static void assert_linearity(linear_map_t A, int n, void *e, int ntrials)
{
int sn = n * sizeof(double);
double *x = xmalloc(sn);
double *y = xmalloc(sn);
double *Ax = xmalloc(sn);
double *Ay = xmalloc(sn);
double *xpy = xmalloc(sn);
double *AxpAy = xmalloc(sn);
double *Axpy = xmalloc(sn);
for (int i = 0; i < ntrials; i++) {
fill_random_vector(x, n);
fill_random_vector(y, n);
vector_sum(xpy, x, y, n);
A(Ax, x, n, e);
A(Ay, y, n, e);
A(Axpy, xpy, n, e);
vector_sum(AxpAy, Ax, Ay, n);
double error = 0;
for (int k = 0; k < n; k++)
error = hypot(error, fabs(AxpAy[k]-Axpy[k]));
fprintf(stderr, "error linearity = %g\n", error);
if (error > 1e-12)
fprintf(stderr, "WARNING: non linear!\n");
}
free(x);
free(y );
free(Ax );
free(Ay );
free(xpy );
free(AxpAy);
free(Axpy );
}
int Runge_Kutta_4b(int n, void (*f)(double,double *,double *,double *,double *,double *,double *),
double *p, double *fld, double *ext, double *extev,
double *y, double x0, double h, double *yout,
double *k1, double *k2, double *k3, double *k4,
double *t1, double *t2, double *t3, double *t4, double *t5, double *t6,
double *t7, double *t8)
{
double h2, h3;
if (n == 0)
{
return 0;
}
// cs: [0,0.333333333333,0.666666666667,1]
// as: <1, []>
// <3, [1]>
// <3, [~1,3]>
// <1, [1,~1,1]>
// bs: <8, [1,3,3,1]>
h2 = 0.333333333333 * h;
h3 = 0.666666666667 * h;
(*f)(x0, p, fld, ext, extev, y, k1);
// printf("c: k1[0] = %g\n", k1[0]);
vector_scale(n, 1.0, k1, t1);
vector_scale(n, h/3.0, t1, t2);
vector_sum(n, y, t2, t3);
(*f)(x0+h2, p, fld, ext, extev, t3, k2);
vector_scale(n, -1.0, k1, t1); vector_scale(n, 3.0, k2, t2);
vector_sum(n, t1, t2, t3);
vector_scale(n, h/3.0, t3, t4); vector_sum(n, y, t4, t5);
(*f)(x0+h3, p, fld, ext, extev, t5, k3);
vector_scale(n, 1.0, k1, t1); vector_scale(n, -1.0, k2, t2);
vector_scale(n, 1.0, k3, t3);
vector_sum(n, t1, t2, t4); vector_sum(n, t3, t4, t5);
vector_scale(n, h, t5, t6); vector_sum(n, y, t6, t7);
(*f)(x0+h, p, fld, ext, extev, t7, k4);
vector_scale(n, 1.0, k1, t1);
vector_scale(n, 3.0, k2, t2);
vector_scale(n, 3.0, k3, t3);
vector_scale(n, 1.0, k4, t4);
vector_sum(n, t1, t2, t5); vector_sum(n, t3, t4, t6);
vector_sum(n, t5, t6, t7);
vector_scale(n, h/8.0, t7, t8);
// printf("c: t6[0] = %g\n", t6[0]);
vector_sum(n, y, t8, yout);
return 0;
}
vector3d ahrs_drift_correction(dataexchange_t *data) {
vector3d corr_vector, acc_g;
corr_vector.x = 0.0;
corr_vector.y = 0.0;
corr_vector.z = 0.0;
//do correction only then acceleration is close to 1G (unreliable if greater)
acc_g = adxl345_raw_to_g(data, SCALE_2G_10B);
double acc_magnitude = vector_magnitude(acc_g);
if (fabs(acc_magnitude - 1.0) <= 0.15) {
float corr_strength = 0.15;
//vectors for rotation matrix
vector3d acc_v, mag_v;
acc_v.x = (*data).acc_x;
acc_v.y = (*data).acc_y;
acc_v.z = (*data).acc_z;
mag_v.x = (*data).mag_x;
mag_v.y = (*data).mag_y;
mag_v.z = (*data).mag_z;
hmc5883l_applyCalibration(&mag_v, calib_ptr);
vector3d down = vector_inv(acc_v);
vector3d east = vector_cross(down, mag_v);
vector3d north = vector_cross(east, down);
//normalize vectors
vector_norm(&down);
vector_norm(&east);
vector_norm(&north);
//matrix from rotation quaternion
matrix3x3d rot_matrix = quaternion_to_matrix((*data).qr);
//correction vector calculation
vector3d sum1 = vector_sum(vector_cross(north, matrix_row_to_vector(&rot_matrix, 1)),
vector_cross(east, matrix_row_to_vector(&rot_matrix, 2)));
vector3d sum2 = vector_sum(sum1, vector_cross(down, matrix_row_to_vector(&rot_matrix, 3)));
