Project Euler problem 11 in C isnt providing any output - c

I have been trying to solve Project Euler problem 11. I have rechecked my code multiple times but still, after debugging, my program is not providing any answers
The question states that we need to find the greatest product possible of 4 consecutive numbers: either vertically, horizontally or diagonally of the matrix given in the code below:
Here is my code.
#include <stdio.h>
#include <stdlib.h>
int main()
{
int matr[20][20] =
{
{8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8},
{49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0},
{81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65},
{52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91},
{22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80},
{24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50},
{32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70},
{67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21},
{24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72},
{21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95},
{78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92},
{16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57},
{86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58},
{19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40},
{4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66},
{88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69},
{4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36},
{20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16},
{20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54},
{1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48}
};
int horProduct=0, verProduct=0, diagright=0, diagleft=0;
int maxProduct = 0;
// horizontal product
for (int i = 0; i < 20; i++)
{
for(int j = 0; j < 17; j++)
{
horProduct = matr[i][j]*matr[i][j+1]*matr[i][j+2]*matr[i][j+3];
}
if(horProduct > maxProduct)
{
maxProduct = horProduct;
}
}
//vertical product
for (int j = 0; j < 20; j++)
{
for(int i = 0; i < 17; i++)
{
verProduct = matr[i][j]*matr[i+1][j]*matr[i+2][j]*matr[i+3][j];
}
if(verProduct > maxProduct)
{
maxProduct = verProduct;
}
}
//diagonal right
for (int i = 0; i < 17; i++)
{
for(int j = 0; j < 17; j++)
{
diagright = matr[i][j]*matr[i+1][j+1]*matr[i+2][j+2]*matr[i+3][j+3];
}
if(diagright > maxProduct)
{
maxProduct = diagright;
}
}
//diagonal left
for (int i = 19; i > 3; i--)
{
for(int j = 19; j > 3; j--)
{
diagleft = matr[i][j]*matr[i-1][j-1]*matr[i-2][j-2]*matr[i-3][j-3];
}
if(diagleft > maxProduct)
{
maxProduct = diagleft;
}
}
printf("final largest product: %d\n", maxProduct);
return 0;
}
kindly let me know what is going wrong here. Why isn't my program able to print any output?


I did a rookie mistake.
The comparison with maxProduct should be inside the second loop.
#include <stdio.h>
#include <stdlib.h>
int main()
{
int matr[20][20] =
{
{8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8},
{49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0},
{81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65},
{52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91},
{22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80},
{24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50},
{32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70},
{67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21},
{24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72},
{21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95},
{78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92},
{16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57},
{86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58},
{19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40},
{4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66},
{88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69},
{4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36},
{20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16},
{20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54},
{1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48}
};
int horProduct=0, verProduct=0, diagright=0, diagleft=0;
int maxProduct = 0;
// horizontal product
for (int i = 0; i < 20; i++)
{
for(int j = 0; j < 17; j++)
{
horProduct = matr[i][j]*matr[i][j+1]*matr[i][j+2]*matr[i][j+3];
if(horProduct > maxProduct)
{
maxProduct = horProduct;
}
}
}
printf("hori: %d\n", maxProduct);
for (int j = 0; j < 20; j++)
{
for(int i = 0; i < 17; i++)
{
verProduct = matr[i][j]*matr[i+1][j]*matr[i+2][j]*matr[i+3][j];
if(verProduct > maxProduct)
{
maxProduct = verProduct;
}
}
}
printf("verti: %d\n", maxProduct);
//diagonal right
for (int i = 0; i < 17; i++)
{
for(int j = 0; j < 17; j++)
{
diagright = matr[i][j]*matr[i+1][j+1]*matr[i+2][j+2]*matr[i+3][j+3];
if(diagright > maxProduct)
{
maxProduct = diagright;
}
}
}
printf("diagright: %d\n", maxProduct);
//diagonal left
for (int i = 0; i < 20 ; i++)
{
for(int j = 0; j < 17; j++)
{
diagleft = matr[i][j]*matr[i+1][j+1]*matr[i+2][j+2]*matr[i+3][j+3];
if(diagleft > maxProduct)
{
maxProduct = diagleft;
}
}
}
printf("diagleft: %d\n", maxProduct);
return 0;
}

