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00013 #ifndef __MATHEMATICS_H_
00014 #define __MATHEMATICS_H_
00015
00016 #include "lib/common.h"
00017 #include "lib/io.h"
00018 #include "lib/lapack.h"
00019 #include "base/SGObject.h"
00020 #include "base/Parallel.h"
00021
00022 #include <math.h>
00023 #include <stdio.h>
00024 #include <float.h>
00025 #include <pthread.h>
00026 #include <unistd.h>
00027 #include <sys/types.h>
00028 #include <sys/time.h>
00029 #include <time.h>
00030
00031 #ifdef SUNOS
00032 #include <ieeefp.h>
00033 #endif
00034
00036 #ifdef log2
00037 #define cygwin_log2 log2
00038 #undef log2
00039 #endif
00040
00041
00042
00044 #ifdef _GLIBCXX_CMATH
00045 #if _GLIBCXX_USE_C99_MATH
00046 #if !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC
00047
00049 using std::signbit;
00050
00051 using std::fpclassify;
00052
00053 using std::isfinite;
00054 using std::isinf;
00055 using std::isnan;
00056 using std::isnormal;
00057
00058 using std::isgreater;
00059 using std::isgreaterequal;
00060 using std::isless;
00061 using std::islessequal;
00062 using std::islessgreater;
00063 using std::isunordered;
00064 #endif
00065 #endif
00066 #endif
00067
00068
00069 #ifdef _WIN32
00070 #ifndef isnan
00071 #define isnan _isnan
00072 #endif
00073
00074 #ifndef isfinite
00075 #define isfinite _isfinite
00076 #endif
00077 #endif //_WIN32
00078
00079 #ifndef NAN
00080 #include <stdlib.h>
00081 #define NAN (strtod("NAN",NULL))
00082 #endif
00083
00084
00085 #define RNG_SEED_SIZE 256
00086
00087
00088 #define RADIX_STACK_SIZE 512
00089
00090
00091 #define radix_push(a, n, i) sp->sa = a, sp->sn = n, (sp++)->si = i
00092 #define radix_pop(a, n, i) a = (--sp)->sa, n = sp->sn, i = sp->si
00093
00094 #ifndef DOXYGEN_SHOULD_SKIP_THIS
00095
00096 template <class T> struct radix_stack_t
00097 {
00099 T *sa;
00101 size_t sn;
00103 uint16_t si;
00104 };
00105
00107
00109 template <class T1, class T2> struct thread_qsort
00110 {
00112 T1* output;
00114 T2* index;
00116 uint32_t size;
00117
00119 int32_t* qsort_threads;
00121 int32_t sort_limit;
00123 int32_t num_threads;
00124 };
00125 #endif // DOXYGEN_SHOULD_SKIP_THIS
00126
00127 namespace shogun
00128 {
00131 class CMath : public CSGObject
00132 {
00133 public:
00137
00138 CMath();
00139
00141 virtual ~CMath();
00143
00147
00149
00150 template <class T>
00151 static inline T min(T a, T b)
00152 {
00153 return (a<=b) ? a : b;
00154 }
00155
00157 template <class T>
00158 static inline T max(T a, T b)
00159 {
00160 return (a>=b) ? a : b;
00161 }
00162
00164 template <class T>
00165 static inline T clamp(T value, T lb, T ub)
00166 {
00167 if (value<=lb)
00168 return lb;
00169 else if (value>=ub)
00170 return ub;
00171 else
00172 return value;
00173 }
00174
00176 template <class T>
00177 static inline T abs(T a)
00178 {
00179
00180
00181 if (a==0)
00182 return 0;
00183 else if (a>0)
00184 return a;
00185 else
00186 return -a;
00187 }
00189
00192
00193 static inline float64_t round(float64_t d)
00194 {
00195 return ::floor(d+0.5);
00196 }
00197
00198 static inline float64_t floor(float64_t d)
00199 {
00200 return ::floor(d);
00201 }
00202
00203 static inline float64_t ceil(float64_t d)
00204 {
00205 return ::ceil(d);
00206 }
00207
00209 template <class T>
00210 static inline T sign(T a)
00211 {
00212 if (a==0)
00213 return 0;
00214 else return (a<0) ? (-1) : (+1);
00215 }
00216
00218 template <class T>
00219 static inline void swap(T &a,T &b)
00220 {
00221 T c=a;
00222 a=b;
00223 b=c;
00224 }
00225
00229 template <class T>
00230 static inline void resize(T* &data, int64_t old_size, int64_t new_size)
00231 {
00232 if (old_size==new_size)
00233 return;
00234 T* new_data = new T[new_size];
00235 for (int64_t i=0; i<old_size && i<new_size; i++)
00236 new_data[i]=data[i];