corr_vector = vector_scale(sum2, corr_strength);
}
return corr_vector;
}
int Runge_Kutta_4b_regime(int n, void (*f)(double,double *,double *,double *,int *,double *,double *,double *,double *),
double *p, double *fld, double *d, int *r, double *ext, double *extev,
double *y, double x0, double h, double *yout,
double *k1, double *k2, double *k3, double *k4,
double *t1, double *t2, double *t3, double *t4, double *t5, double *t6,
double *t7, double* t8)
{
double h2, h3;
if (n == 0)
{
return 0;
}
h2 = 0.333333333333 * h;
h3 = 0.666666666667 * h;
(*f)(x0, p, fld, d, r, ext, extev, y, k1);
// printf("c: k1[0] = %g\n", k1[0]);
vector_scale(n, 1.0, k1, t1);
vector_scale(n, h/3.0, t1, t2);
vector_sum(n, y, t2, t3);
(*f)(x0+h2, p, fld, d, r, ext, extev, t3, k2);
vector_scale(n, -1.0, k1, t1); vector_scale(n, 3.0, k2, t2);
vector_sum(n, t1, t2, t3);
vector_scale(n, h/3.0, t3, t4); vector_sum(n, y, t4, t5);
(*f)(x0+h3, p, fld, d, r, ext, extev, t5, k3);
vector_scale(n, 1.0, k1, t1); vector_scale(n, -1.0, k2, t2);
vector_scale(n, 1.0, k3, t3);
vector_sum(n, t1, t2, t4); vector_sum(n, t3, t4, t5);
vector_scale(n, h, t5, t6); vector_sum(n, y, t6, t7);
(*f)(x0+h, p, fld, d, r, ext, extev, t7, k4);
vector_scale(n, 1.0, k1, t1);
vector_scale(n, 3.0, k2, t2);
vector_scale(n, 3.0, k3, t3);
vector_scale(n, 1.0, k4, t4);
vector_sum(n, t1, t2, t5); vector_sum(n, t3, t4, t6);
vector_sum(n, t5, t6, t7);
vector_scale(n, h/8.0, t7, t8);
// printf("c: t6[0] = %g\n", t6[0]);
vector_sum(n, y, t8, yout);
return 0;
}
int main()
{
float a[N];
float b[N];
float res[N];
float golden_res[N];
unsigned int i, j, errors = 0;
for(i = 0; i < N; i++) {
a[i] = i*1.0;
b[i] = i*2.0;
golden_res[i] = a[i] + b[i];
}
vector_sum(a, b, res);
for(i = 0; i < N; i++) {
if(res[i] != golden_res[i]) {
printf("Error, expected: %f, got: %f \n", golden_res[i], res[i]);
errors++;
}
}
if(errors == 0) {
printf("Test succeeded!\n");
return 0;
} else {
printf("Test failed, %u errors\n", errors);
return 1;
}
}
inline size_t sample_from_likelihoods (
rng_t & rng,
const std::vector<float, Alloc> & likelihoods)
{
float total = vector_sum(likelihoods.size(), likelihoods.data());
return sample_from_likelihoods(rng, likelihoods, total);
}
t_color3 ft_trace_ray(t_object arr[16], t_object light[16], t_ray ray, int depth, float *dist_out, t_env env)
{
t_intersect inter;
t_color3 outcolor;
t_color3 refl_color;
int i;
float dist;
float _dist_out;
if (dist_out == NULL)
dist_out = &_dist_out;
*dist_out = INFINITY;
outcolor = color_new(17, 25, 37);
i = -1;
inter.obj = NULL;
while (++i < 16 && arr[i].type != DEFAULT)
if (env.fctinter[arr[i].type](ray, arr + i, &dist))
if ((!inter.obj || dist < *dist_out) && dist > 0.00001)
{
inter.obj = &arr[i];
*dist_out = dist;
}
if (inter.obj)
{
inter.pos = create_intersect(ray, *dist_out);
inter.v_normal = env.fctnormal[inter.obj->type](ray, inter.pos, inter.obj);
outcolor = getfinalcolor(light, inter);
if (inter.obj->reflection_index != 0.0 && depth < g_death)
{
refl_color = ft_trace_ray(arr, light, create_reflection(ray, inter), depth + 1, NULL, env);
outcolor = vector_sum(outcolor, vector_mul(refl_color, inter.obj->reflection_index));
}
}
return outcolor;
}
int vextra_response_katcl(struct katcl_line *cl, int code, char *fmt, va_list args)
{
int result[3];
char *name, *status;
if(code > KATCP_RESULT_OK){
return -1;
}
name = arg_copy_string_katcl(cl, 0);
if(name == NULL){
return -1;
}
name[0] = KATCP_REPLY;
status = code_to_name_katcm(code);
if(status == NULL){
return -1;
}
