parallel partially done

parallel/para_gibbs.cu

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+/*
+Created by Zebulun Arendsee.
+March 26, 2013
+
+Modified by Will Landau.
+June 30, 2013
+will-landau.com
+landau@iastate.edu
+
+This program implements a MCMC algorithm for the following hierarchical
+model:
+
+y_k     ~ Poisson(n_k * theta_k)     k = 1, ..., K
+theta_k ~ Gamma(a, b)
+a       ~ Unif(0, a0)
+b       ~ Unif(0, b0) 
+
+We let a0 and b0 be arbitrarily large.
+
+Arguments:
+    1) input filename
+        With two space delimited columns holding integer values for
+        y and float values for n.
+    2) number of trials (1000 by default)
+
+Output: A comma delimited file containing a column for a, b, and each
+theta. All output is written to stdout.
+
+Example dataset:
+
+$ head -3 data.txt
+4 0.91643
+23 3.23709
+7 0.40103
+
+Example of compilation and execution:
+
+$ nvcc gibbs_metropolis.cu -o gibbs
+$ ./gibbs mydata.txt 2500 > output.csv
+$
+
+This code borrows from the nVidia developer zone documentation, 
+specifically http://docs.nvidia.com/cuda/curand/index.html#topic_1_2_1
+*/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <cuda.h>
+#include <math.h>
+#include <curand_kernel.h>
+#include <thrust/reduce.h>
+#include <thrust/device_ptr.h>
+#include <thrust/device_vector.h>
+
+#define PI 3.14159265359f
+#define THREADS_PER_BLOCK 64
+
+#define CUDA_CALL(x) {if((x) != cudaSuccess){ \
+  printf("CUDA error at %s:%d\n",__FILE__,__LINE__); \
+  printf("  %s\n", cudaGetErrorString(cudaGetLastError())); \
+  exit(EXIT_FAILURE);}} 
+
+#define CURAND_CALL(x) {if((x) != CURAND_STATUS_SUCCESS) { \
+  printf("Error at %s:%d\n",__FILE__,__LINE__); \
+  printf("  %s\n", cudaGetErrorString(cudaGetLastError())); \
+  exit(EXIT_FAILURE);}}
+
+__host__ void load_data(int argc, char **argv, int *K, int **y, float **n);
+
+__host__ float sample_a(float a, float b, int K, float sum_logs);
+__host__ float sample_b(float a, int K, float flat_sum);
+
+__host__ float rnorm();
+__host__ float rgamma(float a, float b);
+
+__device__ float rgamma(curandState *state, int id, float a, float b);
+
+__global__ void sample_theta(curandState *state, float *theta, float *log_theta, 
+                             int *y, float *n, float a, float b, int K);
+__global__ void setup_kernel(curandState *state, unsigned int seed, int);
+
+
+__global__ void seqMetroProcess(int K, int nBlocks, int *y, float *n, curandState *state, 
+                                float *theta, float *log_theta, 
+                                float a, float b, int trials);
+__device__ void sample_theta_seq(float *theta, float *log_theta, int *y, float *n,
+                             float a, float b, int K, curandState *state);
+
+int main(int argc, char **argv){
+
+  curandState *devStates;
+  float a, b, flat_sum, sum_logs, *n, *dev_n, *dev_theta, *dev_log_theta;
+  int i, K, *y, *dev_y, nBlocks, trials = 1000;
+
+  if(argc > 2)
+    trials = atoi(argv[2]);
+
+  load_data(argc, argv, &K, &y, &n);
+
+  /* starting values of hyperparameters */
+  a = 20; 
+  b = 1;   
+
+  /*------ Allocate memory -----------------------------------------*/
+
+  CUDA_CALL(cudaMalloc((void **)&dev_y, K * sizeof(int)));
+  CUDA_CALL(cudaMemcpy(dev_y, y, K * sizeof(int), 
+            cudaMemcpyHostToDevice));
+
+  CUDA_CALL(cudaMalloc((void **)&dev_n, K * sizeof(float)));
+  CUDA_CALL(cudaMemcpy(dev_n, n, K * sizeof(float), 
+            cudaMemcpyHostToDevice));
+
+  /* Allocate space for theta and log_theta on device and host */
