1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538
|
/*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or
* (at your option) any later version.
*
* Written (W) 1999-2008 Soeren Sonnenburg
* Written (W) 1999-2008 Gunnar Raetsch
* Copyright (C) 1999-2008 Fraunhofer Institute FIRST and Max-Planck-Society
*/
// Math.cpp: implementation of the CMath class.
//
//////////////////////////////////////////////////////////////////////
#include "lib/common.h"
#include "lib/Mathematics.h"
#include "lib/lapack.h"
#include "lib/io.h"
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
//////////////////////////////////////////////////////////////////////
// Construction/Destruction
//////////////////////////////////////////////////////////////////////
#ifdef USE_LOGCACHE
//gene/math specific constants
#ifdef USE_HMMDEBUG
#define MAX_LOG_TABLE_SIZE 10*1024*1024
#define LOG_TABLE_PRECISION 1e-6
#else
#define MAX_LOG_TABLE_SIZE 123*1024*1024
#define LOG_TABLE_PRECISION 1e-15
#endif
INT CMath::LOGACCURACY = 0; // 100000 steps per integer
#endif
INT CMath::LOGRANGE = 0; // range for logtable: log(1+exp(x)) -25 <= x <= 0
const DREAL CMath::INFTY = -log(0.0); // infinity
const DREAL CMath::ALMOST_INFTY = +1e+20; //a large number
const DREAL CMath::ALMOST_NEG_INFTY = -1000;
#ifdef USE_LOGCACHE
DREAL* CMath::logtable = NULL;
#endif
CHAR* CMath::rand_state = NULL;
UINT CMath::seed = 0;
CMath::CMath()
: CSGObject()
{
#ifndef HAVE_SWIG
CSGObject::version.print_version();
#endif
CMath::rand_state=new CHAR[256];
init_random();
#ifndef HAVE_SWIG
SG_PRINT( "( seeding random number generator with %u, ", seed);
#endif
#ifdef USE_LOGCACHE
LOGRANGE=CMath::determine_logrange();
LOGACCURACY=CMath::determine_logaccuracy(LOGRANGE);
#ifndef HAVE_SWIG
SG_PRINT( "initializing log-table (size=%i*%i*%i=%2.1fMB) ... ) ",LOGRANGE,LOGACCURACY,sizeof(DREAL),LOGRANGE*LOGACCURACY*sizeof(DREAL)/(1024.0*1024.0)) ;
#endif
CMath::logtable=new DREAL[LOGRANGE*LOGACCURACY];
init_log_table();
#else
INT i=0;
while ((DREAL)log(1+((DREAL)exp(-DREAL(i)))))
i++;
#ifndef HAVE_SWIG
SG_PRINT("determined range for x in log(1+exp(-x)) is:%d )\n", i);
#endif
LOGRANGE=i;
#endif
}
CMath::~CMath()
{
delete[] CMath::rand_state;
CMath::rand_state=NULL;
#ifdef USE_LOGCACHE
delete[] CMath::logtable;
CMath::logtable=NULL;
#endif
}
#ifdef USE_LOGCACHE
INT CMath::determine_logrange()
{
INT i;
DREAL acc=0;
for (i=0; i<50; i++)
{
acc=((DREAL)log(1+((DREAL)exp(-DREAL(i)))));
if (acc<=(DREAL)LOG_TABLE_PRECISION)
break;
}
SG_INFO( "determined range for x in table log(1+exp(-x)) is:%d (error:%G)\n",i,acc);
return i;
}
INT CMath::determine_logaccuracy(INT range)
{
range=MAX_LOG_TABLE_SIZE/range/((int)sizeof(DREAL));
SG_INFO( "determined accuracy for x in table log(1+exp(-x)) is:%d (error:%G)\n",range,1.0/(double) range);
return range;
}
//init log table of form log(1+exp(x))
void CMath::init_log_table()