result[0] = append_string_katcl(cl, KATCP_FLAG_FIRST, name);
result[1] = append_string_katcl(cl, 0, status);
result[2] = append_vargs_katcl(cl, KATCP_FLAG_LAST, fmt, args);
return vector_sum(result, 3);
}
/*solution saved in b */
void conjugate_gradient(sparse_matrix A, double *b, int size) {
double *x, *r, *p, *Ap, *aux, rnew, rold, alfa;
int i;
x = (double*) malloc(size*sizeof(double));
r = (double*) malloc(size*sizeof(double));
p = (double*) malloc(size*sizeof(double));
Ap = (double*) malloc(size*sizeof(double));
aux = (double*) malloc(size*sizeof(double));
for (i = 0; i < size; i ++) {
x[i] = 0;
r[i] = b[i];
p[i] = b[i];
}
rold = inner_product(r, r, size);
/* result of operations from all void functions used here are stored in the last argument */
while (1) {
matrix_vector_product(A, p, Ap);
alfa = rold / inner_product(p, Ap, size); /*step length*/
vector_scalar_product(p, alfa, size, aux);
vector_sum(x, aux, size, x);
vector_scalar_product(Ap, alfa, size, aux);
vector_subtraction(r, aux, size, r);
rnew = inner_product(r, r, size);
if (sqrt(rnew) < E)
break;
vector_scalar_product(p, rnew / rold, size, p);
vector_sum(p, r, size, p);
rold = rnew;
}
for (i = 0; i < size; i ++) {
b[i] = x[i];
}
free(x);
free(r);
free(p);
free(Ap);
free(aux);
}
int basic_inform_katcl(struct katcl_line *cl, char *name, char *arg)
{
int result[2];
if(arg){
result[0] = append_string_katcl(cl, KATCP_FLAG_FIRST, name);
result[1] = append_string_katcl(cl, KATCP_FLAG_LAST, arg);
return vector_sum(result, 2);
} else {
return append_string_katcl(cl, KATCP_FLAG_FIRST | KATCP_FLAG_LAST, name);
}
}
void WeightMatrix_iter::normalize_row(std::vector<double>& rowvec)
{
double sum_row = vector_sum(rowvec);
// for(int cc=0; cc<_nClass; cc++){
// sum_row += rowvec[cc];
// }
if (sum_row>0){
for(int cc=0; cc<_nClass; cc++){
(rowvec[cc]) /= sum_row;
}
}
}
void
train(const category_index_t &category_index,
const std::vector<fv_t> &data)
{
for (auto l = category_index.begin(); l != category_index.end(); ++l) {
fv_t centroid;
vector_sum(centroid, l->second, data);
vector_normalize_l2(centroid);
m_centroids.push_back(centroid);
m_centroid_labels.push_back(l->first);
}
m_inverted_index.build(&m_centroids);
}
/**
* Create a new leaf node, storing pointers back to the end points for later.
*/
static CIRC_NODE*
circ_node_leaf_new(const POINTARRAY* pa, int i)
{
POINT2D *p1, *p2;
POINT3D q1, q2, c;
GEOGRAPHIC_POINT g1, g2, gc;
CIRC_NODE *node;
double diameter;
p1 = (POINT2D*)getPoint_internal(pa, i);
p2 = (POINT2D*)getPoint_internal(pa, i+1);
geographic_point_init(p1->x, p1->y, &g1);
geographic_point_init(p2->x, p2->y, &g2);
LWDEBUGF(3,"edge #%d (%g %g, %g %g)", i, p1->x, p1->y, p2->x, p2->y);
diameter = sphere_distance(&g1, &g2);
/* Zero length edge, doesn't get a node */
if ( FP_EQUALS(diameter, 0.0) )
return NULL;
/* Allocate */
node = lwalloc(sizeof(CIRC_NODE));
node->p1 = p1;
node->p2 = p2;
/* Convert ends to X/Y/Z, sum, and normalize to get mid-point */
geog2cart(&g1, &q1);
geog2cart(&g2, &q2);
vector_sum(&q1, &q2, &c);
normalize(&c);
cart2geog(&c, &gc);
node->center = gc;
node->radius = diameter / 2.0;
LWDEBUGF(3,"edge #%d CENTER(%g %g) RADIUS=%g", i, gc.lon, gc.lat, node->radius);
/* Leaf has no children */
node->num_nodes = 0;
node->nodes = NULL;
node->edge_num = i;
return node;
}
void construct_cand(vector<int>& nums,int k, int n, vector<int>& cand) {
int nums_len = nums.size();
int max;
if (nums_len > k)//end backtrace.
return;
if (vector_sum(nums) >= n)//pruning.
