InitHEADmain

3 files changed, 182 insertions, 0 deletions

diff --git a/Homework/math4610/inc/lizfcm.h b/Homework/math4610/inc/lizfcm.h
new file mode 100644
index 0000000..1dcdb6b
--- /dev/null
+++ b/Homework/math4610/inc/lizfcm.h
@@ -0,0 +1,100 @@
+#include "macros.h"
+#include "types.h"
+
+#ifndef LIZFCM_H
+#define LIZFCM_H
+
+extern float smaceps();
+extern double dmaceps();
+
+extern double central_derivative_at(double (*f)(double), double a, double h);
+extern double forward_derivative_at(double (*f)(double), double a, double h);
+extern double backward_derivative_at(double (*f)(double), double a, double h);
+
+extern double sum_v(Array_double *v);
+extern Array_double *scale_v(Array_double *v1, double m);
+extern Array_double *add_v(Array_double *v1, Array_double *v2);
+extern Array_double *minus_v(Array_double *v1, Array_double *v2);
+extern double v_dot_v(Array_double *v1, Array_double *v2);
+extern double l2_norm(Array_double *v);
+extern double l1_norm(Array_double *v);
+extern double linf_norm(Array_double *v);
+extern double vector_distance(Array_double *v1, Array_double *v2,
+                              double (*norm)(Array_double *));
+extern double l2_distance(Array_double *v1, Array_double *v2);
+extern double l1_distance(Array_double *v1, Array_double *v2);
+extern double linf_distance(Array_double *v1, Array_double *v2);
+extern Array_double *copy_vector(Array_double *v1);
+extern Array_double *add_element(Array_double *v, double x);
+extern Array_double *slice_element(Array_double *v, size_t x);
+extern void free_vector(Array_double *v);
+extern void format_vector_into(Array_double *v, char *s);
+extern int vector_equal(Array_double *a, Array_double *b);
+
+extern Matrix_double *put_identity_diagonal(Matrix_double *m);
+extern Matrix_double **lu_decomp(Matrix_double *m);
+extern Array_double *bsubst(Matrix_double *u, Array_double *b);
+extern Array_double *fsubst(Matrix_double *l, Array_double *b);
+extern Array_double *solve_matrix_lu_bsubst(Matrix_double *m, Array_double *b);
+extern Matrix_double *gaussian_elimination(Matrix_double *m);
+extern Array_double *solve_matrix_gaussian(Matrix_double *m, Array_double *b);
+extern Array_double *m_dot_v(Matrix_double *m, Array_double *v);
+extern Matrix_double *m_dot_m(Matrix_double *a, Matrix_double *b);
+extern Matrix_double *transpose(Matrix_double *m);
+extern Array_double *col_v(Matrix_double *m, size_t x);
+extern Matrix_double *copy_matrix(Matrix_double *m);
+extern Matrix_double *add_column(Matrix_double *m, Array_double *col);
+extern Matrix_double *slice_column(Matrix_double *m, size_t col);
+extern void free_matrix(Matrix_double *m);
+extern void format_matrix_into(Matrix_double *m, char *s);
+extern int matrix_equal(Matrix_double *a, Matrix_double *b);
+
+extern Line *least_squares_lin_reg(Array_double *x, Array_double *y);
+
+extern Array_double *find_ivt_range(double (*f)(double), double start_x,
+                                    double delta, size_t max_steps);
+extern Array_double *bisect_find_root(double (*f)(double), double a, double b,
+                                      double tolerance, size_t max_iterations);
+extern double bisect_find_root_with_error_assumption(double (*f)(double),
+                                                     double a, double b,
+                                                     double tolerance);
+extern double fixed_point_iteration_method(double (*f)(double),
+                                           double (*g)(double), double x_0,
+                                           double tolerance,
+                                           size_t max_iterations);
+extern double fixed_point_newton_method(double (*f)(double),
+                                        double (*fprime)(double), double x_0,
+                                        double tolerance,
+                                        size_t max_iterations);
+extern double fixed_point_secant_method(double (*f)(double), double x_0,
+                                        double x_1, double tolerance,
+                                        size_t max_iterations);
+extern double fixed_point_secant_bisection_method(double (*f)(double),
+                                                  double x_0, double x_1,
+                                                  double tolerance,
+                                                  size_t max_iterations);
+
+extern double dominant_eigenvalue(Matrix_double *m, Array_double *v,
+                                  double tolerance, size_t max_iterations);
+extern double shift_inverse_power_eigenvalue(Matrix_double *m, Array_double *v,
+                                             double shift, double tolerance,
+                                             size_t max_iterations);
+extern double least_dominant_eigenvalue(Matrix_double *m, Array_double *v,