00237 delete[] data;
00238 data=new_data;
00239 }
00240
00242 template <class T>
00243 static inline T twonorm(T* x, int32_t len)
00244 {
00245 float64_t result=0;
00246 for (int32_t i=0; i<len; i++)
00247 result+=x[i]*x[i];
00248
00249 return CMath::sqrt(result);
00250 }
00251
00253 template <class T>
00254 static inline T qsq(T* x, int32_t len, float64_t q)
00255 {
00256 float64_t result=0;
00257 for (int32_t i=0; i<len; i++)
00258 result+=CMath::pow(x[i], q);
00259
00260 return result;
00261 }
00262
00264 template <class T>
00265 static inline T qnorm(T* x, int32_t len, float64_t q)
00266 {
00267 ASSERT(q!=0);
00268 return CMath::pow(qsq(x, len, q), 1/q);
00269 }
00270
00272 template <class T>
00273 static inline T sq(T x)
00274 {
00275 return x*x;
00276 }
00277
00279 static inline float32_t sqrt(float32_t x)
00280 {
00281 return ::sqrtf(x);
00282 }
00283
00285 static inline float64_t sqrt(float64_t x)
00286 {
00287 return ::sqrt(x);
00288 }
00289
00291 static inline floatmax_t sqrt(floatmax_t x)
00292 {
00293
00294
00295 #ifdef HAVE_SQRTL
00296 return ::sqrtl(x);
00297 #else
00298 return ::sqrt(x);
00299 #endif
00300 }
00301
00302
00304 static inline floatmax_t powl(floatmax_t x, floatmax_t n)
00305 {
00306
00307
00308 #ifdef HAVE_POWL
00309 return ::powl((long double) x, (long double) n);
00310 #else
00311 return ::pow((double) x, (double) n);
00312 #endif
00313 }
00314
00315 static inline int32_t pow(int32_t x, int32_t n)
00316 {
00317 ASSERT(n>=0);
00318 int32_t result=1;
00319 while (n--)
00320 result*=x;
00321
00322 return result;
00323 }
00324
00325 static inline float64_t pow(float64_t x, int32_t n)
00326 {
00327 ASSERT(n>=0);
00328 float64_t result=1;
00329 while (n--)
00330 result*=x;
00331
00332 return result;
00333 }
00334
00335 static inline float64_t pow(float64_t x, float64_t n)
00336 {
00337 return ::pow((double) x, (double) n);
00338 }
00339
00340 static inline float64_t exp(float64_t x)
00341 {
00342 return ::exp((double) x);
00343 }
00344
00345 static inline float64_t log10(float64_t v)
00346 {
00347 return ::log(v)/::log(10.0);
00348 }
00349
00350 static inline float64_t log2(float64_t v)
00351 {
00352 #ifdef HAVE_LOG2
00353 return ::log2(v);
00354 #else
00355 return ::log(v)/::log(2.0);
00356 #endif //HAVE_LOG2
00357 }
00358
00359 static inline float64_t log(float64_t v)
00360 {
00361 return ::log(v);
00362 }
00363
00364 template <class T>
00365 static void transpose_matrix(
00366 T*& matrix, int32_t& num_feat, int32_t& num_vec)
00367 {
00368 T* transposed=new T[num_vec*num_feat];
00369 for (int32_t i=0; i<num_vec; i++)
00370 {
00371 for (int32_t j=0; j<num_feat; j++)
00372 transposed[i+j*num_vec]=matrix[i*num_feat+j];
00373 }
00374
00375 delete[] matrix;
00376 matrix=transposed;
00377
00378 CMath::swap(num_feat, num_vec);
00379 }
00380
00381 #ifdef HAVE_LAPACK
00382
00383
00384 static float64_t* pinv(
00385 float64_t* matrix, int32_t rows, int32_t cols,
00386 float64_t* target=NULL);
00387
00388
00389
00390
00391 static inline void dgemm(
00392 double alpha, const double* A, int rows, int cols,
00393 CBLAS_TRANSPOSE transposeA, double *B, int cols_B,
00394 CBLAS_TRANSPOSE transposeB, double beta, double *C)
00395 {
00396 cblas_dgemm(CblasColMajor, transposeA, transposeB, rows, cols, cols_B,
00397 alpha, A, cols, B, cols_B, beta, C, cols);
00398 }
00399
00400
00401 static inline void dgemv(
00402 double alpha, const double *A, int rows, int cols,
00403 const CBLAS_TRANSPOSE transposeA, const double* X, double beta,
00404 double* Y)
00405 {
00406 cblas_dgemv(CblasColMajor, transposeA,
00407 rows, cols, alpha, A, cols,
00408 X, 1, beta, Y, 1);
00409 }
00410 #endif
00411
00412 static inline int64_t factorial(int32_t n)
00413 {
00414 int64_t res=1;
00415 for (int i=2; i<=n; i++)
