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fjlt.cpp
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fjlt.cpp
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#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <mkl.h>
#include <fftw3.h>
#include <omp.h>
#include "fjlt.h"
#include "io.h"
/*
* Counts number of set bits in an integer
*/
int count_bits(unsigned number) {
unsigned int c; // c accumulates the total bits set in v
while (number) {
c++;
number &= number - 1; // clear the least significant bit set
}
return c;
}
/*
* Uniform Distribution
*
* INPUT: Pointer to hold the distribution data
* Size of Distribution (m,n)
* OUTPUT: Matrix filled with uniform distribution
*
* Algorithm: Nothing Special
*/
void randu(float *data, int m, int n) {
#pragma omp parallel for shared(data)
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
data[i * n + j] = (float) rand() / RAND_MAX;
}
}
}
/*
* Standard Normal Distribution
*
* INPUT: Pointer to hold the distribution date
* Size of Distribution (m,n)
* OUTPUT: Matrix filled with normal distribution
*
* Algorithm: Generate two random numbers R1 and R2 from
* an uniform distribution, then two random normally
* distributed values can be as follows
*
* sqrt(-2*log(R1)) cos(2*pi*R2)
* sqrt(-2*log(R1)) sin(2*pi*R2)
*
* Formula 30.3 of Statistical Distributions (3rd ed)
* Merran Evans, Nicholas Hastings, and Brian Peacock
*/
void randn(float *data, int m, int n) {
float *udata = (float*) malloc((m * n + 1) * sizeof(float));
randu(udata, m * n + 1, 1);
int i, j, k;
float pi = 4 * atan(1);
float square, amp, angle;
k = 0;
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
if (k % 2 == 0) {
square = -2 * log(udata[k]);
if (square < 0)
square = 0;
amp = sqrt(square);
angle = 2 * pi * udata[k + 1];
data[i * n + j] = amp * sin(angle);
} else {
data[i * n + j] = amp * cos(angle);
}
k++;
}
}
free(udata);
}
/*
* Normal Distribution
*
* INPUT: Pointer to hold the distribution data
* Size of Distribution (m,n)
* mean mu, variance var
* OUTPUT: Matrix filled with normal distribution
*
* Algorithm: Uses Standard normal distribution to
* generate an arbitrary normal distribution with
* mean mu and variance var
*/
void randn_mv(float *data, int m, int n, float mu, float var) {
randn(data, m, n);
float sd = sqrt(var);
#pragma omp parallel for shared(data)
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
data[i * n + j] = mu + sd * data[i * n + j];
}
}
}
/*
* Inverse CND for Normal distribution
*
* INPUT: Any value from uniform distribution
* OUPUT: Value from normal distribution
*
* Algorithm: q belongs to (0,1)
* INVCND(q) belongs to normal distribution
*
* We use Moro's Inverse CND approximation as there exists no
* closed form solutions
*/
inline float moroinv_cnd(float P){
const float a1 = 2.50662823884;
const float a2 = -18.61500062529;
const float a3 = 41.39119773534;
const float a4 = -25.44106049637;
const float b1 = -8.4735109309;
const float b2 = 23.08336743743;
const float b3 = -21.06224101826;
const float b4 = 3.13082909833;
const float c1 = 0.337475482272615;
const float c2 = 0.976169019091719;
const float c3 = 0.160797971491821;
const float c4 = 2.76438810333863E-02;
const float c5 = 3.8405729373609E-03;
const float c6 = 3.951896511919E-04;
const float c7 = 3.21767881768E-05;
const float c8 = 2.888167364E-07;
const float c9 = 3.960315187E-07;
float y, z;
if(P <= 0 || P >= 1.0){
//printf("MoroInvCND(): bad parameter %f\n", P);
//Caused by numerical instability of rand
P = 0.9999;
}
y = P - 0.5;
if(fabs(y) < 0.42){
z = y * y;
z = y * (((a4 * z + a3) * z + a2) * z + a1) / ((((b4 * z + b3) * z + b2) * z + b1) * z + 1);
}else{
if(y > 0)
z = log(-log(1.0 - P));
else
z = log(-log(P));
z = c1 + z * (c2 + z * (c3 + z * (c4 + z * (c5 + z * (c6 + z * (c7 + z * (c8 + z * c9)))))));
if(y < 0) z = -z;
}
return z;
}
/*
* Normal Distribution
*
* INPUT: Pointer to hold the distribution data
* Size of Distribution (m,n)
* mean mu, variance var
* OUTPUT: Matrix filled with normal distribution
*
* Algorithm: Uses Moro's Inverse CND distribution to
* generate an arbitrary normal distribution with
* mean mu and variance var
*/
void inv_randn(float *data, int m, int n, float mu, float var){
float sd = sqrt(var);
#pragma omp parallel for shared(data)
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
data[i * n + j] = mu + sd * moroinv_cnd((float)rand()/RAND_MAX);
}
}
}
/*
* Generates P matrix
*
* INPUT: size of distribution (k,d)
* epsilon e
* embedding type p
* number of points n
* OUTPUT: P matrix
*
* Algorithm: P_ij = N(0,1/q) with probability q
