EDIT: I've added the main, factorial, and trapGamma function to give the full picture but I am specifically talking about the for loop for iSum in the I function.
Basically I've run out of ideas and exhausted everywhere I know of to find an answer to this. I need to code a program that will compute a complex function which represents an M/M/1 queue.
The function includes sub functions such as calculating the integral of a gamma function and computing factorials. I've written all the code for the computations but my sum is giving me huge numbers when I would expect nothing higher than about .35
#include <math.h>
#include <stdio.h>
double I(int k, double t);
double trapGamma(double z);
unsigned long long int factorial(unsigned int n);
int main()
{
int k;
int i = 0;
double dt = 0.1;
printf("Ikx = [ \n");
for (t = 14.0 ; t <= 15.0; t += dt)
{
printf("%f " , t);
for (k = 1 ; k <= 10 ; k++)
{
I(k, t);
printf("%f " , I(k, t));
}
printf("\n");
}
printf(" ];\n");
return (0);
}
double I(int k, double t)
{
unsigned long long int x;
unsigned int n = 20;
double numerator, y, pow1, c;
double iSum;
double Ix;
int i = 0;
iSum = 0.0;
Ix = 0.0;
a = .25 * pow(t , 2);
b = pow(a, i);
x = factorial(n);
y = trapGamma(k + i + 1);
iSum = (b / (x * y));
//This is the sum loop that I'm having trouble with, I've broke the iSum equation down for my own readability while coding right above this comment
for (i = 0; i <= 100 ; i++)
{
iSum += i;
}
Ix = (pow((.5 * t), k) ) * iSum;
return Ix;
}
/*
I've checked both the factorial and trapGamma functions and they are giving me the expected results.
*/
unsigned long long int factorial(unsigned int n)
{
if(n <= 1)
return 1;
else
return (n * factorial(n - 1));
}
double trapGamma (double z)
{
int i , N = 100;
double gamma;
double a = 0.0;
double b = 15.0;
double x1, x2, y1, y2;
double areai;
double w = (b - a) / N;
gamma = 0.0;
for (i = 1; i < N; i++)
{
x1 = a + ((i - 1) * w); //the left bound point
x2 = a + (i*w); //the right bound point
y1 = pow(x1,z - 1)*exp(-x1); //the height of our left bound
y2 = pow(x2, z - 1)*exp(-x2); //the height of our right bound
areai = ((y1 + y2) / 2.0) * (x2 - x1);
gamma += areai;
}
return gamma;
}
This is building upon another project where I used a bessel function to create the M/M/1 queue over a 60 second span so I can see what this one is supposed to be. I've checked both my trapGamma and factorial functions results on there own and they are both working as expected.
How are summations supposed to be coded?
If the intent of the posted code is to calculate the modified Bessel function I, there are some pitfalls and useful semplifications to be aware of. Given
Trying to calculate the factorial, the value of the Gamma function, their product and the powers separately for each term of the sum leads to integer overflow sooner than later.
It's better to update the value of each addend of the sum instead.
Also, given that k is a whole, we have Γ(n) = (n - 1)!
The addends are increasingly smaller and, after some iterations, too small to be added to the sum, given the limited precision of type double.
// Evaluates x^k / k! trying not to overflow
double power_over_factorial(double x, int k)
{
double result = 1.0;
for ( int i = 1; i <= k; ++i )
{
result *= x / i;
}
return result;
}
#define MAX_ITERS 20
double modified_Bessel_I(int k, double x)
{
x /= 2;
const double xx = x * x;
double partial = power_over_factorial(x, k);
double old_sum, sum = partial;
int m = 1;
do
{
old_sum = sum;
partial *= xx / ((m + k) * m);
sum += partial;
}
while ( old_sum != sum && ++m < MAX_ITERS );
return sum;
}
Testable here.