return;
if (nums_len == 0)
max = 0;
else
max = nums.at(nums_len-1);
for (int i = max+1; i <= 9; i++)
cand.push_back(i);
}
static t_color3 getfinalcolor(t_object *light, t_intersect inter)
{
t_color3 color;
unsigned int i;
color = color_new(0., 0., 0.);
if (inter.obj)
{
i = 0;
while(light[i].type != DEFAULT)
{
color = vector_sum(iter_light(inter, (t_spotlight *)&light[i]), color);
++i;
}
return (vector_div(color, i));
}
return (color_new(17, 25, 37));
}
int main (int argc, char* argv[]) {
struct timespec start, end;
initOpenCL();
/* START Measurements */
get_date(argc, argv);
clock_gettime(CLOCK_MONOTONIC, &start);
int arraySize = SIZE;
size_t bufferSize = arraySize * sizeof(double);
double* inputA = (double*) malloc (bufferSize);
double* inputB = (double*) malloc (bufferSize);
double* output = (double*) malloc (bufferSize);
/* Initilise data */
initialize_data(arraySize, inputA, inputB);
/* Computation */
vector_sum(arraySize, inputA, inputB, output);
/* END Measurements */
clock_gettime(CLOCK_MONOTONIC, &end);
get_date(argc, argv);
/* Check results */
//check_results(arraySize, inputA, inputB, output);
/* Cleaning */
cleanUpOpenCL();
double res=0;
int i;
for (i = 0; i < arraySize; i++) {
res = res + output[i] ;
}
times = (((double)(end.tv_sec - start.tv_sec)*1000) +
((double)(end.tv_nsec - start.tv_nsec)/1000000));
//cout << "Time to finish: " << times << " ms" << endl;
printf("Time to finish %6.0f ms [check = %e]\n", times, res);
}
static t_color3 getfinalcolor(t_object *arr, t_intersect inter, t_env env)
{
t_color3 color;
t_color3 color_tmp;
float dist[2];
t_ray newray;
float shade;
t_vector3 l;
int i;
int k;
int a;
color_tmp = color_new(0, 0, 0);
a = 0;
if (inter.obj)
{
i = -1;
while(arr[i].type != DEFAULT)
{
shade = 1.0;
if (arr[i].light == TRUE)
{
l = vector_substract(arr[i].pos, inter.pos);
dist[0] = vector_magnitude(l);
newray.pos = vector_substract(inter.pos, vector_mul(inter.v_normal, 1e-4f));
newray.dir = vector_unit(l);
k = -1;
while (++k < 16 && arr[k].type != DEFAULT)
if (env.fctinter[arr[k].type](newray, arr + k, &dist[1]))
{
if (arr[k].light != TRUE && dist[1] <= dist[0])
shade -= 0.3;
}
color_tmp = vector_sum(color_tmp, iter_light(inter, &arr[i], shade));
++a;
}
++i;
}
return (vector_div(color_tmp, a));
}
return (color_new(17, 25, 37));
}
int vlog_message_katcl(struct katcl_line *cl, int level, char *name, char *fmt, va_list args)
{
int result[5];
struct timeval now;
unsigned int milli;
char *subsystem, *logstring;
#ifdef DEBUG
if(level >= KATCP_LEVEL_OFF){
fprintf(stderr, "log: bad form to a message of level off or worse\n");
return -1;
}
#endif
logstring = log_to_string_katcl(level);
if(logstring == NULL){
#ifdef DEBUG
fprintf(stderr, "log: bad log level\n");
abort();
#endif
return -1;
}
subsystem = name ? name : "unknown" ;
gettimeofday(&now, NULL);
milli = now.tv_usec / 1000;
result[0] = append_string_katcl(cl, KATCP_FLAG_FIRST, KATCP_LOG_INFORM);
result[1] = append_string_katcl(cl, 0, logstring);
result[2] = append_args_katcl(cl, 0, "%lu%03d", now.tv_sec, milli);
result[3] = append_string_katcl(cl, 0, subsystem);
#if DEBUG > 1
fprintf(stderr, "log: my fmt string is <%s>, milli=%u\n", fmt, milli);
#endif
result[4] = append_vargs_katcl(cl, KATCP_FLAG_LAST, fmt, args);
/* do the right thing, collect error codes */
return vector_sum(result, 5);
}
quaternion ahrs_orientation(dataexchange_t *data) {
//angle component
vector3d gyr_rad_s = vector_sum(l3g4200d_raw_to_rad(data), ahrs_drift_correction(data));
//vector3d gyr_rad_s = vector_sum(l3g4200d_raw_to_rad(data), ahrs_drift_correction(data));
double angle = vector_magnitude(gyr_rad_s) * (*data).time_period;
//axis, normalized
vector_norm(&gyr_rad_s);