* = 0 elsewhere
*
* q = min( ( e^p-2 * (log n)^p /d ), 1 )
* p belongs to {1,2}
*/
float* generatep(int n, int k, int d, float e, int p) {
float *data = (float*) malloc(k * d * sizeof(float));
memset(data, 0, k * d * sizeof(float));
float q = pow(e, p - 2) * pow(log(n), p) / d;
q = q < 1 ? q : 1;
//printf("Value of q: %f\n", q);
float *rdata = (float*) malloc(k * d * sizeof(float));
//randn_mv(data, k, d, 0, 1 / q);
inv_randn(data, k, d, 0, 1/q);
randu(rdata, k, d);
#pragma omp parallel for shared(data, rdata)
for (int i = 0; i < k; i++) {
for (int j = 0; j < d; j++) {
data[i * d + j] *= (rdata[i * d + j] < q);
}
}
free(rdata);
return data;
}
/*
* Generates Hadamard matrix
*
* INPUT: size of matrix
* OUTPUT: Resultanta H matrix
*
* Algorithm: P_ij = d^-0.5 8 (-1)^<i-1,j-1>
* <i,j> is the dot product of i,j in binary
*
* Not really used because this takes O(d^2) operations
*/
float* generateh(int d) {
float *data = (float*) malloc(d*d*sizeof(float));
float consmul = 1 / (float)sqrt(d);
#pragma omp parallel for shared(data)
for (int i = 0; i < d; i++) {
for (int j = 0; j < d; j++) {
int currpow = count_bits(i & j);
data[i * d + j] = consmul * ((currpow & (currpow - 1)) == 0 ? 1 : -1);
}
}
return data;
}
/*
* Generates diagnol matrix D
*
* INPUT: size of matrix d
* OUTPUT: Matrix D
*
* Algorithm: D_ii = {-1,1} with probability 0.5
*
* Returned as a vector with length d to avoid extra space
*/
float* generated(int d) {
float *data = (float*) malloc(d * sizeof(float));
#pragma omp parallel for shared(data)
for (int i = 0; i < d; i++) {
data[i] = ((float) rand() / RAND_MAX) < 0.5 ? 1 : -1;
}
return data;
}
/*
* Apply FJLT transform on input data
* INPUT: n points of d dimensions
* k required dimension
* OUTPUT: Projected data
*
* Algorithm: FJLT = PHDx
*/
float* FJLT(float *input, int n, int k, int d) {
float *data = (float*) malloc(n * d * sizeof(float));
memcpy(data, input, n * d * sizeof(float));
float eps = (float) sqrt(log(n) / k);
float *D;
D = generated(d);
float *P;
P = generatep(n, k, d, eps, 2);
/*
* Reduced data
*/
float *result;
result = (float*) malloc(n * k * sizeof(float));
memset(result, 0, k * n * sizeof(float));
//float sqrtd = 1 / sqrt(d);
/*
* Process each point at once i.e each column of data
*/
int curr = 0;
#pragma omp parallel for private(curr) shared(data,result)
for(curr=0; curr < n; curr++) {
float *point = data + d * curr;
float *output = result + k * curr;
int a, b, c;
for (a = 0; a < d; a++){
point[a] *= D[a];
}
/*
* Do Fast Walsh transform on the point
*/
int l2 = (int) log2(d);
for (a = 0; a < l2; a++) {
for (b = 0; b < (1 << l2); b += 1 << (a + 1)) {
for (c = 0; c < (1 << a); c++) {
float temp = point[b + c];
point[b + c] += point[b + c + (1 << a)];
point[b + c + (1 << a)] = temp - point[b + c + (1 << a)];
}
}
}
/*
* Multiply with P
*/
cblas_sgemv(CblasRowMajor, CblasNoTrans, k, d, (float)1/d, P, d, point, 1, 0.0, output, 1);
}
free(D);
free(P);
free(data);
return result;
}
/*
* Apply FJLT transform on input data
* INPUT: n points of d dimensions
* k required dimension
* OUTPUT: Projected data
*
* Algorithm: FJLT = PHDx
* Uses FFTW instead of Walsh-Hadamard Transform
*/
float* FJLT_fftw(float *data, int n, int k, int d) {
// k = e^-2 * log(n)
float eps = (float) sqrt(log(n) / k);
float *D;
D = generated(d);
float *P;
P = generatep(n, k, d, eps, 2);
/*
* Reduced data
*/
float *result;
result = (float*) malloc(n * k * sizeof(float));
memset(result, 0, k * n * sizeof(float));
//float sqrtd = 1 / sqrt(d);
/*
* Temp array of size d to copy from fftw_complex to float
*/
float *hdx;
hdx = (float*) malloc(d* sizeof(float));
/*
* Temp arrays for fourier transform results
*/
fftw_complex* in = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * d);
fftw_complex* out = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * d);
/*
* Process each point at once i.e each column of data
*/
int curr = 0;
#pragma omp parallel for private(curr) shared(data,result)
for(curr=0; curr<n; curr++) {
float *x = data + d * curr;
float *y = result + k * curr;
//setup a plan
fftw_plan plan = fftw_plan_dft_1d(d, in, out, FFTW_FORWARD, FFTW_ESTIMATE);
int i;
//First multiply X by D while simultaneosuly pack it in x
for (i = 0; i < d; i++) {
in[i][0] = /*sqrtd * */ D[i] * x[i];
}
//then Fourier transform
fftw_execute_dft( plan, in, out);
//cast from fftw_complex to float
//TODO - Dont know any other way.. going with the normal copy
for (i = 0; i < d; i++) {
hdx[i] = (float)out[i][0];
}
cblas_sgemv(CblasRowMajor, CblasNoTrans, k, d, (float)1/d, P, d, hdx, 1, 0.0, y, 1);
}
return result;
}