00416 res*=i ;
00417 return res ;
00418 }
00419
00420 static void init_random(uint32_t initseed=0)
00421 {
00422 if (initseed==0)
00423 {
00424 struct timeval tv;
00425 gettimeofday(&tv, NULL);
00426 seed=(uint32_t) (4223517*getpid()*tv.tv_sec*tv.tv_usec);
00427 }
00428 else
00429 seed=initseed;
00430 #if !defined(CYGWIN) && !defined(__INTERIX)
00431
00432
00433 initstate(seed, CMath::rand_state, RNG_SEED_SIZE);
00434 #endif
00435 }
00436
00437 static inline int64_t random()
00438 {
00439 #if defined(CYGWIN) || defined(__INTERIX)
00440 return rand();
00441 #else
00442 return ::random();
00443 #endif
00444 }
00445
00446 static inline int32_t random(int32_t min_value, int32_t max_value)
00447 {
00448 int32_t ret = min_value + (int32_t) ((max_value-min_value+1) * (random() / (RAND_MAX+1.0)));
00449 ASSERT(ret>=min_value && ret<=max_value);
00450 return ret ;
00451 }
00452
00453 static inline float32_t random(float32_t min_value, float32_t max_value)
00454 {
00455 float32_t ret = min_value + ((max_value-min_value) * (random() / (1.0*RAND_MAX)));
00456
00457 if (ret<min_value || ret>max_value)
00458 SG_SPRINT("min_value:%10.10f value: %10.10f max_value:%10.10f", min_value, ret, max_value);
00459 ASSERT(ret>=min_value && ret<=max_value);
00460 return ret;
00461 }
00462
00463 static inline float64_t random(float64_t min_value, float64_t max_value)
00464 {
00465 float64_t ret = min_value + ((max_value-min_value) * (random() / (1.0*RAND_MAX)));
00466
00467 if (ret<min_value || ret>max_value)
00468 SG_SPRINT("min_value:%10.10f value: %10.10f max_value:%10.10f", min_value, ret, max_value);
00469 ASSERT(ret>=min_value && ret<=max_value);
00470 return ret;
00471 }
00472
00473 template <class T>
00474 static T* clone_vector(const T* vec, int32_t len)
00475 {
00476 T* result = new T[len];
00477 for (int32_t i=0; i<len; i++)
00478 result[i]=vec[i];
00479
00480 return result;
00481 }
00482 template <class T>
00483 static void fill_vector(T* vec, int32_t len, T value)
00484 {
00485 for (int32_t i=0; i<len; i++)
00486 vec[i]=value;
00487 }
00488 template <class T>
00489 static void range_fill_vector(T* vec, int32_t len, T start=0)
00490 {
00491 for (int32_t i=0; i<len; i++)
00492 vec[i]=i+start;
00493 }
00494
00495 template <class T>
00496 static void random_vector(T* vec, int32_t len, T min_value, T max_value)
00497 {
00498 for (int32_t i=0; i<len; i++)
00499 vec[i]=CMath::random(min_value, max_value);
00500 }
00501
00502 static inline int32_t* randperm(int32_t n)
00503 {
00504 int32_t* perm = new int32_t[n];
00505
00506 if (!perm)
00507 return NULL;
00508 for (int32_t i = 0; i < n; i++)
00509 perm[i] = i;
00510 for (int32_t i = 0; i < n; i++)
00511 swap(perm[random(0, n - 1)], perm[i]);
00512 return perm;
00513 }
00514
00515 static inline int64_t nchoosek(int32_t n, int32_t k)
00516 {
00517 int64_t res=1;
00518
00519 for (int32_t i=n-k+1; i<=n; i++)
00520 res*=i;
00521
00522 return res/factorial(k);
00523 }
00524
00526 template <class T>
00527 static inline void vec1_plus_scalar_times_vec2(T* vec1,
00528 T scalar, const T* vec2, int32_t n)
00529 {
00530 for (int32_t i=0; i<n; i++)
00531 vec1[i]+=scalar*vec2[i];
00532 }
00533
00535 static inline float64_t dot(const bool* v1, const bool* v2, int32_t n)
00536 {
00537 float64_t r=0;
00538 for (int32_t i=0; i<n; i++)
00539 r+=((v1[i]) ? 1 : 0) * ((v2[i]) ? 1 : 0);
00540 return r;
00541 }
00542
00544 static inline floatmax_t dot(const floatmax_t* v1, const floatmax_t* v2, int32_t n)
00545 {
00546 floatmax_t r=0;
00547 for (int32_t i=0; i<n; i++)
00548 r+=v1[i]*v2[i];
00549 return r;
00550 }
00551
00553 static inline float64_t dot(const float64_t* v1, const float64_t* v2, int32_t n)
00554 {
00555 float64_t r=0;
00556 #ifdef HAVE_LAPACK
00557 int32_t skip=1;
00558 r = cblas_ddot(n, v1, skip, v2, skip);
