Merge pull request #13 from kvedala/documentation/fixes

[feat] LU decomposition
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Krishna Vedala 2020-06-07 15:24:51 -04:00 committed by GitHub
commit 2d0ddc3a77
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6 changed files with 131 additions and 9 deletions

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@ -60,11 +60,11 @@ if(USE_OPENMP)
endif()
endif()
add_subdirectory(conversions)
add_subdirectory(misc)
add_subdirectory(project_euler)
add_subdirectory(sorting)
add_subdirectory(searching)
add_subdirectory(conversions)
add_subdirectory(project_euler)
add_subdirectory(machine_learning)
add_subdirectory(numerical_methods)

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@ -242,6 +242,7 @@
* [Gauss Elimination](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/gauss_elimination.c)
* [Gauss Seidel Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/gauss_seidel_method.c)
* [Lagrange Theorem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/lagrange_theorem.c)
* [Lu Decompose](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/lu_decompose.c)
* [Mean](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/mean.c)
* [Median](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/median.c)
* [Newton Raphson Root](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/newton_raphson_root.c)

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@ -38,11 +38,12 @@ char *abbreviate(const char *phrase)
i = 0;
counter++;
char words[counter][80];
char **words = (char **)malloc(counter * sizeof(char *));
/* initalizes words-array with empty strings */
for (i = 0; i < counter; i++)
{
words[i] = (char *)malloc(80 * sizeof(char));
strcpy(words[i], "");
}
@ -83,5 +84,9 @@ char *abbreviate(const char *phrase)
strcat(acr, words[i]);
}
for (i = 0; i < counter; i++)
free(words[i]);
free(words);
return acr;
}
}

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@ -0,0 +1,117 @@
/**
* \file
* \brief [LU decomposition](https://en.wikipedia.org/wiki/LU_decompositon) of a
* square matrix
* \author [Krishna Vedala](https://github.com/kvedala)
*/
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#ifdef _OPENMP
#include <omp.h>
#endif
/** Perform LU decomposition on matrix
* \param[in] A matrix to decompose
* \param[out] L output L matrix
* \param[out] U output U matrix
* \param[in] mat_size input square matrix size
*/
int lu_decomposition(double **A, double **L, double **U, int mat_size)
{
int row, col, j;
// regularize each row
for (row = 0; row < mat_size; row++)
{
// Upper triangular matrix
#ifdef _OPENMP
#pragma omp for
#endif
for (col = row; col < mat_size; col++)
{
// Summation of L[i,j] * U[j,k]
double lu_sum = 0.;
for (j = 0; j < row; j++)
lu_sum += L[row][j] * U[j][col];
// Evaluate U[i,k]
U[row][col] = A[row][col] - lu_sum;
}
// Lower triangular matrix
#ifdef _OPENMP
#pragma omp for
#endif
for (col = row; col < mat_size; col++)
{
if (row == col)
{
L[row][col] = 1.;
continue;
}
// Summation of L[i,j] * U[j,k]
double lu_sum = 0.;
for (j = 0; j < row; j++)
lu_sum += L[col][j] * U[j][row];
// Evaluate U[i,k]
L[col][row] = (A[col][row] - lu_sum) / U[row][row];
}
}
return 0;
}
/** Function to display square matrix */
void display(double **A, int N)
{
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
printf("% 3.3g \t", A[i][j]);
}
putchar('\n');
}
}
/** Main function */
int main(int argc, char **argv)
{
int mat_size = 3; // default matrix size
const int range = 10;
const int range2 = range >> 1;
if (argc == 2)
mat_size = atoi(argv[1]);
srand(time(NULL)); // random number initializer
/* Create a square matrix with random values */
double **A = (double **)malloc(mat_size * sizeof(double *));
double **L = (double **)malloc(mat_size * sizeof(double *)); // output
double **U = (double **)malloc(mat_size * sizeof(double *)); // output
for (int i = 0; i < mat_size; i++)
{
// calloc so that all valeus are '0' by default
A[i] = (double *)calloc(mat_size, sizeof(double));
L[i] = (double *)calloc(mat_size, sizeof(double));
U[i] = (double *)calloc(mat_size, sizeof(double));
for (int j = 0; j < mat_size; j++)
/* create random values in the limits [-range2, range-1] */
A[i][j] = (double)(rand() % range - range2);
}
lu_decomposition(A, L, U, mat_size);
printf("A = \n");
display(A, mat_size);
printf("\nL = \n");
display(L, mat_size);
printf("\nU = \n");
display(U, mat_size);
return 0;
}

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@ -19,6 +19,6 @@ foreach( testsourcefile ${APP_SOURCES} )
if(MATH_LIBRARY)
target_link_libraries(${testname} ${MATH_LIBRARY})
endif()
install(TARGETS ${testname} DESTINATION "bin/misc")
install(TARGETS ${testname} DESTINATION "bin/project_euler")
endforeach( testsourcefile ${APP_SOURCES} )

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@ -26,10 +26,9 @@ long MAX_N = 28123; /**< Limit of numbers to check */
char *abundant_flags = NULL;
/**
* Returns:
* -1 if N is deficient
* 1 if N is abundant
* 0 if N is perfect
* \returns -1 if N is deficient
* \returns 1 if N is abundant
* \returns 0 if N is perfect
**/
char get_perfect_number(unsigned long N)
{