Related

Writing a fast linear system solver in OpenCL C

I'm writing an OpenCL kernel which will involve solving a linear system. Currently my kernel is simply too slow, and improving the performance of the linear system portion seemed like a good place to start.
I should also note that I'm not trying make my linear solver parallel, the problem I'm working on is already embarassingly parallel at a macroscopic level.
The following is C code I wrote for solving Ax=b using Gaussian elimination with partial pivoting,
#import <stdio.h>
#import <math.h>
#import <time.h>
#define K 50
// Solve the system Ax=b using Gaussian elimination with partial pivoting.
void linear_solve(float A[K * K], float b[K])
{
for (long j=0; j<K; j++)
{
// Begin partial pivoting.
float maxval = fabs(A[K * j + j]);
long maxrow = j;
for (long i=j+1; i<K; i++)
{
if (fabs(A[K * j + i]) > maxval)
{
maxval = fabs(A[K * j + i]);
maxrow = i;
}
}
for (long l=0; l<K; l++)
{
float A_temp = A[K * l + maxrow];
A[K * l + maxrow] = A[K * l + j];
A[K * l + j] = A_temp;
}
float b_temp = b[maxrow];
b[maxrow] = b[j];
b[j] = b_temp;
// End partial pivoting.
// Begin putting [A; b] into row echelon form.
for (long i=j; i<K-1; i++)
{
float c = -A[K * j + (i + 1)] / A[K * j + j];
for (long l=j+1; l<K; l++)
A[K * l + (i + 1)] += c * A[K * l + j];
b[i + 1] += c * b[j];
}
// End putting [A; b] into row echelon form.
}
// Begin backsolving for x (by overwritting b).
for (long j=K-1; j>0; j--)
for (long i=j-1; i>=0; i--)
b[i] -= b[j] * A[K * j + i] / A[K * j + j];
for (long j=0; j<K; j++)
b[j] *= 1 / A[K * j + j];
// End backsolving for x.
}
int main()
{
int i, j;
float A[K * K] = {38, 49, 38, 73, 70, 71, 33, 24, 14, 82, 46, 99, 82, 36, 21, 32, 48, 40, 27, 60, 31, 15, 38, 88, 95, 57, 36, 86, 42, 56, 1, 37, 73, 7, 92, 93, 16, 95, 59, 76, 18, 42, 57, 9, 14, 40, 68, 61, 8, 26, 90, 33, 95, 8, 5, 87, 66, 84, 45, 78, 27, 16, 9, 83, 46, 61, 74, 44, 17, 21, 21, 53, 96, 49, 58, 67, 73, 60, 18, 40, 32, 68, 68, 21, 57, 86, 69, 7, 80, 10, 36, 46, 94, 59, 41, 80, 70, 2, 90, 57, 92, 50, 92, 98, 88, 14, 39, 80, 68, 78, 49, 40, 54, 51, 68, 80, 95, 22, 37, 88, 10, 30, 54, 7, 84, 99, 42, 94, 75, 45, 22, 41, 75, 38, 54, 97, 64, 62, 6, 48, 92, 49, 72, 5, 75, 67, 24, 55, 76, 17, 62, 19, 75, 41, 63, 97, 19, 83, 69, 12, 43, 94, 48, 92, 94, 54, 76, 11, 99, 96, 20, 29, 43, 97, 86, 23, 55, 2, 75, 61, 17, 45, 88, 79, 9, 26, 1, 3, 10, 91, 94, 85, 13, 58, 3, 53, 24, 76, 9, 2, 33, 34, 51, 65, 100, 67, 84, 21, 77, 17, 88, 65, 2, 46, 1, 18, 15, 57, 1, 88, 60, 64, 39, 36, 79, 89, 51, 39, 98, 67, 62, 34, 56, 98, 74, 52, 93, 11, 87, 45, 48, 82, 87, 5, 97, 65, 1, 81, 39, 85, 33, 26, 24, 90, 41, 69, 74, 43, 21, 54, 91, 94, 78, 41, 17, 11, 71, 25, 72, 52, 36, 27, 100, 48, 67, 52, 94, 44, 94, 91, 83, 95, 76, 19, 70, 34, 87, 67, 62, 67, 81, 55, 81, 45, 68, 1, 56, 95, 76, 38, 72, 88, 37, 64, 29, 16, 19, 81, 36, 18, 25, 28, 21, 17, 57, 51, 22, 87, 61, 39, 56, 51, 65, 44, 59, 3, 75, 98, 5, 21, 48, 95, 53, 23, 96, 4, 11, 11, 77, 21, 58, 78, 9, 93, 81, 17, 77, 97, 97, 44, 96, 26, 35, 89, 73, 26, 37, 3, 51, 76, 14, 67, 45, 92, 52, 83, 43, 91, 20, 62, 4, 48, 75, 35, 17, 65, 6, 98, 2, 78, 69, 39, 30, 57, 27, 49, 8, 71, 46, 82, 16, 62, 57, 69, 94, 15, 56, 15, 29, 42, 93, 96, 57, 2, 63, 23, 57, 54, 47, 88, 40, 1, 90, 48, 1, 4, 26, 32, 12, 97, 38, 62, 72, 92, 71, 72, 34, 93, 84, 56, 20, 33, 53, 42, 7, 54, 98, 37, 27, 2, 13, 88, 30, 24, 91, 22, 95, 100, 53, 53, 31, 91, 95, 9, 36, 89, 25, 60, 28, 47, 61, 81, 41, 47, 88, 6, 46, 83, 4, 48, 73, 88, 8, 83, 78, 18, 21, 75, 6, 90, 87, 92, 18, 71, 5, 82, 36, 2, 50, 86, 49, 72, 92, 67, 41, 38, 81, 37, 67, 93, 99, 51, 79, 95, 76, 85, 90, 27, 93, 44, 79, 97, 7, 11, 52, 76, 61, 23, 52, 97, 58, 74, 87, 58, 70, 77, 97, 74, 85, 65, 71, 79, 91, 36, 92, 35, 97, 9, 6, 38, 90, 46, 84, 98, 65, 4, 89, 9, 72, 55, 3, 21, 77, 43, 76, 83, 34, 16, 33, 21, 6, 28, 98, 27, 86, 93, 66, 55, 34, 76, 93, 42, 1, 36, 82, 82, 13, 45, 48, 8, 4, 66, 51, 32, 68, 81, 49, 70, 93, 73, 89, 16, 76, 95, 90, 37, 83, 28, 40, 14, 3, 18, 27, 34, 24, 53, 42, 24, 57, 93, 48, 43, 91, 28, 75, 86, 47, 40, 61, 20, 34, 81, 31, 62, 20, 75, 80, 81, 95, 75, 14, 8, 89, 13, 7, 9, 27, 80, 24, 52, 27, 75, 4, 58, 20, 82, 89, 31, 100, 48, 57, 73, 34, 52, 24, 26, 64, 18, 90, 74, 17, 58, 8, 44, 43, 56, 56, 51, 58, 56, 4, 87, 80, 24, 100, 47, 72, 60, 41, 2, 26, 81, 17, 57, 28, 6, 21, 4, 99, 92, 42, 37, 22, 45, 5, 93, 72, 27, 91, 13, 44, 93, 6, 100, 31, 17, 78, 16, 96, 32, 57, 45, 95, 76, 92, 3, 77, 84, 92, 87, 63, 42, 70, 79, 77, 90, 16, 100, 82, 61, 23, 67, 55, 45, 38, 27, 95, 19, 10, 4, 53, 75, 62, 1, 99, 62, 94, 30, 95, 65, 35, 62, 25, 59, 26, 62, 98, 50, 73, 31, 11, 89, 20, 1, 74, 45, 49, 55, 78, 49, 82, 35, 9, 45, 100, 99, 87, 10, 56, 79, 85, 89, 8, 9, 53, 87, 13, 27, 95, 81, 7, 71, 63, 44, 38, 84, 40, 87, 79, 54, 42, 58, 49, 85, 49, 6, 55, 83, 93, 52, 63, 76, 52, 40, 91, 36, 74, 70, 92, 92, 67, 57, 51, 74, 22, 35, 22, 48, 60, 86, 87, 79, 18, 65, 1, 36, 65, 91, 24, 33, 71, 52, 43, 20, 100, 94, 68, 19, 93, 66, 89, 45, 39, 97, 57, 67, 51, 92, 20, 97, 45, 32, 10, 82, 86, 2, 8, 27, 15, 60, 7, 6, 90, 71, 40, 91, 10, 16, 39, 40, 32, 2, 11, 5, 81, 31, 72, 41, 7, 89, 89, 85, 28, 67, 54, 44, 47, 26, 44, 51, 50, 65, 41, 68, 17, 88, 45, 43, 8, 11, 79, 10, 99, 58, 42, 75, 75, 86, 73, 24, 33, 15, 46, 84, 33, 27, 96, 14, 25, 11, 67, 48, 51, 85, 61, 87, 71, 85, 62, 32, 71, 15, 56, 6, 20, 43, 64, 97, 81, 94, 94, 61, 39, 46, 99, 37, 66, 40, 17, 74, 44, 6, 2, 11, 53, 44, 75, 29, 58, 77, 66, 96, 82, 13, 32, 43, 13, 36, 10, 39, 54, 39, 79, 22, 4, 41, 19, 44, 37, 73, 76, 84, 78, 94, 13, 98, 26, 56, 55, 51, 38, 37, 60, 55, 92, 19, 53, 48, 4, 7, 85, 82, 8, 60, 34, 67, 98, 76, 38, 14, 20, 62, 41, 