I need to create a struct that holds a 2D array however the array size can vary so i cannot define it with a constant length. I tried to solve this with a double pointer only to find out the double pointer is not the same as a double array. So how can i do this?
struct GaussianKernel {
int r;
double weightSum;
double **kernel;
};
GaussianKernel initializeKernel2D(jdouble sigma){
int r = (int) ceil(3 * sigma);
int kernelLen = 2 * r + 1;
double G[kernelLen][kernelLen];
double weightSum = 0;
double temp;
for (int y = -r; y <= r; y++)
{
for (int x = -r; x <= r; x++)
{
temp = exp(-(pow(x, 2) + pow(y, 2)) / (2 * pow(sigma, 2))) / (2 * PI * pow(sigma, 2));
G[y + r][x + r] = temp;
weightSum = weightSum + temp;
}
}
struct GaussianKernel GKernel;
GKernel.r = r;
GKernel.kernel = G;
GKernel.weightSum = weightSum;
return GKernel;
}
YOu should allocate your 2D dynamic array as:
GKernel.kernel = malloc(kernelLen * sizeof(double *));
for(i=0;i<kernelLen;i++)
GKernel.kernel[i] = malloc(kernelLen * sizeof(double));
Then you can store values in GKernel.kernel as per logic of your program
I'm currently working on this : I generate a Paraview .vtm file that contains several .vtr files. Each .vtr file contains values, and coordinates, like this, assuming I'm working on a dimension of 8 :
<PointData Scalars="U">
<DataArray type="Float32" Name="U" format="ascii">
<!-- 8*8*8 values -->
</DataArray>
</PointData>
<Coordinates>
<DataArray type="Float32" Name="x" format="ascii">
<!-- 8 x values -->
</DataArray>
<DataArray type="Float32" Name="y" format="ascii">
<!-- 8 y values -->
</DataArray>
<DataArray type="Float32" Name="z" format="ascii">
<!-- 8 z values -->
</DataArray>
</Coordinates>
I use a quadridimensionnal array to store my values : float ****tab, with tab[s][x][y][z], where :
s is the current split step. It increments everytime I start working on the next .vtr file.
x, y, z the values.
Now is what causes me trouble : the coordinates where I have to place these points can be anything. It can be constant (following a step, like 0, 0.1, 0.2, and so on), or not.
I store the coordinates in three arrays : x[], y[], z[]. My goal is to cut the set of values into smaller cubes. Let's assume I split my values into 8 files (2^3 files), I have to retrieve the correct coordinates for 8 small cubes. And I can't find a way to do that.
I'm pretty sure my data structures choice is terrible, could someone give me some help with that ?
EDIT :
Here is the function generating my four-star array :
float**** fill_array_random4d(int split, int size)
{
float**** ret;
ret = malloc(sizeof(float***) * split);
for (int i = 0; i < split; i++)
{
ret[i] = malloc(sizeof (float**) * size);
for (int j = 0; j < size; j++)
{
ret[i][j] = malloc(sizeof (float*) * size);
for (int k = 0; k < size; k++)
{
ret[i][j][k] = malloc(sizeof (float) * size);
for (int l = 0; l < size; l++)
ret[i][j][k][l] = rand() % 100;
}
}
}
return ret;
}
It's a pretty basic stuff. Right now I'm using random values.
Here is how I create and fill my x, y, z arrays :
float *x, *y, *z;
x = malloc(sizeof (float) * size);
y = malloc(sizeof (float) * size);
z = malloc(sizeof (float) * size);
for (int i = 0; i < size * split; i++)
x[i] = step * i;
for (int i = 0; i < size * split; i++)
y[i] = step * i;
for (int i = 0; i < size * split; i++)
z[i] = step * i;
It's still very basic, and finally here is the function printing the coordinates in the file, following the vtk legacy format :
void print_Coordinates(FILE *file, float *x, float *y, float *z, int size, int split)
{
fprintf(file, " <Coordinates>\n");
for (int i = 0; i < 3; i++)
{
const char *text1 = " <DataArray type=\"Float32\" Name=\"";
const char *text2 = "\" format=\"ascii\">\n";
fprintf(file, "%s%c%s", text1, 'x' + i, text2);
for (int j = 0; j < size; j++)
{
if (i == 0)
fprintf(file, " %f\n", x[j]);
else if (i == 1)
fprintf(file, " %f\n", y[j]);
else
fprintf(file, " %f\n", z[j]);
}
fprintf(file, " </DataArray>\n");
}
fprintf(file, " </Coordinates>\n");
}
So, yeah, it doesn't do what I want at all.