//quaternion from axis/angle
quaternion q = quaternion_from_axis_angle(gyr_rad_s, angle);
//normalize
quaternion_norm(&q);
(*data).qr = quaternion_product((*data).qr, q);
return q;
}
int main()
{
srand(1234);
val_t* xs = malloc(n * sizeof(val_t));
if (xs == NULL) {
fprintf(stderr, "Cannot allocate %zu bytes", n * sizeof(val_t));
return 1;
}
size_t i;
for (i = 0; i < n; ++i) {
xs[i] = randval();
}
vector_t* vec = vector_create(xs, n);
if (vec == NULL) {
fprintf(stderr, "Failed to create vector.");
return 1;
}
idx_t u, v;
for (i = 0; i < m; ++i) {
randinterval(n, &u, &v);
val_t true_sum = dense_sum(xs, u, v);
val_t sparse_sum = vector_sum(vec, u, v);
if (true_sum != sparse_sum) {
fprintf(stderr, "Incorrect sum.\n");
return 1;
}
}
vector_free(vec);
free(xs);
return 0;
}
int is_a_solution(vector<int>& nums, int k, int n) {
if (nums.size() == k && vector_sum(nums) == n)
return true;
else
return false;
}
void WeightMatrix_iter::solve(std::map<unsigned int, std::vector<double> >& ret_result)
{
ret_result.clear();
// _prev_result.resize(_nrows);
// _result.resize(_nrows);
_result_parallel.resize(_nrows);
for(size_t i=0; i< _nrows; i++){
// _prev_result[i].resize(_nClass, 0.0 );
// _result[i].resize(_nClass, 0.0 );
_result_parallel[i].resize(_nClass, 0.0 );
}
printf("LabelProp labeled example %u\n", _mapped_trn_idx.size());
reassign_label();
size_t ncores=8;
_maxIter=200;
double max_diff;
for (size_t iter=0; iter< _maxIter; iter++){
max_diff = 0;
// for(size_t row = 0 ; row < _nrows ; row++){
//
// // if ((! _nzd_indicator[row]) || (_trn_indicator[row]))
// if (! _nzd_indicator[row])
// continue;
//
// for(size_t jj=0; jj < _Wnorm[row].size(); jj++){
// unsigned int col = _Wnorm[row][jj].j;
// double val = _Wnorm[row][jj].v;
//
// // if ((! _nzd_indicator[col]) || (_trn_indicator[col]))
// if (! _nzd_indicator[col])
// continue;
//
// for(int cc=0; cc<_nClass; cc++){
// (_result[row][cc]) += (val * _prev_result[col][cc]);
// }
// }
// }
size_t start_row=0;
std::vector< boost::thread* > threads;
size_t chunksz = _nrows/ncores;
if (_nrows> (ncores*chunksz))
ncores++;
for(size_t ichunk=0; ichunk < ncores; ichunk++){
size_t end_row = start_row + chunksz;
if (end_row >=_nrows)
end_row = _nrows;
threads.push_back(new boost::thread(&WeightMatrix_iter::solve_partial, this, start_row, end_row));
start_row = end_row;
}
// printf("Sync all threads \n");
for (size_t ti=0; ti<threads.size(); ti++)
(threads[ti])->join();
// printf("all threads done\n");
// double debug_diff=0;
// for(size_t row = 0 ; row < _nrows ; row++){
// for(int cc=0; cc<_nClass; cc++){
// debug_diff += fabs(_result[row][cc] - _result_parallel[row][cc]);
// }
// }
// if (debug_diff>0)
// printf("Difference between serial and parallel = %f\n",debug_diff);
for(size_t row = 0 ; row < _nrows ; row++){
// normalize_row(_result[row]);
normalize_row(_result_parallel[row]);
}
for(size_t row = 0 ; row < _nrows ; row++){
if (_trn_indicator[row]){
continue;
}
double diff=0;
for(int cc=0; cc<_nClass; cc++){
diff = fabs(_prev_result[row][cc] - _result_parallel[row][cc]);
max_diff = (max_diff>diff) ? max_diff: diff;
_prev_result[row][cc] = _result_parallel[row][cc];
}
}
reassign_label();
if (!(iter%10))
printf("max diff %.5f\n",max_diff);
if (max_diff<EPS)
break;
}
printf("max diff %.5f\n",max_diff);
for(size_t row = 0 ; row < _nrows ; row++){
if ((! _nzd_indicator[row]) || (_trn_indicator[row]))
continue;
if (!(vector_sum(_result_parallel[row])>0))
_result_parallel[row].assign(_nClass, (double)(1.0/_nClass));
ret_result.insert(std::make_pair(row, _result_parallel[row]));
}
}
int main()
{
MPI_Init(NULL, NULL);
int comm_sz;
int my_rank;
int *local_vector;
int local_size;
