version of links when family, link, response e.t.c
|
|
|
1836 all come from the standard places.
|
|
|
1837 */
|
|
|
1838 int stdlinks(res,lfd,sp,i,th,rs)
|
|
|
1839 lfdata *lfd;
|
|
|
1840 smpar *sp;
|
|
|
1841 double th, rs, *res;
|
|
|
1842 int i;
|
|
|
1843 {
|
|
|
1844 return(links(th,resp(lfd,i),fami(sp),link(sp),res,cens(lfd,i),prwt(lfd,i),rs));
|
|
|
1845 }
|
|
|
1846
|
|
|
1847 /*
|
|
|
1848 * functions used in variance, skewness, kurtosis calculations
|
|
|
1849 * in scb corrections.
|
|
|
1850 */
|
|
|
1851
|
|
|
1852 double b2(th,tg,w)
|
|
|
1853 double th, w;
|
|
|
1854 int tg;
|
|
|
1855 { double y;
|
|
|
1856 switch(tg&63)
|
|
|
1857 { case TGAUS: return(w);
|
|
|
1858 case TPOIS: return(w*mut_exp(th));
|
|
|
1859 case TLOGT:
|
|
|
1860 y = expit(th);
|
|
|
1861 return(w*y*(1-y));
|
|
|
1862 }
|
|
|
1863 LERR(("b2: invalid family %d",tg));
|
|
|
1864 return(0.0);
|
|
|
1865 }
|
|
|
1866
|
|
|
1867 double b3(th,tg,w)
|
|
|
1868 double th, w;
|
|
|
1869 int tg;
|
|
|
1870 { double y;
|
|
|
1871 switch(tg&63)
|
|
|
1872 { case TGAUS: return(0.0);
|
|
|
1873 case TPOIS: return(w*mut_exp(th));
|
|
|
1874 case TLOGT:
|
|
|
1875 y = expit(th);
|
|
|
1876 return(w*y*(1-y)*(1-2*y));
|
|
|
1877 }
|
|
|
1878 LERR(("b3: invalid family %d",tg));
|
|
|
1879 return(0.0);
|
|
|
1880 }
|
|
|
1881
|
|
|
1882 double b4(th,tg,w)
|
|
|
1883 double th, w;
|
|
|
1884 int tg;
|
|
|
1885 { double y;
|
|
|
1886 switch(tg&63)
|
|
|
1887 { case TGAUS: return(0.0);
|
|
|
1888 case TPOIS: return(w*mut_exp(th));
|
|
|
1889 case TLOGT:
|
|
|
1890 y = expit(th); y = y*(1-y);
|
|
|
1891 return(w*y*(1-6*y));
|
|
|
1892 }
|
|
|
1893 LERR(("b4: invalid family %d",tg));
|
|
|
1894 return(0.0);
|
|
|
1895 }
|
|
|
1896
|
|
|
1897 int def_check(sp,des,lfd)
|
|
|
1898 smpar *sp;
|
|
|
1899 design *des;
|
|
|
1900 lfdata *lfd;
|
|
|
1901 { switch(link(sp))
|
|
|
1902 { case LLOG: if (des->cf[0]>700) return(LF_OOB);
|
|
|
1903 break;
|
|
|
1904 }
|
|
|
1905 return(LF_OK);
|
|
|
1906 }
|
|
|
1907 extern void setfdensity(), setfgauss(), setfbino(), setfpoisson();
|
|
|
1908 extern void setfgamma(), setfgeom(), setfcirc(), setfweibull();
|
|
|
1909 extern void setfrbino(), setfrobust(), setfcauchy(), setfquant();
|
|
|
1910
|
|
|
1911 void setfamily(sp)
|
|
|
1912 smpar *sp;
|
|
|
1913 { int tg, lnk;
|
|
|
1914 family *f;
|
|
|
1915
|
|
|
1916 tg = fam(sp);
|
|
|
1917 f = fami(sp);
|
|
|
1918 f->quasi = tg&64;
|
|
|
1919 f->robust = tg&128;
|
|
|
1920 f->initial = reginit;
|
|
|
1921 f->like = likereg;
|
|
|
1922 f->pcheck = def_check;
|
|
|
1923
|
|
|
1924 switch(tg&63)
|
|
|
1925 { case TDEN:
|
|
|
1926 case THAZ:
|
|
|
1927 case TRAT: setfdensity(f); break;
|
|
|
1928 case TGAUS: setfgauss(f); break;
|
|
|
1929 case TLOGT: setfbino(f); break;
|
|
|
1930 case TRBIN: setfrbino(f); break;
|
|
|
1931 case TPROB:
|
|
|
1932 case TPOIS: setfpoisson(f); break;
|
|
|
1933 case TGAMM: setfgamma(f); break;
|
|
|
1934 case TGEOM: setfgeom(f); break;
|
|
|
1935 case TWEIB: setfweibull(f);
|
|
|
1936 case TCIRC: setfcirc(f); break;
|
|
|
1937 case TROBT: setfrobust(f); break;
|
|
|
1938 case TCAUC: setfcauchy(f); break;
|
|
|
1939 case TQUANT: setfquant(f); break;
|
|
|
1940 default: LERR(("setfamily: unknown family %d",tg&63));
|
|
|
1941 return;
|
|
|
1942 }
|
|
|
1943
|
|
|
1944 lnk = defaultlink(link(sp),f);
|
|
|
1945 if (!f->vallink(lnk))
|
|
|
1946 { WARN(("setfamily: invalid link %d - revert to default",link(sp)));
|
|
|
1947 link(sp) = f->deflink;
|
|
|
1948 }
|
|
|
1949 else
|
|
|
1950 link(sp) = lnk;
|
|
|
1951 }
|
|
|
1952 /*
|
|
|
1953 * Copyright 1996-2006 Catherine Loader.
|
|
|
1954 */
|
|
|
1955 #include "locf.h"
|
|
|
1956
|
|
|
1957 int pois_vallink(link)
|
|
|
1958 int link;
|
|
|
1959 { return((link==LLOG) | (link==LIDENT) | (link==LSQRT));
|
|
|
1960 }
|
|
|
1961
|
|
|
1962 int pois_fam(y,mean,th,link,res,cens,w)
|
|
|
1963 double y, mean, th, *res, w;
|
|
|
1964 int link, cens;
|
|
|
1965 { double wmu, pt, dp;
|
|
|
1966 if (link==LINIT)
|
|
|
1967 { res[ZDLL] = MAX(y,0.0);
|
|
|
1968 return(LF_OK);
|
|
|
1969 }
|
|
|
1970 wmu = w*mean;
|
|
|
1971 if (inllmix) y = w*y;
|
|
|
1972 if (cens)
|
|
|
1973 { if (y<=0)
|
|
|
1974 { res[ZLIK] = res[ZDLL] = res[ZDDLL] = 0.0;
|
|
|
1975 return(LF_OK);
|
|
|
1976 }
|
|
|
1977 pt = igamma(wmu,y);
|
|
|
1978 dp = dgamma(wmu,y,1.0,0)/pt;
|
|
|
1979 res[ZLIK] = log(pt);
|
|
|
1980 /*
|
|
|
1981 * res[ZDLL] = dp * w*dmu/dth
|
|
|
1982 * res[ZDDLL]= -dp*(w*d2mu/dth2 + (y-1)/mu*(dmu/dth)^2) + res[ZDLL]^2
|
|
|
1983 */
|
|
|
1984 if (link==LLOG)
|
|
|
1985 { res[ZDLL] = dp*wmu;
|
|
|
1986 res[ZDDLL]= -dp*wmu*(y-wmu) + SQR(res[ZDLL]);
|
|
|
1987 return(LF_OK);
|
|
|
1988 }
|
|
|
1989 if (link==LIDENT)
|
|
|
1990 { res[ZDLL] = dp*w;
|
|
|
1991 res[ZDDLL]= -dp*(y-1-wmu)*w/mean + SQR(res[ZDLL]);
|
|
|
1992 return(LF_OK);
|
|
|
1993 }
|
|
|
1994 if (link==LSQRT)
|
|
|
1995 { res[ZDLL] = dp*2*w*th;
|
|
|
1996 res[ZDDLL]= -dp*w*(4*y-2-4*wmu) + SQR(res[ZDLL]);
|
|
|
1997 return(LF_OK);
|
|
|
1998 } }
|
|
|
1999 if (link==LLOG)
|
|
|
2000 { if (y<0) /* goon observation - delete it */
|
|
|
2001 { res[ZLIK] = res[ZDLL] = res[ZDDLL] = 0;
|
|
|
2002 return(LF_OK);
|
|
|
2003 }
|
|
|
2004 res[ZLIK] = res[ZDLL] = y-wmu;
|
|
|
2005 if (y>0) res[ZLIK] += y*(th-log(y/w));
|
|
|
2006 res[ZDDLL] = wmu;
|
|
|
2007 return(LF_OK);
|
|
|
2008 }
|
|
|
2009 if (link==LIDENT)
|
|
|
2010 { if ((mean<=0) && (y>0)) return(LF_BADP);
|
|
|
2011 res[ZLIK] = y-wmu;
|
|
|
2012 res[ZDLL] = -w;
|
|
|
2013 res[ZDDLL] = 0;
|
|
|
2014 if (y>0)
|
|
|
2015 { res[ZLIK] += y*log(wmu/y);
|
|
|
2016 res[ZDLL] += y/mean;
|
|
|
2017 res[ZDDLL]= y/(mean*mean);
|
|
|
2018 }
|
|
|
2019 return(LF_OK);
|
|
|
2020 }
|
|
|
2021 if (link==LSQRT)
|
|
|
2022 { if ((mean<=0) && (y>0)) return(LF_BADP);
|
|
|
2023 res[ZLIK] = y-wmu;
|
|
|
2024 res[ZDLL] = -2*w*th;
|
|
|
2025 res[ZDDLL]= 2*w;
|
|
|
2026 if (y>0)
|
|
|
2027 { res[ZLIK] += y*log(wmu/y);
|
|
|
2028 res[ZDLL] += 2*y/th;
|
|
|
2029 res[ZDDLL]+= 2*y/mean;
|
|
|
2030 }
|
|
|
2031 return(LF_OK);
|
|
|
2032 }
|
|
|
2033 LERR(("link %d invalid for Poisson family",link));
|
|
|
2034 return(LF_LNK);
|
|
|
2035 }
|
|
|
2036
|
|
|
2037 void setfpoisson(fam)
|
|
|
2038 family *fam;
|
|
|
2039 { fam->deflink = LLOG;
|
|
|
2040 fam->canlink = LLOG;
|
|
|
2041 fam->vallink = pois_vallink;
|
|
|
2042 fam->family = pois_fam;
|
|
|
2043 }
|
|
|
2044 /*
|
|
|
2045 * Copyright 1996-2006 Catherine Loader.
|
|
|
2046 */
|
|
|
2047 #include "locf.h"
|
|
|
2048
|
|
|
2049 #define QTOL 1.0e-10
|
|
|
2050 extern int lf_status;
|
|
|
2051 static double q0;
|
|
|
2052
|
|
|
2053 int quant_vallink(int link) { return(1); }
|
|
|
2054
|
|
|
2055 int quant_fam(y,mean,th,link,res,cens,w)
|
|
|
2056 double y, mean, th, *res, w;
|
|
|
2057 int link, cens;
|
|
|
2058 { double z, p;
|
|
|
2059 if (link==LINIT)
|
|
|
2060 { res[ZDLL] = w*y;
|
|
|
2061 return(LF_OK);
|
|
|
2062 }
|
|
|
2063 p = 0.5; /* should be pen(sp) */
|
|
|
2064 z = y-mean;
|
|
|
2065 res[ZLIK] = (z<0) ? (w*z/p) : (-w*z/(1-p));
|
|
|
2066 res[ZDLL] = (z<0) ? -w/p : w/(1-p);
|
|
|
2067 res[ZDDLL]= w/(p*(1-p));
|
|
|
2068 return(LF_OK);
|
|
|
2069 }
|
|
|
2070
|
|
|
2071 int quant_check(sp,des,lfd)
|
|
|
2072 smpar *sp;
|
|
|
2073 design *des;
|
|
|
2074 lfdata *lfd;
|
|
|
2075 { return(LF_DONE);
|
|
|
2076 }
|
|
|
2077
|
|
|
2078 void setfquant(fam)
|
|
|
2079 family *fam;
|
|
|
2080 { fam->deflink = LIDENT;
|
|
|
2081 fam->canlink = LIDENT;
|
|
|
2082 fam->vallink = quant_vallink;
|
|
|
2083 fam->family = quant_fam;
|
|
|
2084 fam->pcheck = quant_check;
|
|
|
2085 }
|
|
|
2086
|
|
|
2087 /*
|
|
|
2088 * cycling rule for choosing among ties.
|
|
|
2089 */
|
|
|
2090 int tiecycle(ind,i0,i1,oi)
|
|
|
2091 int *ind, i0, i1, oi;
|
|
|
2092 { int i, ii, im;
|
|
|
2093 im = ind[i0];
|
|
|
2094 for (i=i0+1; i<=i1; i++)
|
|
|
2095 { ii = ind[i];
|
|
|
2096 if (im<=oi)
|
|
|
2097 { if ((ii<im) | (ii>oi)) im = ii;
|
|
|
2098 }
|
|
|
2099 else
|
|
|
2100 { if ((ii<im) & (ii>oi)) im = ii;
|
|
|
2101 }
|
|
|
2102 }
|
|
|
2103 return(im);
|
|
|
2104 }
|
|
|
2105
|
|
|
2106 /*
|
|
|
2107 * move coefficient vector cf, as far as possible, in direction dc.
|
|
|
2108 */
|
|
|
2109 int movecoef(lfd,des,p,cf,dc,oi)
|
|
|
2110 lfdata *lfd;
|
|
|
2111 design *des;
|
|
|
2112 double p, *cf, *dc;
|
|
|
2113 int oi;
|
|
|
2114 { int i, ii, im, i0, i1, j;
|
|
|
2115 double *lb, *el, e, sp, sn, sw, sum1, sum2, tol1;
|
|
|
2116
|
|
|
2117 lb = des->th;
|
|
|
2118 el = des->res;
|
|
|
2119 sum1 = sum2 = 0.0;
|
|
|
2120
|
|
|
2121 sp = sn = sw = 0.0;
|
|
|
2122 for (i=0; i<des->n; i++)
|
|
|
2123 { ii = des->ind[i];
|
|
|
2124 lb[ii] = innerprod(dc,d_xi(des,ii),des->p);
|
|
|
2125 e = resp(lfd,ii) - innerprod(cf,d_xi(des,ii),des->p);
|
|
|
2126 el[ii] = (fabs(lb[ii])<QTOL) ? 1e100 : e/lb[ii];
|
|
|
2127 if (lb[ii]>0)
|
|
|
2128 sp += prwt(lfd,ii)*wght(des,ii)*lb[ii];
|
|
|
2129 else
|
|
|
2130 sn -= prwt(lfd,ii)*wght(des,ii)*lb[ii];
|
|
|
2131 sw += prwt(lfd,ii)*wght(des,ii);
|
|
|
2132 }
|
|
|
2133 printf("sp %8.5f sn %8.5f\n",sn,sp);
|
|
|
2134 /* if sn, sp are both zero, should return an LF_PF.
|
|
|
2135 * but within numerical tolerance? what does it mean?
|
|
|
2136 */
|
|
|
2137 if (sn+sp <= QTOL*q0) { lf_status = LF_PF; return(0); }
|
|
|
2138
|
|
|
2139 sum1 = sp/(1-p) + sn/p;
|
|
|
2140 tol1 = QTOL*(sp+sn);
|
|
|
2141 mut_order(el,des->ind,0,des->n-1);
|
|
|
2142
|
|
|
2143 for (i=0; i<des->n; i++)
|
|
|
2144 { ii = des->ind[i];
|
|
|
2145 sum2 += prwt(lfd,ii)*wght(des,ii)*((lb[ii]>0) ? lb[ii]/p : -lb[ii]/(1-p) );
|
|
|
2146 sum1 -= prwt(lfd,ii)*wght(des,ii)*((lb[ii]>0) ? lb[ii]/(1-p) : -lb[ii]/p );
|
|
|
2147 if (sum1<=sum2+tol1)
|
|
|
2148 {
|
|
|
2149 /* determine the range of ties [i0,i1]
|
|
|
2150 * el[ind[i0..i1]] = el[ind[i]].
|
|
|
2151 * if sum1==sum2, el[ind[i+1]]..el[ind[i1]]] = el[ind[i1]], else i1 = i.
|
|
|
2152 */
|
|
|
2153 i0 = i1 = i;
|
|
|
2154 while ((i0>0) && (el[des->ind[i0-1]]==el[ii])) i0--;
|
|
|
2155 while ((i1<des->n-1) && (el[des->ind[i1+1]]==el[ii])) i1++;
|
|
|
2156 if (sum1>=sum2-tol1)
|
|
|
2157 while ((i1<des->n-1) && (el[des->ind[i1+1]]==el[des->ind[i+1]])) i1++;
|
|
|
2158
|
|
|
2159 if (i0<i1) ii = tiecycle(des->ind,i0,i1,oi);
|
|
|
2160 for (j=0; j<des->p; j++) cf[j] += el[ii]*dc[j];
|
|
|
2161 return(ii);
|
|
|
2162 }
|
|
|
2163 }
|
|
|
2164 mut_printf("Big finddlt problem.\n");
|
|
|
2165 ii = des->ind[des->n-1];
|
|
|
2166 for (j=0; j<des->p; j++) cf[j] += el[ii]*dc[j];
|
|
|
2167 return(ii);
|
|
|
2168 }
|
|
|
2169
|
|
|
2170 /*
|
|
|
2171 * special version of movecoef for min/max.
|
|
|
2172 */
|
|
|
2173 int movemin(lfd,des,f,cf,dc,oi)
|
|
|
2174 design *des;
|
|
|
2175 lfdata *lfd;
|
|
|
2176 double *cf, *dc, f;
|
|
|
2177 int oi;
|
|
|
2178 { int i, ii, im, p, s, ssum;
|
|
|
2179 double *lb, sum, lb0, lb1, z0, z1;
|
|
|
2180
|
|
|
2181 lb = des->th;
|
|
|
2182 s = (f<=0.0) ? 1 : -1;
|
|
|
2183
|
|
|
2184 /* first, determine whether move should be in positive or negative direction */
|
|
|
2185 p = des->p;
|
|
|
2186 sum = 0;
|
|
|
2187 for (i=0; i<des->n; i++)
|
|
|
2188 { ii = des->ind[i];
|
|
|
2189 lb[ii] = innerprod(dc,d_xi(des,ii),des->p);
|
|
|
2190 sum += prwt(lfd,ii)*wght(des,ii)*lb[ii];
|
|
|
2191 }
|
|
|
2192 if (fabs(sum) <= QTOL*q0)
|
|
|
2193 { lf_status = LF_PF;
|
|
|
2194 return(0);
|
|
|
2195 }
|
|
|
2196 ssum = (sum<=0.0) ? -1 : 1;
|
|
|
2197 if (ssum != s)
|
|
|
2198 for (i=0; i<p; i++) dc[i] = -dc[i];
|
|
|
2199
|
|
|
2200 /* now, move positively. How far can we move? */
|
|
|
2201 lb0 = 1.0e100; im = oi;
|
|
|
2202 for (i=0; i<des->n; i++)
|
|
|
2203 { ii = des->ind[i];
|
|
|
2204 lb[ii] = innerprod(dc,d_xi(des,ii),des->p); /* must recompute - signs! */
|
|
|
2205 if (s*lb[ii]>QTOL) /* should have scale-free tolerance here */
|
|
|
2206 { z0 = innerprod(cf,d_xi(des,ii),p);
|
|
|
2207 lb1 = (resp(lfd,ii) - z0)/lb[ii];
|
|
|
2208 if (lb1<lb0)
|
|
|
2209 { if (fabs(lb1-lb0)<QTOL) /* cycle */
|
|
|
2210 { if (im<=oi)
|
|
|
2211 { if ((ii>oi) | (ii<im)) im = ii; }
|
|
|
2212 else
|
|
|
2213 { if ((ii>oi) & (ii<im)) im = ii; }
|
|
|
2214 }
|
|
|
2215 else
|
|
|
2216 { im = ii; lb0 = lb1; }
|
|
|
2217 }
|
|
|
2218 }
|
|
|
2219 }
|
|
|
2220
|
|
|
2221 for (i=0; i<p; i++) cf[i] = cf[i]+lb0*dc[i];
|
|
|
2222 if (im==-1) lf_status = LF_PF;
|
|
|
2223 return(im);
|
|
|
2224 }
|
|
|
2225
|
|
|
2226 double qll(lfd,spr,des,cf)
|
|
|
2227 lfdata *lfd;
|
|
|
2228 smpar *spr;
|
|
|
2229 design *des;
|
|
|
2230 double *cf;
|
|
|
2231 { int i, ii;
|
|
|
2232 double th, sp, sn, p, e;
|
|
|
2233
|
|
|
2234 p = pen(spr);
|
|
|
2235 sp = sn = 0.0;
|
|
|
2236 for (i=0; i<des->n; i++)
|
|
|
2237 { ii = des->ind[i];
|
|
|
2238 th = innerprod(d_xi(des,ii),cf,des->p);
|
|
|
2239 e = resp(lfd,ii)-th;
|
|
|
2240 if (e<0) sn -= prwt(lfd,ii)*wght(des,ii)*e;
|
|
|
2241 if (e>0) sp += prwt(lfd,ii)*wght(des,ii)*e;
|
|
|
2242 }
|
|
|
2243 if (p<=0.0) return((sn<QTOL) ? -sp : -1e300);
|
|
|
2244 if (p>=1.0) return((sp<QTOL) ? -sn : -1e300);
|
|
|
2245 return(-sp/(1-p)-sn/p);
|
|
|
2246 }
|
|
|
2247
|
|
|
2248 /*
|
|
|
2249 * running quantile smoother.
