Vec/Matrix linear algebra code things
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14
linalg/Makefile
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14
linalg/Makefile
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CC = gcc
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CFLAGS = -Wall -O2
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TARGET = main
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SRC = main.c
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#LDFLAGS =
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$(TARGET): $(SRC)
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@echo CC $@
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@$(CC) $(CFLAGS) -o $@ $^ $(LDFLAGS)
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clean:
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rm -f $(TARGET)
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BIN
linalg/main
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BIN
linalg/main
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238
linalg/main.c
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238
linalg/main.c
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#include <assert.h>
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#include <math.h>
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#include <stdbool.h>
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#include <stdio.h>
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/**
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* @brief A 2×2 matrix stored in row-major order.
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*
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* The elements are laid out as:
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* [ arr[0] arr[1] ]
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* [ arr[2] arr[3] ]
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*/
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typedef struct Mat2 {
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float arr[4];
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} Mat2;
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/**
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* @brief A 3×3 matrix stored in row-major order.
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*
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* The elements are laid out as:
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* [ arr[0] arr[1] arr[2] ]
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* [ arr[3] arr[4] arr[5] ]
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* [ arr[6] arr[7] arr[8] ]
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*/
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typedef struct Mat3 {
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float arr[9];
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} Mat3;
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/**
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* @brief A 2D vector with x and y components.
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*/
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typedef struct Vec2 {
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float x, y;
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} Vec2;
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/**
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* @brief A 3D vector with x, y, and z components.
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*/
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typedef struct Vec3 {
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float x, y, z;
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} Vec3;
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/**
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* @brief Computes the dot product of two 3D vectors.
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*
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* @param a Pointer to the first vector.
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* @param b Pointer to the second vector.
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* @return The dot product (a • b).
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*/
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inline float vec3_dot(const Vec3 *a, const Vec3 *b);
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/**
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* @brief Computes the cross product of two 3D vectors.
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*
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* @param a Pointer to the first vector.
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* @param b Pointer to the second vector.
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* @return The cross product vector (a × b).
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*/
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Vec3 vec3_cross(const Vec3 *a, const Vec3 *b);
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/**
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* @brief Computes the determinant of a 2×2 matrix.
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*
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* @param m Pointer to the matrix.
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* @return The determinant of the matrix.
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*/
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float mat2_det(const Mat2 *m);
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/**
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* @brief Computes the determinant of a 3×3 matrix (row-major order).
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*
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* @param m Pointer to the matrix.
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* @return The determinant of the matrix.
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*/
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float mat3_det2(const Mat3 *m);
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/**
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* @brief Multiplies two 2×2 matrices (row-major order).
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*
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* @param m1 Pointer to the first matrix.
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* @param m2 Pointer to the second matrix.
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* @return The resulting matrix product (m1 × m2).
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*/
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Mat2 mat2_mul(const Mat2 *m1, const Mat2 *m2);
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/**
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* @brief Multiplies two 3×3 matrices (row-major order).
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*
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* @param m1 Pointer to the first matrix.
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* @param m2 Pointer to the second matrix.
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* @return The resulting matrix product (m1 × m2).
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*/
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Mat3 mat3_mul(const Mat3 *m1, const Mat3 *m2);
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/**
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* @brief Checks if two 2×2 matrices are approximately equal.
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*
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* @param a Pointer to the first matrix.
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* @param b Pointer to the second matrix.
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* @param epsilon Tolerance for comparison.
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* @return true if all elements are approximately equal within epsilon.
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*/
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bool mat2_approx_eq(const Mat2 *a, const Mat2 *b, float epsilon);
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/**
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* @brief Checks if two 3×3 matrices are approximately equal.
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*
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* @param a Pointer to the first matrix.
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* @param b Pointer to the second matrix.
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* @param epsilon Tolerance for comparison.
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* @return true if all elements are approximately equal within epsilon.