int sum;
MPI_Status status;
MPI_Comm_size(MPI_COMM_WORLD, &comm_sz);
MPI_Comm_rank(MPI_COMM_WORLD, &my_rank);
if (my_rank == 0)
{
int i;
int *sums = (int*) malloc((comm_sz-1) * sizeof(int));
// Read in vector
int *vector, size=0;
vector = (int*) malloc(MAX_SIZE * sizeof(int));
populate(vector, &size);
local_size = size / comm_sz;
// Start timer
double start, finish;
MPI_Barrier(MPI_COMM_WORLD);
start = MPI_Wtime();
// Broadcast size
MPI_Bcast(&local_size, 1, MPI_INT, 0, MPI_COMM_WORLD);
// Distribute array
for (i = 1; i < comm_sz; i++)
MPI_Send(vector+i*local_size, local_size, MPI_INT, i, TAG, MPI_COMM_WORLD);
// Sum local vector
sum = vector_sum(vector, local_size);
// Read sums
for (i = 1; i < comm_sz; i++)
MPI_Recv(sums+(i-1), 1, MPI_INT, MPI_ANY_SOURCE, TAG, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
// Sum sums
sum += vector_sum(sums, comm_sz-1);
// Stop timer
MPI_Barrier(MPI_COMM_WORLD);
finish = MPI_Wtime();
printf("Sum: %d\nTime: %fs\n", sum, finish-start);
free(sums);
free(vector);
}
else
{
// Wait for timer
MPI_Barrier(MPI_COMM_WORLD);
// Get local_size
MPI_Bcast(&local_size, 1, MPI_INT, 0, MPI_COMM_WORLD);
// Read into local array
local_vector = (int*) malloc(local_size * sizeof(int));
MPI_Recv(local_vector, local_size, MPI_INT, 0, TAG, MPI_COMM_WORLD, &status);
// Sum local array
sum = vector_sum(local_vector, local_size);
// Send sum
MPI_Send(&sum, 1, MPI_INT, 0, TAG, MPI_COMM_WORLD);
MPI_Barrier(MPI_COMM_WORLD);
free(local_vector);
}
MPI_Finalize();
}
int Dormand_Prince_5_4(int n, void (*f)(double,double *,double *,double *,double *,double *,double *),
double *p, double *fld, double *ext, double *extev,
double *y, double x0, double h, double *yout, double *err,
double *k1, double *k2, double *k3, double *k4, double *k5, double *k6, double *k7,
double *t1, double *t2, double *t3, double *t4, double *t5, double *t6, double *t7, double *t8, double *t9, double *t10,
double *t11, double *t12)
{
double h2, h3, h4, h5;
if (n == 0)
{
return 0;
}
h2 = 0.2 * h;
h3 = 0.3 * h;
h4 = 0.8 * h;
h5 = 0.888888888889 * h;
//printf("c: h = %g\n", h);
//printf("c: y[0] = %g\n", y[0]);
(*f)(x0, p, fld, ext, extev, y, k1);
// printf("c: k1[0] = %g\n", k1[0]);
vector_scale(n, 1.0, k1, t1);
// printf("c: t1[0] = %g\n", t1[0]);
vector_scale(n, h/5.0, t1, t2);
vector_sum(n, y, t2, t3);
// printf("c: t2[0] = %g\n", t2[0]);
// printf("c: k2 = %p\n", k2);
// printf("c: k2[0] = %g\n", k2[0]);
(*f)(x0+h2, p, fld, ext, extev, t3, k2);
// printf("c: k2[0] = %g\n", k2[0]);
// printf("c: k2[0] = %g\n", k2[0]);
vector_scale(n, 3.0, k1, t1);
vector_scale(n, 9.0, k2, t2);
vector_sum(n, t1, t2, t3); vector_scale(n, h/40.0, t3, t4); vector_sum(n, y, t4, t5);
(*f)(x0+h3, p, fld, ext, extev, t5, k3);
// printf("c: k3[0] = %g\n", k3[0]);
vector_scale(n, 44.0, k1, t1);
vector_scale(n, -168.0, k2, t2);
vector_scale(n, 160.0, k3, t3);
// printf("c: t1[0] = %g\n", t1[0]);
// printf("c: t2[0] = %g\n", t2[0]);
// printf("c: t3[0] = %g\n", t3[0]);
vector_sum(n, t1, t2, t4); vector_sum(n, t3, t4, t5);
vector_scale(n, h/45.0, t5, t6); vector_sum(n, y, t6, t7);
// printf("c: t4[0] = %g\n", t4[0]);
// printf("c: t5[0] = %g\n", t5[0]);
// printf("c: t6[0] = %g\n", t6[0]);
// printf("c: t7[0] = %g\n", t7[0]);
(*f)(x0+h4, p, fld, ext, extev, t7, k4);
// printf("c: k4 = %p\n", k4);
// printf("c: k4[0] = %g\n", k4[0]);
vector_scale(n, 19372.0, k1, t1);
vector_scale(n, -76080.0, k2, t2);
vector_scale(n, 64448.0, k3, t3);
vector_scale(n, -1908.0, k4, t4);
vector_sum(n, t1, t2, t5); vector_sum(n, t3, t4, t6); vector_sum(n, t5, t6, t7);
vector_scale(n, h/6561.0, t7, t8);
// printf("c: t8[0] = %g\n", t8[0]);
vector_sum(n, y, t8, t9);