|
|
|
2250 */
|
|
|
2251 void lfquantile(lfd,sp,des,maxit)
|
|
|
2252 lfdata *lfd;
|
|
|
2253 smpar *sp;
|
|
|
2254 design *des;
|
|
|
2255 int maxit;
|
|
|
2256 { int i, ii, im, j, k, p, *ci, (*mover)();
|
|
|
2257 double *cf, *db, *dc, *cm, f, q1, q2, l0;
|
|
|
2258
|
|
|
2259 printf("in lfquantile\n");
|
|
|
2260 f = pen(sp);
|
|
|
2261 p = des->p;
|
|
|
2262 cf = des->cf;
|
|
|
2263 dc = des->oc;
|
|
|
2264 db = des->ss;
|
|
|
2265 setzero(cf,p);
|
|
|
2266 setzero(dc,p);
|
|
|
2267 cm = des->V;
|
|
|
2268 setzero(cm,p*p);
|
|
|
2269 ci = (int *)des->fix;
|
|
|
2270
|
|
|
2271 q1 = -qll(lfd,sp,des,cf);
|
|
|
2272 if (q1==0.0) { lf_status = LF_PF; return; }
|
|
|
2273 for (i=0; i<p; i++) cm[i*(p+1)] = 1;
|
|
|
2274 mover = movecoef;
|
|
|
2275 if ((f<=0.0) | (f>=1.0)) mover = movemin;
|
|
|
2276
|
|
|
2277 dc[0] = 1.0;
|
|
|
2278 im = mover(lfd,des,f,cf,dc,-1);
|
|
|
2279 if (lf_status != LF_OK) return;
|
|
|
2280 ci[0] = im;
|
|
|
2281 printf("init const %2d\n",ci[0]);
|
|
|
2282 q0 = -qll(lfd,sp,des,cf);
|
|
|
2283 if (q0<QTOL*q1) { lf_status = LF_PF; return; }
|
|
|
2284
|
|
|
2285 printf("loop 0\n"); fflush(stdout);
|
|
|
2286 for (i=1; i<p; i++)
|
|
|
2287 {
|
|
|
2288 printf("i %2d\n",i);
|
|
|
2289 memcpy(&cm[(i-1)*p],d_xi(des,im),p*sizeof(double));
|
|
|
2290 setzero(db,p);
|
|
|
2291 db[i] = 1.0;
|
|
|
2292 resproj(db,cm,dc,p,i);
|
|
|
2293 printf("call mover\n"); fflush(stdout);
|
|
|
2294 im = mover(lfd,des,f,cf,dc,-1);
|
|
|
2295 if (lf_status != LF_OK) return;
|
|
|
2296 printf("mover %2d\n",im); fflush(stdout);
|
|
|
2297 ci[i] = im;
|
|
|
2298 }
|
|
|
2299 printf("call qll\n"); fflush(stdout);
|
|
|
2300 q1 = qll(lfd,sp,des,cf);
|
|
|
2301
|
|
|
2302 printf("loop 1 %d %d %d %d\n",ci[0],ci[1],ci[2],ci[3]); fflush(stdout);
|
|
|
2303 for (k=0; k<maxit; k++)
|
|
|
2304 { for (i=0; i<p; i++)
|
|
|
2305 { for (j=0; j<p; j++)
|
|
|
2306 if (j!=i) memcpy(&cm[(j-(j>i))*p],d_xi(des,ci[j]),p*sizeof(double));
|
|
|
2307 memcpy(db,d_xi(des,ci[i]),p*sizeof(double));
|
|
|
2308 resproj(db,cm,dc,p,p-1);
|
|
|
2309 printf("call mover\n"); fflush(stdout);
|
|
|
2310 im = mover(lfd,des,f,cf,dc,ci[i]);
|
|
|
2311 if (lf_status != LF_OK) return;
|
|
|
2312 printf("mover %2d\n",im); fflush(stdout);
|
|
|
2313 ci[i] = im;
|
|
|
2314 }
|
|
|
2315 q2 = qll(lfd,sp,des,cf);
|
|
|
2316 /*
|
|
|
2317 * convergence: require no change -- reasonable, since discrete?
|
|
|
2318 * remember we're maximizing, and q's are negative.
|
|
|
2319 */
|
|
|
2320 if (q2 <= q1) return;
|
|
|
2321 q1 = q2;
|
|
|
2322 }
|
|
|
2323 printf("loop 2\n");
|
|
|
2324 mut_printf("Warning: lfquantile not converged.\n");
|
|
|
2325 }
|
|
|
2326 /*
|
|
|
2327 * Copyright 1996-2006 Catherine Loader.
|
|
|
2328 */
|
|
|
2329 #include "locf.h"
|
|
|
2330
|
|
|
2331 extern double links_rs;
|
|
|
2332
|
|
|
2333 int robust_vallink(link)
|
|
|
2334 int link;
|
|
|
2335 { return(link==LIDENT);
|
|
|
2336 }
|
|
|
2337
|
|
|
2338 int robust_fam(y,mean,th,link,res,cens,w)
|
|
|
2339 double y, mean, th, *res, w;
|
|
|
2340 int link, cens;
|
|
|
2341 { double z, sw;
|
|
|
2342 if (link==LINIT)
|
|
|
2343 { res[ZDLL] = w*y;
|
|
|
2344 return(LF_OK);
|
|
|
2345 }
|
|
|
2346 sw = (w==1.0) ? 1.0 : sqrt(w); /* don't want unnecess. sqrt! */
|
|
|
2347 z = sw*(y-mean)/links_rs;
|
|
|
2348 res[ZLIK] = (fabs(z)<HUBERC) ? -z*z/2 : HUBERC*(HUBERC/2.0-fabs(z));
|
|
|
2349 if (z< -HUBERC)
|
|
|
2350 { res[ZDLL] = -sw*HUBERC/links_rs;
|
|
|
2351 res[ZDDLL]= 0.0;
|
|
|
2352 return(LF_OK);
|
|
|
2353 }
|
|
|
2354 if (z> HUBERC)
|
|
|
2355 { res[ZDLL] = sw*HUBERC/links_rs;
|
|
|
2356 res[ZDDLL]= 0.0;
|
|
|
2357 return(LF_OK);
|
|
|
2358 }
|
|
|
2359 res[ZDLL] = sw*z/links_rs;
|
|
|
2360 res[ZDDLL] = w/(links_rs*links_rs);
|
|
|
2361 return(LF_OK);
|
|
|
2362 }
|
|
|
2363
|
|
|
2364 int cauchy_fam(y,p,th,link,res,cens,w)
|
|
|
2365 double y, p, th, *res, w;
|
|
|
2366 int link, cens;
|
|
|
2367 { double z;
|
|
|
2368 if (link!=LIDENT)
|
|
|
2369 { LERR(("Invalid link in famcauc"));
|
|
|
2370 return(LF_LNK);
|
|
|
2371 }
|
|
|
2372 z = w*(y-th)/links_rs;
|
|
|
2373 res[ZLIK] = -log(1+z*z);
|
|
|
2374 res[ZDLL] = 2*w*z/(links_rs*(1+z*z));
|
|
|
2375 res[ZDDLL] = 2*w*w*(1-z*z)/(links_rs*links_rs*(1+z*z)*(1+z*z));
|
|
|
2376 return(LF_OK);
|
|
|
2377 }
|
|
|
2378
|
|
|
2379 extern double lf_tol;
|
|
|
2380 int robust_init(lfd,des,sp)
|
|
|
2381 lfdata *lfd;
|
|
|
2382 design *des;
|
|
|
2383 smpar *sp;
|
|
|
2384 { int i;
|
|
|
2385 for (i=0; i<des->n; i++)
|
|
|
2386 des->res[i] = resp(lfd,(int)des->ind[i]) - base(lfd,(int)des->ind[i]);
|
|
|
2387 des->cf[0] = median(des->res,des->n);
|
|
|
2388 for (i=1; i<des->p; i++) des->cf[i] = 0.0;
|
|
|
2389 lf_tol = 1.0e-6;
|
|
|
2390 return(LF_OK);
|
|
|
2391 }
|
|
|
2392
|
|
|
2393 void setfrobust(fam)
|
|
|
2394 family *fam;
|
|
|
2395 { fam->deflink = LIDENT;
|
|
|
2396 fam->canlink = LIDENT;
|
|
|
2397 fam->vallink = robust_vallink;
|
|
|
2398 fam->family = robust_fam;
|
|
|
2399 fam->initial = robust_init;
|
|
|
2400 fam->robust = 0;
|
|
|
2401 }
|
|
|
2402
|
|
|
2403 void setfcauchy(fam)
|
|
|
2404 family *fam;
|
|
|
2405 { fam->deflink = LIDENT;
|
|
|
2406 fam->canlink = LIDENT;
|
|
|
2407 fam->vallink = robust_vallink;
|
|
|
2408 fam->family = cauchy_fam;
|
|
|
2409 fam->initial = robust_init;
|
|
|
2410 fam->robust = 0;
|
|
|
2411 }
|
|
|
2412 /*
|
|
|
2413 * Copyright 1996-2006 Catherine Loader.
|
|
|
2414 */
|
|
|
2415 #include "locf.h"
|
|
|
2416
|
|
|
2417 int weibull_vallink(link)
|
|
|
2418 int link;
|
|
|
2419 { return((link==LIDENT) | (link==LLOG) | (link==LLOGIT));
|
|
|
2420 }
|
|
|
2421
|
|
|
2422 int weibull_fam(y,mean,th,link,res,cens,w)
|
|
|
2423 double y, mean, th, *res, w;
|
|
|
2424 int link, cens;
|
|
|
2425 { double yy;
|
|
|
2426 yy = pow(y,w);
|
|
|
2427 if (link==LINIT)
|
|
|
2428 { res[ZDLL] = MAX(yy,0.0);
|
|
|
2429 return(LF_OK);
|
|
|
2430 }
|
|
|
2431 if (cens)
|
|
|
2432 { res[ZLIK] = -yy/mean;
|
|
|
2433 res[ZDLL] = res[ZDDLL] = yy/mean;
|
|
|
2434 return(LF_OK);
|
|
|
2435 }
|
|
|
2436 res[ZLIK] = 1-yy/mean-th;
|
|
|
2437 if (yy>0) res[ZLIK] += log(w*yy);
|
|
|
2438 res[ZDLL] = -1+yy/mean;
|
|
|
2439 res[ZDDLL]= yy/mean;
|
|
|
2440 return(LF_OK);
|
|
|
2441 }
|
|
|
2442
|
|
|
2443 void setfweibull(fam)
|
|
|
2444 family *fam;
|
|
|
2445 { fam->deflink = LLOG;
|
|
|
2446 fam->canlink = LLOG;
|
|
|
2447 fam->vallink = weibull_vallink;
|
|
|
2448 fam->family = weibull_fam;
|
|
|
2449 fam->robust = 0;
|
|
|
2450 }
|
|
|
2451 /*
|
|
|
2452 * Copyright 1996-2006 Catherine Loader.
|
|
|
2453 */
|
|
|
2454 /*
|
|
|
2455 Functions implementing the adaptive bandwidth selection.
|
|
|
2456 Will make the final call to nbhd() to set smoothing weights
|
|
|
2457 for selected bandwidth, But will **not** make the
|
|
|
2458 final call to locfit().
|
|
|
2459 */
|
|
|
2460
|
|
|
2461 #include "locf.h"
|
|
|
2462
|
|
|
2463 static double hmin;
|
|
|
2464
|
|
|
2465 #define NACRI 5
|
|
|
2466 static char *atype[NACRI] = { "none", "cp", "ici", "mindex", "ok" };
|
|
|
2467 static int avals[NACRI] = { ANONE, ACP, AKAT, AMDI, AOK };
|
|
|
2468 int lfacri(char *z)
|
|
|
2469 { return(pmatch(z, atype, avals, NACRI, ANONE));
|
|
|
2470 }
|
|
|
2471
|
|
|
2472 double adcri(lk,t0,t2,pen)
|
|
|
2473 double lk, t0, t2, pen;
|
|
|
2474 { double y;
|
|
|
2475 /* return(-2*lk/(t0*exp(pen*log(1-t2/t0)))); */
|
|
|
2476 /* return((-2*lk+pen*t2)/t0); */
|
|
|
2477 y = (MAX(-2*lk,t0-t2)+pen*t2)/t0;
|
|
|
2478 return(y);
|
|
|
2479 }
|
|
|
2480
|
|
|
2481 double mmse(lfd,sp,dv,des)
|
|
|
2482 lfdata *lfd;
|
|
|
2483 smpar *sp;
|
|
|
2484 deriv *dv;
|
|
|
2485 design *des;
|
|
|
2486 { int i, ii, j, p, p1;
|
|
|
2487 double sv, sb, *l, dp;
|
|
|
2488
|
|
|
2489 l = des->wd;
|
|
|
2490 wdiag(lfd, sp, des,l,dv,0,1,0);
|
|
|
2491 sv = sb = 0;
|
|
|
2492 p = npar(sp);
|
|
|
2493 for (i=0; i<des->n; i++)
|
|
|
2494 { sv += l[i]*l[i];
|
|
|
2495 ii = des->ind[i];
|
|
|
2496 dp = dist(des,ii);
|
|
|
2497 for (j=0; j<deg(sp); j++) dp *= dist(des,ii);
|
|
|
2498 sb += fabs(l[i])*dp;
|
|
|
2499 }
|
|
|
2500 p1 = factorial(deg(sp)+1);
|
|
|
2501 printf("%8.5f sv %8.5f sb %8.5f %8.5f\n",des->h,sv,sb,sv+sb*sb*pen(sp)*pen(sp)/(p1*p1));
|
|
|
2502 return(sv+sb*sb*pen(sp)*pen(sp)/(p1*p1));
|
|
|
2503 }
|
|
|
2504
|
|
|
2505 static double mcp, clo, cup;
|
|
|
2506
|
|
|
2507 /*
|
|
|
2508 Initial bandwidth will be (by default)
|
|
|
2509 k-nearest neighbors for k small, just large enough to
|
|
|
2510 get defined estimate (unless user provided nonzero nn or fix-h components)
|
|
|
2511 */
|
|
|
2512
|
|
|
2513 int ainitband(lfd,sp,dv,des)
|
|
|
2514 lfdata *lfd;
|
|
|
2515 smpar *sp;
|
|
|
2516 deriv *dv;
|
|
|
2517 design *des;
|
|
|
2518 { int lf_status, p, z, cri, noit, redo;
|
|
|
2519 double ho, t[6];
|
|
|
2520
|
|
|
2521 if (lf_debug >= 2) mut_printf("ainitband:\n");
|
|
|
2522 p = des->p;
|
|
|
2523 cri = acri(sp);
|
|
|
2524 noit = (cri!=AOK);
|
|
|
2525 z = (int)(lfd->n*nn(sp));
|
|
|
2526 if ((noit) && (z<p+2)) z = p+2;
|
|
|
2527 redo = 0; ho = -1;
|
|
|
2528 do
|
|
|
2529 {
|
|
|
2530 nbhd(lfd,des,z,redo,sp);
|
|
|
2531 if (z<des->n) z = des->n;
|
|
|
2532 if (des->h>ho) lf_status = locfit(lfd,des,sp,noit,0,0);
|
|
|
2533 z++;
|
|
|
2534 redo = 1;
|
|
|
2535 } while ((z<=lfd->n) && ((des->h==0)||(lf_status!=LF_OK)));
|
|
|
2536 hmin = des->h;
|
|
|
2537
|
|
|
2538 switch(cri)
|
|
|
2539 { case ACP:
|
|
|
2540 local_df(lfd,sp,des,t);
|
|
|
2541 mcp = adcri(des->llk,t[0],t[2],pen(sp));
|
|
|
2542 return(lf_status);
|
|
|
2543 case AKAT:
|
|
|
2544 local_df(lfd,sp,des,t);
|
|
|
2545 clo = des->cf[0]-pen(sp)*t[5];
|
|
|
2546 cup = des->cf[0]+pen(sp)*t[5];
|
|
|
2547 return(lf_status);
|
|
|
2548 case AMDI:
|
|
|
2549 mcp = mmse(lfd,sp,dv,des);
|
|
|
2550 return(lf_status);
|
|
|
2551 case AOK: return(lf_status);
|
|
|
2552 }
|
|
|
2553 LERR(("aband1: unknown criterion"));
|
|
|
2554 return(LF_ERR);
|
|
|
2555 }
|
|
|
2556
|
|
|
2557 /*
|
|
|
2558 aband2 increases the initial bandwidth until lack of fit results,
|
|
|
2559 or the fit is close to a global fit. Increase h by 1+0.3/d at
|
|
|
2560 each iteration.