58, 29, 70, 71, 16, 60, 26, 8, 64, 92, 17, 26, 40, 12, 59, 69, 97, 63, 52, 81, 27, 10, 99, 73, 74, 68, 8, 44, 70, 38, 65, 3, 27, 80, 90, 8, 64, 98, 89, 10, 45, 42, 55, 61, 49, 45, 82, 48, 27, 22, 16, 50, 58, 41, 92, 64, 54, 35, 65, 23, 66, 22, 9, 68, 79, 45, 69, 71, 94, 24, 41, 55, 48, 84, 12, 80, 71, 41, 91, 77, 83, 2, 12, 55, 21, 100, 99, 65, 20, 77, 37, 29, 75, 6, 59, 84, 25, 70, 40, 31, 73, 26, 61, 77, 16, 73, 41, 5, 83, 51, 9, 60, 97, 44, 21, 21, 87, 20, 74, 91, 43, 10, 69, 67, 14, 30, 71, 31, 20, 21, 98, 58, 21, 51, 83, 20, 69, 70, 13, 8, 62, 66, 28, 46, 75, 66, 65, 21, 32, 83, 7, 62, 4, 46, 98, 89, 20, 11, 57, 93, 72, 14, 80, 57, 10, 53, 67, 52, 88, 21, 97, 67, 42, 14, 86, 5, 12, 44, 35, 82, 3, 69, 87, 32, 10, 15, 54, 40, 60, 11, 46, 23, 77, 97, 46, 61, 90, 74, 82, 50, 15, 73, 59, 83, 68, 52, 54, 54, 89, 99, 44, 7, 85, 29, 65, 87, 20, 57, 5, 45, 98, 36, 98, 36, 99, 3, 54, 78, 100, 91, 73, 77, 63, 30, 11, 31, 21, 12, 78, 66, 36, 6, 50, 27, 55, 97, 79, 85, 29, 91, 72, 64, 18, 78, 77, 93, 74, 76, 33, 68, 71, 48, 10, 4, 19, 32, 53, 87, 75, 11, 25, 71, 23, 55, 16, 74, 28, 66, 90, 49, 75, 95, 19, 50, 75, 49, 52, 28, 57, 90, 20, 77, 52, 9, 42, 4, 20, 49, 78, 99, 78, 38, 100, 90, 7, 12, 8, 35, 26, 49, 54, 78, 43, 86, 23, 55, 11, 79, 20, 56, 61, 26, 81, 42, 93, 4, 3, 84, 3, 55, 46, 27, 67, 74, 28, 100, 44, 5, 14, 65, 22, 71, 13, 61, 65, 53, 14, 44, 53, 67, 69, 2, 76, 76, 90, 63, 21, 46, 46, 96, 19, 40, 12, 22, 45, 98, 6, 81, 7, 70, 51, 16, 62, 66, 33, 21, 69, 34, 24, 92, 23, 14, 51, 84, 36, 73, 83, 45, 52, 93, 20, 21, 61, 58, 75, 85, 36, 92, 29, 26, 100, 86, 79, 46, 43, 95, 9, 8, 98, 29, 27, 70, 93, 60, 20, 14, 10, 77, 71, 12, 38, 91, 59, 57, 84, 77, 15, 81, 17, 10, 42, 89, 4, 72, 16, 85, 27, 80, 85, 85, 9, 94, 3, 59, 30, 43, 30, 87, 20, 19, 33, 92, 8, 52, 46, 67, 26, 76, 3, 21, 71, 10, 37, 49, 61, 15, 70, 57, 66, 55, 52, 87, 36, 18, 30, 69, 28, 68, 26, 82, 86, 87, 16, 15, 46, 92, 54, 100, 92, 89, 52, 97, 53, 21, 31, 51, 31, 17, 46, 68, 53, 93, 64, 87, 43, 39, 94, 2, 38, 30, 87, 35, 53, 97, 28, 54, 58, 42, 55, 23, 27, 2, 27, 4, 78, 31, 14, 87, 21, 75, 26, 28, 67, 56, 65, 80, 10, 21, 48, 71, 52, 24, 67, 38, 62, 68, 93, 17, 56, 85, 87, 75, 62, 68, 45, 88, 49, 97, 78, 14, 94, 3, 67, 86, 9, 24, 92, 2, 12, 89, 73, 94, 63, 89, 65, 92, 61, 100, 90, 44, 57, 17, 74, 59, 5, 63, 5, 73, 46, 76, 69, 12, 97, 91, 9, 6, 61, 37, 5, 20, 39, 32, 19, 14, 46, 2, 46, 41, 28, 39, 29, 41, 59, 25, 97, 94, 63, 31, 64, 63, 72, 41, 46, 58, 79, 79, 35, 49, 42, 43, 82, 32, 41, 37, 84, 96, 100, 33, 87, 38, 89, 97, 25, 56, 61, 4, 100, 9, 83, 66, 77, 65, 22, 81, 52, 27, 6, 79, 29, 34, 15, 64, 22, 80, 61, 10, 74, 1, 68, 80, 74, 86, 98, 9, 24, 76, 57, 23, 5, 50, 7, 11, 80, 39, 10, 75, 38, 73, 8, 47, 3, 92, 90, 51, 42, 22, 45, 63, 27, 62, 78, 38, 5, 46, 46, 80, 51, 6, 43, 43, 7, 13, 50, 10, 64, 4, 67, 94, 69, 58, 58, 77, 71, 42, 80, 35, 15, 34, 65, 23, 43, 21, 24, 69, 24, 37, 68, 11, 38, 18, 12, 37, 41, 81, 12, 3, 91, 44, 98, 5, 1, 90, 53, 100, 90, 26, 36, 23, 14, 76, 23, 70, 58, 7, 35, 42, 11, 19, 48, 11, 24, 61, 49, 52, 69, 68, 82, 11, 57, 87, 65, 68, 54, 69, 39, 99, 1, 86, 44, 35, 36, 58, 73, 17, 14, 14, 87, 20, 57, 11, 65, 98, 77, 10, 51, 45, 50, 28, 56, 23, 64, 6, 11, 15, 93, 32, 77, 45, 57, 84, 49, 66, 98, 71, 8, 35, 62, 23, 82, 30, 75, 41, 15, 52, 22, 93, 68, 12, 83, 76, 19, 93, 67, 19, 35, 76, 49, 95, 40, 21, 78, 76, 86, 26, 31, 85, 15, 29, 82, 68, 54, 29, 70, 79, 93, 35, 2, 60, 78, 74, 32, 77, 94, 21, 21, 87, 48, 58, 76, 5, 87, 41, 6, 74, 83, 2, 56, 8, 2, 81, 3, 59, 7, 49, 62, 72, 98, 81, 68, 6, 82, 20, 97, 71, 16, 10, 58, 37, 98, 49, 23, 61, 80, 15, 77, 26, 56, 99, 21, 19, 60, 80, 61, 31, 6, 59, 70, 7, 87, 41, 9, 2, 34, 43, 84, 12, 24, 67, 63, 40, 78, 3, 100, 22, 100, 61, 59, 92, 26, 9, 39, 56, 93, 74, 47, 21, 71, 67, 81, 40, 74, 56, 34, 35, 82, 94, 35, 35, 15, 52, 44, 5, 83, 30, 10, 18, 65, 31, 45, 49, 100, 41, 26, 51, 3, 86, 17, 62, 13, 92, 58, 76, 53, 34, 81, 98, 57, 99, 81, 67, 23, 25, 99, 88, 62, 99, 37, 85, 17, 60, 23, 56, 97, 65, 41, 91, 16, 90, 47, 86, 56, 99, 44, 28, 18, 89, 27, 43, 43, 14, 64, 96, 8, 92, 74, 65, 24, 26, 96, 92, 19, 57, 24, 25, 3, 80, 99, 89, 78, 78, 80, 89, 27, 6, 49, 78, 81, 75, 99, 21, 64, 51, 98, 32, 53, 59, 74, 33, 1, 93, 9, 1, 24, 15, 8, 55, 76, 51, 98, 41, 77, 48, 81, 47, 76, 47, 65, 25, 2, 80, 67, 9, 85, 18, 73, 35, 50, 69, 46, 33, 14, 47, 25, 93, 28, 39, 12, 87, 85, 81, 16, 51, 91, 93, 32, 60, 55, 43, 54, 32, 57, 4, 30, 20, 15, 96, 64, 3, 99, 41, 5, 78, 28, 52, 39, 45, 41, 54, 1, 13, 53, 84, 75, 24, 100, 44, 8, 18, 46, 42, 86, 65, 27, 74, 1, 75, 99, 90, 33, 31, 4, 22, 17, 30, 44, 36, 72, 47, 75, 100, 47, 85, 86, 59, 37, 32, 30, 67, 98, 94, 85, 93, 1, 81, 60, 33, 97, 88, 73, 68, 8, 35, 30, 83, 19, 99, 74, 21, 93, 42, 80, 95, 27, 65, 24, 73, 31, 43, 92, 81, 24, 70, 67, 78, 48, 47, 70, 76, 12, 79, 89, 7, 28, 83, 78, 22, 25, 32, 17, 4, 68, 42, 15, 1, 3, 18, 43, 75, 48, 84, 17, 60, 100, 73, 59, 80, 68, 13, 89, 7, 93, 16, 22, 1, 58, 92, 87, 90, 23, 95, 76, 67, 10, 14, 70, 17, 99, 77, 6, 63, 69, 2, 93, 27, 29, 88, 39, 35, 25, 50, 91, 13, 16, 91, 50, 53, 54, 12, 53, 25, 11, 6, 10, 44, 36, 87, 67, 69, 5, 5, 78, 25, 19, 24, 50, 88, 62, 24, 89, 39, 86, 6, 7, 70, 56, 92, 18, 76, 57, 50, 28, 71, 50, 74, 19, 89, 49, 8, 76, 92, 80, 41, 34, 33, 63, 88, 31, 95, 97, 71, 52, 36, 26, 99, 72, 50, 76, 33, 62, 79, 11, 76, 54, 64, 42, 76, 5, 45, 79, 61, 39, 66, 72, 74, 76, 25, 63, 35, 100, 42, 61, 12, 9, 41, 95, 90, 48, 24, 8, 66, 65, 29, 74, 97, 54, 51, 31, 31, 51, 30, 63, 32, 70, 79, 49, 7, 35, 53, 76, 83, 62, 20, 13, 92, 95, 40, 99, 10, 98, 13, 7, 88, 16, 40, 10, 22, 29, 88, 64, 39, 13, 26, 12, 27, 69, 70, 23, 41, 67, 50, 96, 24, 97, 29, 31, 42, 27, 90, 50, 69, 42, 92, 22, 88, 23, 35, 83, 82, 74, 50, 72, 98, 94, 94, 46, 82, 16, 35, 88, 46, 89, 77, 86, 19, 17, 20, 5, 13, 25, 69, 79, 90, 55, 88, 71, 13, 30};