00559 #else
00560 for (int32_t i=0; i<n; i++)
00561 r+=v1[i]*v2[i];
00562 #endif
00563 return r;
00564 }
00565
00567 static inline float32_t dot(
00568 const float32_t* v1, const float32_t* v2, int32_t n)
00569 {
00570 float64_t r=0;
00571 #ifdef HAVE_LAPACK
00572 int32_t skip=1;
00573 r = cblas_sdot(n, v1, skip, v2, skip);
00574 #else
00575 for (int32_t i=0; i<n; i++)
00576 r+=v1[i]*v2[i];
00577 #endif
00578 return r;
00579 }
00580
00582 static inline float64_t dot(
00583 const uint64_t* v1, const uint64_t* v2, int32_t n)
00584 {
00585 float64_t r=0;
00586 for (int32_t i=0; i<n; i++)
00587 r+=((float64_t) v1[i])*v2[i];
00588
00589 return r;
00590 }
00592 static inline float64_t dot(
00593 const int64_t* v1, const int64_t* v2, int32_t n)
00594 {
00595 float64_t r=0;
00596 for (int32_t i=0; i<n; i++)
00597 r+=((float64_t) v1[i])*v2[i];
00598
00599 return r;
00600 }
00601
00603 static inline float64_t dot(
00604 const int32_t* v1, const int32_t* v2, int32_t n)
00605 {
00606 float64_t r=0;
00607 for (int32_t i=0; i<n; i++)
00608 r+=((float64_t) v1[i])*v2[i];
00609
00610 return r;
00611 }
00612
00614 static inline float64_t dot(
00615 const uint32_t* v1, const uint32_t* v2, int32_t n)
00616 {
00617 float64_t r=0;
00618 for (int32_t i=0; i<n; i++)
00619 r+=((float64_t) v1[i])*v2[i];
00620
00621 return r;
00622 }
00623
00625 static inline float64_t dot(
00626 const uint16_t* v1, const uint16_t* v2, int32_t n)
00627 {
00628 float64_t r=0;
00629 for (int32_t i=0; i<n; i++)
00630 r+=((float64_t) v1[i])*v2[i];
00631
00632 return r;
00633 }
00634
00636 static inline float64_t dot(
00637 const int16_t* v1, const int16_t* v2, int32_t n)
00638 {
00639 float64_t r=0;
00640 for (int32_t i=0; i<n; i++)
00641 r+=((float64_t) v1[i])*v2[i];
00642
00643 return r;
00644 }
00645
00647 static inline float64_t dot(
00648 const char* v1, const char* v2, int32_t n)
00649 {
00650 float64_t r=0;
00651 for (int32_t i=0; i<n; i++)
00652 r+=((float64_t) v1[i])*v2[i];
00653
00654 return r;
00655 }
00656
00658 static inline float64_t dot(
00659 const uint8_t* v1, const uint8_t* v2, int32_t n)
00660 {
00661 float64_t r=0;
00662 for (int32_t i=0; i<n; i++)
00663 r+=((float64_t) v1[i])*v2[i];
00664
00665 return r;
00666 }
00667
00669 static inline float64_t dot(
00670 const float64_t* v1, const char* v2, int32_t n)
00671 {
00672 float64_t r=0;
00673 for (int32_t i=0; i<n; i++)
00674 r+=((float64_t) v1[i])*v2[i];
00675
00676 return r;
00677 }
00678
00680 template <class T>
00681 static inline void add(
00682 T* target, T alpha, const T* v1, T beta, const T* v2,
00683 int32_t len)
00684 {
00685 for (int32_t i=0; i<len; i++)
00686 target[i]=alpha*v1[i]+beta*v2[i];
00687 }
00688
00690 template <class T>
00691 static inline void add_scalar(T alpha, T* vec, int32_t len)
00692 {
00693 for (int32_t i=0; i<len; i++)
00694 vec[i]+=alpha;
00695 }
00696
00698 template <class T>
00699 static inline void scale_vector(T alpha, T* vec, int32_t len)
00700 {
00701 for (int32_t i=0; i<len; i++)
00702 vec[i]*=alpha;
00703 }
00704
00706 template <class T>
00707 static inline T sum(T* vec, int32_t len)
00708 {
00709 T result=0;
00710 for (int32_t i=0; i<len; i++)
00711 result+=vec[i];
00712
00713 return result;
00714 }
00715
00717 template <class T>
00718 static inline T max(T* vec, int32_t len)
00719 {
00720 ASSERT(len>0);
00721 T maxv=vec[0];
00722
00723 for (int32_t i=1; i<len; i++)
00724 maxv=CMath::max(vec[i], maxv);
00725
00726 return maxv;
00727 }
00728
00730 template <class T>
00731 static inline T sum_abs(T* vec, int32_t len)
00732 {
00733 T result=0;
00734 for (int32_t i=0; i<len; i++)
00735 result+=CMath::abs(vec[i]);
00736
00737 return result;
00738 }
00739
00741 template <class T>
00742 static inline bool fequal(T x, T y, float64_t precision=1e-6)