|
|
|
2561 */
|
|
|
2562
|
|
|
2563 double aband2(lfd,sp,dv,des,h0)
|
|
|
2564 lfdata *lfd;
|
|
|
2565 smpar *sp;
|
|
|
2566 deriv *dv;
|
|
|
2567 design *des;
|
|
|
2568 double h0;
|
|
|
2569 { double t[6], h1, nu1, cp, ncp, tlo, tup;
|
|
|
2570 int d, inc, n, p, done;
|
|
|
2571
|
|
|
2572 if (lf_debug >= 2) mut_printf("aband2:\n");
|
|
|
2573 d = lfd->d; n = lfd->n; p = npar(sp);
|
|
|
2574 h1 = des->h = h0;
|
|
|
2575 done = 0; nu1 = 0.0;
|
|
|
2576 inc = 0; ncp = 0.0;
|
|
|
2577 while ((!done) & (nu1<(n-p)*0.95))
|
|
|
2578 { fixh(sp) = (1+0.3/d)*des->h;
|
|
|
2579 nbhd(lfd,des,0,1,sp);
|
|
|
2580 if (locfit(lfd,des,sp,1,0,0) > 0) WARN(("aband2: failed fit"));
|
|
|
2581 local_df(lfd,sp,des,t);
|
|
|
2582 nu1 = t[0]-t[2]; /* tr(A) */
|
|
|
2583 switch(acri(sp))
|
|
|
2584 { case AKAT:
|
|
|
2585 tlo = des->cf[0]-pen(sp)*t[5];
|
|
|
2586 tup = des->cf[0]+pen(sp)*t[5];
|
|
|
2587 /* mut_printf("h %8.5f tlo %8.5f tup %8.5f\n",des->h,tlo,tup); */
|
|
|
2588 done = ((tlo>cup) | (tup<clo));
|
|
|
2589 if (!done)
|
|
|
2590 { clo = MAX(clo,tlo);
|
|
|
2591 cup = MIN(cup,tup);
|
|
|
2592 h1 = des->h;
|
|
|
2593 }
|
|
|
2594 break;
|
|
|
2595 case ACP:
|
|
|
2596 cp = adcri(des->llk,t[0],t[2],pen(sp));
|
|
|
2597 /* mut_printf("h %8.5f lk %8.5f t0 %8.5f t2 %8.5f cp %8.5f\n",des->h,des->llk,t[0],t[2],cp); */
|
|
|
2598 if (cp<mcp) { mcp = cp; h1 = des->h; }
|
|
|
2599 if (cp>=ncp) inc++; else inc = 0;
|
|
|
2600 ncp = cp;
|
|
|
2601 done = (inc>=10) | ((inc>=3) & ((t[0]-t[2])>=10) & (cp>1.5*mcp));
|
|
|
2602 break;
|
|
|
2603 case AMDI:
|
|
|
2604 cp = mmse(lfd,sp,dv,des);
|
|
|
2605 if (cp<mcp) { mcp = cp; h1 = des->h; }
|
|
|
2606 if (cp>ncp) inc++; else inc = 0;
|
|
|
2607 ncp = cp;
|
|
|
2608 done = (inc>=3);
|
|
|
2609 break;
|
|
|
2610 }
|
|
|
2611 }
|
|
|
2612 return(h1);
|
|
|
2613 }
|
|
|
2614
|
|
|
2615 /*
|
|
|
2616 aband3 does a finer search around best h so far. Try
|
|
|
2617 h*(1-0.2/d), h/(1-0.1/d), h*(1+0.1/d), h*(1+0.2/d)
|
|
|
2618 */
|
|
|
2619 double aband3(lfd,sp,dv,des,h0)
|
|
|
2620 lfdata *lfd;
|
|
|
2621 smpar *sp;
|
|
|
2622 deriv *dv;
|
|
|
2623 design *des;
|
|
|
2624 double h0;
|
|
|
2625 { double t[6], h1, cp, tlo, tup;
|
|
|
2626 int i, i0, d, n;
|
|
|
2627
|
|
|
2628 if (lf_debug >= 2) mut_printf("aband3:\n");
|
|
|
2629 d = lfd->d; n = lfd->n;
|
|
|
2630 h1 = h0;
|
|
|
2631 i0 = (acri(sp)==AKAT) ? 1 : -2;
|
|
|
2632 if (h0==hmin) i0 = 1;
|
|
|
2633
|
|
|
2634 for (i=i0; i<=2; i++)
|
|
|
2635 { if (i==0) i++;
|
|
|
2636 fixh(sp) = h0*(1+0.1*i/d);
|
|
|
2637 nbhd(lfd,des,0,1,sp);
|
|
|
2638 if (locfit(lfd,des,sp,1,0,0) > 0) WARN(("aband3: failed fit"));
|
|
|
2639 local_df(lfd,sp,des,t);
|
|
|
2640 switch (acri(sp))
|
|
|
2641 { case AKAT:
|
|
|
2642 tlo = des->cf[0]-pen(sp)*t[5];
|
|
|
2643 tup = des->cf[0]+pen(sp)*t[5];
|
|
|
2644 if ((tlo>cup) | (tup<clo)) /* done */
|
|
|
2645 i = 2;
|
|
|
2646 else
|
|
|
2647 { h1 = des->h;
|
|
|
2648 clo = MAX(clo,tlo);
|
|
|
2649 cup = MIN(cup,tup);
|
|
|
2650 }
|
|
|
2651 break;
|
|
|
2652 case ACP:
|
|
|
2653 cp = adcri(des->llk,t[0],t[2],pen(sp));
|
|
|
2654 if (cp<mcp) { mcp = cp; h1 = des->h; }
|
|
|
2655 else
|
|
|
2656 { if (i>0) i = 2; }
|
|
|
2657 break;
|
|
|
2658 case AMDI:
|
|
|
2659 cp = mmse(lfd,sp,dv,des);
|
|
|
2660 if (cp<mcp) { mcp = cp; h1 = des->h; }
|
|
|
2661 else
|
|
|
2662 { if (i>0) i = 2; }
|
|
|
2663 }
|
|
|
2664 }
|
|
|
2665 return(h1);
|
|
|
2666 }
|
|
|
2667
|
|
|
2668 int alocfit(lfd,sp,dv,des,cv)
|
|
|
2669 lfdata *lfd;
|
|
|
2670 smpar *sp;
|
|
|
2671 deriv *dv;
|
|
|
2672 design *des;
|
|
|
2673 int cv;
|
|
|
2674 { int lf_status;
|
|
|
2675 double h0;
|
|
|
2676
|
|
|
2677 lf_status = ainitband(lfd,sp,dv,des);
|
|
|
2678 if (lf_error) return(lf_status);
|
|
|
2679 if (acri(sp) == AOK) return(lf_status);
|
|
|
2680
|
|
|
2681 h0 = fixh(sp);
|
|
|
2682 fixh(sp) = aband2(lfd,sp,dv,des,des->h);
|
|
|
2683 fixh(sp) = aband3(lfd,sp,dv,des,fixh(sp));
|
|
|
2684 nbhd(lfd,des,0,1,sp);
|
|
|
2685 lf_status = locfit(lfd,des,sp,0,0,cv);
|
|
|
2686 fixh(sp) = h0;
|
|
|
2687
|
|
|
2688 return(lf_status);
|
|
|
2689 }
|
|
|
2690 /*
|
|
|
2691 * Copyright 1996-2006 Catherine Loader.
|
|
|
2692 */
|
|
|
2693 /*
|
|
|
2694 *
|
|
|
2695 * Evaluate the locfit fitting functions.
|
|
|
2696 * calcp(sp,d)
|
|
|
2697 * calculates the number of fitting functions.
|
|
|
2698 * makecfn(sp,des,dv,d)
|
|
|
2699 * makes the coef.number vector.
|
|
|
2700 * fitfun(lfd, sp, x,t,f,dv)
|
|
|
2701 * lfd is the local fit structure.
|
|
|
2702 * sp smoothing parameter structure.
|
|
|
2703 * x is the data point.
|
|
|
2704 * t is the fitting point.
|
|
|
2705 * f is a vector to return the results.
|
|
|
2706 * dv derivative structure.
|
|
|
2707 * designmatrix(lfd, sp, des)
|
|
|
2708 * is a wrapper for fitfun to build the design matrix.
|
|
|
2709 *
|
|
|
2710 */
|
|
|
2711
|
|
|
2712 #include "locf.h"
|
|
|
2713
|
|
|
2714 int calcp(sp,d)
|
|
|
2715 smpar *sp;
|
|
|
2716 int d;
|
|
|
2717 { int i, k;
|
|
|
2718
|
|
|
2719 if (ubas(sp)) return(npar(sp));
|
|
|
2720
|
|
|
2721 switch (kt(sp))
|
|
|
2722 { case KSPH:
|
|
|
2723 case KCE:
|
|
|
2724 k = 1;
|
|
|
2725 for (i=1; i<=deg(sp); i++) k = k*(d+i)/i;
|
|
|
2726 return(k);
|
|
|
2727 case KPROD: return(d*deg(sp)+1);
|
|
|
2728 case KLM: return(d);
|
|
|
2729 case KZEON: return(1);
|
|
|
2730 }
|
|
|
2731 LERR(("calcp: invalid kt %d",kt(sp)));
|
|
|
2732 return(0);
|
|
|
2733 }
|
|
|
2734
|
|
|
2735 int coefnumber(dv,kt,d,deg)
|
|
|
2736 int kt, d, deg;
|
|
|
2737 deriv *dv;
|
|
|
2738 { int d0, d1, t;
|
|
|
2739
|
|
|
2740 if (d==1)
|
|
|
2741 { if (dv->nd<=deg) return(dv->nd);
|
|
|
2742 return(-1);
|
|
|
2743 }
|
|
|
2744
|
|
|
2745 if (dv->nd==0) return(0);
|
|
|
2746 if (deg==0) return(-1);
|
|
|
2747 if (dv->nd==1) return(1+dv->deriv[0]);
|
|
|
2748 if (deg==1) return(-1);
|
|
|
2749 if (kt==KPROD) return(-1);
|
|
|
2750
|
|
|
2751 if (dv->nd==2)
|
|
|
2752 { d0 = dv->deriv[0]; d1 = dv->deriv[1];
|
|
|
2753 if (d0<d1) { t = d0; d0 = d1; d1 = t; }
|
|
|
2754 return((d+1)*(d0+1)-d0*(d0+3)/2+d1);
|
|
|
2755 }
|
|
|
2756 if (deg==2) return(-1);
|
|
|
2757
|
|
|
2758 LERR(("coefnumber not programmed for nd>=3"));
|
|
|
2759 return(-1);
|
|
|
2760 }
|
|
|
2761
|
|
|
2762 void makecfn(sp,des,dv,d)
|
|
|
2763 smpar *sp;
|
|
|
2764 design *des;
|
|
|
2765 deriv *dv;
|
|
|
2766 int d;
|
|
|
2767 { int i, nd;
|
|
|
2768
|
|
|
2769 nd = dv->nd;
|
|
|
2770
|
|
|
2771 des->cfn[0] = coefnumber(dv,kt(sp),d,deg(sp));
|
|
|
2772 des->ncoef = 1;
|
|
|
2773 if (nd >= deg(sp)) return;
|
|
|
2774 if (kt(sp)==KZEON) return;
|
|
|
2775
|
|
|
2776 if (d>1)
|
|
|
2777 { if (nd>=2) return;
|
|
|
2778 if ((nd>=1) && (kt(sp)==KPROD)) return;
|
|
|
2779 }
|
|
|
2780
|
|
|
2781 dv->nd = nd+1;
|
|
|
2782 for (i=0; i<d; i++)
|
|
|
2783 { dv->deriv[nd] = i;
|
|
|
2784 des->cfn[i+1] = coefnumber(dv,kt(sp),d,deg(sp));
|
|
|
2785 }
|
|
|
2786 dv->nd = nd;
|
|
|
2787
|
|
|
2788 des->ncoef = 1+d;
|
|
|
2789 }
|
|
|
2790
|
|
|
2791 void fitfunangl(dx,ff,sca,cd,deg)
|
|
|
2792 double dx, *ff, sca;
|
|
|
2793 int deg, cd;
|
|
|
2794 {
|
|
|
2795 if (deg>=3) WARN(("Can't handle angular model with deg>=3"));
|
|
|
2796
|
|
|
2797 switch(cd)
|
|
|
2798 { case 0:
|
|
|
2799 ff[0] = 1;
|
|
|
2800 ff[1] = sin(dx/sca)*sca;
|
|
|
2801 ff[2] = (1-cos(dx/sca))*sca*sca;
|
|
|
2802 return;
|
|
|
2803 case 1:
|
|
|
2804 ff[0] = 0;
|
|
|
2805 ff[1] = cos(dx/sca);
|
|
|
2806 ff[2] = sin(dx/sca)*sca;
|
|
|
2807 return;
|
|
|
2808 case 2:
|
|
|
2809 ff[0] = 0;
|
|
|
2810 ff[1] = -sin(dx/sca)/sca;
|
|
|
2811 ff[2] = cos(dx/sca);
|
|
|
2812 return;
|
|
|
2813 default: WARN(("Can't handle angular model with >2 derivs"));
|
|
|
2814 }
|
|
|
2815 }
|
|
|
2816
|
|
|
2817 void fitfun(lfd,sp,x,t,f,dv)
|
|
|
2818 lfdata *lfd;
|
|
|
2819 smpar *sp;
|
|
|
2820 double *x, *t, *f;
|
|
|
2821 deriv *dv;
|
|
|
2822 { int d, deg, nd, m, i, j, k, ct_deriv[MXDIM];
|
|
|
2823 double ff[MXDIM][1+MXDEG], dx[MXDIM], *xx[MXDIM];
|
|
|
2824
|
|
|
2825 if (ubas(sp))
|
|
|
2826 { for (i=0; i<lfd->d; i++) xx[i] = &x[i];
|
|
|
2827 i = 0;
|
|
|
2828 sp->vbasis(xx,t,1,lfd->d,1,npar(sp),f);
|
|
|
2829 return;
|
|
|
2830 }
|
|
|
2831
|
|
|
2832 d = lfd->d;
|
|
|
2833 deg = deg(sp);
|
|
|
2834 m = 0;
|
|
|
2835 nd = (dv==NULL) ? 0 : dv->nd;
|
|
|
2836
|
|
|
2837 if (kt(sp)==KZEON)
|
|
|
2838 { f[0] = 1.0;
|
|
|
2839 return;
|
|
|
2840 }
|
|
|
2841
|
|
|
2842 if (kt(sp)==KLM)
|
|
|
2843 { for (i=0; i<d; i++) f[m++] = x[i];
|
|
|
2844 return;
|
|
|
2845 }
|
|
|
2846
|
|
|
2847 f[m++] = (nd==0);
|
|
|
2848 if (deg==0) return;
|
|
|
2849
|
|
|
2850 for (i=0; i<d; i++)
|
|
|
2851 { ct_deriv[i] = 0;
|
|
|
2852 dx[i] = (t==NULL) ? x[i] : x[i]-t[i];
|
|
|
2853 }
|
|
|
2854 for (i=0; i<nd; i++) ct_deriv[dv->deriv[i]]++;
|
|
|
2855
|
|
|
2856 for (i=0; i<d; i++)
|
|
|
2857 { switch(lfd->sty[i])
|
|
|
2858 {
|
|
|
2859 case STANGL:
|
|
|
2860 fitfunangl(dx[i],ff[i],lfd->sca[i],ct_deriv[i],deg(sp));
|
|
|
2861 break;
|
|
|
2862 default:
|
|
|
2863 for (j=0; j<ct_deriv[i]; j++) ff[i][j] = 0.0;
|
|
|
2864 ff[i][ct_deriv[i]] = 1.0;
|
|
|
2865 for (j=ct_deriv[i]+1; j<=deg; j++)
|
|
|
2866 ff[i][j] = ff[i][j-1]*dx[i]/(j-ct_deriv[i]);
|
|
|
2867 }
|
|
|
2868 }
|
|
|
2869
|
|
|
2870 /*
|
|
|
2871 * Product kernels. Note that if ct_deriv[i] != nd, that implies
|
|
|
2872 * there is differentiation wrt another variable, and all components
|
|
|
2873 * involving x[i] are 0.
|
|
|
2874 */
|
|
|
2875 if ((d==1) || (kt(sp)==KPROD))
|
|
|
2876 { for (j=1; j<=deg; j++)
|
|
|
2877 for (i=0; i<d; i++)
|
|
|
2878 f[m++] = (ct_deriv[i]==nd) ? ff[i][j] : 0.0;
|
|
|
2879 return;
|
|
|
2880 }
|
|
|
2881
|
|
|
2882 /*
|
|
|
2883 * Spherical kernels with the full polynomial basis.
|
|
|
2884 * Presently implemented up to deg=3.
|
|
|
2885 */
|
|
|
2886 for (i=0; i<d; i++)
|
|
|
2887 f[m++] = (ct_deriv[i]==nd) ? ff[i][1] : 0.0;
|
|
|
2888 if (deg==1) return;
|
|
|
2889
|
|
|
2890 for (i=0; i<d; i++)
|
|
|
2891 {
|
|
|
2892 /* xi^2/2 terms. */
|
|
|
2893 f[m++] = (ct_deriv[i]==nd) ? ff[i][2] : 0.0;
|
|
|
2894
|
|
|
2895 /* xi xj terms */
|
|
|
2896 for (j=i+1; j<d; j++)
|
|
|
2897 f[m++] = (ct_deriv[i]+ct_deriv[j]==nd) ? ff[i][1]*ff[j][1] : 0.0;
|
|
|
2898 }
|
|
|
2899 if (deg==2) return;
|
|
|
2900
|
|
|
2901 for (i=0; i<d; i++)
|
|
|
2902 {
|
|
|
2903 /* xi^3/6 terms */
|
|
|
2904 f[m++] = (ct_deriv[i]==nd) ? ff[i][3] : 0.0;
|
|
|
2905
|
|
|
2906 /* xi^2/2 xk terms */
|
|
|
2907 for (k=i+1; k<d; k++)
|
|
|
2908 f[m++] = (ct_deriv[i]+ct_deriv[k]==nd) ? ff[i][2]*ff[k][1] : 0.0;
|
|
|
2909
|
|
|
2910 /* xi xj xk terms */
|
|
|
2911 for (j=i+1; j<d; j++)
|
|
|
2912 { f[m++] = (ct_deriv[i]+ct_deriv[j]==nd) ? ff[i][1]*ff[j][2] : 0.0;
|
|
|
2913 for (k=j+1; k<d; k++)
|
|
|
2914 f[m++] = (ct_deriv[i]+ct_deriv[j]+ct_deriv[k]==nd) ?
|
|
|
2915 ff[i][1]*ff[j][1]*ff[k][1] : 0.0;
|
|
|
2916 }
|
|
|
2917 }
|
|
|
2918 if (deg==3) return;
|
|
|
2919
|
|
|
2920 LERR(("fitfun: can't handle deg=%d for spherical kernels",deg));
|
|
|
2921 }
|
|
|
2922
|
|
|
2923 /*
|
|
|
2924 * Build the design matrix. Assumes des->ind contains the indices of
|
|
|
2925 * the required data points; des->n the number of points; des->xev
|
|
|
2926 * the fitting point.
|
|
|
2927 */
|
|
|
2928 void designmatrix(lfd,sp,des)
|
|
|
2929 lfdata *lfd;
|
|
|
2930 smpar *sp;
|
|
|
2931 design *des;
|
|
|
2932 { int i, ii, j, p;
|
|
|
2933 double *X, u[MXDIM];
|
|
|
2934
|
|
|
2935 X = d_x(des);
|
|
|
2936 p = des->p;
|
|
|
2937
|
|
|
2938 if (ubas(sp))
|
|
|
2939 {
|
|
|
2940 sp->vbasis(lfd->x,des->xev,lfd->n,lfd->d,des->n,p,X);
|
|
|
2941 return;
|
|
|
2942 }
|
|
|
2943
|
|
|
2944 for (i=0; i<des->n; i++)
|
|
|
2945 { ii = des->ind[i];
|
|
|
2946 for (j=0; j<lfd->d; j++) u[j] = datum(lfd,j,ii);
|
|
|
2947 fitfun(lfd,sp,u,des->xev,&X[ii*p],NULL);
|
|
|
2948 }
|
|
|
2949 }
|
|
|
2950 /*
|
|
|
2951 * Copyright 1996-2006 Catherine Loader.
|
|
|
2952 */
|
|
|
2953 /*
|
|
|
2954 *
|
|
|
2955 *
|
|
|
2956 * Functions for determining bandwidth; smoothing neighborhood
|
|
|
2957 * and smoothing weights.