float b[K] = {66, 97, 50, 69, 24, 42, 23, 82, 25, 79, 66, 26, 76, 25, 75, 25, 43, 40, 55, 8, 20, 53, 66, 94, 57, 10, 39, 70, 5, 57, 22, 36, 45, 94, 24, 44, 89, 41, 14, 87, 9, 46, 74, 23, 72, 62, 52, 74, 36, 13};
clock_t begin = clock();
linear_solve(A, b);
clock_t end = clock();
double time_spent = (double)(end - begin) / CLOCKS_PER_SEC;
printf("seconds: %f\n", time_spent);
printf("Result vector is: ");
for (i=0; i<K; i++)
{
printf("%f,", b[i]);
}
printf("\n");
return 0;
}
The following is Julia code for solving Ax=b, by calling LAPACK (LU-decomp followed by upper/lower triangular solver),
using BenchmarkTools
A = reshape(Float64[38, 49, 38, 73, 70, 71, 33, 24, 14, 82, 46, 99, 82, 36, 21, 32, 48, 40, 27, 60, 31, 15, 38, 88, 95, 57, 36, 86, 42, 56, 1, 37, 73, 7, 92, 93, 16, 95, 59, 76, 18, 42, 57, 9, 14, 40, 68, 61, 8, 26, 90, 33, 95, 8, 5, 87, 66, 84, 45, 78, 27, 16, 9, 83, 46, 61, 74, 44, 17, 21, 21, 53, 96, 49, 58, 67, 73, 60, 18, 40, 32, 68, 68, 21, 57, 86, 69, 7, 80, 10, 36, 46, 94, 59, 41, 80, 70, 2, 90, 57, 92, 50, 92, 98, 88, 14, 39, 80, 68, 78, 49, 40, 54, 51, 68, 80, 95, 22, 37, 88, 10, 30, 54, 7, 84, 99, 42, 94, 75, 45, 22, 41, 75, 38, 54, 97, 64, 62, 6, 48, 92, 49, 72, 5, 75, 67, 24, 55, 76, 17, 62, 19, 75, 41, 63, 97, 19, 83, 69, 12, 43, 94, 48, 92, 94, 54, 76, 11, 99, 96, 20, 29, 43, 97, 86, 23, 55, 2, 75, 61, 17, 45, 88, 79, 9, 26, 1, 3, 10, 91, 94, 85, 13, 58, 3, 53, 24, 76, 9, 2, 33, 34, 51, 65, 100, 67, 84, 21, 77, 17, 88, 65, 2, 46, 1, 18, 15, 57, 1, 88, 60, 64, 39, 36, 79, 89, 51, 39, 98, 67, 62, 34, 56, 98, 74, 52, 93, 11, 87, 45, 48, 82, 87, 5, 97, 65, 1, 81, 39, 85, 33, 26, 24, 90, 41, 69, 74, 43, 21, 54, 91, 94, 78, 41, 17, 11, 71, 25, 72, 52, 36, 27, 100, 48, 67, 52, 94, 44, 94, 91, 83, 95, 76, 19, 70, 34, 87, 67, 62, 67, 81, 55, 81, 45, 68, 1, 56, 95, 76, 38, 72, 88, 37, 64, 29, 16, 19, 81, 36, 18, 25, 28, 21, 17, 57, 51, 22, 87, 61, 39, 56, 51, 65, 44, 59, 3, 75, 98, 5, 21, 48, 95, 53, 23, 96, 4, 11, 11, 77, 21, 58, 78, 9, 93, 81, 17, 77, 97, 97, 44, 96, 26, 35, 89, 73, 26, 37, 3, 51, 76, 14, 67, 45, 92, 52, 83, 43, 91, 20, 62, 4, 48, 75, 35, 17, 65, 6, 98, 2, 78, 69, 39, 30, 57, 27, 49, 8, 71, 46, 82, 16, 62, 57, 69, 94, 15, 56, 15, 29, 42, 93, 96, 57, 2, 63, 23, 57, 54, 47, 88, 40, 1, 90, 48, 1, 4, 26, 32, 12, 97, 38, 62, 72, 92, 71, 72, 34, 93, 84, 56, 20, 33, 53, 42, 7, 54, 98, 37, 27, 2, 13, 88, 30, 24, 91, 22, 95, 100, 53, 53, 31, 91, 95, 9, 36, 89, 25, 60, 28, 47, 61, 81, 41, 47, 88, 6, 46, 83, 4, 48, 73, 88, 8, 83, 78, 18, 21, 75, 6, 90, 87, 92, 18, 71, 5, 82, 36, 2, 50, 86, 49, 72, 92, 67, 41, 38, 81, 37, 67, 93, 99, 51, 79, 95, 76, 85, 90, 27, 93, 44, 79, 97, 7, 11, 52, 76, 61, 23, 52, 97, 58, 74, 87, 58, 70, 77, 97, 74, 85, 65, 71, 79, 91, 36, 92, 35, 97, 9, 6, 38, 90, 46, 84, 98, 65, 4, 89, 9, 72, 55, 3, 21, 77, 43, 76, 83, 34, 16, 33, 21, 6, 28, 98, 27, 86, 93, 66, 55, 34, 76, 93, 42, 1, 36, 82, 82, 13, 45, 48, 8, 4, 66, 51, 32, 68, 81, 49, 70, 93, 73, 89, 16, 76, 95, 90, 37, 83, 28, 40, 14, 3, 18, 27, 34, 24, 53, 42, 24, 57, 93, 48, 43, 91, 28, 75, 86, 47, 40, 61, 20, 34, 81, 31, 62, 20, 75, 80, 81, 95, 75, 14, 8, 89, 13, 7, 9, 27, 80, 24, 52, 27, 75, 4, 58, 20, 82, 89, 31, 100, 48, 57, 73, 34, 52, 24, 26, 64, 18, 90, 74, 17, 58, 8, 44, 43, 56, 56, 51, 58, 56, 4, 87, 80, 24, 100, 47, 72, 60, 41, 2, 26, 81, 17, 57, 28, 6, 21, 4, 99, 92, 42, 37, 22, 45, 5, 93, 72, 27, 91, 13, 44, 93, 6, 100, 31, 17, 78, 16, 96, 32, 57, 45, 95, 76, 92, 3, 77, 84, 92, 87, 63, 42, 70, 79, 77, 90, 16, 100, 82, 61, 23, 67, 55, 45, 38, 27, 95, 19, 10, 4, 53, 75, 62, 1, 99, 62, 94, 30, 95, 65, 35, 62, 25, 59, 26, 62, 98, 50, 73, 31, 11, 89, 20, 1, 74, 45, 49, 55, 78, 49, 82, 35, 9, 45, 100, 99, 87, 10, 56, 79, 85, 89, 8, 9, 53, 87, 13, 27, 95, 81, 7, 71, 63, 44, 38, 84, 40, 87, 79, 54, 42, 58, 49, 85, 49, 6, 55, 83, 93, 52, 63, 76, 52, 40, 91, 36, 74, 70, 92, 92, 67, 57, 51, 74, 22, 35, 22, 48, 60, 86, 87, 79, 18, 65, 1, 36, 65, 91, 24, 33, 71, 52, 43, 20, 100, 94, 68, 19, 93, 66, 89, 45, 39, 97, 57, 67, 51, 92, 20, 97, 45, 32, 10, 82, 86, 2, 8, 27, 15, 60, 7, 6, 90, 71, 40, 91, 10, 16, 39, 40, 32, 2, 11, 5, 81, 31, 72, 41, 7, 89, 89, 85, 28, 67, 54, 44, 47, 26, 44, 51, 50, 65, 41, 68, 17, 88, 45, 43, 8, 11, 79, 10, 99, 58, 42, 75, 75, 86, 73, 24, 33, 15, 46, 84, 33, 27, 96, 14, 25, 11, 67, 48, 51, 85, 61, 87, 71, 85, 62, 32, 71, 15, 56, 6, 20, 43, 64, 97, 81, 94, 94, 61, 39, 46, 99, 37, 66, 40, 17, 74, 44, 6, 2, 11, 53, 44, 75, 29, 58, 77, 66, 96, 82, 13, 32, 43, 13, 36, 10, 39, 54, 39, 79, 22, 4, 41, 19, 44, 37, 73, 76, 84, 78, 94, 13, 98, 26, 56, 55, 51, 38, 37, 60, 55, 92, 19, 53, 48, 4, 7, 85, 82, 8, 60, 34, 67, 98, 76, 38, 14, 20, 62, 41, 58, 29, 70, 71, 16, 60, 26, 8, 64, 92, 17, 26, 40, 12, 59, 69, 97, 63, 52, 81, 27, 10, 99, 73, 74, 68, 8, 44, 70, 38, 65, 3, 27, 80, 90, 8, 64, 98, 89, 10, 45, 42, 55, 61, 49, 45, 82, 48, 27, 22, 16, 50, 58, 41, 92, 64, 54, 35, 65, 23, 66, 22, 9, 68, 79, 45, 69, 71, 94, 24, 41, 55, 48, 84, 12, 80, 71, 41, 91, 77, 83, 2, 12, 55, 21, 100, 99, 65, 20, 77, 37, 29, 75, 6, 59, 84, 25, 70, 40, 31, 73, 26, 61, 77, 16, 73, 41, 5, 83, 51, 9, 60, 97, 44, 21, 21, 87, 20, 74, 91, 43, 10, 69, 67, 14, 30, 71, 31, 20, 21, 98, 58, 21, 51, 83, 20, 69, 70, 13, 8, 62, 66, 28, 46, 75, 66, 65, 21, 32, 83, 7, 62, 4, 46, 98, 89, 20, 11, 57, 93, 72, 14, 80, 57, 10, 53, 67, 52, 88, 21, 97, 67, 42, 14, 86, 5, 12, 44, 35, 82, 3, 69, 87, 32, 10, 15, 54, 40, 60, 11, 46, 23, 77, 97, 46, 61, 90, 74, 82, 50, 15, 73, 59, 83, 68, 52, 54, 54, 89, 99, 44, 7, 85, 29, 65, 87, 20, 57, 5, 45, 98, 36, 