00743 {
00744 return CMath::abs(x-y)<precision;
00745 }
00746
00747 static inline float64_t mean(float64_t* vec, int32_t len)
00748 {
00749 ASSERT(vec);
00750 ASSERT(len>0);
00751
00752 float64_t mean=0;
00753 for (int32_t i=0; i<len; i++)
00754 mean+=vec[i];
00755 return mean/len;
00756 }
00757
00758 static inline float64_t trace(
00759 float64_t* mat, int32_t cols, int32_t rows)
00760 {
00761 float64_t trace=0;
00762 for (int32_t i=0; i<rows; i++)
00763 trace+=mat[i*cols+i];
00764 return trace;
00765 }
00766
00770 static void sort(int32_t *a, int32_t cols, int32_t sort_col=0);
00771 static void sort(float64_t *a, int32_t*idx, int32_t N);
00772
00773
00774
00775
00776
00777
00778
00780 template <class T>
00781 inline static void radix_sort(T* array, int32_t size)
00782 {
00783 radix_sort_helper(array,size,0);
00784 }
00785
00786 template <class T>
00787 static inline uint8_t byte(T word, uint16_t p)
00788 {
00789 return (word >> (sizeof(T)-p-1) * 8) & 0xff;
00790 }
00791
00792 template <class T>
00793 static void radix_sort_helper(T* array, int32_t size, uint16_t i)
00794 {
00795 static size_t count[256], nc, cmin;
00796 T *ak;
00797 uint8_t c=0;
00798 radix_stack_t<T> s[RADIX_STACK_SIZE], *sp, *olds, *bigs;
00799 T *an, *aj, *pile[256];
00800 size_t *cp, cmax;
00801
00802
00803 sp = s;
00804 radix_push(array, size, i);
00805
00806
00807 while (sp>s) {
00808 radix_pop(array, size, i);
00809 an = array + size;
00810
00811
00812 if (nc == 0) {
00813 cmin = 0xff;
00814 for (ak = array; ak < an; ak++) {
00815 c = byte(*ak, i);
00816 count[c]++;
00817 if (count[c] == 1) {
00818
00819 if (c < cmin)
00820 cmin = c;
00821 nc++;
00822 }
00823 }
00824
00825
00826 if (sp + nc > s + RADIX_STACK_SIZE) {
00827 radix_sort_helper(array, size, i);
00828 continue;
00829 }
00830 }
00831
00832
00833
00834
00835
00836
00837
00838 olds = bigs = sp;
00839 cmax = 2;
00840 ak = array;
00841 pile[0xff] = an;
00842 for (cp = count + cmin; nc > 0; cp++) {
00843
00844 while (*cp == 0)
00845 cp++;
00846
00847 if (*cp > 1) {
00848
00849 if (*cp > cmax) {
00850 cmax = *cp;
00851 bigs = sp;
00852 }
00853
00854 if (i < sizeof(T)-1)
00855 radix_push(ak, *cp, (uint16_t) (i + 1));
00856 }
00857 pile[cp - count] = ak += *cp;
00858 nc--;
00859 }
00860
00861
00862 swap(*olds, *bigs);
00863
00864
00865
00866
00867
00868
00869
00870
00871
00872
00873
00874
00875
00876 aj = array;
00877 while (aj<an)
00878 {
00879 T r;
00880
00881 for (r = *aj; aj < (ak = --pile[c = byte(r, i)]);)
00882 swap(*ak, r);
00883
00884 *aj = r;
00885 aj += count[c];
00886 count[c] = 0;
00887 }
00888 }
00889 }
00890
00893 template <class T>
00894 static void insertion_sort(T* output, int32_t size)
00895 {
00896 for (int32_t i=0; i<size-1; i++)
00897 {
00898 int32_t j=i-1;
00899 T value=output[i];
00900 while (j >= 0 && output[j] > value)
00901 {
00902 output[j+1] = output[j];
00903 j--;
00904 }
00905 output[j+1]=value;
00906 }
00907 }
00908
00909
00912 template <class T>
00913 static void qsort(T* output, int32_t size)
00914 {
00915 if (size==2)
00916 {
00917 if (output[0] > output [1])
00918 swap(output[0],output[1]);
00919 return;
00920 }
00921
00922 T split=output[size/2];
00923
00924 int32_t left=0;
00925 int32_t right=size-1;
00926
00927 while (left<=right)
00928 {
00929 while (output[left] < split)
00930 left++;
00931 while (output[right] > split)
00932 right--;
00933
00934 if (left<=right)
00935 {
00936 swap(output[left],output[right]);
00937 left++;
00938 right--;
00939 }
00940 }
00941
00942 if (right+1> 1)
00943 qsort(output,right+1);
00944
00945 if (size-left> 1)
00946 qsort(&output[left],size-left);
00947 }
00948
00950 template <class T> static void display_bits(T word, int32_t width=8*sizeof(T))
00951 {
00952 ASSERT(width>=0);