|
|
|
2958 */
|
|
|
2959
|
|
|
2960 #include "locf.h"
|
|
|
2961
|
|
|
2962 double rho(x,sc,d,kt,sty) /* ||x|| for appropriate distance metric */
|
|
|
2963 double *x, *sc;
|
|
|
2964 int d, kt, *sty;
|
|
|
2965 { double rhoi[MXDIM], s;
|
|
|
2966 int i;
|
|
|
2967 for (i=0; i<d; i++)
|
|
|
2968 { if (sty!=NULL)
|
|
|
2969 { switch(sty[i])
|
|
|
2970 { case STANGL: rhoi[i] = 2*sin(x[i]/(2*sc[i])); break;
|
|
|
2971 case STCPAR: rhoi[i] = 0; break;
|
|
|
2972 default: rhoi[i] = x[i]/sc[i];
|
|
|
2973 } }
|
|
|
2974 else rhoi[i] = x[i]/sc[i];
|
|
|
2975 }
|
|
|
2976
|
|
|
2977 if (d==1) return(fabs(rhoi[0]));
|
|
|
2978
|
|
|
2979 s = 0;
|
|
|
2980 if (kt==KPROD)
|
|
|
2981 { for (i=0; i<d; i++)
|
|
|
2982 { rhoi[i] = fabs(rhoi[i]);
|
|
|
2983 if (rhoi[i]>s) s = rhoi[i];
|
|
|
2984 }
|
|
|
2985 return(s);
|
|
|
2986 }
|
|
|
2987
|
|
|
2988 if (kt==KSPH)
|
|
|
2989 { for (i=0; i<d; i++)
|
|
|
2990 s += rhoi[i]*rhoi[i];
|
|
|
2991 return(sqrt(s));
|
|
|
2992 }
|
|
|
2993
|
|
|
2994 LERR(("rho: invalid kt"));
|
|
|
2995 return(0.0);
|
|
|
2996 }
|
|
|
2997
|
|
|
2998 double kordstat(x,k,n,ind)
|
|
|
2999 double *x;
|
|
|
3000 int k, n, *ind;
|
|
|
3001 { int i, i0, i1, l, r;
|
|
|
3002 double piv;
|
|
|
3003 if (k<1) return(0.0);
|
|
|
3004 i0 = 0; i1 = n-1;
|
|
|
3005 while (1)
|
|
|
3006 { piv = x[ind[(i0+i1)/2]];
|
|
|
3007 l = i0; r = i1;
|
|
|
3008 while (l<=r)
|
|
|
3009 { while ((l<=i1) && (x[ind[l]]<=piv)) l++;
|
|
|
3010 while ((r>=i0) && (x[ind[r]]>piv)) r--;
|
|
|
3011 if (l<=r) ISWAP(ind[l],ind[r]);
|
|
|
3012 } /* now, x[ind[i0..r]] <= piv < x[ind[l..i1]] */
|
|
|
3013 if (r<k-1) i0 = l; /* go right */
|
|
|
3014 else /* put pivots in middle */
|
|
|
3015 { for (i=i0; i<=r; )
|
|
|
3016 if (x[ind[i]]==piv) { ISWAP(ind[i],ind[r]); r--; }
|
|
|
3017 else i++;
|
|
|
3018 if (r<k-1) return(piv);
|
|
|
3019 i1 = r;
|
|
|
3020 }
|
|
|
3021 }
|
|
|
3022 }
|
|
|
3023
|
|
|
3024 /* check if i'th data point is in limits */
|
|
|
3025 int inlim(lfd,i)
|
|
|
3026 lfdata *lfd;
|
|
|
3027 int i;
|
|
|
3028 { int d, j, k;
|
|
|
3029 double *xlim;
|
|
|
3030
|
|
|
3031 xlim = lfd->xl;
|
|
|
3032 d = lfd->d;
|
|
|
3033 k = 1;
|
|
|
3034 for (j=0; j<d; j++)
|
|
|
3035 { if (xlim[j]<xlim[j+d])
|
|
|
3036 k &= ((datum(lfd,j,i)>=xlim[j]) & (datum(lfd,j,i)<=xlim[j+d]));
|
|
|
3037 }
|
|
|
3038 return(k);
|
|
|
3039 }
|
|
|
3040
|
|
|
3041 double compbandwid(di,ind,x,n,d,nn,fxh)
|
|
|
3042 double *di, *x, fxh;
|
|
|
3043 int n, d, nn, *ind;
|
|
|
3044 { int i;
|
|
|
3045 double nnh;
|
|
|
3046
|
|
|
3047 if (nn==0) return(fxh);
|
|
|
3048
|
|
|
3049 if (nn<n)
|
|
|
3050 nnh = kordstat(di,nn,n,ind);
|
|
|
3051 else
|
|
|
3052 { nnh = 0;
|
|
|
3053 for (i=0; i<n; i++) nnh = MAX(nnh,di[i]);
|
|
|
3054 nnh = nnh*exp(log(1.0*nn/n)/d);
|
|
|
3055 }
|
|
|
3056 return(MAX(fxh,nnh));
|
|
|
3057 }
|
|
|
3058
|
|
|
3059 /*
|
|
|
3060 fast version of nbhd for ordered 1-d data
|
|
|
3061 */
|
|
|
3062 void nbhd1(lfd,sp,des,k)
|
|
|
3063 lfdata *lfd;
|
|
|
3064 smpar *sp;
|
|
|
3065 design *des;
|
|
|
3066 int k;
|
|
|
3067 { double x, h, *xd, sc;
|
|
|
3068 int i, l, r, m, n, z;
|
|
|
3069
|
|
|
3070 n = lfd->n;
|
|
|
3071 x = des->xev[0];
|
|
|
3072 xd = dvari(lfd,0);
|
|
|
3073 sc = lfd->sca[0];
|
|
|
3074
|
|
|
3075 /* find closest data point to x */
|
|
|
3076 if (x<=xd[0]) z = 0;
|
|
|
3077 else
|
|
|
3078 if (x>=xd[n-1]) z = n-1;
|
|
|
3079 else
|
|
|
3080 { l = 0; r = n-1;
|
|
|
3081 while (r-l>1)
|
|
|
3082 { z = (r+l)/2;
|
|
|
3083 if (xd[z]>x) r = z;
|
|
|
3084 else l = z;
|
|
|
3085 }
|
|
|
3086 /* now, xd[0..l] <= x < x[r..n-1] */
|
|
|
3087 if ((x-xd[l])>(xd[r]-x)) z = r; else z = l;
|
|
|
3088 }
|
|
|
3089 /* closest point to x is xd[z] */
|
|
|
3090
|
|
|
3091 if (nn(sp)<0) /* user bandwidth */
|
|
|
3092 h = sp->vb(des->xev);
|
|
|
3093 else
|
|
|
3094 { if (k>0) /* set h to nearest neighbor bandwidth */
|
|
|
3095 { l = r = z;
|
|
|
3096 if (l==0) r = k-1;
|
|
|
3097 if (r==n-1) l = n-k;
|
|
|
3098 while (r-l<k-1)
|
|
|
3099 { if ((x-xd[l-1])<(xd[r+1]-x)) l--; else r++;
|
|
|
3100 if (l==0) r = k-1;
|
|
|
3101 if (r==n-1) l = n-k;
|
|
|
3102 }
|
|
|
3103 h = x-xd[l];
|
|
|
3104 if (h<xd[r]-x) h = xd[r]-x;
|
|
|
3105 }
|
|
|
3106 else h = 0;
|
|
|
3107 h /= sc;
|
|
|
3108 if (h<fixh(sp)) h = fixh(sp);
|
|
|
3109 }
|
|
|
3110
|
|
|
3111 m = 0;
|
|
|
3112 if (xd[z]>x) z--; /* so xd[z]<=x */
|
|
|
3113 /* look left */
|
|
|
3114 for (i=z; i>=0; i--) if (inlim(lfd,i))
|
|
|
3115 { dist(des,i) = (x-xd[i])/sc;
|
|
|
3116 wght(des,i) = weight(lfd, sp, &xd[i], &x, h, 1, dist(des,i));
|
|
|
3117 if (wght(des,i)>0)
|
|
|
3118 { des->ind[m] = i;
|
|
|
3119 m++;
|
|
|
3120 } else i = 0;
|
|
|
3121 }
|
|
|
3122 /* look right */
|
|
|
3123 for (i=z+1; i<n; i++) if (inlim(lfd,i))
|
|
|
3124 { dist(des,i) = (xd[i]-x)/sc;
|
|
|
3125 wght(des,i) = weight(lfd, sp, &xd[i], &x, h, 1, dist(des,i));
|
|
|
3126 if (wght(des,i)>0)
|
|
|
3127 { des->ind[m] = i;
|
|
|
3128 m++;
|
|
|
3129 } else i = n;
|
|
|
3130 }
|
|
|
3131
|
|
|
3132 des->n = m;
|
|
|
3133 des->h = h;
|
|
|
3134 }
|
|
|
3135
|
|
|
3136 void nbhd_zeon(lfd,des)
|
|
|
3137 lfdata *lfd;
|
|
|
3138 design *des;
|
|
|
3139 { int i, j, m, eq;
|
|
|
3140
|
|
|
3141 m = 0;
|
|
|
3142 for (i=0; i<lfd->n; i++)
|
|
|
3143 { eq = 1;
|
|
|
3144 for (j=0; j<lfd->d; j++) eq = eq && (des->xev[j] == datum(lfd,j,i));
|
|
|
3145 if (eq)
|
|
|
3146 { wght(des,i) = 1;
|
|
|
3147 des->ind[m] = i;
|
|
|
3148 m++;
|
|
|
3149 }
|
|
|
3150 }
|
|
|
3151 des->n = m;
|
|
|
3152 des->h = 1.0;
|
|
|
3153 }
|
|
|
3154
|
|
|
3155 void nbhd(lfd,des,nn,redo,sp)
|
|
|
3156 lfdata *lfd;
|
|
|
3157 design *des;
|
|
|
3158 int redo, nn;
|
|
|
3159 smpar *sp;
|
|
|
3160 { int d, i, j, m, n;
|
|
|
3161 double h, u[MXDIM];
|
|
|
3162
|
|
|
3163 if (lf_debug>1) mut_printf("nbhd: nn %d fixh %8.5f\n",nn,fixh(sp));
|
|
|
3164
|
|
|
3165 d = lfd->d; n = lfd->n;
|
|
|
3166
|
|
|
3167 if (ker(sp)==WPARM)
|
|
|
3168 { for (i=0; i<n; i++)
|
|
|
3169 { wght(des,i) = 1.0;
|
|
|
3170 des->ind[i] = i;
|
|
|
3171 }
|
|
|
3172 des->n = n;
|
|
|
3173 return;
|
|
|
3174 }
|
|
|
3175
|
|
|
3176 if (kt(sp)==KZEON)
|
|
|
3177 { nbhd_zeon(lfd,des);
|
|
|
3178 return;
|
|
|
3179 }
|
|
|
3180
|
|
|
3181 if (kt(sp)==KCE)
|
|
|
3182 { des->h = 0.0;
|
|
|
3183 return;
|
|
|
3184 }
|
|
|
3185
|
|
|
3186 /* ordered 1-dim; use fast searches */
|
|
|
3187 if ((nn<=n) & (lfd->ord) & (ker(sp)!=WMINM) & (lfd->sty[0]!=STANGL))
|
|
|
3188 { nbhd1(lfd,sp,des,nn);
|
|
|
3189 return;
|
|
|
3190 }
|
|
|
3191
|
|
|
3192 if (!redo)
|
|
|
3193 { for (i=0; i<n; i++)
|
|
|
3194 { for (j=0; j<d; j++) u[j] = datum(lfd,j,i)-des->xev[j];
|
|
|
3195 dist(des,i) = rho(u,lfd->sca,d,kt(sp),lfd->sty);
|
|
|
3196 des->ind[i] = i;
|
|
|
3197 }
|
|
|
3198 }
|
|
|
3199 else
|
|
|
3200 for (i=0; i<n; i++) des->ind[i] = i;
|
|
|
3201
|
|
|
3202 if (ker(sp)==WMINM)
|
|
|
3203 { des->h = minmax(lfd,des,sp);
|
|
|
3204 return;
|
|
|
3205 }
|
|
|
3206
|
|
|
3207 if (nn<0)
|
|
|
3208 h = sp->vb(des->xev);
|
|
|
3209 else
|
|
|
3210 h = compbandwid(des->di,des->ind,des->xev,n,lfd->d,nn,fixh(sp));
|
|
|
3211 m = 0;
|
|
|
3212 for (i=0; i<n; i++) if (inlim(lfd,i))
|
|
|
3213 { for (j=0; j<d; j++) u[j] = datum(lfd,j,i);
|
|
|
3214 wght(des,i) = weight(lfd, sp, u, des->xev, h, 1, dist(des,i));
|
|
|
3215 if (wght(des,i)>0)
|
|
|
3216 { des->ind[m] = i;
|
|
|
3217 m++;
|
|
|
3218 }
|
|
|
3219 }
|
|
|
3220 des->n = m;
|
|
|
3221 des->h = h;
|
|
|
3222 }
|
|
|
3223 /*
|
|
|
3224 * Copyright 1996-2006 Catherine Loader.
|
|
|
3225 */
|
|
|
3226 /*
|
|
|
3227 *
|
|
|
3228 * This file includes functions to solve for the scale estimate in
|
|
|
3229 * local robust regression and likelihood. The main entry point is
|
|
|
3230 * lf_robust(lfd,sp,des,mxit),
|
|
|
3231 * called from the locfit() function.
|
|
|
3232 *
|
|
|
3233 * The update_rs(x) accepts a residual scale x as the argument (actually,
|
|
|
3234 * it works on the log-scale). The function computes the local fit
|
|
|
3235 * assuming this residual scale, and re-estimates the scale from this
|
|
|
3236 * new fit. The final solution satisfies the fixed point equation
|
|
|
3237 * update_rs(x)=x. The function lf_robust() automatically calls
|
|
|
3238 * update_rs() through the fixed point iterations.
|
|
|
3239 *
|
|
|
3240 * The estimation of the scale from the fit is based on the sqrt of
|
|
|
3241 * the median deviance of observations with non-zero weights (in the
|
|
|
3242 * gaussian case, this is the median absolute residual).
|
|
|
3243 *
|
|
|
3244 * TODO:
|
|
|
3245 * Should use smoothing weights in the median.
|
|
|
3246 */
|
|
|
3247
|
|
|
3248 #include "locf.h"
|
|
|
3249
|
|
|
3250 extern int lf_status;
|
|
|
3251 double robscale;
|
|
|
3252
|
|
|
3253 static lfdata *rob_lfd;
|
|
|
3254 static smpar *rob_sp;
|
|
|
3255 static design *rob_des;
|
|
|
3256 static int rob_mxit;
|
|
|
3257
|
|
|
3258 double median(x,n)
|
|
|
3259 double *x;
|
|
|
3260 int n;
|
|
|
3261 { int i, j, lt, eq, gt;
|
|
|
3262 double lo, hi, s;
|
|
|
3263 lo = hi = x[0];
|
|
|
3264 for (i=0; i<n; i++)
|
|
|
3265 { lo = MIN(lo,x[i]);
|
|
|
3266 hi = MAX(hi,x[i]);
|
|
|
3267 }
|
|
|
3268 if (lo==hi) return(lo);
|
|
|
3269 lo -= (hi-lo);
|
|
|
3270 hi += (hi-lo);
|
|
|
3271 for (i=0; i<n; i++)
|
|
|
3272 { if ((x[i]>lo) & (x[i]<hi))
|
|
|
3273 { s = x[i]; lt = eq = gt = 0;
|
|
|
3274 for (j=0; j<n; j++)
|
|
|
3275 { lt += (x[j]<s);
|
|
|
3276 eq += (x[j]==s);
|
|
|
3277 gt += (x[j]>s);
|
|
|
3278 }
|
|
|
3279 if ((2*(lt+eq)>n) && (2*(gt+eq)>n)) return(s);
|
|
|
3280 if (2*(lt+eq)<=n) lo = s;
|
|
|
3281 if (2*(gt+eq)<=n) hi = s;
|
|
|
3282 }
|
|
|
3283 }
|
|
|
3284 return((hi+lo)/2);
|
|
|
3285 }
|
|
|
3286
|
|
|
3287 double nrobustscale(lfd,sp,des,rs)
|
|
|
3288 lfdata *lfd;
|
|
|
3289 smpar *sp;
|
|
|
3290 design *des;
|
|
|
3291 double rs;
|
|
|
3292 { int i, ii, p;
|
|
|
3293 double link[LLEN], sc, sd, sw, e;
|
|
|
3294 p = des->p; sc = sd = sw = 0.0;
|
|
|
3295 for (i=0; i<des->n; i++)
|
|
|
3296 { ii = des->ind[i];
|
|
|
3297 fitv(des,ii) = base(lfd,ii)+innerprod(des->cf,d_xi(des,ii),p);
|
|
|
3298 e = resp(lfd,ii)-fitv(des,ii);
|
|
|
3299 stdlinks(link,lfd,sp,ii,fitv(des,ii),rs);
|
|
|
3300 sc += wght(des,ii)*e*link[ZDLL];
|
|
|
3301 sd += wght(des,ii)*e*e*link[ZDDLL];
|
|
|
3302 sw += wght(des,ii);
|
|
|
3303 }
|
|
|
3304
|
|
|
3305 /* newton-raphson iteration for log(s)
|
|
|
3306 -psi(ei/s) - log(s); s = e^{-th}
|
|
|
3307 */
|
|
|
3308 rs *= exp((sc-sw)/(sd+sc));
|
|
|
3309 return(rs);
|
|
|
3310 }
|
|
|
3311
|
|
|
3312 double robustscale(lfd,sp,des)
|
|
|
3313 lfdata *lfd;
|
|
|
3314 smpar *sp;
|
|
|
3315 design *des;
|
|
|
3316 { int i, ii, p, fam, lin, or;
|
|
|
3317 double rs, link[LLEN];
|
|
|
3318 p = des->p;
|
|
|
3319 fam = fam(sp);
|
|
|
3320 lin = link(sp);
|
|
|
3321 or = fami(sp)->robust;
|
|
|
3322 fami(sp)->robust = 0;
|
|
|
3323
|
|
|
3324 for (i=0; i<des->n; i++)
|
|
|
3325 { ii = des->ind[i];
|
|
|
3326 fitv(des,ii) = base(lfd,ii) + innerprod(des->cf,d_xi(des,ii),p);
|
|
|
3327 links(fitv(des,ii),resp(lfd,ii),fami(sp),lin,link,cens(lfd,ii),prwt(lfd,ii),1.0);
|
|
|
3328 des->res[i] = -2*link[ZLIK];
|
|
|
3329 }
|
|
|
3330 fami(sp)->robust = or;
|
|
|
3331 rs = sqrt(median(des->res,des->n));
|
|
|
3332
|
|
|
3333 if (rs==0.0) rs = 1.0;
|
|
|
3334 return(rs);
|
|
|
3335 }
|
|
|
3336
|
|
|
3337 double update_rs(x)
|
|
|
3338 double x;
|
|
|
3339 { double nx;
|
|
|
3340 if (lf_status != LF_OK) return(x);
|
|
|
3341 robscale = exp(x);
|
|
|
3342 lfiter(rob_lfd,rob_sp,rob_des,rob_mxit);
|
|
|
3343 if (lf_status != LF_OK) return(x);
|
|
|
3344
|
|
|
3345 nx = log(robustscale(rob_lfd,rob_sp,rob_des));
|
|
|
3346 if (nx<x-0.2) nx = x-0.2;
|
|
|
3347 return(nx);
|
|
|
3348 }
|
|
|
3349
|
|
|
3350 void lf_robust(lfd,sp,des,mxit)
|
|
|
3351 lfdata *lfd;
|
|
|
3352 design *des;
|
|
|
3353 smpar *sp;
|
|
|
3354 int mxit;
|
|
|
3355 { double x;
|
|
|
3356 rob_lfd = lfd;
|
|
|
3357 rob_des = des;
|
|
|
3358 rob_sp = sp;
|
|
|
3359 rob_mxit = mxit;
|
|
|
3360 lf_status = LF_OK;
|
|
|
3361
|
|
|
3362 x = log(robustscale(lfd,sp,des));
|
|
|
3363
|
|
|
3364 solve_fp(update_rs, x, 1.0e-6, mxit);
|
|
|
3365 }
|
|
|
3366 /*
|
|
|
3367 * Copyright 1996-2006 Catherine Loader.
|
|
|
3368 */
|
|
|
3369 /*
|
|
|
3370 * Post-fitting functions to compute the local variance and
|
|
|
3371 * influence functions. Also the local degrees of freedom
|
|
|
3372 * calculations for adaptive smoothing.
|
|
|
3373 */
|
|
|
3374
|
|
|
3375 #include "locf.h"
|
|
|
3376
|
|
|
3377 extern double robscale;
|
|
|
3378
|
|
|
3379 /*
|
|
|
3380 vmat() computes (after the local fit..) the matrix
|
|
|
3381 M2 = X^T W^2 V X.
|
|
|
3382 M12 = (X^T W V X)^{-1} M2
|
|
|
3383 Also, for convenience, tr[0] = sum(wi) tr[1] = sum(wi^2).
|
|
|
3384 */
|
|
|
3385 void vmat(lfd, sp, des, M12, M2)
|
|
|
3386 lfdata *lfd;
|
|
|
3387 smpar *sp;
|
|
|
3388 design *des;
|
|
|
3389 double *M12, *M2;
|
|
|
3390 { int i, ii, p, nk, ok;
|
|
|
3391 double link[LLEN], h, ww, tr0, tr1;
|
|
|
3392 p = des->p;
|
|
|
3393 setzero(M2,p*p);
|
|
|
3394
|
|
|
3395 nk = -1;
|
|
|
3396
|
|
|
3397 /* for density estimation, use integral rather than
|
|
|
3398 sum form, if W^2 is programmed...
|
|
|
3399 */
|
|
|
3400 if ((fam(sp)<=THAZ) && (link(sp)==LLOG))
|
|
|
3401 { switch(ker(sp))
|
|
|
3402 { case WGAUS: nk = WGAUS; h = des->h/SQRT2; break;
|
|
|
3403 case WRECT: nk = WRECT; h = des->h; break;
|
|
|
3404 case WEPAN: nk = WBISQ; h = des->h; break;
|
|
|
3405 case WBISQ: nk = WQUQU; h = des->h; break;
|
|
|
3406 case WTCUB: nk = W6CUB; h = des->h; break;
|
|
|
3407 case WEXPL: nk = WEXPL; h = des->h/2; break;
|
|
|
3408 }
|
|
|
3409 }
|
|
|
3410
|
|
|
3411 tr0 = tr1 = 0.0;
|
|
|
3412 if (nk != -1)
|
|
|
3413 { ok = ker(sp); ker(sp) = nk;
|
|
|
3414 /* compute M2 using integration. Use M12 as work matrix. */
|
|
|
3415 (des->itype)(des->xev, M2, M12, des->cf, h);
|
|
|
3416 ker(sp) = ok;
|
|
|
3417 if (fam(sp)==TDEN) multmatscal(M2,des->smwt,p*p);
|
|
|
3418 tr0 = des->ss[0];
|
|
|
3419 tr1 = M2[0]; /* n int W e^<a,A> */
|
|
|
3420 }
|
|
|
3421 else
|
|
|
3422 { for (i=0; i<des->n; i++)
|
|
|
3423 { ii = des->ind[i];
|
|
|
3424 stdlinks(link,lfd,sp,ii,fitv(des,ii),robscale);
|
|
|
3425 ww = SQR(wght(des,ii))*link[ZDDLL];
|
|
|
3426 tr0 += wght(des,ii);
|
|
|
3427 tr1 += SQR(wght(des,ii));
|
|
|
3428 addouter(M2,d_xi(des,ii),d_xi(des,ii),p,ww);
|
|
|
3429 }
|
|
|
3430 }
|
|
|
3431 des->tr0 = tr0;
|
|
|
3432 des->tr1 = tr1;
|
|
|
3433
|
|
|
3434 memcpy(M12,M2,p*p*sizeof(double));
|
|
|
3435 for (i=0; i<p; i++)
|
|
|
3436 jacob_solve(&des->xtwx,&M12[i*p]);
|
|
|
3437 }
|
|
|
3438
|
|
|
3439 void lf_vcov(lfd,sp,des)
|
|
|
3440 lfdata *lfd;
|
|
|
3441 smpar *sp;
|
|
|
3442 design *des;
|
|
|
3443 { int i, j, k, p;
|
|
|
3444 double *M12, *M2;
|
|
|
3445 M12 = des->V; M2 = des->P; p = des->p;
|
|
|
3446 vmat(lfd,sp,des,M12,M2); /* M2 = X^T W^2 V X tr0=sum(W) tr1=sum(W*W) */
|
|
|
3447 des->tr2 = m_trace(M12,p); /* tr (XTWVX)^{-1}(XTW^2VX) */
|
|
|
3448
|
|
|
3449 /*
|
|
|
3450 * Covariance matrix is M1^{-1} * M2 * M1^{-1}
|
|
|
3451 * We compute this using the cholesky decomposition of
|
|
|
3452 * M2; premultiplying by M1^{-1} and squaring. This
|
|
|
3453 * is more stable than direct computation in near-singular cases.