+  CUDA_CALL(cudaMalloc((void **)&dev_theta, K * sizeof(float)));
+  CUDA_CALL(cudaMalloc((void **)&dev_log_theta, K * sizeof(float)));
+
+  /* Allocate space for random states on device */
+  CUDA_CALL(cudaMalloc((void **)&devStates, K * sizeof(curandState)));
+
+
+  /*------ Setup random number generators (one per thread) ---------*/
+
+  //nBlocks = (K + THREADS_PER_BLOCK - 1) / THREADS_PER_BLOCK;
+  nBlocks = 500;
+  setup_kernel<<<nBlocks, THREADS_PER_BLOCK>>>(devStates, 0, K);
+  seqMetroProcess<<<nBlocks,1>>>(K,nBlocks,dev_y,dev_n,devStates,dev_theta,dev_log_theta,a,b,trials);
+
+ /*------ Free Memory -------------------------------------------*/
+
+  free(y);
+  free(n);
+
+  CUDA_CALL(cudaFree(devStates));
+  CUDA_CALL(cudaFree(dev_theta));
+  CUDA_CALL(cudaFree(dev_log_theta));
+  CUDA_CALL(cudaFree(dev_y));
+  CUDA_CALL(cudaFree(dev_n));
+
+  return EXIT_SUCCESS;
+}
+
+
+/*
+ *  Sample each theta from the appropriate gamma distribution
+ */
+
+__device__ void sample_theta_seq(float *theta, float *log_theta, int *y, float *n,
+                             float a, float b, int K, curandState *state){
+
+  float hyperA, hyperB;
+
+  for ( int i = 0; i < K; i++ ){
+    hyperA = a + y[i];
+    hyperB = b + n[i];
+    theta[i] = rgamma(state,i,hyperA, hyperB);
+    log_theta[i] = log(theta[i]);
+  }
+}
+
+__global__ void seqMetroProcess(int K, int nBlocks, int *y, float *n, curandState *state, 
+                             float *theta, float *log_theta, 
+                             float a, float b, int trials){
+  /*------ MCMC ----------------------------------------------------*/
+  int i;
+
+  int start = blockIdx.x * K/nBlocks;
+  int lengthPerBlock = K/nBlocks;   
+  //partition the data
+  int *yy = &y[start];
+  float *nn = &n[start];
+  float *sTheta = &theta[start];
+  float *sLogTheta = &log_theta[start]; 
+
+  printf("block id:%d\n",blockIdx.x);
+  for(int j = 0; j < lengthPerBlock ; j++) {
+        printf("%d ", yy[j]);
+    }
+  printf("alpha, beta\n");
+
+
+
+  /* Steps of MCMC */
+
+
+  for(i = 0; i < trials; i++){    
+    //sample_theta<<<nBlocks, THREADS_PER_BLOCK>>>(devStates, dev_theta, dev_log_theta, dev_y, dev_n, a, b, K);
+      sample_theta_seq(sTheta, sLogTheta, yy, nn, a, b, K, state);
+       /* Make iterators for thetas and log thetas. */
+   // thrust::device_ptr<float> theta(dev_theta);
+   // thrust::device_ptr<float> log_theta(dev_log_theta);
+
+    /* Compute pairwise sums of thetas and log_thetas. */
+   // flat_sum = thrust::reduce(theta, theta + K);
+   // sum_logs = thrust::reduce(log_theta, log_theta + K);
+
+    /* Sample hyperparameters. */
+   // a = sample_a(a, b, K, sum_logs);
+   // b = sample_b(a, K, flat_sum);
+
+    /* print hyperparameters. */
+    printf("%f, %f\n", a, b); 
+  }
+}
+
+
+/*
+ *  Read in data.
+ */
+
+__host__ void load_data(int argc, char **argv, int *K, int **y, float **n){
+  int k;
+  char line[128];
+  FILE *fp;    
+
+  if(argc > 1){
+    fp = fopen(argv[1], "r");
+  } else {
+    printf("Please provide input filename\n");
+    exit(EXIT_FAILURE);
+  }
+
+  if(fp == NULL){
+    printf("Cannot read file \n");
+    exit(EXIT_FAILURE);
+  }
+
+  *K = 0;
+  while( fgets (line, sizeof line, fp) != NULL )
+    (*K)++; 
+
+  rewind(fp);
+
+  *y = (int*) malloc((*K) * sizeof(int));
+  *n = (float*) malloc((*K) * sizeof(float)); 
+
+  for(k = 0; k < *K; k++)
+    fscanf(fp, "%d %f", *y + k, *n + k);    
+
+  fclose(fp);
+}
+
+
+/*
+ *  Metropolis algorithm for producing random a values. 
+ *  The proposal distribution in normal with a variance that
+ *  is adjusted at each step.