98, 36, 99, 3, 54, 78, 100, 91, 73, 77, 63, 30, 11, 31, 21, 12, 78, 66, 36, 6, 50, 27, 55, 97, 79, 85, 29, 91, 72, 64, 18, 78, 77, 93, 74, 76, 33, 68, 71, 48, 10, 4, 19, 32, 53, 87, 75, 11, 25, 71, 23, 55, 16, 74, 28, 66, 90, 49, 75, 95, 19, 50, 75, 49, 52, 28, 57, 90, 20, 77, 52, 9, 42, 4, 20, 49, 78, 99, 78, 38, 100, 90, 7, 12, 8, 35, 26, 49, 54, 78, 43, 86, 23, 55, 11, 79, 20, 56, 61, 26, 81, 42, 93, 4, 3, 84, 3, 55, 46, 27, 67, 74, 28, 100, 44, 5, 14, 65, 22, 71, 13, 61, 65, 53, 14, 44, 53, 67, 69, 2, 76, 76, 90, 63, 21, 46, 46, 96, 19, 40, 12, 22, 45, 98, 6, 81, 7, 70, 51, 16, 62, 66, 33, 21, 69, 34, 24, 92, 23, 14, 51, 84, 36, 73, 83, 45, 52, 93, 20, 21, 61, 58, 75, 85, 36, 92, 29, 26, 100, 86, 79, 46, 43, 95, 9, 8, 98, 29, 27, 70, 93, 60, 20, 14, 10, 77, 71, 12, 38, 91, 59, 57, 84, 77, 15, 81, 17, 10, 42, 89, 4, 72, 16, 85, 27, 80, 85, 85, 9, 94, 3, 59, 30, 43, 30, 87, 20, 19, 33, 92, 8, 52, 46, 67, 26, 76, 3, 21, 71, 10, 37, 49, 61, 15, 70, 57, 66, 55, 52, 87, 36, 18, 30, 69, 28, 68, 26, 82, 86, 87, 16, 15, 46, 92, 54, 100, 92, 89, 52, 97, 53, 21, 31, 51, 31, 17, 46, 68, 53, 93, 64, 87, 43, 39, 94, 2, 38, 30, 87, 35, 53, 97, 28, 54, 58, 42, 55, 23, 27, 2, 27, 4, 78, 31, 14, 87, 21, 75, 26, 28, 67, 56, 65, 80, 10, 21, 48, 71, 52, 24, 67, 38, 62, 68, 93, 17, 56, 85, 87, 75, 62, 68, 45, 88, 49, 97, 78, 14, 94, 3, 67, 86, 9, 24, 92, 2, 12, 89, 73, 94, 63, 89, 65, 92, 61, 100, 90, 44, 57, 17, 74, 59, 5, 63, 5, 73, 46, 76, 69, 12, 97, 91, 9, 6, 61, 37, 5, 20, 39, 32, 19, 14, 46, 2, 46, 41, 28, 39, 29, 41, 59, 25, 97, 94, 63, 31, 64, 63, 72, 41, 46, 58, 79, 79, 35, 49, 42, 43, 82, 32, 41, 37, 84, 96, 100, 33, 87, 38, 89, 97, 25, 56, 61, 4, 100, 9, 83, 66, 77, 65, 22, 81, 52, 27, 6, 79, 29, 34, 15, 64, 22, 80, 61, 10, 74, 1, 68, 80, 74, 86, 98, 9, 24, 76, 57, 23, 5, 50, 7, 11, 80, 39, 10, 75, 38, 73, 8, 47, 3, 92, 90, 51, 42, 22, 45, 63, 27, 62, 78, 38, 5, 46, 46, 80, 51, 6, 43, 43, 7, 13, 50, 10, 64, 4, 67, 94, 69, 58, 58, 77, 71, 42, 80, 35, 15, 34, 65, 23, 43, 21, 24, 69, 24, 37, 68, 11, 38, 18, 12, 37, 41, 81, 12, 3, 91, 44, 98, 5, 1, 90, 53, 100, 90, 26, 36, 23, 14, 76, 23, 70, 58, 7, 35, 42, 11, 19, 48, 11, 24, 61, 49, 52, 69, 68, 82, 11, 57, 87, 65, 68, 54, 69, 39, 99, 1, 86, 44, 35, 36, 58, 73, 17, 14, 14, 87, 20, 57, 11, 65, 98, 77, 10, 51, 45, 50, 28, 56, 23, 64, 6, 11, 15, 93, 32, 77, 45, 57, 84, 49, 66, 98, 71, 8, 35, 62, 23, 82, 30, 75, 41, 15, 52, 22, 93, 68, 12, 83, 76, 19, 93, 67, 19, 35, 76, 49, 95, 40, 21, 78, 76, 86, 26, 31, 85, 15, 29, 82, 68, 54, 29, 70, 79, 93, 35, 2, 60, 78, 74, 32, 77, 94, 21, 21, 87, 48, 58, 76, 5, 87, 41, 6, 74, 83, 2, 56, 8, 2, 81, 3, 59, 7, 49, 62, 72, 98, 81, 68, 6, 82, 20, 97, 71, 16, 10, 58, 37, 98, 49, 23, 61, 80, 15, 77, 26, 56, 99, 21, 19, 60, 80, 61, 31, 6, 59, 70, 7, 87, 41, 9, 2, 34, 43, 84, 12, 24, 67, 63, 40, 78, 3, 100, 22, 100, 61, 59, 92, 26, 9, 39, 56, 93, 74, 47, 21, 71, 67, 81, 40, 74, 56, 34, 35, 82, 94, 35, 35, 15, 52, 44, 5, 83, 30, 10, 18, 65, 31, 45, 49, 100, 41, 26, 51, 3, 86, 17, 62, 13, 92, 58, 76, 53, 34, 81, 98, 57, 99, 81, 67, 23, 25, 99, 88, 62, 99, 37, 85, 17, 60, 23, 56, 97, 65, 41, 91, 16, 90, 47, 86, 56, 99, 44, 28, 18, 89, 27, 43, 43, 14, 64, 96, 8, 92, 74, 65, 24, 26, 96, 92, 19, 57, 24, 25, 3, 80, 99, 89, 78, 78, 80, 89, 27, 6, 49, 78, 81, 75, 99, 21, 64, 51, 98, 32, 53, 59, 74, 33, 1, 93, 9, 1, 24, 15, 8, 55, 76, 51, 98, 41, 77, 48, 81, 47, 76, 47, 65, 25, 2, 80, 67, 9, 85, 18, 73, 35, 50, 69, 46, 33, 14, 47, 25, 93, 28, 39, 12, 87, 85, 81, 16, 51, 91, 93, 32, 60, 55, 43, 54, 32, 57, 4, 30, 20, 15, 96, 64, 3, 99, 41, 5, 78, 28, 52, 39, 45, 41, 54, 1, 13, 53, 84, 75, 24, 100, 44, 8, 18, 46, 42, 86, 65, 27, 74, 1, 75, 99, 90, 33, 31, 4, 22, 17, 30, 44, 36, 72, 47, 75, 100, 47, 85, 86, 59, 37, 32, 30, 67, 98, 94, 85, 93, 1, 81, 60, 33, 97, 88, 73, 68, 8, 35, 30, 83, 19, 99, 74, 21, 93, 42, 80, 95, 27, 65, 24, 73, 31, 43, 92, 81, 24, 70, 67, 78, 48, 47, 70, 76, 12, 79, 89, 7, 28, 83, 78, 22, 25, 32, 17, 4, 68, 42, 15, 1, 3, 18, 43, 75, 48, 84, 17, 60, 100, 73, 59, 80, 68, 13, 89, 7, 93, 16, 22, 1, 58, 92, 87, 90, 23, 95, 76, 67, 10, 14, 70, 17, 99, 77, 6, 63, 69, 2, 93, 27, 29, 88, 39, 35, 25, 50, 91, 13, 16, 91, 50, 53, 54, 12, 53, 25, 11, 6, 10, 44, 36, 87, 67, 69, 5, 5, 78, 25, 19, 24, 50, 88, 62, 24, 89, 39, 86, 6, 7, 70, 56, 92, 18, 76, 57, 50, 28, 71, 50, 74, 19, 89, 49, 8, 76, 92, 80, 41, 34, 33, 63, 88, 31, 95, 97, 71, 52, 36, 26, 99, 72, 50, 76, 33, 62, 79, 11, 76, 54, 64, 42, 76, 5, 45, 79, 61, 39, 66, 72, 74, 76, 25, 63, 35, 100, 42, 61, 12, 9, 41, 95, 90, 48, 24, 8, 66, 65, 29, 74, 97, 54, 51, 31, 31, 51, 30, 63, 32, 70, 79, 49, 7, 35, 53, 76, 83, 62, 20, 13, 92, 95, 40, 99, 10, 98, 13, 7, 88, 16, 40, 10, 22, 29, 88, 64, 39, 13, 26, 12, 27, 69, 70, 23, 41, 67, 50, 96, 24, 97, 29, 31, 42, 27, 90, 50, 69, 42, 92, 22, 88, 23, 35, 83, 82, 74, 50, 72, 98, 94, 94, 46, 82, 16, 35, 88, 46, 89, 77, 86, 19, 17, 20, 5, 13, 25, 69, 79, 90, 55, 88, 71, 13, 30], (50,50))
b = Float64[66, 97, 50, 69, 24, 42, 23, 82, 25, 79, 66, 26, 76, 25, 75, 25, 43, 40, 55, 8, 20, 53, 66, 94, 57, 10, 39, 70, 5, 57, 22, 36, 45, 94, 24, 44, 89, 41, 14, 87, 9, 46, 74, 23, 72, 62, 52, 74, 36, 13]
linear_solve(A, b) = A \ b
#benchmark linear_solve(A, b)
The C code runs in approximately 166 microseconds, while the LAPACK (via Julia) code runs in an average of 33 microseconds (5 times faster!).
I suppose this is a testament to the quality of LAPACK and the associated Julia wrapper.
Unfortunately since this C code is to be part of an OpenCL kernel, I can't really take advantage of either, is there a way to make my C code more performant? So that it achieves a performance more similar to that of LAPACK?