{
for (INT i=0; i< LOGACCURACY*LOGRANGE; i++)
logtable[i]=log(1+exp(DREAL(-i)/DREAL(LOGACCURACY)));
}
#endif
void CMath::sort(INT *a, INT cols, INT sort_col)
{
INT changed=1;
if (a[0]==-1) return ;
while (changed)
{
changed=0; INT i=0 ;
while ((a[(i+1)*cols]!=-1) && (a[(i+1)*cols+1]!=-1)) // to be sure
{
if (a[i*cols+sort_col]>a[(i+1)*cols+sort_col])
{
for (INT j=0; j<cols; j++)
CMath::swap(a[i*cols+j],a[(i+1)*cols+j]) ;
changed=1 ;
} ;
i++ ;
} ;
} ;
}
void CMath::sort(DREAL *a, INT* idx, INT N)
{
INT changed=1;
while (changed)
{
changed=0;
for (INT i=0; i<N-1; i++)
{
if (a[i]>a[i+1])
{
swap(a[i],a[i+1]) ;
swap(idx[i],idx[i+1]) ;
changed=1 ;
} ;
} ;
} ;
}
DREAL CMath::Align(CHAR * seq1, CHAR* seq2, INT l1, INT l2, DREAL gapCost)
{
DREAL actCost=0 ;
INT i1, i2 ;
DREAL* const gapCosts1 = new DREAL[ l1 ];
DREAL* const gapCosts2 = new DREAL[ l2 ];
DREAL* costs2_0 = new DREAL[ l2 + 1 ];
DREAL* costs2_1 = new DREAL[ l2 + 1 ];
// initialize borders
for( i1 = 0; i1 < l1; ++i1 ) {
gapCosts1[ i1 ] = gapCost * i1;
}
costs2_1[ 0 ] = 0;
for( i2 = 0; i2 < l2; ++i2 ) {
gapCosts2[ i2 ] = gapCost * i2;
costs2_1[ i2+1 ] = costs2_1[ i2 ] + gapCosts2[ i2 ];
}
// compute alignment
for( i1 = 0; i1 < l1; ++i1 ) {
swap( costs2_0, costs2_1 );
actCost = costs2_0[ 0 ] + gapCosts1[ i1 ];
costs2_1[ 0 ] = actCost;
for( i2 = 0; i2 < l2; ++i2 ) {
const DREAL actMatch = costs2_0[ i2 ] + ( seq1[i1] == seq2[i2] );
const DREAL actGap1 = costs2_0[ i2+1 ] + gapCosts1[ i1 ];
const DREAL actGap2 = actCost + gapCosts2[ i2 ];
const DREAL actGap = min( actGap1, actGap2 );
actCost = min( actMatch, actGap );
costs2_1[ i2+1 ] = actCost;
}
}
delete [] gapCosts1;
delete [] gapCosts2;
delete [] costs2_0;
delete [] costs2_1;
// return the final cost
return actCost;
}
//plot x- axis false positives (fp) 1-Specificity
//plot y- axis true positives (tp) Sensitivity
INT CMath::calcroc(DREAL* fp, DREAL* tp, DREAL* output, INT* label, INT& size, INT& possize, INT& negsize, DREAL& tresh, FILE* rocfile)
{
INT left=0;
INT right=size-1;
INT i;
for (i=0; i<size; i++)
{
if (!(label[i]== -1 || label[i]==1))
return -1;
}
//sort data such that -1 labels first +1 behind
while (left<right)
{
while ((label[left] < 0) && (left<right))
left++;
while ((label[right] > 0) && (left<right)) //warning: label must be either -1 or +1
right--;
swap(output[left],output[right]);
swap(label[left], label[right]);
}
// neg/pos sizes
negsize=left;
possize=size-left;
DREAL* negout=output;
DREAL* posout=&output[left];
// sort the pos and neg outputs separately
qsort(negout, negsize);
qsort(posout, possize);
// set minimum+maximum values for decision-treshhold
DREAL minimum=min(negout[0], posout[0]);
DREAL maximum=minimum;
if (negsize>0)
maximum=max(maximum,negout[negsize-1]);
if (possize>0)
maximum=max(maximum,posout[possize-1]);
DREAL treshhold=minimum;
DREAL old_treshhold=treshhold;
//clear array.