Here is a screenshot of the result :
All the cubes are on top of each other. With the code I was using earlier, I had several cubes (one per file), but they were aligned on a diagonal (which is not good either).
As you have admitted, there are some problems with your data structure:
The first dimension s seems incongruent: Should the data structure include the original and the smaller cube? That's not easy to do, because the smaller cubes have other dimensions.
You have many separate data: The (random) data, the coordinates and the array dimensions. In order to represent the cube, you need to keep track of all of these. I recommend to create a structure to keep the relevant data together.
There isn't anything per se wrong with your approach to represent the three-dimensional array with a triple pointer, but the design leads to many fragmented allocations. A multi-dimensional array with constant dimensions is probably better represented as one "flat" memory block.
I suggest two structures:
typedef struct Cube Cube;
typedef struct Axis Axis;
struct Axis {
int n; /* number of values */
float *data; /* graduation values */
};
struct Cube {
Axis *x, *y, *z; /* Axes of the cube */
float *data; /* x-major data */
};
An "axis" stores the values along one of the axes. The cube itself doesn't worry about the axis-related code and just delegates it to its three member axes. A "cube" is your data object. (In the implementation below, the data representation is x-major, meaning the x loop is the outermost, the z loop is the innermost. You can chnage that by swapping the loops.)
If you have a populated cube object, you can the extract sub-cubes by creating a cube of a smaller dimension and copying the relevant data ranges from the axes and from the cube data. If you want to cover the whole cube, you can either extract and write the cubes as you go or store them in an array of cubes, e.g. Cube *small[8] for splitting in half for each direction. (This would be like your original s index, only that each cube may have its own dimension.)
An implementation of this behaviour with an (addmittedly simple) test main is below:
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
typedef struct Cube Cube;
typedef struct Axis Axis;
struct Axis {
int n; /* number of values */
float *data; /* graduation values */
};
struct Cube {
Axis *x, *y, *z; /* Axes of the cube */
float *data; /* x-major data */
};
/*
* Create a new axis with a constant step.
*/
Axis *axis_new(int n, float start, float step)
{
Axis *axis = malloc(sizeof(*axis));
float *p;
axis->n = n;
axis->data = malloc(n * sizeof(*axis->data));
p = axis->data;
while (n--) {
*p = start;
start += step;
p++;
}
return axis;
}
/*
* Destroy and clean up axis
*/
void axis_delete(Axis *axis)
{
if (axis) {
free(axis->data);
free(axis);
}
}
/*
* Write axis in XML format to given file
*/
void axis_write(const Axis *axis, FILE *f, const char *name)
{
float *p = axis->data;
int n = axis->n;
fprintf(f, " <DataArray type=\"Float32\" "
"Name=\"%s\" format=\"ascii\">\n", name);
fprintf(f, " ");
while (n--) {
fprintf(f, " %g", *p++);
}
fprintf(f, "\n");
fprintf(f, " </DataArray>\n");
}
/*
* Create a new axis that is a sub-axis of orig.