+                                        double tolerance,
+                                        size_t max_iterations);
+extern Array_double *partition_find_eigenvalues(Matrix_double *m,
+                                                Matrix_double *guesses,
+                                                double tolerance,
+                                                size_t max_iterations);
+extern Matrix_double *leslie_matrix(Array_double *age_class_surivor_ratio,
+                                    Array_double *age_class_offspring);
+
+extern double rand_from(double min, double max);
+
+extern Array_double *jacobi_solve(Matrix_double *m, Array_double *b,
+                                  double tolerance, size_t max_iterations);
+extern Array_double *gauss_siedel_solve(Matrix_double *m, Array_double *b,
+                                        double l2_convergence_tolerance,
+                                        size_t max_iterations);
+
+#endif // LIZFCM_H
diff --git a/Homework/math4610/inc/macros.h b/Homework/math4610/inc/macros.h
new file mode 100644
index 0000000..d081869
--- /dev/null
+++ b/Homework/math4610/inc/macros.h
@@ -0,0 +1,58 @@
+#include <stddef.h>
+#include <stdlib.h>
+#include <string.h>
+
+#ifndef MACROS_H
+#define MACROS_H
+
+#define DEFINE_ARRAY(TYPE)                                                     \
+  typedef struct {                                                             \
+    TYPE *data;                                                                \
+    size_t size;                                                               \
+  } Array_##TYPE
+
+#define DEFINE_MATRIX(TYPE)                                                    \
+  typedef struct {                                                             \
+    Array_##TYPE **data;                                                       \
+    size_t cols;                                                               \
+    size_t rows;                                                               \
+  } Matrix_##TYPE
+
+#define InitArray(TYPE, ...)                                                   \
+  ({                                                                           \
+    TYPE temp[] = __VA_ARGS__;                                                 \
+    Array_##TYPE *arr = malloc(sizeof(Array_##TYPE));                          \
+    arr->size = sizeof(temp) / sizeof(temp[0]);                                \
+    arr->data = malloc(arr->size * sizeof(TYPE));                              \
+    memcpy(arr->data, temp, arr->size * sizeof(TYPE));                         \
+    arr;                                                                       \
+  })
+
+#define InitArrayWithSize(TYPE, SIZE, INIT_VALUE)                              \
+  ({                                                                           \
+    Array_##TYPE *arr = malloc(sizeof(Array_##TYPE));                          \
+    arr->size = SIZE;                                                          \
+    arr->data = malloc(arr->size * sizeof(TYPE));                              \
+    for (size_t i = 0; i < arr->size; i++)                                     \
+      arr->data[i] = INIT_VALUE;                                               \
+    arr;                                                                       \
+  })
+
+#define InitMatrixWithSize(TYPE, ROWS, COLS, INIT_VALUE)                       \
+  ({                                                                           \
+    Matrix_##TYPE *matrix = malloc(sizeof(Matrix_##TYPE));                     \
+    matrix->rows = ROWS;                                                       \
+    matrix->cols = COLS;                                                       \
+    matrix->data = malloc(matrix->rows * sizeof(Array_##TYPE *));              \
+    for (size_t y = 0; y < matrix->rows; y++)                                  \
+      matrix->data[y] = InitArrayWithSize(TYPE, COLS, INIT_VALUE);             \
+    matrix;                                                                    \
+  })
+
+#define c_max(x, y) (((x) >= (y)) ? (x) : (y))
+#define c_min(x, y) (((x) <= (y)) ? (x) : (y))
+
+#define true 1
+#define false 0
+
+#endif // MACROS_H
diff --git a/Homework/math4610/inc/types.h b/Homework/math4610/inc/types.h
new file mode 100644
index 0000000..95ab96d
--- /dev/null
+++ b/Homework/math4610/inc/types.h
@@ -0,0 +1,24 @@
+#include "macros.h"
+#include <stdint.h>
+
+#ifndef TYPES_H
+#define TYPES_H
+
+DEFINE_ARRAY(int);
+DEFINE_ARRAY(uint32_t);
+DEFINE_ARRAY(int32_t);
+DEFINE_ARRAY(float);
+DEFINE_ARRAY(double);
+
+DEFINE_MATRIX(int);
+DEFINE_MATRIX(uint32_t);
+DEFINE_MATRIX(int32_t);
+DEFINE_MATRIX(float);
+DEFINE_MATRIX(double);
+
+typedef struct Line {
+  double m;
+  double a;
+} Line;
+
+#endif // TYPES_H