for (i=0; i<size; i++)
{
fp[i]=1.0;
tp[i]=1.0;
}
//start with fp=1.0 tp=1.0 which is posidx=0, negidx=0
//everything right of {pos,neg}idx is considered to beLONG to +1
INT posidx=0;
INT negidx=0;
INT iteration=1;
INT returnidx=-1;
DREAL minerr=10;
while (iteration < size && treshhold<=maximum)
{
old_treshhold=treshhold;
while (treshhold==old_treshhold && treshhold<=maximum)
{
if (posidx<possize && negidx<negsize)
{
if (posout[posidx]<negout[negidx])
{
if (posout[posidx]==treshhold)
posidx++;
else
treshhold=posout[posidx];
}
else
{
if (negout[negidx]==treshhold)
negidx++;
else
treshhold=negout[negidx];
}
}
else
{
if (posidx>=possize && negidx<negsize-1)
{
negidx++;
treshhold=negout[negidx];
}
else if (negidx>=negsize && posidx<possize-1)
{
posidx++;
treshhold=posout[posidx];
}
else if (negidx<negsize && treshhold!=negout[negidx])
treshhold=negout[negidx];
else if (posidx<possize && treshhold!=posout[posidx])
treshhold=posout[posidx];
else
{
treshhold=2*(maximum+100); // force termination
posidx=possize;
negidx=negsize;
break;
}
}
}
//calc tp,fp
tp[iteration]=(possize-posidx)/(DREAL (possize));
fp[iteration]=(negsize-negidx)/(DREAL (negsize));
//choose poINT with minimal error
if (minerr > negsize*fp[iteration]/size+(1-tp[iteration])*possize/size )
{
minerr=negsize*fp[iteration]/size+(1-tp[iteration])*possize/size;
tresh=(old_treshhold+treshhold)/2;
returnidx=iteration;
}
iteration++;
}
// set new size
size=iteration;
if (rocfile)
{
const CHAR id[]="ROC";
fwrite(id, sizeof(char), sizeof(id), rocfile);
fwrite(fp, sizeof(DREAL), size, rocfile);
fwrite(tp, sizeof(DREAL), size, rocfile);
}
return returnidx;
}
UINT CMath::crc32(BYTE *data, INT len)
{
UINT result;
INT i,j;
BYTE octet;
result = 0-1;
for (i=0; i<len; i++)
{
octet = *(data++);
for (j=0; j<8; j++)
{
if ((octet >> 7) ^ (result >> 31))
{
result = (result << 1) ^ 0x04c11db7;
}
else
{
result = (result << 1);
}
octet <<= 1;
}
}
return ~result;
}
double CMath::mutual_info(DREAL* p1, DREAL* p2, INT len)
{
double e=0;
for (INT i=0; i<len; i++)
for (INT j=0; j<len; j++)
e+=exp(p2[j*len+i])*(p2[j*len+i]-p1[i]-p1[j]);
return e;
}
double CMath::relative_entropy(DREAL* p, DREAL* q, INT len)
{
double e=0;
for (INT i=0; i<len; i++)
e+=exp(p[i])*(p[i]-q[i]);
return e;
}
double CMath::entropy(DREAL* p, INT len)
{
double e=0;
for (INT i=0; i<len; i++)
e-=exp(p[i])*p[i];
return e;
}
//Howto construct the pseudo inverse (from "The Matrix Cookbook")
//
//Assume A does not have full rank, i.e. A is n \times m and rank(A) = r < min(n;m).
//
//The matrix A+ known as the pseudo inverse is unique and does always exist.
