Numen - SIMD optimized math library

Matrix Multiplication

Hadamard Matrix

• Reference

int mat2Hadamard(Mat2 *mat1, Mat2 *mat2, Mat2 *mOut);
int mat3Hadamard(Mat3 *mat1, Mat3 *mat2, Mat3 *mOut);
int mat4Hadamard(Mat4 *mat1, Mat4 *mat2, Mat4 *mOut);

• Parameters

  • mat1: First Matrix Operand
  • mat2: Second Matrix Operand
  • mOut: A new matrix that is the result of Hadamard Product

• Return Value

  • int: Error code

• Example

nml_t arr1[9] = {1.0, 4.0, 7.0,
                 2.0, 5.0, 8.0,
                 3.0, 6.0, 9.0};
nml_t arr2[9] = {9.0, 6.0, 3.0,
                 8.0, 5.0, 2.0,
                 7.0, 4.0, 1.0};
nml_t expected[9] = {9.0, 24.0, 21.0,
                     16.0, 25.0, 16.0,
                     21.0, 24.0, 9.0};
Mat mat2, mat2, result;
mat2Init(arr, &A);
mat2Init(arr, &B);
mat2Hadamard(&A, &B, &result);

• Representation \[ \text{mat1}\odot\text{mat2}=\text{result} \]

\[ \begin{bmatrix} 1.0 & 4.0 & 7.0 \ 2.0 & 5.0 & 8.0 \ 3.0 & 6.0 & 9.0 \end{bmatrix} \quad \odot \quad \begin{bmatrix} 9.0 & 6.0 & 3.0 \ 8.0 & 5.0 & 2.0 \ 7.0 & 4.0 & 1.0 \end{bmatrix} \quad \text{=} \quad \begin{bmatrix} 9.0 & 24.0 & 21.0 \ 16.0 & 25.0 & 16.0 \ 21.0 & 24.0 & 9.0 \end{bmatrix} \quad \]

Matrix-Vector Multiplication

• Reference

int mat2MulMat2(Mat2 *mat, Vec2 *vec, Vec2 *vOut);
int mat3MulMat3(Mat3 *mat, Vec3 *vec, Vec3 *vOut);
int mat4MulMat4(Mat4 *mat, Vec4 *vec, Vec4 *vOut);

• Parameters

  • mat : Matrix Operand
  • vec : Vector Operand
  • vOut: A new vector that is the result of Matrix-Vector Multiplication

• Return Value

  • int: Error code

• Example

nml_t mat_arr[9] = {1.0, 4.0, 7.0,
                    2.0, 5.0, 8.0,
                    3.0, 6.0, 9.0};

Mat3 mat;
Vec3 vec, result;
mat3Init(mat_arr, &mat);
vec3Init(2.0, 3.0, 4.0, &vec);
mat3MulVec3(&mat, &vec, &result);

• Representation \[ \text{mat}\cdot\text{vec}=\text{result} \]

\[ \begin{bmatrix} 1.0 & 4.0 & 7.0 \ 2.0 & 5.0 & 8.0 \ 3.0 & 6.0 & 9.0 \end{bmatrix} \quad \text{x} \quad \begin{pmatrix} 2.0 \ 3 0 \ 4.0 \ \end{pmatrix} \quad \text{=} \quad \begin{pmatrix} 20.0 \ 47.0 \ 74.0 \end{pmatrix} \quad \]

Matrix-Matrix Multiplication

• Reference

int mat2MulMat2(Mat2 *mat1, Mat2 *mat2, Mat2 *mOut);
int mat3MulMat3(Mat3 *mat1, Mat3 *mat2, Mat3 *mOut);
int mat4MulMat4(Mat4 *mat1, Mat4 *mat2, Mat4 *mOut);

• Parameters

  • mat1: First Matrix Operand
  • mat2: Second Matrix Operand
  • mOut: A new matrix that is the result of Matrix-Matrix Multiplication

• Return Value

  • int: Error code

• Example

nml_t arr1[4] = {1.0, 3.0,
                 2.0, 4.0};
nml_t arr2[4] = {4.0, 2.0,
                 3.0, 1.0};
Mat mat1, mat2, result;
mat2Init(arr, &mat1);
mat2Init(arr, &mat2);
mat2Hadamard(&mat1, &mat2, &result);

• Representation \[ \text{mat}\cdot\text{vec}=\text{result} \]

\[ \begin{bmatrix} 1.0 & 3.0 \ 2.0 & 4.0 \end{bmatrix} \quad \text{+} \quad \begin{bmatrix} 4.0 & 2.0 \ 3.0 & 1.0 \end{bmatrix} \quad \text{=} \quad \begin{bmatrix} 8.0 & 20.0 \ 5.0 & 13.0 \end{bmatrix} \quad \]