// printf("c: t9[0] = %g\n", t9[0]);
(*f)(x0+h5, p, fld, ext, extev, t9, k5);
// printf("c: k5[0] = %g\n", k5[0]);
vector_scale(n, 477901.0, k1, t1);
vector_scale(n, -1806240.0, k2, t2);
vector_scale(n, 1495424.0, k3, t3);
vector_scale(n, 46746.0, k4, t4);
vector_scale(n, -45927.0, k5, t5);
vector_sum(n, t1, t2, t6); vector_sum(n, t3, t4, t7); vector_sum(n, t5, t6, t8); vector_sum(n, t7, t8, t9);
vector_scale(n, h/167904.0, t9, t10);
vector_sum(n, y, t10, t11);
(*f)(x0+h, p, fld, ext, extev, t11, k6 );
// printf("c: k6[0] = %g\n", k6[0]);
vector_scale(n, 12985.0, k1, t1);
vector_scale(n, 64000.0, k3, t3);
vector_scale(n, 92750.0, k4, t4);
vector_scale(n, -45927.0, k5, t5);
vector_scale(n, 18656.0, k6, t6);
vector_sum(n, t1, t3, t7); vector_sum(n, t4, t5, t8); vector_sum(n, t6, t7, t9); vector_sum(n, t8, t9, t10);
vector_scale(n, h/142464.0, t10, t11);
vector_sum(n, y, t11, t12);
(*f)(x0+h, p, fld, ext, extev, t12, k7 );
// printf("c: k7[0] = %g\n", k7[0]);
vector_sum(n, y, t11, yout);
// printf("c: yout[0] = %g\n", yout[0]);
vector_scale(n, 26341.0, k1, t1);
vector_scale(n, -90880.0, k3, t3);
vector_scale(n, 790230.0, k4, t4);
vector_scale(n, -1086939.0, k5, t5);
vector_scale(n, 895488.0, k6, t6);
vector_scale(n, -534240.0, k7, t7);
vector_sum(n, t1, t3, t8); vector_sum(n, t4, t5, t9); vector_sum(n, t6, t7, t10); vector_sum(n, t8, t9, t11);
vector_sum(n, t10, t11, t12);
vector_scale(n, h/21369600.0, t12, err);
//printf("c: xn = %g err[0] = %g\n", x0+h, err[0]);
return 0;
}
Vector vector_average(Vector* data, int len) {
Vector sum = vector_sum(data, len);
return vector_scale(sum, 1.0 / (double) len);
}
/* main: application entry point.
* @argc: the number of commandline arguments.
* @argv: the commandline argument string array.
*/
int main (int argc, char **argv) {
/* declare required variables. */
struct vector *x, *y, *z, *u;
struct matrix *V, *R, *C;
double theta;
char *smean, *svar, *label;
unsigned long n;
int i;
/* initialize the random number generator. */
rand_init (time (NULL));
/* parse the command-line arguments. */
if (!opts_init (argc, argv)) {
/* output an error message and exit. */
ferror ("failed to parse arguments");
fprintf (stdout, HELP);
return 1;
}
/* see if we should display the help message. */
if (opts_geti (OPTS_S_HELP)) {
/* print the help message and quit. */
fprintf (stdout, HELP);
return 0;
}
/* get the number of points to produce. */
n = opts_geti (OPTS_S_COUNT);
/* ensure the point count is valid. */
if (!n) {
/* output an error message and exit. */
ferror ("invalid point count (%lu)", n);
fprintf (stdout, HELP);
return 1;
}
/* get the points label. */
label = opts_gets (OPTS_S_LABEL);
/* ensure the points label is valid. */
if (!label) {
/* output an error message and exit. */
ferror ("invalid label '%s'", label);
fprintf (stdout, HELP);
return 1;
}
/* allocate the math structures. */
x = vector_new (2);
y = vector_new (2);
z = vector_new (2);
u = vector_new (2);
V = matrix_new (2, 2);
R = matrix_new (2, 2);
C = matrix_new (2, 2);
/* ensure we allocated the math structures. */
if (!x || !y || !z || !u || !V || !R || !C) {
/* output an error message and exit. */
ferror ("failed to allocate math structures");
return 1;
}
/* get the mean string. */
smean = opts_gets (OPTS_S_MEAN);
/* did we get a mean string? */
if (smean) {
/* try to parse the string. */
if (sscanf (smean, "(%lf,%lf)", &u->d[0], &u->d[1]) != 2) {
/* output an error message and exit. */
ferror ("failed to parse mean string '%s'", smean);
fprintf (stdout, HELP);
return 1;
}
}
else {
/* initialize to the origin. */
u->d[0] = u->d[1] = 0.0;
}
/* get the variance string. */
svar = opts_gets (OPTS_S_VAR);
/* did we get a variance string? */