//
//The pseudo inverse A+ can be constructed from the singular value
//decomposition A = UDV^T , by A^+ = V(D+)U^T.
#ifdef HAVE_LAPACK
DREAL* CMath::pinv(DREAL* matrix, INT rows, INT cols, DREAL* target)
{
if (!target)
target=new DREAL[rows*cols];
char jobu='A';
char jobvt='A';
int m=rows;
int n=cols;
int lda=m;
int ldu=m;
int ldvt=n;
int info=-1;
int lsize=CMath::min(m,n);
double* s=new double[lsize];
double* u=new double[m*m];
double* vt=new double[n*n];
wrap_dgesvd(jobu, jobvt, m, n, matrix, lda, s, u, ldu, vt, ldvt, &info);
ASSERT(info==0);
for (INT i=0; i<n; i++)
{
for (INT j=0; j<lsize; j++)
vt[i*n+j]=vt[i*n+j]/s[j];
}
cblas_dgemm(CblasColMajor, CblasTrans, CblasTrans, m, n, m, 1.0, vt, ldvt, u, ldu, 0, target, m);
delete[] u;
delete[] vt;
delete[] s;
return target;
}
#endif
template <>
void CMath::display_vector(BYTE* vector, INT n, const char* name)
{
ASSERT(n>=0);
SG_SPRINT("%s=[", name);
for (INT i=0; i<n; i++)
SG_SPRINT("%d%s", vector[i], i==n-1? "" : ",");
SG_SPRINT("]\n");
}
template <>
void CMath::display_vector(INT* vector, INT n, const char* name)
{
ASSERT(n>=0);
SG_SPRINT("%s=[", name);
for (INT i=0; i<n; i++)
SG_SPRINT("%d%s", vector[i], i==n-1? "" : ",");
SG_SPRINT("]\n");
}
template <>
void CMath::display_vector(LONG* vector, INT n, const char* name)
{
ASSERT(n>=0);
SG_SPRINT("%s=[", name);
for (INT i=0; i<n; i++)
SG_SPRINT("%lld%s", vector[i], i==n-1? "" : ",");
SG_SPRINT("]\n");
}
template <>
void CMath::display_vector(SHORTREAL* vector, INT n, const char* name)
{
ASSERT(n>=0);
SG_SPRINT("%s=[", name);
for (INT i=0; i<n; i++)
SG_SPRINT("%10.10f%s", vector[i], i==n-1? "" : ",");
SG_SPRINT("]\n");
}
template <>
void CMath::display_vector(DREAL* vector, INT n, const char* name)
{
ASSERT(n>=0);
SG_SPRINT("%s=[", name);
for (INT i=0; i<n; i++)
SG_SPRINT("%10.10f%s", vector[i], i==n-1? "" : ",");
SG_SPRINT("]\n");
}
template <>
void CMath::display_matrix(INT* matrix, INT rows, INT cols, const char* name)
{
ASSERT(rows>=0 && cols>=0);
SG_SPRINT("%s=[\n", name);
for (INT i=0; i<rows; i++)
{
SG_SPRINT("[");
for (INT j=0; j<cols; j++)
SG_SPRINT("\t%d%s", matrix[j*rows+i],
j==cols-1? "" : ",");
SG_SPRINT("]%s\n", i==rows-1? "" : ",");
}
SG_SPRINT("]\n");
}
template <>
void CMath::display_matrix(DREAL* matrix, INT rows, INT cols, const char* name)
{
ASSERT(rows>=0 && cols>=0);
SG_SPRINT("%s=[\n", name);
for (INT i=0; i<rows; i++)
{
SG_SPRINT("[");
for (INT j=0; j<cols; j++)
SG_SPRINT("\t%lf%s", (double) matrix[j*rows+i],
j==cols-1? "" : ",");
SG_SPRINT("]%s\n", i==rows-1? "" : ",");
}
SG_SPRINT("]\n");
}
|