TL;DR: The current C code is inefficient on a modern hardware. Moreover, using OpenCL on dedicated GPUs or CUDA will only be fast for quite big matrices here (ie. not 50x50 ones).
The biggest problem in the C code comes from the line A[K * l + (i + 1)] += c * A[K * l + j];. Indeed, as the loop iterator is l, the memory access pattern is not contiguous but strided. Strided memory access pattern is much more inefficient than a contiguous ones on modern hardware architectures (due to code vectorization, cache lines, memory prefetching, etc.). This is especially true on GPUs.
You can fix this problem by transposing the A matrix. Here is the modified version:
// Naive (inefficient) transposition
// Please use the much faster BLAS function to do this (if possible)
void transpose(float A[K * K])
{
for (long j=0; j<K; ++j)
{
for (long i=j+1; i<K; ++i)
{
float tmp = A[K * i + j];
A[K * i + j] = A[K * j + i];
A[K * j + i] = tmp;
}
}
}
// Solve the system Ax=b using Gaussian elimination with partial pivoting.
// Work directly on the transposed version of A rather than transposing A every time should be much faster (especially for small matrices).
void fast_linear_solve(float A[K * K], float b[K])
{
// Not useful if A is already transposed
transpose(A);
for (long j=0; j<K; j++)
{
// Begin partial pivoting.
float maxval = fabs(A[K * j + j]);
long maxrow = j;
for (long i=j+1; i<K; i++)
{
if (fabs(A[K * i + j]) > maxval)
{
maxval = fabs(A[K * i + j]);
maxrow = i;
}
}
for (long l=0; l<K; l++)
{
float A_temp = A[K * maxrow + l];
A[K * maxrow + l] = A[K * j + l];
A[K * j + l] = A_temp;
}
float b_temp = b[maxrow];
b[maxrow] = b[j];
b[j] = b_temp;
// End partial pivoting.
// Begin putting [A; b] into row echelon form.
for (long i=j; i<K-1; i++)
{
float c = -A[K * (i + 1) + j] / A[K * j + j];
for (long l=j+1; l<K; l++)
A[K * (i + 1) + l] += c * A[K * j + l];
b[i + 1] += c * b[j];
}
// End putting [A; b] into row echelon form.
}
// Begin backsolving for x (by overwritting b).
for (long j=K-1; j>0; j--)
for (long i=j-1; i>=0; i--)
b[i] -= b[j] * A[K * i + j] / A[K * j + j];
for (long j=0; j<K; j++)
b[j] *= 1 / A[K * j + j];
// End backsolving for x.
// Not useful if A is already transposed
transpose(A);
}
Another problem comes from the way the benchmark is performed. Indeed, Julia run multiple time the code while the C code is executed once and with the clock function. To have a more fair comparison with the Julia implementation, the linear_solve function of the C implementation must be evaluated multiple times (by putting it in a loop and taking care of possible clever compiler optimizations that could add some biases). gettimeofday should be preferred over clock (as the former compute the wall-clock time and the latter compute the sum of the user time and the system time).
Here are (average) results with a 50x50 matrix on my machine (with GCC 9.3 using -O3, Clang 9.0 using -O3 too, and with Julia 1.4):
Original C code (GCC): 25 us | Original C code (Clang): 25 us
New C code (GCC): 11 us | New C code (Clang): 12 us
Julia code: 80 us
Here are results with a 500x500 random matrix:
Original C code (GCC): 37.9 ms | Original C code (Clang): 38.8 ms
New C code (GCC): 6.7 ms | New C code (Clang): 6.1 ms
Julia code: 2.3 ms
There is still a room for improvement for big matrices: the C code can be improved using loop tiling for example (at the cost of decreasing the code readability and maintainability).
One should keep in mind that although using (dedicated) GPUs should improves performance for big matrices, it should however not be the case for small matrices due to the relatively high latency of GPUs (eg. data transfers, synchronizations, memory latency) unless batch processing is used on many small matrices.