|
|
|
3454 */
|
|
|
3455 chol_dec(M2,p,p);
|
|
|
3456 for (i=0; i<p; i++)
|
|
|
3457 for (j=0; j<i; j++)
|
|
|
3458 { M2[j*p+i] = M2[i*p+j];
|
|
|
3459 M2[i*p+j] = 0.0;
|
|
|
3460 }
|
|
|
3461 for (i=0; i<p; i++) jacob_solve(&des->xtwx,&M2[i*p]);
|
|
|
3462 for (i=0; i<p; i++)
|
|
|
3463 { for (j=0; j<p; j++)
|
|
|
3464 { M12[i*p+j] = 0;
|
|
|
3465 for (k=0; k<p; k++)
|
|
|
3466 M12[i*p+j] += M2[k*p+i]*M2[k*p+j]; /* ith column of covariance */
|
|
|
3467 }
|
|
|
3468 }
|
|
|
3469 if ((fam(sp)==TDEN) && (link(sp)==LIDENT))
|
|
|
3470 multmatscal(M12,1/SQR(des->smwt),p*p);
|
|
|
3471
|
|
|
3472 /* this computes the influence function as des->f1[0]. */
|
|
|
3473 unitvec(des->f1,0,des->p);
|
|
|
3474 jacob_solve(&des->xtwx,des->f1);
|
|
|
3475 }
|
|
|
3476
|
|
|
3477 /* local_df computes:
|
|
|
3478 * tr[0] = trace(W)
|
|
|
3479 * tr[1] = trace(W*W)
|
|
|
3480 * tr[2] = trace( M1^{-1} M2 )
|
|
|
3481 * tr[3] = trace( M1^{-1} M3 )
|
|
|
3482 * tr[4] = trace( (M1^{-1} M2)^2 )
|
|
|
3483 * tr[5] = var(theta-hat).
|
|
|
3484 */
|
|
|
3485 void local_df(lfd,sp,des,tr)
|
|
|
3486 lfdata *lfd;
|
|
|
3487 smpar *sp;
|
|
|
3488 design *des;
|
|
|
3489 double *tr;
|
|
|
3490 { int i, ii, j, p;
|
|
|
3491 double *m2, *V, ww, link[LLEN];
|
|
|
3492
|
|
|
3493 tr[0] = tr[1] = tr[2] = tr[3] = tr[4] = tr[5] = 0.0;
|
|
|
3494 m2 = des->V; V = des->P; p = des->p;
|
|
|
3495
|
|
|
3496 vmat(lfd,sp,des,m2,V); /* M = X^T W^2 V X tr0=sum(W) tr1=sum(W*W) */
|
|
|
3497 tr[0] = des->tr0;
|
|
|
3498 tr[1] = des->tr1;
|
|
|
3499 tr[2] = m_trace(m2,p); /* tr (XTWVX)^{-1}(XTW^2VX) */
|
|
|
3500
|
|
|
3501 unitvec(des->f1,0,p);
|
|
|
3502 jacob_solve(&des->xtwx,des->f1);
|
|
|
3503 for (i=0; i<p; i++)
|
|
|
3504 for (j=0; j<p; j++)
|
|
|
3505 { tr[4] += m2[i*p+j]*m2[j*p+i]; /* tr(M^2) */
|
|
|
3506 tr[5] += des->f1[i]*V[i*p+j]*des->f1[j]; /* var(thetahat) */
|
|
|
3507 }
|
|
|
3508 tr[5] = sqrt(tr[5]);
|
|
|
3509
|
|
|
3510 setzero(m2,p*p);
|
|
|
3511 for (i=0; i<des->n; i++)
|
|
|
3512 { ii = des->ind[i];
|
|
|
3513 stdlinks(link,lfd,sp,ii,fitv(des,ii),robscale);
|
|
|
3514 ww = wght(des,ii)*wght(des,ii)*wght(des,ii)*link[ZDDLL];
|
|
|
3515 addouter(m2,d_xi(des,ii),d_xi(des,ii),p,ww);
|
|
|
3516 }
|
|
|
3517 for (i=0; i<p; i++)
|
|
|
3518 { jacob_solve(&des->xtwx,&m2[i*p]);
|
|
|
3519 tr[3] += m2[i*(p+1)];
|
|
|
3520 }
|
|
|
3521
|
|
|
3522 return;
|
|
|
3523 }
|
|
|
3524 /*
|
|
|
3525 * Copyright 1996-2006 Catherine Loader.
|
|
|
3526 */
|
|
|
3527 /*
|
|
|
3528 * Routines for computing weight diagrams.
|
|
|
3529 * wdiag(lf,des,lx,deg,ty,exp)
|
|
|
3530 * Must locfit() first, unless ker==WPARM and has par. comp.
|
|
|
3531 *
|
|
|
3532 */
|
|
|
3533
|
|
|
3534 #include "locf.h"
|
|
|
3535
|
|
|
3536 static double *wd;
|
|
|
3537 extern double robscale;
|
|
|
3538 void nnresproj(lfd,sp,des,u,m,p)
|
|
|
3539 lfdata *lfd;
|
|
|
3540 smpar *sp;
|
|
|
3541 design *des;
|
|
|
3542 double *u;
|
|
|
3543 int m, p;
|
|
|
3544 { int i, ii, j;
|
|
|
3545 double link[LLEN];
|
|
|
3546 setzero(des->f1,p);
|
|
|
3547 for (j=0; j<m; j++)
|
|
|
3548 { ii = des->ind[j];
|
|
|
3549 stdlinks(link,lfd,sp,ii,fitv(des,ii),robscale);
|
|
|
3550 for (i=0; i<p; i++) des->f1[i] += link[ZDDLL]*d_xij(des,j,ii)*u[j];
|
|
|
3551 }
|
|
|
3552 jacob_solve(&des->xtwx,des->f1);
|
|
|
3553 for (i=0; i<m; i++)
|
|
|
3554 { ii = des->ind[i];
|
|
|
3555 u[i] -= innerprod(des->f1,d_xi(des,ii),p)*wght(des,ii);
|
|
|
3556 }
|
|
|
3557 }
|
|
|
3558
|
|
|
3559 void wdexpand(l,n,ind,m)
|
|
|
3560 double *l;
|
|
|
3561 int *ind, n, m;
|
|
|
3562 { int i, j, t;
|
|
|
3563 double z;
|
|
|
3564 for (j=m; j<n; j++) { l[j] = 0.0; ind[j] = -1; }
|
|
|
3565 j = m-1;
|
|
|
3566 while (j>=0)
|
|
|
3567 { if (ind[j]==j) j--;
|
|
|
3568 else
|
|
|
3569 { i = ind[j];
|
|
|
3570 z = l[j]; l[j] = l[i]; l[i] = z;
|
|
|
3571 t = ind[j]; ind[j] = ind[i]; ind[i] = t;
|
|
|
3572 if (ind[j]==-1) j--;
|
|
|
3573 }
|
|
|
3574 }
|
|
|
3575
|
|
|
3576 /* for (i=n-1; i>=0; i--)
|
|
|
3577 { l[i] = ((j>=0) && (ind[j]==i)) ? l[j--] : 0.0; } */
|
|
|
3578 }
|
|
|
3579
|
|
|
3580 int wdiagp(lfd,sp,des,lx,pc,dv,deg,ty,exp)
|
|
|
3581 lfdata *lfd;
|
|
|
3582 smpar *sp;
|
|
|
3583 design *des;
|
|
|
3584 paramcomp *pc;
|
|
|
3585 deriv *dv;
|
|
|
3586 double *lx;
|
|
|
3587 int deg, ty, exp;
|
|
|
3588 { int i, j, p, nd;
|
|
|
3589 double *l1;
|
|
|
3590
|
|
|
3591 p = des->p;
|
|
|
3592
|
|
|
3593 fitfun(lfd,sp,des->xev,pc->xbar,des->f1,dv);
|
|
|
3594 if (exp)
|
|
|
3595 { jacob_solve(&pc->xtwx,des->f1);
|
|
|
3596 for (i=0; i<lfd->n; i++)
|
|
|
3597 lx[i] = innerprod(des->f1,d_xi(des,des->ind[i]),p);
|
|
|
3598 return(lfd->n);
|
|
|
3599 }
|
|
|
3600 jacob_hsolve(&pc->xtwx,des->f1);
|
|
|
3601 for (i=0; i<p; i++) lx[i] = des->f1[i];
|
|
|
3602
|
|
|
3603 nd = dv->nd;
|
|
|
3604 dv->nd = nd+1;
|
|
|
3605 if (deg>=1)
|
|
|
3606 for (i=0; i<lfd->d; i++)
|
|
|
3607 { dv->deriv[nd] = i;
|
|
|
3608 l1 = &lx[(i+1)*p];
|
|
|
3609 fitfun(lfd,sp,des->xev,pc->xbar,l1,dv);
|
|
|
3610 jacob_hsolve(&pc->xtwx,l1);
|
|
|
3611 }
|
|
|
3612
|
|
|
3613 dv->nd = nd+2;
|
|
|
3614 if (deg>=2)
|
|
|
3615 for (i=0; i<lfd->d; i++)
|
|
|
3616 { dv->deriv[nd] = i;
|
|
|
3617 for (j=0; j<lfd->d; j++)
|
|
|
3618 { dv->deriv[nd+1] = j;
|
|
|
3619 l1 = &lx[(i*lfd->d+j+lfd->d+1)*p];
|
|
|
3620 fitfun(lfd,sp,des->xev,pc->xbar,l1,dv);
|
|
|
3621 jacob_hsolve(&pc->xtwx,l1);
|
|
|
3622 } }
|
|
|
3623 dv->nd = nd;
|
|
|
3624 return(p);
|
|
|
3625 }
|
|
|
3626
|
|
|
3627 int wdiag(lfd,sp,des,lx,dv,deg,ty,exp)
|
|
|
3628 lfdata *lfd;
|
|
|
3629 smpar *sp;
|
|
|
3630 design *des;
|
|
|
3631 deriv *dv;
|
|
|
3632 double *lx;
|
|
|
3633 int deg, ty, exp;
|
|
|
3634 /* deg=0: l(x) only.
|
|
|
3635 deg=1: l(x), l'(x)
|
|
|
3636 deg=2: l(x), l'(x), l''(x)
|
|
|
3637 ty = 1: e1 (X^T WVX)^{-1} X^T W -- hat matrix
|
|
|
3638 ty = 2: e1 (X^T WVX)^{-1} X^T WV^{1/2} -- scb's
|
|
|
3639 */
|
|
|
3640 { double w, *X, *lxd, *lxdd, wdd, wdw, *ulx, link[LLEN], h;
|
|
|
3641 double dfx[MXDIM], hs[MXDIM];
|
|
|
3642 int i, ii, j, k, l, m, d, p, nd;
|
|
|
3643
|
|
|
3644 h = des->h;
|
|
|
3645 nd = dv->nd;
|
|
|
3646 wd = des->wd;
|
|
|
3647 d = lfd->d; p = des->p; X = d_x(des);
|
|
|
3648 ulx = des->res;
|
|
|
3649 m = des->n;
|
|
|
3650 for (i=0; i<d; i++) hs[i] = h*lfd->sca[i];
|
|
|
3651 if (deg>0)
|
|
|
3652 { lxd = &lx[m];
|
|
|
3653 setzero(lxd,m*d);
|
|
|
3654 if (deg>1)
|
|
|
3655 { lxdd = &lxd[d*m];
|
|
|
3656 setzero(lxdd,m*d*d);
|
|
|
3657 } }
|
|
|
3658
|
|
|
3659 if (nd>0) fitfun(lfd,sp,des->xev,des->xev,des->f1,dv); /* c(0) */
|
|
|
3660 else unitvec(des->f1,0,p);
|
|
|
3661 jacob_solve(&des->xtwx,des->f1); /* c(0) (X^TWX)^{-1} */
|
|
|
3662 for (i=0; i<m; i++)
|
|
|
3663 { ii = des->ind[i];
|
|
|
3664 lx[i] = innerprod(des->f1,&X[ii*p],p); /* c(0)(XTWX)^{-1}X^T */
|
|
|
3665 if (deg>0)
|
|
|
3666 { wd[i] = Wd(dist(des,ii)/h,ker(sp));
|
|
|
3667 for (j=0; j<d; j++)
|
|
|
3668 { dfx[j] = datum(lfd,j,ii)-des->xev[j];
|
|
|
3669 lxd[j*m+i] = lx[i]*wght(des,ii)*weightd(dfx[j],lfd->sca[j],
|
|
|
3670 d,ker(sp),kt(sp),h,lfd->sty[j],dist(des,ii));
|
|
|
3671 /* c(0) (XTWX)^{-1}XTW' */
|
|
|
3672 }
|
|
|
3673 if (deg>1)
|
|
|
3674 { wdd = Wdd(dist(des,ii)/h,ker(sp));
|
|
|
3675 for (j=0; j<d; j++)
|
|
|
3676 for (k=0; k<d; k++)
|
|
|
3677 { w = (dist(des,ii)==0) ? 0 : h/dist(des,ii);
|
|
|
3678 w = wdd * (des->xev[k]-datum(lfd,k,ii)) * (des->xev[j]-datum(lfd,j,ii))
|
|
|
3679 * w*w / (hs[k]*hs[k]*hs[j]*hs[j]);
|
|
|
3680 if (j==k) w += wd[i]/(hs[j]*hs[j]);
|
|
|
3681 lxdd[(j*d+k)*m+i] = lx[i]*w;
|
|
|
3682 /* c(0)(XTWX)^{-1}XTW'' */
|
|
|
3683 }
|
|
|
3684 }
|
|
|
3685 }
|
|
|
3686 lx[i] *= wght(des,ii);
|
|
|
3687 }
|
|
|
3688
|
|
|
3689 dv->nd = nd+1;
|
|
|
3690 if (deg==2)
|
|
|
3691 { for (i=0; i<d; i++)
|
|
|
3692 { dv->deriv[nd] = i;
|
|
|
3693 fitfun(lfd,sp,des->xev,des->xev,des->f1,dv);
|
|
|
3694 for (k=0; k<m; k++)
|
|
|
3695 { ii = des->ind[i];
|
|
|
3696 stdlinks(link,lfd,sp,ii,fitv(des,ii),robscale);
|
|
|
3697 for (j=0; j<p; j++)
|
|
|
3698 des->f1[j] -= link[ZDDLL]*lxd[i*m+k]*X[ii*p+j];
|
|
|
3699 /* c'(x)-c(x)(XTWX)^{-1}XTW'X */
|
|
|
3700 }
|
|
|
3701 jacob_solve(&des->xtwx,des->f1); /* (...)(XTWX)^{-1} */
|
|
|
3702 for (j=0; j<m; j++)
|
|
|
3703 { ii = des->ind[j];
|
|
|
3704 ulx[j] = innerprod(des->f1,&X[ii*p],p); /* (...)XT */
|
|
|
3705 }
|
|
|
3706 for (j=0; j<d; j++)
|
|
|
3707 for (k=0; k<m; k++)
|
|
|
3708 { ii = des->ind[k];
|
|
|
3709 dfx[j] = datum(lfd,j,ii)-des->xev[j];
|
|
|
3710 wdw = wght(des,ii)*weightd(dfx[j],lfd->sca[j],d,ker(sp),
|
|
|
3711 kt(sp),h,lfd->sty[j],dist(des,ii));
|
|
|
3712 lxdd[(i*d+j)*m+k] += ulx[k]*wdw;
|
|
|
3713 lxdd[(j*d+i)*m+k] += ulx[k]*wdw;
|
|
|
3714 } /* + 2(c'-c(XTWX)^{-1}XTW'X)(XTWX)^{-1}XTW' */
|
|
|
3715 }
|
|
|
3716 for (j=0; j<d*d; j++) nnresproj(lfd,sp,des,&lxdd[j*m],m,p);
|
|
|
3717 /* * (I-X(XTWX)^{-1} XTW */
|
|
|
3718 }
|
|
|
3719 if (deg>0)
|
|
|
3720 { for (j=0; j<d; j++) nnresproj(lfd,sp,des,&lxd[j*m],m,p);
|
|
|
3721 /* c(0)(XTWX)^{-1}XTW'(I-X(XTWX)^{-1}XTW) */
|
|
|
3722 for (i=0; i<d; i++)
|
|
|
3723 { dv->deriv[nd]=i;
|
|
|
3724 fitfun(lfd,sp,des->xev,des->xev,des->f1,dv);
|
|
|
3725 jacob_solve(&des->xtwx,des->f1);
|
|
|
3726 for (k=0; k<m; k++)
|
|
|
3727 { ii = des->ind[k];
|
|
|
3728 for (l=0; l<p; l++)
|
|
|
3729 lxd[i*m+k] += des->f1[l]*X[ii*p+l]*wght(des,ii);
|
|
|
3730 } /* add c'(0)(XTWX)^{-1}XTW */
|
|
|
3731 }
|
|
|
3732 }
|
|
|
3733
|
|
|
3734 dv->nd = nd+2;
|
|
|
3735 if (deg==2)
|
|
|
3736 { for (i=0; i<d; i++)
|
|
|
3737 { dv->deriv[nd]=i;
|
|
|
3738 for (j=0; j<d; j++)
|
|
|
3739 { dv->deriv[nd+1]=j;
|
|
|
3740 fitfun(lfd,sp,des->xev,des->xev,des->f1,dv);
|
|
|
3741 jacob_solve(&des->xtwx,des->f1);
|
|
|
3742 for (k=0; k<m; k++)
|
|
|
3743 { ii = des->ind[k];
|
|
|
3744 for (l=0; l<p; l++)
|
|
|
3745 lxdd[(i*d+j)*m+k] += des->f1[l]*X[ii*p+l]*wght(des,ii);
|
|
|
3746 } /* + c''(x)(XTWX)^{-1}XTW */
|
|
|
3747 }
|
|
|
3748 }
|
|
|
3749 }
|
|
|
3750 dv->nd = nd;
|
|
|
3751
|
|
|
3752 k = 1+d*(deg>0)+d*d*(deg==2);
|
|
|
3753
|
|
|
3754 if (exp) wdexpand(lx,lfd->n,des->ind,m);
|
|
|
3755
|
|
|
3756 if (ty==1) return(m);
|
|
|
3757 for (i=0; i<m; i++)
|
|
|
3758 { ii = des->ind[i];
|
|
|
3759 stdlinks(link,lfd,sp,ii,fitv(des,ii),robscale);
|
|
|
3760 link[ZDDLL] = sqrt(fabs(link[ZDDLL]));
|
|
|
3761 for (j=0; j<k; j++) lx[j*m+i] *= link[ZDDLL];
|
|
|
3762 }
|
|
|
3763 return(m);
|
|
|
3764 }
|
|
|
3765 /*
|
|
|
3766 * Copyright 1996-2006 Catherine Loader.
|
|
|
3767 */
|
|
|
3768 /*
|
|
|
3769 * String matching functions. For a given argument string, find
|
|
|
3770 * the best match from an array of possibilities. Is there a library
|
|
|
3771 * function somewhere to do something like this?
|
|
|
3772 *
|
|
|
3773 * return values of -1 indicate failure/unknown string.