if (svar) {
/* try to parse the string. */
if (sscanf (svar, "(%lf,%lf)", &V->d[0][0], &V->d[1][1]) != 2) {
/* output an error message and exit. */
ferror ("failed to parse variance string '%s'", svar);
fprintf (stdout, HELP);
return 1;
}
}
else {
/* initialize to unit variances. */
V->d[0][0] = V->d[1][1] = 1.0;
}
/* get the rotation value. */
theta = opts_getf (OPTS_S_ROT) / 180.0 * M_PI;
/* build the rotation matrix. */
R->d[0][0] = cos (theta);
R->d[0][1] = -sin (theta);
R->d[1][0] = sin (theta);
R->d[1][1] = cos (theta);
/* calculate the covariance matrix. */
if (!matrix_matrix_mul (1.0, R, V, C)) {
/* output an error message and exit. */
ferror ("failed to calculate covariance matrix");
return 1;
}
/* see if we should produce a header. */
if (opts_geti (OPTS_S_HEADER)) {
/* yep. print one. */
fprintf (stdout,
"Obs ID (Primary)\tObs ID (Obs. Sec. ID:1)\tM1.t[2]\tM1.t[1]\n");
}
/* loop a set number of times. */
for (i = 0; i < n; i++) {
/* calculate the two values. */
x->d[0] = randnormal ();
x->d[1] = randnormal ();
/* scale the values. */
if (!matrix_vector_mul (1.0, C, x, y)) {
/* output an error message and exit. */
ferror ("failed to scale random variate %d", i + 1);
return 1;
}
/* translate the values. */
if (!vector_sum (1.0, y, 1.0, u, z)) {
/* output an error message and exit. */
ferror ("failed to translate random variate %d", i + 1);
return 1;
}
/* print the values. */
fprintf (stdout, "%d\t%s\t%lf\t%lf\n", i + 1, label, z->d[0], z->d[1]);
}
/* free the math structures. */
vector_free (x);
vector_free (y);
vector_free (z);
vector_free (u);
matrix_free (V);
matrix_free (R);
matrix_free (C);
/* return success. */
return 0;
}
int Bogacki_Shampine_3_2(int n, void (*f)(double,double *,double *,double *,double *,double *,double *),
double *p, double *fld, double *ext, double *extev,
double *y, double x0, double h, double *yout, double *err,
double *k1, double *k2, double *k3, double *k4,
double *t1, double *t2, double *t3, double *t4, double *t5, double *t6, double *t7)
{
double h2, h3;
if (n == 0)
{
return 0;
}
h2 = 0.5 * h;
h3 = 0.75 * h;
//printf("c: h = %g\n", h);
//printf("c: y[0] = %g\n", y[0]);
(*f)(x0, p, fld, ext, extev, y, k1);
// printf("c: k1[0] = %g\n", k1[0]);
vector_scale(n, 1.0, k1, t1);
// printf("c: t1[0] = %g\n", t1[0]);
vector_scale(n, h/2.0, t1, t2);
vector_sum(n, y, t2, t3);
// printf("c: t2[0] = %g\n", t2[0]);
// printf("c: k2 = %p\n", k2);
// printf("c: k2[0] = %g\n", k2[0]);
(*f)(x0+h2, p, fld, ext, extev, t3, k2);
// printf("c: k2[0] = %g\n", k2[0]);
// printf("c: k2[0] = %g\n", k2[0]);
vector_scale(n, 3.0, k2, t2);
vector_scale(n, h/4.0, t2, t3); vector_sum(n, y, t3, t4);
(*f)(x0+h3, p, fld, ext, extev, t4, k3);
// printf("c: k3[0] = %g\n", k3[0]);
vector_scale(n, 2.0, k1, t1);
vector_scale(n, 3.0, k2, t2);
vector_scale(n, 4.0, k3, t3);
// printf("c: t1[0] = %g\n", t1[0]);
// printf("c: t2[0] = %g\n", t2[0]);
// printf("c: t3[0] = %g\n", t3[0]);
vector_sum(n, t1, t2, t4); vector_sum(n, t3, t4, t5);
vector_scale(n, h/9.0, t5, t6); vector_sum(n, y, t6, t7);
// printf("c: t4[0] = %g\n", t4[0]);
// printf("c: t5[0] = %g\n", t5[0]);
// printf("c: t6[0] = %g\n", t6[0]);
// printf("c: t7[0] = %g\n", t7[0]);
(*f)(x0+h, p, fld, ext, extev, t7, k4);
// printf("c: k4 = %p\n", k4);
// printf("c: k4[0] = %g\n", k4[0]);
vector_sum(n, y, t6, yout);
// printf("c: yout[0] = %g\n", yout[0]);
vector_scale(n, -5.0, k1, t1);
vector_scale(n, 6.0, k2, t2);
vector_scale(n, 8.0, k3, t3);
vector_scale(n, -9.0, k4, t4);
vector_sum(n, t1, t2, t5); vector_sum(n, t3, t4, t6);
vector_sum(n, t5, t6, t7);
vector_scale(n, h/72.0, t7, err);
//printf("c: xn = %g err[0] = %g\n", x0+h, err[0]);
return 0;
}