*/
Axis *axis_slice(const Axis *orig, int start, int len)
{
Axis *axis = axis_new(len, 0, 0);
memcpy(axis->data, orig->data + start, len * sizeof(*axis->data));
return axis;
}
/*
* Create a cube of zero values for the given axes
*/
Cube *cube_new(Axis *x, Axis *y, Axis *z)
{
Cube *cube = malloc(sizeof(*cube));
int dim = x->n * y->n * z->n;
cube->x = x;
cube->y = y;
cube->z = z;
cube->data = malloc(dim * sizeof(*cube->data));
return cube;
}
/*
* Destroy and clean up cube
*/
void cube_delete(Cube *cube)
{
if (cube) {
axis_delete(cube->x);
axis_delete(cube->y);
axis_delete(cube->z);
free(cube->data);
free(cube);
}
}
float *cube_at(const Cube *cube, int x, int y, int z)
{
int pos = (x * cube->y->n + y) * cube->z->n + z;
return cube->data + pos;
}
/*
* Populate all x, y, z values according to the function func.
*/
void cube_populate(Cube *cube, float (*func)(float x, float y, float z))
{
int i, j, k;
float *p = cube->data;
for (i = 0; i < cube->x->n; i++) {
float x = cube->x->data[i];
for (j = 0; j < cube->y->n; j++) {
float y = cube->y->data[j];
for (k = 0; k < cube->z->n; k++) {
float z = cube->z->data[k];
*p++ = func(x, y, z);
}
}
}
}
/*
* Write cube to given file.
*/
void cube_write(const Cube *cube, FILE *f)
{
float *p = cube->data;
int n = cube->x->n * cube->y->n * cube->z->n;
fprintf(f, "<PointData Scalars=\"U\">\n");
fprintf(f, " <DataArray type=\"Float32\" Name=\"U\" format=\"ascii\">\n");
while (n--) {
fprintf(f, " %g", *p++);
}
fprintf(f, "\n");
fprintf(f, " </DataArray>\n");
fprintf(f, "</PointData>\n");
fprintf(f, "<Coordinates>\n");
axis_write(cube->x, f, "x");
axis_write(cube->y, f, "y");
axis_write(cube->z, f, "z");
fprintf(f, "</Coordinates>\n");
}
/*
* Create a new cube that is a sub-cube of orig.
*/
Cube *cube_slice(const Cube *orig,
int x, int dx, int y, int dy, int z, int dz)
{
Cube *cube;
float *p;
int i, j, k;
if (x + dx > orig->x->n) return NULL;
if (y + dy > orig->y->n) return NULL;
if (z + dz > orig->z->n) return NULL;
cube = cube_new(
axis_slice(orig->x, x, dx),
axis_slice(orig->y, y, dy),
axis_slice(orig->z, z, dz));
p = cube->data;
for (i = 0; i < dx; i++) {
for (j = 0; j < dy; j++) {
for (k = 0; k < dz; k++) {
*p++ = *cube_at(orig, x + i, y + j, z + k);
}
}
}
return cube;
}
/*
* Example appliaction
*/
float dist2(float x, float y, float z)
{
return x*x + y*y + z*z;
}
int main()
{
Cube *cube = cube_new(
axis_new(4, 0, 0.1),
axis_new(4, 0, 0.1),
axis_new(4, 0, 0.1));
int i, j, k;
cube_populate(cube, dist2);
for (i = 0; i < 2; i++) {
for (j = 0; j < 2; j++) {
for (k = 0; k < 2; k++) {
Cube *sub = cube_slice(cube, 2*i, 2, 2*j, 2, 2*k, 2);
cube_write(sub, stdout);
printf("--\n");
cube_delete(sub);
}
}
}
cube_delete(cube);
return 0;
}
I have a square rotating in the console, but I get some holes. How can I fill it correctly?