00953 for (int i=0; i<width; i++)
00954 {
00955 T mask = ((T) 1)<<(sizeof(T)*8-1);
00956 while (mask)
00957 {
00958 if (mask & word)
00959 SG_SPRINT("1");
00960 else
00961 SG_SPRINT("0");
00962
00963 mask>>=1;
00964 }
00965 }
00966 }
00967
00969 template <class T> static void display_vector(
00970 const T* vector, int32_t n, const char* name="vector");
00971
00973 template <class T> static void display_matrix(
00974 const T* matrix, int32_t rows, int32_t cols, const char* name="matrix");
00975
00981 template <class T1,class T2>
00982 static void qsort_index(T1* output, T2* index, uint32_t size);
00983
00989 template <class T1,class T2>
00990 static void qsort_backward_index(
00991 T1* output, T2* index, int32_t size);
00992
01000 template <class T1,class T2>
01001 inline static void parallel_qsort_index(T1* output, T2* index, uint32_t size, int32_t n_threads, int32_t limit=262144)
01002 {
01003 int32_t n=0;
01004 thread_qsort<T1,T2> t;
01005 t.output=output;
01006 t.index=index;
01007 t.size=size;
01008 t.qsort_threads=&n;
01009 t.sort_limit=limit;
01010 t.num_threads=n_threads;
01011 parallel_qsort_index<T1,T2>(&t);
01012 }
01013
01014
01015 template <class T1,class T2>
01016 static void* parallel_qsort_index(void* p);
01017
01018
01019
01020
01021 template <class T>
01022 static void min(float64_t* output, T* index, int32_t size);
01023
01024
01025
01026 template <class T>
01027 static void nmin(
01028 float64_t* output, T* index, int32_t size, int32_t n);
01029
01030
01031
01032 template <class T>
01033 static int32_t unique(T* output, int32_t size)
01034 {
01035 qsort(output, size);
01036 int32_t i,j=0 ;
01037 for (i=0; i<size; i++)
01038 if (i==0 || output[i]!=output[i-1])
01039 output[j++]=output[i];
01040 return j ;
01041 }
01042
01043
01044
01045 template <class T>
01046 static int32_t binary_search_helper(T* output, int32_t size, T elem)
01047 {
01048 int32_t start=0;
01049 int32_t end=size-1;
01050
01051 if (size<1)
01052 return 0;
01053
01054 while (start<end)
01055 {
01056 int32_t middle=(start+end)/2;
01057
01058 if (output[middle]>elem)
01059 end=middle-1;
01060 else if (output[middle]<elem)
01061 start=middle+1;
01062 else
01063 return middle;
01064 }
01065
01066 return start;
01067 }
01068
01069
01070
01071 template <class T>
01072 static inline int32_t binary_search(T* output, int32_t size, T elem)
01073 {
01074 int32_t ind = binary_search_helper(output, size, elem);
01075 if (ind >= 0 && output[ind] == elem)
01076 return ind;
01077 return -1;
01078 }
01079
01080
01081
01082
01083
01084 template <class T>
01085 static int32_t binary_search_max_lower_equal(
01086 T* output, int32_t size, T elem)
01087 {
01088 int32_t ind = binary_search_helper(output, size, elem);
01089
01090 if (output[ind]<=elem)
01091 return ind;
01092 if (ind>0 && output[ind-1] <= elem)
01093 return ind-1;
01094 return -1;
01095 }
01096
01099 static float64_t Align(
01100 char * seq1, char* seq2, int32_t l1, int32_t l2, float64_t gapCost);
01101
01106 static int32_t calcroc(
01107 float64_t* fp, float64_t* tp, float64_t* output, int32_t* label,
01108 int32_t& size, int32_t& possize, int32_t& negsize,
01109 float64_t& tresh, FILE* rocfile);
01111
01114 static float64_t mutual_info(float64_t* p1, float64_t* p2, int32_t len);
01115
01118 static float64_t relative_entropy(
01119 float64_t* p, float64_t* q, int32_t len);
01120
01122 static float64_t entropy(float64_t* p, int32_t len);
01123
01125 inline static uint32_t get_seed()
01126 {
01127 return CMath::seed;
01128 }
01129
01131 inline static int is_finite(double f)
01132 {
01133 #if defined(isfinite) && !defined(SUNOS)
01134 return isfinite(f);
01135 #else
01136 return finite(f);
01137 #endif
01138 }
01139
01141 inline static int is_infinity(double f)
01142 {
01143 #ifdef SUNOS
