mirror of https://github.com/TheAlgorithms/C
Merge pull request #13 from kvedala/documentation/fixes
[feat] LU decomposition
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commit
2d0ddc3a77
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@ -60,11 +60,11 @@ if(USE_OPENMP)
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endif()
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endif()
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add_subdirectory(conversions)
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add_subdirectory(misc)
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add_subdirectory(project_euler)
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add_subdirectory(sorting)
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add_subdirectory(searching)
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add_subdirectory(conversions)
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add_subdirectory(project_euler)
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add_subdirectory(machine_learning)
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add_subdirectory(numerical_methods)
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@ -242,6 +242,7 @@
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* [Gauss Elimination](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/gauss_elimination.c)
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* [Gauss Seidel Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/gauss_seidel_method.c)
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* [Lagrange Theorem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/lagrange_theorem.c)
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* [Lu Decompose](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/lu_decompose.c)
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* [Mean](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/mean.c)
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* [Median](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/median.c)
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* [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)
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i = 0;
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counter++;
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char words[counter][80];
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char **words = (char **)malloc(counter * sizeof(char *));
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/* initalizes words-array with empty strings */
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for (i = 0; i < counter; i++)
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{
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words[i] = (char *)malloc(80 * sizeof(char));
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strcpy(words[i], "");
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}
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@ -83,5 +84,9 @@ char *abbreviate(const char *phrase)
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strcat(acr, words[i]);
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}
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for (i = 0; i < counter; i++)
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free(words[i]);
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free(words);
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return acr;
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}
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}
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@ -0,0 +1,117 @@
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/**
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* \file
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* \brief [LU decomposition](https://en.wikipedia.org/wiki/LU_decompositon) of a
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* square matrix
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* \author [Krishna Vedala](https://github.com/kvedala)
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*/
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#include <stdio.h>
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#include <stdlib.h>
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#include <time.h>
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#ifdef _OPENMP
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#include <omp.h>
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#endif
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/** Perform LU decomposition on matrix
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* \param[in] A matrix to decompose
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* \param[out] L output L matrix
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* \param[out] U output U matrix
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* \param[in] mat_size input square matrix size
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*/
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int lu_decomposition(double **A, double **L, double **U, int mat_size)
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{
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int row, col, j;
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// regularize each row
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for (row = 0; row < mat_size; row++)
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{
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// Upper triangular matrix
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#ifdef _OPENMP
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#pragma omp for
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#endif
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for (col = row; col < mat_size; col++)
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{
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// Summation of L[i,j] * U[j,k]
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double lu_sum = 0.;
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for (j = 0; j < row; j++)
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lu_sum += L[row][j] * U[j][col];
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// Evaluate U[i,k]
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U[row][col] = A[row][col] - lu_sum;
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}
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// Lower triangular matrix
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#ifdef _OPENMP
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#pragma omp for
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#endif
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for (col = row; col < mat_size; col++)
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{
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if (row == col)
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{
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L[row][col] = 1.;
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continue;
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}
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// Summation of L[i,j] * U[j,k]
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double lu_sum = 0.;
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for (j = 0; j < row; j++)
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lu_sum += L[col][j] * U[j][row];
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// Evaluate U[i,k]
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L[col][row] = (A[col][row] - lu_sum) / U[row][row];
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}
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}
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return 0;
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}
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/** Function to display square matrix */
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void display(double **A, int N)
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{
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for (int i = 0; i < N; i++)
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{
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for (int j = 0; j < N; j++)
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{
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printf("% 3.3g \t", A[i][j]);
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}
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putchar('\n');
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}
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}
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/** Main function */
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int main(int argc, char **argv)
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{
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int mat_size = 3; // default matrix size
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const int range = 10;
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const int range2 = range >> 1;
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if (argc == 2)
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mat_size = atoi(argv[1]);
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srand(time(NULL)); // random number initializer
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/* Create a square matrix with random values */
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double **A = (double **)malloc(mat_size * sizeof(double *));
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double **L = (double **)malloc(mat_size * sizeof(double *)); // output
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double **U = (double **)malloc(mat_size * sizeof(double *)); // output
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for (int i = 0; i < mat_size; i++)
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{
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// calloc so that all valeus are '0' by default
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A[i] = (double *)calloc(mat_size, sizeof(double));
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L[i] = (double *)calloc(mat_size, sizeof(double));
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U[i] = (double *)calloc(mat_size, sizeof(double));
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for (int j = 0; j < mat_size; j++)
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/* create random values in the limits [-range2, range-1] */
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A[i][j] = (double)(rand() % range - range2);
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}
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lu_decomposition(A, L, U, mat_size);
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printf("A = \n");
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display(A, mat_size);
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printf("\nL = \n");
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display(L, mat_size);
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printf("\nU = \n");
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display(U, mat_size);
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return 0;
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}
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@ -19,6 +19,6 @@ foreach( testsourcefile ${APP_SOURCES} )
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if(MATH_LIBRARY)
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target_link_libraries(${testname} ${MATH_LIBRARY})
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endif()
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install(TARGETS ${testname} DESTINATION "bin/misc")
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install(TARGETS ${testname} DESTINATION "bin/project_euler")
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endforeach( testsourcefile ${APP_SOURCES} )
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@ -26,10 +26,9 @@ long MAX_N = 28123; /**< Limit of numbers to check */
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char *abundant_flags = NULL;
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/**
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* Returns:
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* -1 if N is deficient
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* 1 if N is abundant
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* 0 if N is perfect
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* \returns -1 if N is deficient
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* \returns 1 if N is abundant
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* \returns 0 if N is perfect
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**/
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char get_perfect_number(unsigned long N)
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{
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