Merge pull request #13 from kvedala/documentation/fixes

[feat] LU decomposition

CMakeLists.txt

@@ -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)
 

DIRECTORY.md

@@ -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)

exercism/acronym/acronym.c

@@ -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;
 }

numerical_methods/lu_decompose.c

@@ -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;
+}

project_euler/CMakeLists.txt

@@ -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} )

project_euler/problem_23/sol2.c

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