|
|
|
3774 */
|
|
|
3775
|
|
|
3776 #include "locf.h"
|
|
|
3777
|
|
|
3778 int ct_match(z1, z2)
|
|
|
3779 char *z1, *z2;
|
|
|
3780 { int ct = 0;
|
|
|
3781 while (z1[ct]==z2[ct])
|
|
|
3782 { if (z1[ct]=='\0') return(ct+1);
|
|
|
3783 ct++;
|
|
|
3784 }
|
|
|
3785 return(ct);
|
|
|
3786 }
|
|
|
3787
|
|
|
3788 int pmatch(z, strings, vals, n, def)
|
|
|
3789 char *z, **strings;
|
|
|
3790 int *vals, n, def;
|
|
|
3791 { int i, ct, best, best_ct;
|
|
|
3792 best = -1;
|
|
|
3793 best_ct = 0;
|
|
|
3794
|
|
|
3795 for (i=0; i<n; i++)
|
|
|
3796 { ct = ct_match(z,strings[i]);
|
|
|
3797 if (ct==strlen(z)+1) return(vals[i]);
|
|
|
3798 if (ct>best_ct) { best = i; best_ct = ct; }
|
|
|
3799 }
|
|
|
3800 if (best==-1) return(def);
|
|
|
3801 return(vals[best]);
|
|
|
3802 }
|
|
|
3803 /*
|
|
|
3804 * Copyright 1996-2006 Catherine Loader.
|
|
|
3805 */
|
|
|
3806 #include "locf.h"
|
|
|
3807
|
|
|
3808 int lf_maxit = 20;
|
|
|
3809 int lf_debug = 0;
|
|
|
3810 int lf_error = 0;
|
|
|
3811
|
|
|
3812 double s0, s1;
|
|
|
3813 static lfdata *lf_lfd;
|
|
|
3814 static design *lf_des;
|
|
|
3815 static smpar *lf_sp;
|
|
|
3816 int lf_status;
|
|
|
3817 int ident=0;
|
|
|
3818 double lf_tol;
|
|
|
3819 extern double robscale;
|
|
|
3820
|
|
|
3821 void lfdata_init(lfd)
|
|
|
3822 lfdata *lfd;
|
|
|
3823 { int i;
|
|
|
3824 for (i=0; i<MXDIM; i++)
|
|
|
3825 { lfd->sty[i] = 0;
|
|
|
3826 lfd->sca[i] = 1.0;
|
|
|
3827 lfd->xl[i] = lfd->xl[i+MXDIM] = 0.0;
|
|
|
3828 }
|
|
|
3829 lfd->y = lfd->w = lfd->c = lfd->b = NULL;
|
|
|
3830 lfd->d = lfd->n = 0;
|
|
|
3831 }
|
|
|
3832
|
|
|
3833 void smpar_init(sp,lfd)
|
|
|
3834 smpar *sp;
|
|
|
3835 lfdata *lfd;
|
|
|
3836 { nn(sp) = 0.7;
|
|
|
3837 fixh(sp)= 0.0;
|
|
|
3838 pen(sp) = 0.0;
|
|
|
3839 acri(sp)= ANONE;
|
|
|
3840 deg(sp) = deg0(sp) = 2;
|
|
|
3841 ubas(sp) = 0;
|
|
|
3842 kt(sp) = KSPH;
|
|
|
3843 ker(sp) = WTCUB;
|
|
|
3844 fam(sp) = 64+TGAUS;
|
|
|
3845 link(sp)= LDEFAU;
|
|
|
3846 npar(sp) = calcp(sp,lfd->d);
|
|
|
3847 }
|
|
|
3848
|
|
|
3849 void deriv_init(dv)
|
|
|
3850 deriv *dv;
|
|
|
3851 { dv->nd = 0;
|
|
|
3852 }
|
|
|
3853
|
|
|
3854 int des_reqd(n,p)
|
|
|
3855 int n, p;
|
|
|
3856 {
|
|
|
3857 return(n*(p+5)+2*p*p+4*p + jac_reqd(p));
|
|
|
3858 }
|
|
|
3859 int des_reqi(n,p)
|
|
|
3860 int n, p;
|
|
|
3861 { return(n+p);
|
|
|
3862 }
|
|
|
3863
|
|
|
3864 void des_init(des,n,p)
|
|
|
3865 design *des;
|
|
|
3866 int n, p;
|
|
|
3867 { double *z;
|
|
|
3868 int k;
|
|
|
3869
|
|
|
3870 if (n<=0) WARN(("des_init: n <= 0"));
|
|
|
3871 if (p<=0) WARN(("des_init: p <= 0"));
|
|
|
3872
|
|
|
3873 if (des->des_init_id != DES_INIT_ID)
|
|
|
3874 { des->lwk = des->lind = 0;
|
|
|
3875 des->des_init_id = DES_INIT_ID;
|
|
|
3876 }
|
|
|
3877
|
|
|
3878 k = des_reqd(n,p);
|
|
|
3879 if (k>des->lwk)
|
|
|
3880 { des->wk = (double *)calloc(k,sizeof(double));
|
|
|
3881 if ( des->wk == NULL ) {
|
|
|
3882 printf("Problem allocating memory for des->wk\n");fflush(stdout);
|
|
|
3883 }
|
|
|
3884 des->lwk = k;
|
|
|
3885 }
|
|
|
3886 z = des->wk;
|
|
|
3887
|
|
|
3888 des->X = z; z += n*p;
|
|
|
3889 des->w = z; z += n;
|
|
|
3890 des->res=z; z += n;
|
|
|
3891 des->di =z; z += n;
|
|
|
3892 des->th =z; z += n;
|
|
|
3893 des->wd =z; z += n;
|
|
|
3894 des->V =z; z += p*p;
|
|
|
3895 des->P =z; z += p*p;
|
|
|
3896 des->f1 =z; z += p;
|
|
|
3897 des->ss =z; z += p;
|
|
|
3898 des->oc =z; z += p;
|
|
|
3899 des->cf =z; z += p;
|
|
|
3900
|
|
|
3901 z = jac_alloc(&des->xtwx,p,z);
|
|
|
3902
|
|
|
3903 k = des_reqi(n,p);
|
|
|
3904 if (k>des->lind)
|
|
|
3905 {
|
|
|
3906 des->ind = (int *)calloc(k,sizeof(int));
|
|
|
3907 if ( des->ind == NULL ) {
|
|
|
3908 printf("Problem allocating memory for des->ind\n");fflush(stdout);
|
|
|
3909 }
|
|
|
3910 des->lind = k;
|
|
|
3911 }
|
|
|
3912 des->fix = &des->ind[n];
|
|
|
3913 for (k=0; k<p; k++) des->fix[k] = 0;
|
|
|
3914
|
|
|
3915 des->n = n; des->p = p;
|
|
|
3916 des->smwt = n;
|
|
|
3917 des->xtwx.p = p;
|
|
|
3918 }
|
|
|
3919
|
|
|
3920 void deschk(des,n,p)
|
|
|
3921 design *des;
|
|
|
3922 int n, p;
|
|
|
3923 { WARN(("deschk deprecated - use des_init()"));
|
|
|
3924 des_init(des,n,p);
|
|
|
3925 }
|
|
|
3926
|
|
|
3927 int likereg(coef, lk0, f1, Z)
|
|
|
3928 double *coef, *lk0, *f1, *Z;
|
|
|
3929 { int i, ii, j, p;
|
|
|
3930 double lk, ww, link[LLEN], *X;
|
|
|
3931
|
|
|
3932 if (lf_debug>2) mut_printf(" likereg: %8.5f\n",coef[0]);
|
|
|
3933 lf_status = LF_OK;
|
|
|
3934 lk = 0.0; p = lf_des->p;
|
|
|
3935 setzero(Z,p*p);
|
|
|
3936 setzero(f1,p);
|
|
|
3937 for (i=0; i<lf_des->n; i++)
|
|
|
3938 {
|
|
|
3939 ii = lf_des->ind[i];
|
|
|
3940 X = d_xi(lf_des,ii);
|
|
|
3941 fitv(lf_des,ii) = base(lf_lfd,ii)+innerprod(coef,X,p);
|
|
|
3942 lf_status = stdlinks(link,lf_lfd,lf_sp,ii,fitv(lf_des,ii),robscale);
|
|
|
3943 if (lf_status == LF_BADP)
|
|
|
3944 { *lk0 = -1.0e300;
|
|
|
3945 return(NR_REDUCE);
|
|
|
3946 }
|
|
|
3947 if (lf_error) lf_status = LF_ERR;
|
|
|
3948 if (lf_status != LF_OK) return(NR_BREAK);
|
|
|
3949
|
|
|
3950 ww = wght(lf_des,ii);
|
|
|
3951 lk += ww*link[ZLIK];
|
|
|
3952 for (j=0; j<p; j++)
|
|
|
3953 f1[j] += X[j]*ww*link[ZDLL];
|
|
|
3954 addouter(Z, X, X, p, ww*link[ZDDLL]);
|
|
|
3955 }
|
|
|
3956 for (i=0; i<p; i++) if (lf_des->fix[i])
|
|
|
3957 { for (j=0; j<p; j++) Z[i*p+j] = Z[j*p+i] = 0.0;
|
|
|
3958 Z[i*p+i] = 1.0;
|
|
|
3959 f1[i] = 0.0;
|
|
|
3960 }
|
|
|
3961
|
|
|
3962 if (lf_debug>4) prresp(coef,Z,p);
|
|
|
3963 if (lf_debug>3) mut_printf(" likelihood: %8.5f\n",lk);
|
|
|
3964 *lk0 = lf_des->llk = lk;
|
|
|
3965
|
|
|
3966 lf_status = fami(lf_sp)->pcheck(lf_sp,lf_des,lf_lfd);
|
|
|
3967 switch(lf_status)
|
|
|
3968 { case LF_DONE: return(NR_BREAK);
|
|
|
3969 case LF_OOB: return(NR_REDUCE);
|
|
|
3970 case LF_PF: return(NR_REDUCE);
|
|
|
3971 case LF_NSLN: return(NR_BREAK);
|
|
|
3972 }
|
|
|
3973
|
|
|
3974 return(NR_OK);
|
|
|
3975 }
|
|
|
3976
|
|
|
3977 int reginit(lfd,des,sp)
|
|
|
3978 lfdata *lfd;
|
|
|
3979 design *des;
|
|
|
3980 smpar *sp;
|
|
|
3981 { int i, ii;
|
|
|
3982 double sb, link[LLEN];
|
|
|
3983 s0 = s1 = sb = 0;
|
|
|
3984 for (i=0; i<des->n; i++)
|
|
|
3985 { ii = des->ind[i];
|
|
|
3986 links(base(lfd,ii),resp(lfd,ii),fami(sp),LINIT,link,cens(lfd,ii),prwt(lfd,ii),1.0);
|
|
|
3987 s1 += wght(des,ii)*link[ZDLL];
|
|
|
3988 s0 += wght(des,ii)*prwt(lfd,ii);
|
|
|
3989 sb += wght(des,ii)*prwt(lfd,ii)*base(lfd,ii);
|
|
|
3990 }
|
|
|
3991 if (s0==0) return(LF_NOPT); /* no observations with W>0 */
|
|
|
3992 setzero(des->cf,des->p);
|
|
|
3993 lf_tol = 1.0e-6*s0;
|
|
|
3994 switch(link(sp))
|
|
|
3995 { case LIDENT:
|
|
|
3996 des->cf[0] = (s1-sb)/s0;
|
|
|
3997 return(LF_OK);
|
|
|
3998 case LLOG:
|
|
|
3999 if (s1<=0.0)
|
|
|
4000 { des->cf[0] = -1000;
|
|
|
4001 return(LF_INFA);
|
|
|
4002 }
|
|
|
4003 des->cf[0] = log(s1/s0) - sb/s0;
|
|
|
4004 return(LF_OK);
|
|
|
4005 case LLOGIT:
|
|
|
4006 if (s1<=0.0)
|
|
|
4007 { des->cf[0] = -1000;
|
|
|
4008 return(LF_INFA);
|
|
|
4009 }
|
|
|
4010 if (s1>=s0)
|
|
|
4011 { des->cf[0] = 1000;
|
|
|
4012 return(LF_INFA);
|
|
|
4013 }
|
|
|
4014 des->cf[0] = logit(s1/s0)-sb/s0;
|
|
|
4015 return(LF_OK);
|
|
|
4016 case LINVER:
|
|
|
4017 if (s1<=0.0)
|
|
|
4018 { des->cf[0] = 1e100;
|
|
|
4019 return(LF_INFA);
|
|
|
4020 }
|
|
|
4021 des->cf[0] = s0/s1-sb/s0;
|
|
|
4022 return(LF_OK);
|
|
|
4023 case LSQRT:
|
|
|
4024 des->cf[0] = sqrt(s1/s0)-sb/s0;
|
|
|
4025 return(LF_OK);
|
|
|
4026 case LASIN:
|
|
|
4027 des->cf[0] = asin(sqrt(s1/s0))-sb/s0;
|
|
|
4028 return(LF_OK);
|
|
|
4029 default:
|
|
|
4030 LERR(("reginit: invalid link %d",link(sp)));
|
|
|
4031 return(LF_ERR);
|
|
|
4032 }
|
|
|
4033 }
|
|
|
4034
|
|
|
4035 int lfinit(lfd,sp,des)
|
|
|
4036 lfdata *lfd;
|
|
|
4037 smpar *sp;
|
|
|
4038 design *des;
|
|
|
4039 { int initstat;
|
|
|
4040 des->xtwx.sm = (deg0(sp)<deg(sp)) ? JAC_CHOL : JAC_EIGD;
|
|
|
4041
|
|
|
4042 designmatrix(lfd,sp,des);
|
|
|
4043 setfamily(sp);
|
|
|
4044 initstat = fami(sp)->initial(lfd,des,sp);
|
|
|
4045
|
|
|
4046 return(initstat);
|
|
|
4047 }
|
|
|
4048
|
|
|
4049 void lfiter(lfd,sp,des,maxit)
|
|
|
4050 lfdata *lfd;
|
|
|
4051 smpar *sp;
|
|
|
4052 design *des;
|
|
|
4053 int maxit;
|
|
|
4054 { int err;
|
|
|
4055 if (lf_debug>1) mut_printf(" lfiter: %8.5f\n",des->cf[0]);
|
|
|
4056
|
|
|
4057 lf_des = des;
|
|
|
4058 lf_lfd = lfd;
|
|
|
4059 lf_sp = sp;
|
|
|
4060
|
|
|
4061 max_nr(fami(sp)->like, des->cf, des->oc, des->res, des->f1,
|
|
|
4062 &des->xtwx, des->p, maxit, lf_tol, &err);
|
|
|
4063 switch(err)
|
|
|
4064 { case NR_OK: return;
|
|
|
4065 case NR_NCON:
|
|
|
4066 WARN(("max_nr not converged"));
|
|
|
4067 return;
|
|
|
4068 case NR_NDIV:
|
|
|
4069 WARN(("max_nr reduction problem"));
|
|
|
4070 return;
|
|
|
4071 }
|
|
|
4072 WARN(("max_nr return status %d",err));
|
|
|
4073 }
|
|
|
4074
|
|
|
4075 int use_robust_scale(int tg)
|
|
|
4076 { if ((tg&64)==0) return(0); /* not quasi - no scale */
|
|
|
4077 if (((tg&128)==0) & (((tg&63)!=TROBT) & ((tg&63)!=TCAUC))) return(0);
|
|
|
4078 return(1);
|
|
|
4079 }
|
|
|
4080
|
|
|
4081 /*
|
|
|
4082 * noit not really needed any more, since
|
|
|
4083 * gauss->pcheck returns LF_DONE, and likereg NR_BREAK
|
|
|
4084 * in gaussian case.
|
|
|
4085 * nb: 0/1: does local neighborhood and weights need computing?
|
|
|
4086 * cv: 0/1: is variance/covariance matrix needed?
|
|
|
4087 */
|
|
|
4088 int locfit(lfd,des,sp,noit,nb,cv)
|
|
|
4089 lfdata *lfd;
|
|
|
4090 design *des;
|
|
|
4091 smpar *sp;
|
|
|
4092 int noit, nb, cv;
|
|
|
4093 { int i;
|
|
|
4094
|
|
|
4095 if (des->xev==NULL)
|
|
|
4096 { LERR(("locfit: NULL evaluation point?"));
|
|
|
4097 return(246);
|
|
|
4098 }
|
|
|
4099
|
|
|
4100 if (lf_debug>0)
|
|
|
4101 { mut_printf("locfit: ");
|
|
|
4102 for (i=0; i<lfd->d; i++) mut_printf(" %10.6f",des->xev[i]);
|
|
|
4103 mut_printf("\n");
|
|
|
4104 }
|
|
|
4105
|
|
|
4106 /* the 1e-12 avoids problems that can occur with roundoff */
|
|
|
4107 if (nb) nbhd(lfd,des,(int)(lfd->n*nn(sp)+1e-12),0,sp);
|
|
|
4108
|
|
|
4109 lf_status = lfinit(lfd,sp,des);
|
|
|
4110
|
|
|
4111 if (lf_status == LF_OK)
|
|
|
4112 { if (use_robust_scale(fam(sp)))
|
|
|
4113 lf_robust(lfd,sp,des,lf_maxit);
|
|
|
4114 else
|
|
|
4115 { if ((fam(sp)&63)==TQUANT)
|
|
|
4116 lfquantile(lfd,sp,des,lf_maxit);
|
|
|
4117 else
|
|
|
4118 { robscale = 1.0;
|
|
|
4119 lfiter(lfd,sp,des,lf_maxit);
|
|
|
4120 }
|
|
|
4121 }
|
|
|
4122 }
|
|
|
4123
|
|
|
4124 if (lf_status == LF_DONE) lf_status = LF_OK;
|
|
|
4125 if (lf_status == LF_OOB) lf_status = LF_OK;
|
|
|
4126
|
|
|
4127 if ((fam(sp)&63)==TDEN) /* convert from rate to density */
|
|
|
4128 { switch(link(sp))
|
|
|
4129 { case LLOG:
|
|
|
4130 des->cf[0] -= log(des->smwt);
|
|
|
4131 break;
|
|
|
4132 case LIDENT:
|
|
|
4133 multmatscal(des->cf,1.0/des->smwt,des->p);
|
|
|
4134 break;
|
|
|
4135 default: LERR(("Density adjustment; invalid link"));
|
|
|
4136 }
|
|
|
4137 }
|
|
|
4138
|
|
|
4139 /* variance calculations, if requested */
|
|
|
4140 if (cv)
|
|
|
4141 { switch(lf_status)
|
|
|
4142 { case LF_PF: /* for these cases, variance calc. would likely fail. */
|
|
|
4143 case LF_NOPT:
|
|
|
4144 case LF_NSLN:
|
|
|
4145 case LF_INFA:
|
|
|
4146 case LF_DEMP:
|
|
|
4147 case LF_XOOR:
|
|
|
4148 case LF_DNOP:
|
|
|
4149 case LF_BADP:
|
|
|
4150 des->llk = des->tr0 = des->tr1 = des->tr2 = 0.0;
|
|
|
4151 setzero(des->V,des->p*des->p);
|
|
|
4152 setzero(des->f1,des->p);
|
|
|
4153 break;
|
|
|
4154 default: lf_vcov(lfd,sp,des);
|
|
|
4155 }
|
|
|
4156 }
|
|
|
4157
|
|
|
4158 return(lf_status);
|
|
|
4159 }
|
|
|
4160
|
|
|
4161 void lf_status_msg(status)
|
|
|
4162 int status;
|
|
|
4163 { switch(status)
|
|
|
4164 { case LF_OK: return;
|
|
|
4165 case LF_NCON: WARN(("locfit did not converge")); return;
|
|
|
4166 case LF_OOB: WARN(("parameters out of bounds")); return;
|
|
|
4167 case LF_PF: WARN(("perfect fit")); return;
|
|
|
4168 case LF_NOPT: WARN(("no points with non-zero weight")); return;
|
|
|
4169 case LF_NSLN: WARN(("no solution")); return;
|
|
|
4170 case LF_INFA: WARN(("initial value problem")); return;
|
|
|
4171 case LF_DEMP: WARN(("density estimate, empty integration region")); return;
|
|
|
4172 case LF_XOOR: WARN(("procv: fit point outside xlim region")); return;
|
|
|
4173 case LF_DNOP: WARN(("density estimation -- insufficient points in smoothing window")); return;
|
|
|
4174 case LF_BADP: WARN(("bad parameters")); return;
|
|
|
4175 default: WARN(("procv: unknown return code %d",status)); return;
|
|
|
4176 } }
|
|
|
4177 /*
|
|
|
4178 * Copyright 1996-2006 Catherine Loader.
|
|
|
4179 */
|
|
|
4180 /*
|
|
|
4181 * Compute minimax weights for local regression.