+ */
+
+__host__ float sample_a(float a, float b, int K, float sum_logs){
+
+  static float sigma = 2;
+  float U, log_acceptance_ratio, proposal = rnorm() * sigma + a;
+
+  if(proposal <= 0) 
+    return a;
+
+  log_acceptance_ratio = (proposal - a) * sum_logs +
+                         K * (proposal - a) * log(b) -
+                         K * (lgamma(proposal) - lgamma(a));
+
+  U = rand() / float(RAND_MAX);
+
+  if(log(U) < log_acceptance_ratio){
+    sigma *= 1.1;
+    return proposal;
+  } else {
+    sigma /= 1.1;
+    return a;
+  }
+}
+
+
+/*
+ *  Sample b from a gamma distribution.
+ */
+
+__host__ float sample_b(float a, int K, float flat_sum){
+
+  float hyperA = K * a + 1;
+  float hyperB = flat_sum;
+  return rgamma(hyperA, hyperB);
+}
+
+
+/* 
+ *  Box-Muller Transformation: Generate one standard normal variable.
+ *
+ *  This algorithm can be more efficiently used by producing two
+ *  random normal variables. However, for the CPU, much faster
+ *  algorithms are possible (e.g. the Ziggurat Algorithm);
+ *
+ *  This is actually the algorithm chosen by NVIDIA to calculate
+ *  normal random variables on the GPU.
+ */
+
+__host__ float rnorm(){
+
+  float U1 = rand() / float(RAND_MAX);
+  float U2 = rand() / float(RAND_MAX);
+  float V1 = sqrt(-2 * log(U1)) * cos(2 * PI * U2);
+  /* float V2 = sqrt(-2 * log(U2)) * cos(2 * PI * U1); */
+  return V1;
+}
+
+
+/*
+ *  See device rgamma function. This is probably not the
+ *   fastest way to generate random gamma variables on a CPU.
+ */
+
+__host__ float rgamma(float a, float b){
+
+  float d = a - 1.0 / 3;
+  float Y, U, v;
+
+  while(1){
+    Y = rnorm();
+    v = pow((1 + Y / sqrt(9 * d)), 3);
+
+    // Necessary to avoid taking the log of a negative number later. 
+    if(v <= 0) 
+      continue;
+
+    U = rand() / float(RAND_MAX);
+
+    // Accept the sample under the following condition. 
+    //   Otherwise repeat loop. 
+    if(log(U) < 0.5 * pow(Y,2) + d * (1 - v + log(v)))
+            return d * v / b;
+  }
+}
+
+/* 
+ *  Generate a single Gamma distributed random variable by the Marsoglia 
+ *  algorithm (George Marsaglia, Wai Wan Tsang; 2001).
+ *
+ *  Zeb chose this algorithm because it has a very high acceptance rate (>96%),
+ *  so this while loop will usually only need to run a few times. Many other 
+ *  algorithms, while perhaps faster on a CPU, have acceptance rates on the 
+ *  order of 50% (very bad in a massively parallel context).
+ */
+
+__device__ float rgamma(curandState *state, int id, float a, float b){
+
+  float d = a - 1.0 / 3;
+  float Y, U, v;
+
+  while(1){   
+    Y = curand_normal(&state[id]);
+    v = pow((1 + Y / sqrt(9 * d)), 3);
+
+    /* Necessary to avoid taking the log of a negative number later. */
+    if(v <= 0) 
+      continue;
+
+    U = curand_uniform(&state[id]);
+
+    /* Accept the sample under the following condition. 
+       Otherwise repeat loop. */
+    if(log(U) < 0.5 * pow(Y,2) + d * (1 - v + log(v)))
+      return d * v / b;
+  }
+}
+
+
+/*
+ *  Sample each theta from the appropriate gamma distribution
+ */
+
+__global__ void sample_theta(curandState *state, 
+                             float *theta, float *log_theta, int *y, float *n, 
+                             float a, float b, int K){
+
+  int id = threadIdx.x + blockIdx.x * blockDim.x;
+  float hyperA, hyperB;
+
+  if(id < K){
+    hyperA = a + y[id];
+    hyperB = b + n[id];
+    theta[id] = rgamma(state, id, hyperA, hyperB);
+    log_theta[id] = log(theta[id]);
+  }
+}
+
+
+/* 
+ *  Initialize GPU random number generators 
+ */
+
+__global__ void setup_kernel(curandState *state, unsigned int seed, int K){
+
+  int id = threadIdx.x + blockIdx.x * blockDim.x;
+
+  if(id < K)
+    curand_init(seed, id, 0, &state[id]);
+}