Split string to a 2-dimensional array in Scala

In Scala:
Is there a way to directly split a string that contains 72 numeric values separated by ; into a 2-dimensional array of 9 rows and 8 columns with those numeric values -in numeric data type-?

val input = List.tabulate(72)(_.toString).mkString(";")
input.split(";").map(_.toInt).grouped(9).toArray
transforms
0;1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21;22;23;24;25;26;27;28;29;30;31;32;33;34;35;36;37;38;39;40;41;42;43;44;45;46;47;48;49;50;51;52;53;54;55;56;57;58;59;60;61;62;63;64;65;66;67;68;69;70;71
into
Array(
Array(0, 1, 2, 3, 4, 5, 6, 7, 8),
Array(9, 10, 11, 12, 13, 14, 15, 16, 17),
Array(18, 19, 20, 21, 22, 23, 24, 25, 26),
Array(27, 28, 29, 30, 31, 32, 33, 34, 35),
Array(36, 37, 38, 39, 40, 41, 42, 43, 44),
Array(45, 46, 47, 48, 49, 50, 51, 52, 53),
Array(54, 55, 56, 57, 58, 59, 60, 61, 62),
Array(63, 64, 65, 66, 67, 68, 69, 70, 71)
)
If you want to swap the dimensions of rows/columns, replace 9 by 8.

using Range and grouped functions
scala> val a = (0 to 71).map(_.toString).toArray.mkString(";")
a: String = 0;1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21;22;23;24;25;26;27;28;29;30;31;32;33;34;35;36;37;38;39;40;41;42;43;44;45;46;47;48;49;50;51;52;53;54;55;56;57;58;59;60;61;62;63;64;65;66;67;68;69;70;71
scala> a.split(";").map(_.toInt).sliding(9,9).toArray
res269: Array[Array[Int]] = Array(Array(0, 1, 2, 3, 4, 5, 6, 7, 8), Array(9, 10, 11, 12, 13, 14, 15, 16, 17), Array(18, 19, 20, 21, 22, 23, 24, 25, 26), Array(27, 28, 29, 30, 31, 32, 33, 34, 35), Array(36, 37, 38, 39, 40, 41, 42, 43, 44), Array(45, 46, 47, 48, 49, 50, 51, 52, 53), Array(54, 55, 56, 57, 58, 59, 60, 61, 62), Array(63, 64, 65, 66, 67, 68, 69, 70, 71))
scala>

appIdentityService.signForApp (Java) and app_identity.sign_blob (Python) results are different