|
|
|
4182 */
|
|
|
4183
|
|
|
4184 #include "locf.h"
|
|
|
4185 #define NR_EMPTY 834
|
|
|
4186
|
|
|
4187 int mmsm_ct;
|
|
|
4188
|
|
|
4189 static int debug=0;
|
|
|
4190 #define CONVTOL 1.0e-8
|
|
|
4191 #define SINGTOL 1.0e-10
|
|
|
4192 #define NR_SINGULAR 100
|
|
|
4193
|
|
|
4194 static lfdata *mm_lfd;
|
|
|
4195 static design *mm_des;
|
|
|
4196 static double mm_gam, mmf, lb;
|
|
|
4197 static int st;
|
|
|
4198
|
|
|
4199 double ipower(x,n) /* use for n not too large!! */
|
|
|
4200 double x;
|
|
|
4201 int n;
|
|
|
4202 { if (n==0) return(1.0);
|
|
|
4203 if (n<0) return(1/ipower(x,-n));
|
|
|
4204 return(x*ipower(x,n-1));
|
|
|
4205 }
|
|
|
4206
|
|
|
4207 double setmmwt(des,a,gam)
|
|
|
4208 design *des;
|
|
|
4209 double *a, gam;
|
|
|
4210 { double ip, w0, w1, sw, wt;
|
|
|
4211 int i;
|
|
|
4212 sw = 0.0;
|
|
|
4213 for (i=0; i<mm_lfd->n; i++)
|
|
|
4214 { ip = innerprod(a,d_xi(des,i),des->p);
|
|
|
4215 wt = prwt(mm_lfd,i);
|
|
|
4216 w0 = ip - gam*des->wd[i];
|
|
|
4217 w1 = ip + gam*des->wd[i];
|
|
|
4218 wght(des,i) = 0.0;
|
|
|
4219 if (w0>0) { wght(des,i) = w0; sw += wt*w0*w0; }
|
|
|
4220 if (w1<0) { wght(des,i) = w1; sw += wt*w1*w1; }
|
|
|
4221 }
|
|
|
4222 return(sw/2-a[0]);
|
|
|
4223 }
|
|
|
4224
|
|
|
4225 /* compute sum_{w!=0} AA^T; e1-sum wA */
|
|
|
4226 int mmsums(des,coef,f,z,J)
|
|
|
4227 design *des;
|
|
|
4228 double *coef, *f, *z;
|
|
|
4229 jacobian *J;
|
|
|
4230 { int ct, i, j, p, sing;
|
|
|
4231 double *A;
|
|
|
4232
|
|
|
4233 mmsm_ct++;
|
|
|
4234 A = J->Z;
|
|
|
4235 *f = setmmwt(des,coef,mm_gam);
|
|
|
4236
|
|
|
4237 p = des->p;
|
|
|
4238 setzero(A,p*p);
|
|
|
4239 setzero(z,p);
|
|
|
4240 z[0] = 1.0;
|
|
|
4241 ct = 0;
|
|
|
4242
|
|
|
4243 for (i=0; i<mm_lfd->n; i++)
|
|
|
4244 if (wght(des,i)!=0.0)
|
|
|
4245 { addouter(A,d_xi(des,i),d_xi(des,i),p,prwt(mm_lfd,i));
|
|
|
4246 for (j=0; j<p; j++) z[j] -= prwt(mm_lfd,i)*wght(des,i)*d_xij(des,i,j);
|
|
|
4247 ct++;
|
|
|
4248 }
|
|
|
4249 if (ct==0) return(NR_EMPTY);
|
|
|
4250
|
|
|
4251 J->st = JAC_RAW;
|
|
|
4252 J->p = p;
|
|
|
4253 jacob_dec(J,JAC_EIGD);
|
|
|
4254
|
|
|
4255 sing = 0;
|
|
|
4256 for (i=0; i<p; i++) sing |= (J->Z[i*p+i]<SINGTOL);
|
|
|
4257 if ((debug) & (sing)) mut_printf("SINGULAR!!!!\n");
|
|
|
4258
|
|
|
4259 return((sing) ? NR_SINGULAR : NR_OK);
|
|
|
4260 }
|
|
|
4261
|
|
|
4262 int descenddir(des,coef,dlt,f,af)
|
|
|
4263 design *des;
|
|
|
4264 double *coef, *dlt, *f;
|
|
|
4265 int af;
|
|
|
4266 { int i, p;
|
|
|
4267 double f0, *oc;
|
|
|
4268
|
|
|
4269 if (debug) mut_printf("descenddir: %8.5f %8.5f\n",dlt[0],dlt[1]);
|
|
|
4270
|
|
|
4271 f0 = *f;
|
|
|
4272 oc = des->oc;
|
|
|
4273 p = des->p;
|
|
|
4274 memcpy(oc,coef,p*sizeof(double));
|
|
|
4275
|
|
|
4276 for (i=0; i<p; i++) coef[i] = oc[i]+lb*dlt[i];
|
|
|
4277 st = mmsums(des,coef,f,des->f1,&des->xtwx);
|
|
|
4278
|
|
|
4279 if (*f>f0) /* halve till we drop */
|
|
|
4280 { while (*f>f0)
|
|
|
4281 { lb = lb/2.0;
|
|
|
4282 for (i=0; i<p; i++) coef[i] = oc[i]+lb*dlt[i];
|
|
|
4283 st = mmsums(des,coef,f,des->f1,&des->xtwx);
|
|
|
4284 }
|
|
|
4285 return(st);
|
|
|
4286 }
|
|
|
4287
|
|
|
4288 if (!af) return(st);
|
|
|
4289
|
|
|
4290 /* double */
|
|
|
4291 while (*f<f0)
|
|
|
4292 { f0 = *f;
|
|
|
4293 lb *= 2.0;
|
|
|
4294 for (i=0; i<p; i++) coef[i] = oc[i]+lb*dlt[i];
|
|
|
4295 st = mmsums(des,coef,f,des->f1,&des->xtwx);
|
|
|
4296 }
|
|
|
4297
|
|
|
4298 lb /= 2.0;
|
|
|
4299 for (i=0; i<p; i++) coef[i] = oc[i]+lb*dlt[i];
|
|
|
4300 st = mmsums(des,coef,f,des->f1,&des->xtwx);
|
|
|
4301
|
|
|
4302 return(st);
|
|
|
4303 }
|
|
|
4304
|
|
|
4305 int mm_initial(des)
|
|
|
4306 design *des;
|
|
|
4307 { double *dlt;
|
|
|
4308
|
|
|
4309 dlt = des->ss;
|
|
|
4310
|
|
|
4311 setzero(des->cf,des->p);
|
|
|
4312 st = mmsums(des,des->cf,&mmf,des->f1,&des->xtwx);
|
|
|
4313
|
|
|
4314 setzero(dlt,des->p);
|
|
|
4315 dlt[0] = 1;
|
|
|
4316 lb = 1.0;
|
|
|
4317 st = descenddir(des,des->cf,dlt,&mmf,1);
|
|
|
4318 return(st);
|
|
|
4319 }
|
|
|
4320
|
|
|
4321 void getsingdir(des,dlt)
|
|
|
4322 design *des;
|
|
|
4323 double *dlt;
|
|
|
4324 { double f, sw, c0;
|
|
|
4325 int i, j, p, sd;
|
|
|
4326
|
|
|
4327 sd = -1; p = des->p;
|
|
|
4328 setzero(dlt,p);
|
|
|
4329 for (i=0; i<p; i++) if (des->xtwx.Z[i*p+i]<SINGTOL) sd = i;
|
|
|
4330 if (sd==-1)
|
|
|
4331 { mut_printf("getsingdir: nonsing?\n");
|
|
|
4332 return;
|
|
|
4333 }
|
|
|
4334 if (des->xtwx.dg[sd]>0)
|
|
|
4335 for (i=0; i<p; i++) dlt[i] = des->xtwx.Q[p*i+sd]*des->xtwx.dg[i];
|
|
|
4336 else
|
|
|
4337 { dlt[sd] = 1.0;
|
|
|
4338 }
|
|
|
4339
|
|
|
4340 c0 = innerprod(dlt,des->f1,p);
|
|
|
4341 if (c0<0) for (i=0; i<p; i++) dlt[i] = -dlt[i];
|
|
|
4342 }
|
|
|
4343
|
|
|
4344 void mmax(coef, old_coef, delta, J, p, maxit, tol, err)
|
|
|
4345 double *coef, *old_coef, *delta, tol;
|
|
|
4346 int p, maxit, *err;
|
|
|
4347 jacobian *J;
|
|
|
4348 { double old_f, lambda;
|
|
|
4349 int i, j;
|
|
|
4350
|
|
|
4351 *err = NR_OK;
|
|
|
4352
|
|
|
4353 for (j=0; j<maxit; j++)
|
|
|
4354 { memcpy(old_coef,coef,p*sizeof(double));
|
|
|
4355 old_f = mmf;
|
|
|
4356
|
|
|
4357 if (st == NR_SINGULAR)
|
|
|
4358 {
|
|
|
4359 getsingdir(mm_des,delta);
|
|
|
4360 st = descenddir(mm_des,coef,delta,&mmf,1);
|
|
|
4361 }
|
|
|
4362 if (st == NR_EMPTY)
|
|
|
4363 {
|
|
|
4364 setzero(delta,p);
|
|
|
4365 delta[0] = 1.0;
|
|
|
4366 st = descenddir(mm_des,coef,delta,&mmf,1);
|
|
|
4367 }
|
|
|
4368 if (st == NR_OK)
|
|
|
4369 {
|
|
|
4370 lb = 1.0;
|
|
|
4371 jacob_solve(J,mm_des->f1);
|
|
|
4372 memcpy(delta,mm_des->f1,p*sizeof(double));
|
|
|
4373 st = descenddir(mm_des,coef,delta,&mmf,0);
|
|
|
4374 }
|
|
|
4375
|
|
|
4376 if ((j>0) & (fabs(mmf-old_f)<tol)) return;
|
|
|
4377 }
|
|
|
4378 WARN(("findab not converged"));
|
|
|
4379 *err = NR_NCON;
|
|
|
4380 return;
|
|
|
4381 }
|
|
|
4382
|
|
|
4383 double findab(gam)
|
|
|
4384 double gam;
|
|
|
4385 { double sl;
|
|
|
4386 int i, p, nr_stat;
|
|
|
4387
|
|
|
4388 if (debug) mut_printf(" findab: gam %8.5f\n",gam);
|
|
|
4389 mm_gam = gam;
|
|
|
4390 p = mm_des->p;
|
|
|
4391 lb = 1.0;
|
|
|
4392 st = mm_initial(mm_des);
|
|
|
4393
|
|
|
4394 mmax(mm_des->cf, mm_des->oc, mm_des->ss,
|
|
|
4395 &mm_des->xtwx, p, lf_maxit, CONVTOL, &nr_stat);
|
|
|
4396
|
|
|
4397 sl = 0.0;
|
|
|
4398 for (i=0; i<mm_lfd->n; i++) sl += fabs(wght(mm_des,i))*mm_des->wd[i];
|
|
|
4399
|
|
|
4400 if (debug) mut_printf(" sl %8.5f gam %8.5f %8.5f %d\n", sl,gam,sl-gam,nr_stat);
|
|
|
4401 return(sl-gam);
|
|
|
4402 }
|
|
|
4403
|
|
|
4404 double weightmm(coef,di,ff,gam)
|
|
|
4405 double *coef, di, *ff, gam;
|
|
|
4406 { double y1, y2, ip;
|
|
|
4407 ip = innerprod(ff,coef,mm_des->p);
|
|
|
4408 y1 = ip-gam*di; if (y1>0) return(y1/ip);
|
|
|
4409 y2 = ip+gam*di; if (y2<0) return(y2/ip);
|
|
|
4410 return(0.0);
|
|
|
4411 }
|
|
|
4412
|
|
|
4413 double minmax(lfd,des,sp)
|
|
|
4414 lfdata *lfd;
|
|
|
4415 design *des;
|
|
|
4416 smpar *sp;
|
|
|
4417 { double h, u[MXDIM], gam;
|
|
|
4418 int i, j, m, d1, p1, err_flag;
|
|
|
4419
|
|
|
4420 if (debug) mut_printf("minmax: x %8.5f\n",des->xev[0]);
|
|
|
4421 mm_lfd = lfd;
|
|
|
4422 mm_des = des;
|
|
|
4423
|
|
|
4424 mmsm_ct = 0;
|
|
|
4425 d1 = deg(sp)+1;
|
|
|
4426 p1 = factorial(d1);
|
|
|
4427 for (i=0; i<lfd->n; i++)
|
|
|
4428 { for (j=0; j<lfd->d; j++) u[j] = datum(lfd,j,i);
|
|
|
4429 des->wd[i] = sp->nn/p1*ipower(dist(des,i),d1);
|
|
|
4430 des->ind[i] = i;
|
|
|
4431 fitfun(lfd, sp, u,des->xev,d_xi(des,i),NULL);
|
|
|
4432 }
|
|
|
4433
|
|
|
4434 /* find gamma (i.e. solve eqn 13.17 from book), using the secant method.
|
|
|
4435 * As a side effect, this finds the other minimax coefficients.
|
|
|
4436 * Note that 13.17 is rewritten as
|
|
|
4437 * g2 = sum |l_i(x)| (||xi-x||^(p+1) M/(s*(p+1)!))
|
|
|
4438 * where g2 = gamma * s * (p+1)! / M. The gam variable below is g2.
|
|
|
4439 * The smoothing parameter is sp->nn == M/s.
|
|
|
4440 */
|
|
|
4441 gam = solve_secant(findab, 0.0, 0.0,1.0, 0.0000001, BDF_EXPRIGHT, &err_flag);
|
|
|
4442
|
|
|
4443 /*
|
|
|
4444 * Set the smoothing weights, in preparation for the actual fit.
|
|
|
4445 */
|
|
|
4446 h = 0.0; m = 0;
|
|
|
4447 for (i=0; i<lfd->n; i++)
|
|
|
4448 { wght(des,i) = weightmm(des->cf, des->wd[i],d_xi(des,i),gam);
|
|
|
4449 if (wght(des,i)>0)
|
|
|
4450 { if (dist(des,i)>h) h = dist(des,i);
|
|
|
4451 des->ind[m] = i;
|
|
|
4452 m++;
|
|
|
4453 }
|
|
|
4454 }
|
|
|
4455 des->n = m;
|
|
|
4456 return(h);
|
|
|
4457 }
|
|
|
4458 /*
|
|
|
4459 * Copyright 1996-2006 Catherine Loader.
|
|
|
4460 */
|
|
|
4461 /*
|
|
|
4462 *
|
|
|
4463 * Defines the weight functions and related quantities used
|
|
|
4464 * in LOCFIT.
|
|
|
4465 */
|
|
|
4466
|
|
|
4467 #include "locf.h"
|
|
|
4468
|
|
|
4469 /*
|
|
|
4470 * convert kernel and kernel type strings to numeric codes.
|
|
|
4471 */
|
|
|
4472 #define NWFUNS 13
|
|
|
4473 static char *wfuns[NWFUNS] = {
|
|
|
4474 "rectangular", "epanechnikov", "bisquare", "tricube",
|
|
|
4475 "triweight", "gaussian", "triangular", "ququ",
|
|
|
4476 "6cub", "minimax", "exponential", "maclean", "parametric" };
|
|
|
4477 static int wvals[NWFUNS] = { WRECT, WEPAN, WBISQ, WTCUB,
|
|
|
4478 WTRWT, WGAUS, WTRIA, WQUQU, W6CUB, WMINM, WEXPL, WMACL, WPARM };
|
|
|
4479 int lfkernel(char *z)
|
|
|
4480 { return(pmatch(z, wfuns, wvals, NWFUNS, WTCUB));
|
|
|
4481 }
|
|
|
4482
|
|
|
4483 #define NKTYPE 5
|
|
|
4484 static char *ktype[NKTYPE] = { "spherical", "product", "center", "lm", "zeon" };
|
|
|
4485 static int kvals[NKTYPE] = { KSPH, KPROD, KCE, KLM, KZEON };
|
|
|
4486 int lfketype(char *z)
|
|
|
4487 { return(pmatch(z, ktype, kvals, NKTYPE, KSPH));
|
|
|
4488 }
|
|
|
4489
|
|
|
4490 /* The weight functions themselves. Used everywhere. */
|
|
|
4491 double W(u,ker)
|
|
|
4492 double u;
|
|
|
4493 int ker;
|
|
|
4494 { u = fabs(u);
|
|
|
4495 switch(ker)
|
|
|
4496 { case WRECT: return((u>1) ? 0.0 : 1.0);
|
|
|
4497 case WEPAN: return((u>1) ? 0.0 : 1-u*u);
|
|
|
4498 case WBISQ: if (u>1) return(0.0);
|
|
|
4499 u = 1-u*u; return(u*u);
|
|
|
4500 case WTCUB: if (u>1) return(0.0);
|
|
|
4501 u = 1-u*u*u; return(u*u*u);
|
|
|
4502 case WTRWT: if (u>1) return(0.0);
|
|
|
4503 u = 1-u*u; return(u*u*u);
|
|
|
4504 case WQUQU: if (u>1) return(0.0);
|
|
|
4505 u = 1-u*u; return(u*u*u*u);
|
|
|
4506 case WTRIA: if (u>1) return(0.0);
|
|
|
4507 return(1-u);
|
|
|
4508 case W6CUB: if (u>1) return(0.0);
|
|
|
4509 u = 1-u*u*u; u = u*u*u; return(u*u);
|
|
|
4510 case WGAUS: return(exp(-SQR(GFACT*u)/2.0));
|
|
|
4511 case WEXPL: return(exp(-EFACT*u));
|
|
|
4512 case WMACL: return(1/((u+1.0e-100)*(u+1.0e-100)));
|
|
|
4513 case WMINM: LERR(("WMINM in W"));
|
|
|
4514 return(0.0);
|
|
|
4515 case WPARM: return(1.0);
|
|
|
4516 }
|
|
|
4517 LERR(("W(): Unknown kernel %d\n",ker));
|
|
|
4518 return(1.0);
|
|
|
4519 }
|
|
|
4520
|
|
|
4521 int iscompact(ker)
|
|
|
4522 int ker;
|
|
|
4523 { if ((ker==WEXPL) | (ker==WGAUS) | (ker==WMACL) | (ker==WPARM)) return(0);
|
|
|
4524 return(1);
|
|
|
4525 }
|
|
|
4526
|
|
|
4527 double weightprod(lfd,u,h,ker)
|
|
|
4528 lfdata *lfd;
|
|
|
4529 double *u, h;
|
|
|
4530 int ker;
|
|
|
4531 { int i;
|
|
|
4532 double sc, w;
|
|
|
4533 w = 1.0;
|
|
|
4534 for (i=0; i<lfd->d; i++)
|
|
|
4535 { sc = lfd->sca[i];
|
|
|
4536 switch(lfd->sty[i])
|
|
|
4537 { case STLEFT:
|
|
|
4538 if (u[i]>0) return(0.0);
|
|
|
4539 w *= W(-u[i]/(h*sc),ker);
|
|
|
4540 break;
|
|
|
4541 case STRIGH:
|
|
|
4542 if (u[i]<0) return(0.0);
|
|
|
4543 w *= W(u[i]/(h*sc),ker);
|
|
|
4544 break;
|
|
|
4545 case STANGL:
|
|
|
4546 w *= W(2*fabs(sin(u[i]/(2*sc)))/h,ker);
|
|
|
4547 break;
|
|
|
4548 case STCPAR:
|
|
|
4549 break;
|
|
|
4550 default:
|
|
|
4551 w *= W(fabs(u[i])/(h*sc),ker);
|
|
|
4552 }
|
|
|
4553 if (w==0.0) return(w);
|
|
|
4554 }
|
|
|
4555 return(w);
|
|
|
4556 }
|
|
|
4557
|
|
|
4558 double weightsph(lfd,u,h,ker, hasdi,di)
|
|
|
4559 lfdata *lfd;
|
|
|
4560 double *u, h, di;
|
|
|
4561 int ker, hasdi;
|
|
|
4562 { int i;
|
|
|
4563
|
|
|
4564 if (!hasdi) di = rho(u,lfd->sca,lfd->d,KSPH,lfd->sty);
|
|
|
4565
|
|
|
4566 for (i=0; i<lfd->d; i++)
|
|
|
4567 { if ((lfd->sty[i]==STLEFT) && (u[i]>0.0)) return(0.0);
|
|
|
4568 if ((lfd->sty[i]==STRIGH) && (u[i]<0.0)) return(0.0);
|
|
|
4569 }
|
|
|
4570 if (h==0) return((di==0.0) ? 1.0 : 0.0);
|
|
|
4571
|
|
|
4572 return(W(di/h,ker));
|
|
|
4573 }
|
|
|
4574
|
|
|
4575 double weight(lfd,sp,x,t,h, hasdi,di)
|
|
|
4576 lfdata *lfd;
|
|
|
4577 smpar *sp;
|
|
|
4578 double *x, *t, h, di;
|
|
|
4579 int hasdi;
|
|
|
4580 { double u[MXDIM];
|
|
|
4581 int i;
|
|
|
4582 for (i=0; i<lfd->d; i++) u[i] = (t==NULL) ? x[i] : x[i]-t[i];
|
|
|
4583 switch(kt(sp))
|
|
|
4584 { case KPROD: return(weightprod(lfd,u,h,ker(sp)));
|
|
|
4585 case KSPH: return(weightsph(lfd,u,h,ker(sp), hasdi,di));
|
|
|
4586 }
|
|
|
4587 LERR(("weight: unknown kernel type %d",kt(sp)));
|
|
|
4588 return(1.0);
|
|
|
4589 }
|
|
|
4590
|
|
|
4591 double sgn(x)
|
|
|
4592 double x;
|
|
|
4593 { if (x>0) return(1.0);
|
|
|
4594 if (x<0) return(-1.0);
|
|
|
4595 return(0.0);
|
|
|
4596 }
|
|
|
4597
|
|
|
4598 double WdW(u,ker) /* W'(u)/W(u) */
|
|
|
4599 double u;
|
|
|
4600 int ker;
|
|
|
4601 { double eps=1.0e-10;
|
|
|
4602 if (ker==WGAUS) return(-GFACT*GFACT*u);
|
|
|
4603 if (ker==WPARM) return(0.0);
|
|
|
4604 if (fabs(u)>=1) return(0.0);
|
|
|
4605 switch(ker)
|
|
|
4606 { case WRECT: return(0.0);
|
|
|
4607 case WTRIA: return(-sgn(u)/(1-fabs(u)+eps));
|
|
|
4608 case WEPAN: return(-2*u/(1-u*u+eps));
|
|
|
4609 case WBISQ: return(-4*u/(1-u*u+eps));
|
|
|
4610 case WTRWT: return(-6*u/(1-u*u+eps));
|
|
|
4611 case WTCUB: return(-9*sgn(u)*u*u/(1-u*u*fabs(u)+eps));
|
|
|
4612 case WEXPL: return((u>0) ? -EFACT : EFACT);
|
|
|
4613 }
|
|
|
4614 LERR(("WdW: invalid kernel"));
|
|
|
4615 return(0.0);