01144 if (fpclass(f) == FP_NINF || fpclass(f) == FP_PINF)
01145 return 1;
01146 else
01147 return 0;
01148 #else
01149 return isinf(f);
01150 #endif
01151 }
01152
01154 inline static int is_nan(double f)
01155 {
01156 #ifdef SUNOS
01157 return isnand(f);
01158 #else
01159 return isnan(f);
01160 #endif
01161 }
01162
01163
01174 #ifdef USE_LOGCACHE
01175 static inline float64_t logarithmic_sum(float64_t p, float64_t q)
01176 {
01177 float64_t diff;
01178
01179 if (!CMath::finite(p))
01180 return q;
01181
01182 if (!CMath::finite(q))
01183 {
01184 SG_SWARNING("INVALID second operand to logsum(%f,%f) expect undefined results\n", p, q);
01185 return NAN;
01186 }
01187 diff = p - q;
01188 if (diff > 0)
01189 return diff > LOGRANGE? p : p + logtable[(int)(diff * LOGACCURACY)];
01190 return -diff > LOGRANGE? q : q + logtable[(int)(-diff * LOGACCURACY)];
01191 }
01192
01194 static void init_log_table();
01195
01197 static int32_t determine_logrange();
01198
01200 static int32_t determine_logaccuracy(int32_t range);
01201 #else
01202 static inline float64_t logarithmic_sum(
01203 float64_t p, float64_t q)
01204 {
01205 float64_t diff;
01206
01207 if (!CMath::is_finite(p))
01208 return q;
01209 if (!CMath::is_finite(q))
01210 return p;
01211 diff = p - q;
01212 if (diff > 0)
01213 return diff > LOGRANGE? p : p + log(1 + exp(-diff));
01214 return -diff > LOGRANGE? q : q + log(1 + exp(diff));
01215 }
01216 #endif
01217 #ifdef LOG_SUM_ARRAY
01218
01223 static inline float64_t logarithmic_sum_array(
01224 float64_t *p, int32_t len)
01225 {
01226 if (len<=2)
01227 {
01228 if (len==2)
01229 return logarithmic_sum(p[0],p[1]) ;
01230 if (len==1)
01231 return p[0];
01232 return -INFTY ;
01233 }
01234 else
01235 {
01236 register float64_t *pp=p ;
01237 if (len%2==1) pp++ ;
01238 for (register int32_t j=0; j < len>>1; j++)
01239 pp[j]=logarithmic_sum(pp[j<<1], pp[1+(j<<1)]) ;
01240 }
01241 return logarithmic_sum_array(p,len%2+len>>1) ;
01242 }
01243 #endif
01244
01245
01247 inline virtual const char* get_name() const { return "Mathematics"; }
01248 public:
01251
01252 static const float64_t INFTY;
01253 static const float64_t ALMOST_INFTY;
01254
01256 static const float64_t ALMOST_NEG_INFTY;
01257
01259 static int32_t LOGRANGE;
01260
01262 static uint32_t seed;
01263 static char* rand_state;
01264
01265 #ifdef USE_LOGCACHE
01266
01268 static int32_t LOGACCURACY;
01270 protected:
01272 static float64_t* logtable;
01273 #endif
01274 };
01275
01276
01277 template <class T1,class T2>
01278 void* CMath::parallel_qsort_index(void* p)
01279 {
01280 struct thread_qsort<T1,T2>* ps=(thread_qsort<T1,T2>*) p;
01281 T1* output=ps->output;
01282 T2* index=ps->index;
01283 uint32_t size=ps->size;
01284 int32_t* qsort_threads=ps->qsort_threads;
01285 int32_t sort_limit=ps->sort_limit;
01286 int32_t num_threads=ps->num_threads;
01287
01288 if (size==2)
01289 {
01290 if (output[0] > output [1])
01291 {
01292 swap(output[0], output[1]);
01293 swap(index[0], index[1]);
01294 }
01295 return NULL;
01296 }
01297
01298 T1 split=output[size/2];
01299
01300 int32_t left=0;
01301 int32_t right=size-1;
01302
01303 while (left<=right)
01304 {
01305 while (output[left] < split)
01306 left++;
01307 while (output[right] > split)
01308 right--;
01309
01310 if (left<=right)
01311 {
01312 swap(output[left], output[right]);
01313 swap(index[left], index[right]);
01314 left++;
01315 right--;
01316 }
01317 }
01318 bool lthread_start=false;
01319 bool rthread_start=false;
01320 pthread_t lthread;
01321 pthread_t rthread;
01322 struct thread_qsort<T1,T2> t1;
01323 struct thread_qsort<T1,T2> t2;
01324
01325 if (right+1> 1 && (right+1< sort_limit || *qsort_threads >= num_threads-1))
01326 qsort_index(output,index,right+1);
01327 else if (right+1> 1)
01328 {