I need to sign JWT using Google Cloud appIdentity.
I tried using python agent and it is working. But the Java client gives signature error.
So I run test code to get signature of same input from Java and Python. It returns different result.
python code
import array
from google.appengine.api import app_identity
header_and_payload = "test"
(key_name, signature) = app_identity.sign_blob(header_and_payload)
print array.array('B', signature)
java code
import com.google.appengine.api.appidentity.AppIdentityService;
import com.google.appengine.api.appidentity.AppIdentityServiceFactory;
headerAndPayload = "test";
AppIdentityService appIdentityService = AppIdentityServiceFactory.getAppIdentityService();
AppIdentityService.SigningResult signingResult = appIdentityService.signForApp(headerAndPayload.getBytes());
System.out.println(Arrays.toString(signingResult.getSignature()));
Python output
[205, 130, 214, 28, 19, 7, 233, 69, 92, 161, 8, 160, 36, 162, 149, 125, 5, 100, 8, 219, 244, 235, 188, 126, 118, 45, 176, 63, 61, 88, 91, 151, 151, 114, 228, 31, 85, 209, 117, 134, 66, 120, 13, 159, 10, 155, 70, 16, 110, 56, 212, 79, 165, 40, 222, 46, 26, 74, 182, 80, 223, 57, 244, 44, 224, 122, 230, 184, 114, 236, 158, 204, 145, 152, 133, 131, 115, 43, 224, 132, 219, 232, 186, 237, 82, 86, 243, 194, 155, 127, 26, 227, 19, 165, 142, 216, 238, 163, 99, 251, 41, 191, 164, 206, 85, 239, 64, 133, 41, 49, 120, 235, 120, 226, 96, 224, 105, 68, 81, 186, 184, 65, 233, 129, 211, 231, 211, 135, 15, 88, 35, 20, 217, 95, 56, 215, 134, 71, 210, 28, 43, 22, 231, 69, 134, 116, 227, 161, 202, 94, 54, 222, 132, 158, 108, 45, 73, 68, 240, 90, 59, 139, 222, 118, 6, 82, 162, 198, 143, 7, 233, 148, 233, 232, 101, 135, 182, 71, 148, 136, 246, 168, 5, 28, 94, 11, 10, 78, 147, 4, 200, 36, 79, 244, 117, 223, 114, 33, 2, 206, 13, 66, 204, 201, 102, 147, 237, 83, 83, 17, 221, 16, 136, 206, 115, 141, 32, 149, 131, 136, 183, 96, 51, 31, 212, 174, 245, 120, 18, 120, 191, 174, 90, 111, 122, 136, 96, 152, 81, 8, 72, 52, 33, 46, 227, 241, 41, 77, 40, 176, 97, 189, 195, 197, 202, 71]
java output
[10, -64, 92, 105, 15, 35, -32, -101, 47, 111, -1, -72, 110, 105, -77, -117, 23, 69, 113, -49, -14, -104, 110, 78, 84, -78, 30, 26, 38, -43, 36, 112, 33, -10, -5, -63, -11, 47, -53, -116, -71, 2, -64, -16, 36, 122, 45, 79, 3, 49, -7, 120, -10, 125, 92, 43, -43, -34, 100, 75, -54, -36, 5, 106, -128, 106, -120, 36, 59, -31, -2, 100, 79, 65, -118, -50, -83, 11, -19, -28, -80, -125, -8, 59, -94, -125, 91, -104, -96, -12, 14, 31, -108, 61, 12, 6, 90, -6, -24, -47, -57, 55, -64, -50, 41, 26, -46, -81, -124, 122, 82, -120, 31, 19, 85, -7, -17, 40, -18, -118, -64, 114, -76, -60, 116, -12, -16, 12, -91, 55, -57, -61, 108, 88, -13, 80, -38, 100, 121, -11, -20, -5, -105, 20, 87, 60, -125, 33, -11, 111, -115, -69, 24, 0, -113, -24, 49, 21, -27, 96, 27, 12, 72, 50, 12, 15, -61, -40, -52, -76, -63, 29, -99, 114, 88, 41, 111, 9, 127, 96, -123, 58, 92, -91, 17, 114, -11, -105, -79, -110, -100, -35, 16, 103, 27, -21, -50, 7, -28, 117, 119, -124, -127, -115, -116, 86, 74, 57, -46, 114, 102, -18, -73, 97, 10, -113, 119, -1, -68, -18, -16, -119, 49, -120, 104, 121, 113, -82, -42, -119, -81, 95, -114, 16, -11, -58, 36, -24, 58, -50, 101, -117, -55, -101, -19, 62, -53, 30, -59, 106, 37, 98, 102, 75, -9, 91]
What is the issue in Java code? Thank you.

In the line:
print array.array('B', signature)
you are using the option 'B' for unsigned char according to the docs. If you use the option 'b' (for signed char) like in
print array.array('b', signature)
you will get the same results for both the Java and the python versions.
I performed tests with the sample codes for Python and Java. In the Python example I set the message variable to the same value as in Java:
message = "abcdefg"
and added this line:
self.response.write('Signature Array: {}\n'.format(array.array('b', signature)))
Hope this helps.

Multiple JSONArray to Array or List

I have saved my JSONs in a database and I want to get specific objects from every entry.
I'll show it:
[
{
"Messungen":[
{
"car":"no Car choosed",
"g":0.2,
"time":"[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]",
"max":66,
"secondText":"0 - 200 km\/h",
"speed":"[63, 61, 63, 62, 63, 64, 65, 65, 66, 66, 66, 64, 63, 63]",
"tosecond":"\/",
"to100":"\/",
"way":209,
"avg":63
}
]
},
{
"Messungen":[
{
"car":"no Car choosed",
"g":0.2,
"time":"[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44]",
"max":70,
"secondText":"0 - 200 km\/h",
"speed":"[59, 61, 61, 61, 62, 60, 61, 62, 61, 62, 63, 63, 64, 64, 63, 63, 64, 65, 65, 65, 65, 65, 66, 66, 67, 69, 69, 67, 67, 67, 67, 67, 68, 68, 69, 70, 70, 69, 69, 69, 69, 69, 68, 66, 66]",
"tosecond":"\/",
"to100":"\/",
"way":808,
"avg":65
}
]
}
]
I want to get the way and the car from the Array Messungen as a List or Array.
Is that possible or should I make two new entries in the database with these two types?
Thanks :)

Databases are designed to be good at managing many, many rows. Use the power of the database. Create a table called "Messung" and make each observation (car, g, way, u.s.w) a column in the table.

How to convert body of ADF mobile log output

When I debug my ADF mobile application, I write command tail -f /var/log/system.log in terminal. And I get following output.
May 6 11:32:42 evosys-iMacs-iMac.local manager[507]: Obj-C [CH-1, State=created ableToSend=Yes]: Message arrived - VMMessage [
type: Plain[0x00]
prinorty: 2
channelID: -1
messageID: 3
length: 137
body: {41, 44, 46, 4D, 53, 47, 20, 31, 30, 30, 30, 30, 20, 20, 20, 35, 31,
31, 20, 20, 20, 35, 31, 31, 20, 20, 20, 20, 20, 30, 20, 20, 20, 31,
30, 31, 7B, 22, 72, 65, 73, 75, 6C, 74, 22, 3A, 5B, 5D, 2C, 22, 64,
61, 74, 61, 43, 68, 61, 6E, 67, 65, 45, 76, 65, 6E, 74, 22, 3A, 7B,
22, 76, 61, 72, 69, 61, 62, 6C, 65, 43, 68, 61, 6E, 67, 65, 73, 22,
3A, 7B, 22, 76, 69, 65, 77, 53, 63, 6F, 70, 65, 22, 3A, 7B, 22, 2E,
6E, 75, 6C, 6C, 22, 3A, 74, 72, 75, 65, 7D, 7D, 2C, 22, 70, 72, 6F,
76, 69, 64, 65, 72, 43, 68, 61, 6E, 67, 65, 73, 22, 3A, 7B, 7D, 7D, 7D}
]
I have no idea how to convert body into string,

I am sure a better awk way can do this, but in the interest of a quick answer
egrep -o '[[:xdigit:]]{2}[,}]' system.log | while read foo
do
printf "\x${foo::2}"
done
Yields
ADFMSG 10000 511 511 0 101{"result":[],"dataChangeEvent":
{"variableChanges":{"viewScope":{".null":true}},"providerChanges":{}}}

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