|
|
|
4616 }
|
|
|
4617
|
|
|
4618 /* deriv. weights .. spherical, product etc
|
|
|
4619 u, sc, sty needed only in relevant direction
|
|
|
4620 Acutally, returns (d/dx W(||x||/h) ) / W(.)
|
|
|
4621 */
|
|
|
4622 double weightd(u,sc,d,ker,kt,h,sty,di)
|
|
|
4623 double u, sc, h, di;
|
|
|
4624 int d, ker, kt, sty;
|
|
|
4625 { if (sty==STANGL)
|
|
|
4626 { if (kt==KPROD)
|
|
|
4627 return(-WdW(2*sin(u/(2*sc)),ker)*cos(u/(2*sc))/(h*sc));
|
|
|
4628 if (di==0.0) return(0.0);
|
|
|
4629 return(-WdW(di/h,ker)*sin(u/sc)/(h*sc*di));
|
|
|
4630 }
|
|
|
4631 if (sty==STCPAR) return(0.0);
|
|
|
4632 if (kt==KPROD)
|
|
|
4633 return(-WdW(u/(h*sc),ker)/(h*sc));
|
|
|
4634 if (di==0.0) return(0.0);
|
|
|
4635 return(-WdW(di/h,ker)*u/(h*di*sc*sc));
|
|
|
4636 }
|
|
|
4637
|
|
|
4638 double weightdd(u,sc,d,ker,kt,h,sty,di,i0,i1)
|
|
|
4639 double *u, *sc, h, di;
|
|
|
4640 int d, ker, kt, i0, i1, *sty;
|
|
|
4641 { double w;
|
|
|
4642 w = 1;
|
|
|
4643 if (kt==KPROD)
|
|
|
4644 {
|
|
|
4645 w = WdW(u[i0]/(h*sc[i0]),ker)*WdW(u[i1]/(h*sc[i1]),ker)/(h*h*sc[i0]*sc[i1]);
|
|
|
4646 }
|
|
|
4647 return(0.0);
|
|
|
4648 }
|
|
|
4649
|
|
|
4650 /* Derivatives W'(u)/u.
|
|
|
4651 Used in simult. conf. band computations,
|
|
|
4652 and kernel density bandwidth selectors. */
|
|
|
4653 double Wd(u,ker)
|
|
|
4654 double u;
|
|
|
4655 int ker;
|
|
|
4656 { double v;
|
|
|
4657 if (ker==WGAUS) return(-SQR(GFACT)*exp(-SQR(GFACT*u)/2));
|
|
|
4658 if (ker==WPARM) return(0.0);
|
|
|
4659 if (fabs(u)>1) return(0.0);
|
|
|
4660 switch(ker)
|
|
|
4661 { case WEPAN: return(-2.0);
|
|
|
4662 case WBISQ: return(-4*(1-u*u));
|
|
|
4663 case WTCUB: v = 1-u*u*u;
|
|
|
4664 return(-9*v*v*u);
|
|
|
4665 case WTRWT: v = 1-u*u;
|
|
|
4666 return(-6*v*v);
|
|
|
4667 default: LERR(("Invalid kernel %d in Wd",ker));
|
|
|
4668 }
|
|
|
4669 return(0.0);
|
|
|
4670 }
|
|
|
4671
|
|
|
4672 /* Second derivatives W''(u)-W'(u)/u.
|
|
|
4673 used in simult. conf. band computations in >1 dimension. */
|
|
|
4674 double Wdd(u,ker)
|
|
|
4675 double u;
|
|
|
4676 int ker;
|
|
|
4677 { double v;
|
|
|
4678 if (ker==WGAUS) return(SQR(u*GFACT*GFACT)*exp(-SQR(u*GFACT)/2));
|
|
|
4679 if (ker==WPARM) return(0.0);
|
|
|
4680 if (u>1) return(0.0);
|
|
|
4681 switch(ker)
|
|
|
4682 { case WBISQ: return(12*u*u);
|
|
|
4683 case WTCUB: v = 1-u*u*u;
|
|
|
4684 return(-9*u*v*v+54*u*u*u*u*v);
|
|
|
4685 case WTRWT: return(24*u*u*(1-u*u));
|
|
|
4686 default: LERR(("Invalid kernel %d in Wdd",ker));
|
|
|
4687 }
|
|
|
4688 return(0.0);
|
|
|
4689 }
|
|
|
4690
|
|
|
4691 /* int u1^j1..ud^jd W(u) du.
|
|
|
4692 Used for local log-linear density estimation.
|
|
|
4693 Assume all j_i are even.
|
|
|
4694 Also in some bandwidth selection.
|
|
|
4695 */
|
|
|
4696 double wint(d,j,nj,ker)
|
|
|
4697 int d, *j, nj, ker;
|
|
|
4698 { double I, z;
|
|
|
4699 int k, dj;
|
|
|
4700 dj = d;
|
|
|
4701 for (k=0; k<nj; k++) dj += j[k];
|
|
|
4702 switch(ker) /* int_0^1 u^(dj-1) W(u)du */
|
|
|
4703 { case WRECT: I = 1.0/dj; break;
|
|
|
4704 case WEPAN: I = 2.0/(dj*(dj+2)); break;
|
|
|
4705 case WBISQ: I = 8.0/(dj*(dj+2)*(dj+4)); break;
|
|
|
4706 case WTCUB: I = 162.0/(dj*(dj+3)*(dj+6)*(dj+9)); break;
|
|
|
4707 case WTRWT: I = 48.0/(dj*(dj+2)*(dj+4)*(dj+6)); break;
|
|
|
4708 case WTRIA: I = 1.0/(dj*(dj+1)); break;
|
|
|
4709 case WQUQU: I = 384.0/(dj*(dj+2)*(dj+4)*(dj+6)*(dj+8)); break;
|
|
|
4710 case W6CUB: I = 524880.0/(dj*(dj+3)*(dj+6)*(dj+9)*(dj+12)*(dj+15)*(dj+18)); break;
|
|
|
4711 case WGAUS: switch(d)
|
|
|
4712 { case 1: I = S2PI/GFACT; break;
|
|
|
4713 case 2: I = 2*PI/(GFACT*GFACT); break;
|
|
|
4714 default: I = exp(d*log(S2PI/GFACT)); /* for nj=0 */
|
|
|
4715 }
|
|
|
4716 for (k=0; k<nj; k++) /* deliberate drop */
|
|
|
4717 switch(j[k])
|
|
|
4718 { case 4: I *= 3.0/(GFACT*GFACT);
|
|
|
4719 case 2: I /= GFACT*GFACT;
|
|
|
4720 }
|
|
|
4721 return(I);
|
|
|
4722 case WEXPL: I = factorial(dj-1)/ipower(EFACT,dj); break;
|
|
|
4723 default: LERR(("Unknown kernel %d in exacint",ker));
|
|
|
4724 }
|
|
|
4725 if ((d==1) && (nj==0)) return(2*I); /* common case quick */
|
|
|
4726 z = (d-nj)*LOGPI/2-mut_lgammai(dj);
|
|
|
4727 for (k=0; k<nj; k++) z += mut_lgammai(j[k]+1);
|
|
|
4728 return(2*I*exp(z));
|
|
|
4729 }
|
|
|
4730
|
|
|
4731 /* taylor series expansion of weight function around x.
|
|
|
4732 0 and 1 are common arguments, so are worth programming
|
|
|
4733 as special cases.
|
|
|
4734 Used in density estimation.
|
|
|
4735 */
|
|
|
4736 int wtaylor(f,x,ker)
|
|
|
4737 double *f, x;
|
|
|
4738 int ker;
|
|
|
4739 { double v;
|
|
|
4740 switch(ker)
|
|
|
4741 { case WRECT:
|
|
|
4742 f[0] = 1.0;
|
|
|
4743 return(1);
|
|
|
4744 case WEPAN:
|
|
|
4745 f[0] = 1-x*x; f[1] = -2*x; f[2] = -1;
|
|
|
4746 return(3);
|
|
|
4747 case WBISQ:
|
|
|
4748 v = 1-x*x;
|
|
|
4749 f[0] = v*v; f[1] = -4*x*v; f[2] = 4-6*v;
|
|
|
4750 f[3] = 4*x; f[4] = 1;
|
|
|
4751 return(5);
|
|
|
4752 case WTCUB:
|
|
|
4753 if (x==1.0)
|
|
|
4754 { f[0] = f[1] = f[2] = 0; f[3] = -27; f[4] = -81; f[5] = -108;
|
|
|
4755 f[6] = -81; f[7] = -36; f[8] = -9; f[9] = -1; return(10); }
|
|
|
4756 if (x==0.0)
|
|
|
4757 { f[1] = f[2] = f[4] = f[5] = f[7] = f[8] = 0;
|
|
|
4758 f[0] = 1; f[3] = -3; f[6] = 3; f[9] = -1; return(10); }
|
|
|
4759 v = 1-x*x*x;
|
|
|
4760 f[0] = v*v*v; f[1] = -9*v*v*x*x; f[2] = x*v*(27-36*v);
|
|
|
4761 f[3] = -27+v*(108-84*v); f[4] = -3*x*x*(27-42*v);
|
|
|
4762 f[5] = x*(-108+126*v); f[6] = -81+84*v;
|
|
|
4763 f[7] = -36*x*x; f[8] = -9*x; f[9] = -1;
|
|
|
4764 return(10);
|
|
|
4765 case WTRWT:
|
|
|
4766 v = 1-x*x;
|
|
|
4767 f[0] = v*v*v; f[1] = -6*x*v*v; f[2] = v*(12-15*v);
|
|
|
4768 f[3] = x*(20*v-8); f[4] = 15*v-12; f[5] = -6; f[6] = -1;
|
|
|
4769 return(7);
|
|
|
4770 case WTRIA:
|
|
|
4771 f[0] = 1-x; f[1] = -1;
|
|
|
4772 return(2);
|
|
|
4773 case WQUQU:
|
|
|
4774 v = 1-x*x;
|
|
|
4775 f[0] = v*v*v*v; f[1] = -8*x*v*v*v; f[2] = v*v*(24-28*v);
|
|
|
4776 f[3] = v*x*(56*v-32); f[4] = (70*v-80)*v+16; f[5] = x*(32-56*v);
|
|
|
4777 f[6] = 24-28*v; f[7] = 8*x; f[8] = 1;
|
|
|
4778 return(9);
|
|
|
4779 case W6CUB:
|
|
|
4780 v = 1-x*x*x;
|
|
|
4781 f[0] = v*v*v*v*v*v;
|
|
|
4782 f[1] = -18*x*x*v*v*v*v*v;
|
|
|
4783 f[2] = x*v*v*v*v*(135-153*v);
|
|
|
4784 f[3] = v*v*v*(-540+v*(1350-816*v));
|
|
|
4785 f[4] = x*x*v*v*(1215-v*(4050-v*3060));
|
|
|
4786 f[5] = x*v*(-1458+v*(9234+v*(-16254+v*8568)));
|
|
|
4787 f[6] = 729-v*(10206-v*(35154-v*(44226-v*18564)));
|
|
|
4788 f[7] = x*x*(4374-v*(30132-v*(56862-v*31824)));
|
|
|
4789 f[8] = x*(12393-v*(61479-v*(92664-v*43758)));
|
|
|
4790 f[9] = 21870-v*(89100-v*(115830-v*48620));
|
|
|
4791 f[10]= x*x*(26730-v*(69498-v*43758));
|
|
|
4792 f[11]= x*(23814-v*(55458-v*31824));
|
|
|
4793 f[12]= 15849-v*(34398-v*18564);
|
|
|
4794 f[13]= x*x*(7938-8568*v);
|
|
|
4795 f[14]= x*(2970-3060*v);
|
|
|
4796 f[15]= 810-816*v;
|
|
|
4797 f[16]= 153*x*x;
|
|
|
4798 f[17]= 18*x;
|
|
|
4799 f[18]= 1;
|
|
|
4800 return(19);
|
|
|
4801 }
|
|
|
4802 LERR(("Invalid kernel %d in wtaylor",ker));
|
|
|
4803 return(0);
|
|
|
4804 }
|
|
|
4805
|
|
|
4806 /* convolution int W(x)W(x+v)dx.
|
|
|
4807 used in kde bandwidth selection.
|
|
|
4808 */
|
|
|
4809 double Wconv(v,ker)
|
|
|
4810 double v;
|
|
|
4811 int ker;
|
|
|
4812 { double v2;
|
|
|
4813 switch(ker)
|
|
|
4814 { case WGAUS: return(SQRPI/GFACT*exp(-SQR(GFACT*v)/4));
|
|
|
4815 case WRECT:
|
|
|
4816 v = fabs(v);
|
|
|
4817 if (v>2) return(0.0);
|
|
|
4818 return(2-v);
|
|
|
4819 case WEPAN:
|
|
|
4820 v = fabs(v);
|
|
|
4821 if (v>2) return(0.0);
|
|
|
4822 return((2-v)*(16+v*(8-v*(16-v*(2+v))))/30);
|
|
|
4823 case WBISQ:
|
|
|
4824 v = fabs(v);
|
|
|
4825 if (v>2) return(0.0);
|
|
|
4826 v2 = 2-v;
|
|
|
4827 return(v2*v2*v2*v2*v2*(16+v*(40+v*(36+v*(10+v))))/630);
|
|
|
4828 }
|
|
|
4829 LERR(("Wconv not implemented for kernel %d",ker));
|
|
|
4830 return(0.0);
|
|
|
4831 }
|
|
|
4832
|
|
|
4833 /* derivative of Wconv.
|
|
|
4834 1/v d/dv int W(x)W(x+v)dx
|
|
|
4835 used in kde bandwidth selection.
|
|
|
4836 */
|
|
|
4837 double Wconv1(v,ker)
|
|
|
4838 double v;
|
|
|
4839 int ker;
|
|
|
4840 { double v2;
|
|
|
4841 v = fabs(v);
|
|
|
4842 switch(ker)
|
|
|
4843 { case WGAUS: return(-0.5*SQRPI*GFACT*exp(-SQR(GFACT*v)/4));
|
|
|
4844 case WRECT:
|
|
|
4845 if (v>2) return(0.0);
|
|
|
4846 return(1.0);
|
|
|
4847 case WEPAN:
|
|
|
4848 if (v>2) return(0.0);
|
|
|
4849 return((-16+v*(12-v*v))/6);
|
|
|
4850 case WBISQ:
|
|
|
4851 if (v>2) return(0.0);
|
|
|
4852 v2 = 2-v;
|
|
|
4853 return(-v2*v2*v2*v2*(32+v*(64+v*(24+v*3)))/210);
|
|
|
4854 }
|
|
|
4855 LERR(("Wconv1 not implemented for kernel %d",ker));
|
|
|
4856 return(0.0);
|
|
|
4857 }
|
|
|
4858
|
|
|
4859 /* 4th derivative of Wconv.
|
|
|
4860 used in kde bandwidth selection (BCV, SJPI, GKK)
|
|
|
4861 */
|
|
|
4862 double Wconv4(v,ker)
|
|
|
4863 double v;
|
|
|
4864 int ker;
|
|
|
4865 { double gv;
|
|
|
4866 switch(ker)
|
|
|
4867 { case WGAUS:
|
|
|
4868 gv = GFACT*v;
|
|
|
4869 return(exp(-SQR(gv)/4)*GFACT*GFACT*GFACT*(12-gv*gv*(12-gv*gv))*SQRPI/16);
|
|
|
4870 }
|
|
|
4871 LERR(("Wconv4 not implemented for kernel %d",ker));
|
|
|
4872 return(0.0);
|
|
|
4873 }
|
|
|
4874
|
|
|
4875 /* 5th derivative of Wconv.
|
|
|
4876 used in kde bandwidth selection (BCV method only)
|
|
|
4877 */
|
|
|
4878 double Wconv5(v,ker) /* (d/dv)^5 int W(x)W(x+v)dx */
|
|
|
4879 double v;
|
|
|
4880 int ker;
|
|
|
4881 { double gv;
|
|
|
4882 switch(ker)
|
|
|
4883 { case WGAUS:
|
|
|
4884 gv = GFACT*v;
|
|
|
4885 return(-exp(-SQR(gv)/4)*GFACT*GFACT*GFACT*GFACT*gv*(60-gv*gv*(20-gv*gv))*SQRPI/32);
|
|
|
4886 }
|
|
|
4887 LERR(("Wconv5 not implemented for kernel %d",ker));
|
|
|
4888 return(0.0);
|
|
|
4889 }
|
|
|
4890
|
|
|
4891 /* 6th derivative of Wconv.
|
|
|
4892 used in kde bandwidth selection (SJPI)
|
|
|
4893 */
|
|
|
4894 double Wconv6(v,ker)
|
|
|
4895 double v;
|
|
|
4896 int ker;
|
|
|
4897 { double gv, z;
|
|
|
4898 switch(ker)
|
|
|
4899 { case WGAUS:
|
|
|
4900 gv = GFACT*v;
|
|
|
4901 gv = gv*gv;
|
|
|
4902 z = exp(-gv/4)*(-120+gv*(180-gv*(30-gv)))*0.02769459142;
|
|
|
4903 gv = GFACT*GFACT;
|
|
|
4904 return(z*gv*gv*GFACT);
|
|
|
4905 }
|
|
|
4906 LERR(("Wconv6 not implemented for kernel %d",ker));
|
|
|
4907 return(0.0);
|
|
|
4908 }
|
|
|
4909
|
|
|
4910 /* int W(v)^2 dv / (int v^2 W(v) dv)^2
|
|
|
4911 used in some bandwidth selectors
|
|
|
4912 */
|
|
|
4913 double Wikk(ker,deg)
|
|
|
4914 int ker, deg;
|
|
|
4915 { switch(deg)
|
|
|
4916 { case 0:
|
|
|
4917 case 1: /* int W(v)^2 dv / (int v^2 W(v) dv)^2 */
|
|
|
4918 switch(ker)
|
|
|
4919 { case WRECT: return(4.5);
|
|
|
4920 case WEPAN: return(15.0);
|
|
|
4921 case WBISQ: return(35.0);
|
|
|
4922 case WGAUS: return(0.2820947918*GFACT*GFACT*GFACT*GFACT*GFACT);
|
|
|
4923 case WTCUB: return(34.152111046847892); /* 59049 / 1729 */
|
|
|
4924 case WTRWT: return(66.083916083916080); /* 9450/143 */
|
|
|
4925 }
|
|
|
4926 case 2:
|
|
|
4927 case 3: /* 4!^2/8*int(W1^2)/int(v^4W1)^2
|
|
|
4928 W1=W*(n4-v^2n2)/(n0n4-n2n2) */
|
|
|
4929 switch(ker)
|
|
|
4930 { case WRECT: return(11025.0);
|
|
|
4931 case WEPAN: return(39690.0);
|
|
|
4932 case WBISQ: return(110346.9231);
|
|
|
4933 case WGAUS: return(14527.43412);
|
|
|
4934 case WTCUB: return(126500.5904);
|
|
|
4935 case WTRWT: return(254371.7647);
|
|
|
4936 }
|
|
|
4937 }
|
|
|
4938 LERR(("Wikk not implemented for kernel %d, deg %d",ker,deg));
|
|
|
4939 return(0.0);
|
|
|
4940 }
|