01329 (*qsort_threads)++;
01330 lthread_start=true;
01331 t1.output=output;
01332 t1.index=index;
01333 t1.size=right+1;
01334 t1.qsort_threads=qsort_threads;
01335 t1.sort_limit=sort_limit;
01336 t1.num_threads=num_threads;
01337 if (pthread_create(<hread, NULL, parallel_qsort_index<T1,T2>, &t1) != 0)
01338 {
01339 lthread_start=false;
01340 (*qsort_threads)--;
01341 qsort_index(output,index,right+1);
01342 }
01343 }
01344
01345
01346 if (size-left> 1 && (size-left< sort_limit || *qsort_threads >= num_threads-1))
01347 qsort_index(&output[left],&index[left], size-left);
01348 else if (size-left> 1)
01349 {
01350 (*qsort_threads)++;
01351 rthread_start=true;
01352 t2.output=&output[left];
01353 t2.index=&index[left];
01354 t2.size=size-left;
01355 t2.qsort_threads=qsort_threads;
01356 t2.sort_limit=sort_limit;
01357 t2.num_threads=num_threads;
01358 if (pthread_create(&rthread, NULL, parallel_qsort_index<T1,T2>, &t2) != 0)
01359 {
01360 rthread_start=false;
01361 (*qsort_threads)--;
01362 qsort_index(&output[left],&index[left], size-left);
01363 }
01364 }
01365
01366 if (lthread_start)
01367 {
01368 pthread_join(lthread, NULL);
01369 (*qsort_threads)--;
01370 }
01371
01372 if (rthread_start)
01373 {
01374 pthread_join(rthread, NULL);
01375 (*qsort_threads)--;
01376 }
01377
01378 return NULL;
01379 }
01380
01381 template <class T1,class T2>
01382 void CMath::qsort_index(T1* output, T2* index, uint32_t size)
01383 {
01384 if (size==2)
01385 {
01386 if (output[0] > output [1])
01387 {
01388 swap(output[0],output[1]);
01389 swap(index[0],index[1]);
01390 }
01391 return;
01392 }
01393
01394 T1 split=output[size/2];
01395
01396 int32_t left=0;
01397 int32_t right=size-1;
01398
01399 while (left<=right)
01400 {
01401 while (output[left] < split)
01402 left++;
01403 while (output[right] > split)
01404 right--;
01405
01406 if (left<=right)
01407 {
01408 swap(output[left],output[right]);
01409 swap(index[left],index[right]);
01410 left++;
01411 right--;
01412 }
01413 }
01414
01415 if (right+1> 1)
01416 qsort_index(output,index,right+1);
01417
01418 if (size-left> 1)
01419 qsort_index(&output[left],&index[left], size-left);
01420 }
01421
01422 template <class T1,class T2>
01423 void CMath::qsort_backward_index(T1* output, T2* index, int32_t size)
01424 {
01425 if (size==2)
01426 {
01427 if (output[0] < output [1])
01428 {
01429 swap(output[0],output[1]);
01430 swap(index[0],index[1]);
01431 }
01432 return;
01433 }
01434
01435
01436 T1 split=output[size/2];
01437
01438 int32_t left=0;
01439 int32_t right=size-1;
01440
01441 while (left<=right)
01442 {
01443 while (output[left] > split)
01444 left++;
01445 while (output[right] < split)
01446 right--;
01447
01448 if (left<=right)
01449 {
01450 swap(output[left],output[right]);
01451 swap(index[left],index[right]);
01452 left++;
01453 right--;
01454 }
01455 }
01456
01457 if (right+1> 1)
01458 qsort_backward_index(output,index,right+1);
01459
01460 if (size-left> 1)
01461 qsort_backward_index(&output[left],&index[left], size-left);
01462 }
01463
01464 template <class T>
01465 void CMath::nmin(float64_t* output, T* index, int32_t size, int32_t n)
01466 {
01467 if (6*n*size<13*size*CMath::log(size))
01468 for (int32_t i=0; i<n; i++)
01469 min(&output[i], &index[i], size-i) ;
01470 else
01471 qsort_index(output, index, size) ;
01472 }
01473
01474
01475 template <class T>
01476 void CMath::min(float64_t* output, T* index, int32_t size)
01477 {
01478 if (size<=1)
01479 return;
01480 float64_t min_elem=output[0];
01481 int32_t min_index=0;
01482 for (int32_t i=1; i<size; i++)
01483 {
01484 if (output[i]<min_elem)
01485 {
01486 min_index=i;
01487 min_elem=output[i];
01488 }
01489 }
01490 swap(output[0], output[min_index]);
01491 swap(index[0], index[min_index]);
01492 }
01493 }
01494 #endif