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*/
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bool mat3_approx_eq(const Mat3 *a, const Mat3 *b, float epsilon);
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#define MAT2_AT(m, row, col) ((m)->arr[(col) * 2 + (row)])
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#define MAT3_AT(m, row, col) ((m)->arr[(col) * 3 + (row)])
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/* Header end... */
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float mat3_det(const Mat3 *m) {
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float m00 = MAT3_AT(m, 0, 0);
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float m01 = MAT3_AT(m, 0, 1);
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float m02 = MAT3_AT(m, 0, 2);
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float m10 = MAT3_AT(m, 1, 0);
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float m11 = MAT3_AT(m, 1, 1);
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float m12 = MAT3_AT(m, 1, 2);
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float m20 = MAT3_AT(m, 2, 0);
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float m21 = MAT3_AT(m, 2, 1);
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float m22 = MAT3_AT(m, 2, 2);
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return m00 * (m11 * m22 - m12 * m21) - m01 * (m10 * m22 - m12 * m20) +
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m02 * (m10 * m21 - m11 * m20);
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}
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inline float vec3_dot(const struct Vec3 *a, const struct Vec3 *b) {
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return a->x * b->x + a->y * b->y + a->z * b->z;
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}
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struct Vec3 vec3_cross(const struct Vec3 *a, const struct Vec3 *b) {
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struct Vec3 res = {.x = a->y * b->z - a->z * b->y,
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.y = a->x * b->z - a->z * b->x,
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.z = a->x * b->y - a->y * b->x};
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return res;
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}
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Mat2 mat2_mul(const Mat2 *m1, const Mat2 *m2) {
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Mat2 m3 = {.arr = {
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MAT2_AT(m1, 0, 0) * MAT2_AT(m2, 0, 0) +
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MAT2_AT(m1, 0, 1) * MAT2_AT(m2, 1, 0),
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MAT2_AT(m1, 1, 0) * MAT2_AT(m2, 0, 0) +
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MAT2_AT(m1, 1, 1) * MAT2_AT(m2, 1, 0),
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MAT2_AT(m1, 0, 0) * MAT2_AT(m2, 0, 1) +
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MAT2_AT(m1, 0, 1) * MAT2_AT(m2, 1, 1),
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MAT2_AT(m1, 1, 0) * MAT2_AT(m2, 0, 1) +
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MAT2_AT(m1, 1, 1) * MAT2_AT(m2, 1, 1),
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}};
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return m3;
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}
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Mat3 mat3_mul(const Mat3 *m1, const Mat3 *m2) {
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Mat3 m3;
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for (int col = 0; col < 3; ++col) {
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for (int row = 0; row < 3; ++row) {
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float sum = 0.0f;
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for (int k = 0; k < 3; ++k) {
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sum += MAT3_AT(m1, row, k) * MAT3_AT(m2, k, col);
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}
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m3.arr[col * 3 + row] = sum;
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}
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}
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return m3;
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}
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void mat3_print(const Mat3 *m) {
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for (int row = 0; row < 3; ++row) {
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printf("| ");
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for (int col = 0; col < 3; ++col) {
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printf("%8.3f ", MAT3_AT(m, row, col));
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}
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printf("|\n");
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}
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}
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bool mat2_approx_eq(const Mat2 *a, const Mat2 *b, float epsilon) {
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for (int i = 0; i < 4; ++i) {
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if (fabsf(a->arr[i] - b->arr[i]) > epsilon)
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return false;
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}
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return true;
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}
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bool mat3_approx_eq(const Mat3 *a, const Mat3 *b, float epsilon) {
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for (int i = 0; i < 9; ++i) {
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if (fabsf(a->arr[i] - b->arr[i]) > epsilon)
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return false;
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}
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return true;
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}
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/* Implem end */
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int main(void) {
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{
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Mat3 m = {{1, 0, 0, 0, 1, 0, 0, 0, 1}};
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Mat3 m3 = mat3_mul(&m, &m);
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assert(mat3_approx_eq(&m3, &m, 0.01));
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}
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{
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Mat3 m = {{1, 0, 0, 0, 1, 0, 0, 0, 1}};
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float d = mat3_det(&m);
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printf("Determinant: %f\n", d);
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MAT3_AT(&m, 0, 0) = 2;
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d = mat3_det(&m);
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printf("Determinant: %f\n", d);
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}
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{
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struct Vec3 a = {10, 10, 10};
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struct Vec3 b = {5, 5, 5};
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struct Vec3 c = vec3_cross(&a, &b);
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printf("{ Vec3: %f, %f, %f }\n", c.x, c.y, c.z);
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}
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{
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struct Vec3 a = {0, 1, 0};
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struct Vec3 b = {0, 0, 1};
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struct Vec3 c = vec3_cross(&a, &b);
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printf("{ Vec3: %f, %f, %f }\n", c.x, c.y, c.z);
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}
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return 0;
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}
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