#include <stdio.h>
#include <Windows.h>
#include <math.h>
void moveTo (int x, int y)
{
COORD coord = { x, y };
SetConsoleCursorPosition(GetStdHandle(STD_OUTPUT_HANDLE), coord);
}
double round (double number)
{
return number < 0.0 ? ceil(number - 0.5) : floor(number + 0.5);
}
double deg2rad (double a)
{
double pi = 3.14159265358979323846;
return a * pi / 180.0;
}
int main ()
{
int w = 8;
int h = 8;
int cx = 20;
int cy = 10;
double a = 0;
while (1)
{
system("cls");
for (int y = 0; y < h; y++)
{
for (int x = 0; x < w; x++)
{
double xx = x - 4;
double yy = y - 4;
double fx = xx * cos(a) - yy * sin(a);
double fy = xx * sin(a) + yy * cos(a);
int ix = cx + round(fx);
int iy = cy + round(fy);
moveTo(ix, iy);
printf("X");
}
}
a += deg2rad(15.0);
Sleep(100);
}
return 0;
}
Not an actual answer
Aparently your code will always print the same number of X in the screen, even though this might not be always the case.
I think you shouldn't be recalculating the positions of each predefinedX but instead calculate the geometry of the lines around the square and fill the space between with Xs, as many as necessary until it hit the opposite border or something.
An alternative solution could be doubling the "density" of your square:
int w = 8*2;
int h = 8*2;
int cx = 20*2;
int cy = 10*2;
...
moveTo(ix/2, iy/2);
This should double print some dots, but should also fill gaps.
I have a homework to implement an FIR filter in C and I wonder whether you think I understood the assignment correctly. The program I wrote that I think solves the problem is:
#include <stdio.h>
float FIRfloats[5];
void floatFIR(float newsample)
{
int i;
float sum=0;
FIRfloats[0]=newsample*0.0299;
FIRfloats[1]=FIRfloats[2]*0.4701;
FIRfloats[2]=FIRfloats[3]*0.4701;
FIRfloats[3]=FIRfloats[4]*0.0299;
/* sum */
for(i=0;i<5;i++)
{
sum=sum+FIRfloats[i];
}
printf("Sum: %f\n", sum);
}
int main ()
{
float n=0.0f;
while (scanf("%f", &n) > 0)
{
floatFIR(n);
}
return 0;
}
And the specification is
Before a new sample xk arrives the old samples are shifted to the
right and then each sample is scaled with a coefficient before the
result yk, the total sum of all scaled samples, is calculated
Coefficients should be c0=0.0299, c1=0.4701, c2=0.4701, c3=0.0299.
Do you think that I solved the assignment correctly? I think it seemed too easy and therefore I wonder.
I'm afraid the implementation provided in the question will not provide the correct results.
In FIR (Finite Impulse Response) filter with 4 coefficients the output series (y) for input series (x) is:
y[t] = c0*x[t] + c1*x[t-1] + c2*x[t-2] + c3*x[t-3]
Therefore the implementation should be similar to:
/* add includes (stdio.h and whatever else you'll need...) */
float floatFIR(float inVal, float* x, float* coef, int len)
{
float y = 0.0;
for (int i = (len-1) ; i > 0 ; i--)
{
x[i] = x[i-1];
y = y + (coef[i] * x[i]);
}
x[0] = inVal;
y = y + (coef[0] * x[0]);
return y;
}
main(int argc, char** argv)
{
float coef[4] = {0.0299, 0.4701, 0.4701, 0.0299};
float x[4] = {0, 0, 0, 0}; /* or any other initial condition*/
float y;
float inVal;
while (scanf("%f", &inVal) > 0)
{
y = floatFIR(inVal, x, coef, 4);
}
return 0;
}
This does the shift and multiplication at the same loop (which does not affect results - only is more efficient.)
If you want to follow the spec exactly, you can change floatFir like this:
float floatFIR(float inVal, float* x, float* coef, int len)
{
float y = 0.0;
for (int i = (len-1) ; i > 0 ; i--)
{
x[i] = x[i-1];
}
x[0] = inVal;
for (int i = 0 ; i < len ; i++)
{
y = y + (coef[i] * x[i]);
}
return y;
}