Numen - SIMD optimized math library

Basic Matrix Operations

Matrix Addition

• Reference

int mat2Add(Mat2 *mat1, Mat2 *mat2, Mat2 *mOut);
int mat3Add(Mat3 *mat1, Mat3 *mat2, Mat3 *mOut);
int mat4Add(Mat4 *mat1, Mat4 *mat2, Mat4 *mOut);

• Parameters

  • mat1: First matrix operand
  • mat2: Second matrix operand
  • mOut: A new matrix that is the result of element-wise addition of mat1 and mat2

• Return Value

  • int: Error code

• Example

Mat2 mat1, mat2, result;
mat2Identity(&mat1);
mat2Diagonal(2.0, &mat2);
mat2Add(&mat1, &mat2, &result);

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

\[ \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix} \quad \text{+} \quad \begin{bmatrix} 2 & 0 \ 0 & 2 \end{bmatrix} \quad \text{=} \quad \begin{bmatrix} 3 & 0 \ 0 & 3 \end{bmatrix} \]

Matrix Subtraction

• Reference

int mat2Sub(Mat2 *mat1, Mat2 *mat2, Mat2 *mOut);
int mat3Sub(Mat3 *mat1, Mat3 *mat2, Mat3 *mOut);
int mat4Sub(Mat4 *mat1, Mat4 *mat2, Mat4 *mOut);

• Parameters

  • mat1: First matrix operand (minuend)
  • mat2: Second matrix operand (subtrahend)
  • mOut: A new matrix that is the result of element-wise subtraction of mat2 from mat1

• Return Value

  • int: Error code

• Example

Mat3 mat1, mat2, result;
mat3Diagonal(5.0, &mat1);
mat3Identity(&mat2);
mat3Sub(&mat1, &mat2, &result);

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

\[ \begin{bmatrix} 5 & 0 & 0 \ 0 & 5 & 0 \ 0 & 0 & 5 \end{bmatrix} \quad \text{-} \quad \begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix} \quad \text{=} \quad \begin{bmatrix} 4 & 0 & 0 \ 0 & 4 & 0 \ 0 & 0 & 4 \end{bmatrix} \]

Matrix Scaling

• Reference

int mat2Scale(Mat2 *mat, nml_t s, Mat2 *mOut);
int mat3Scale(Mat3 *mat, nml_t s, Mat3 *mOut);
int mat4Scale(Mat4 *mat, nml_t s, Mat4 *mOut);

• Parameters

  • mat: Matrix to be scaled
  • s: Scalar value
  • mOut: A new matrix with all elements of mat multiplied by scalar s

• Return Value

  • int: Error code

• Example

Mat4 mat, scaled;
mat4Identity(&mat);
mat4Scale(mat, 3.0, &scaled);

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

\[ \text{3.0} \quad \cdot \quad \begin{bmatrix} 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{bmatrix} \quad \text{=} \quad \begin{bmatrix} 3 & 0 & 0 & 0 \ 0 & 3 & 0 & 0 \ 0 & 0 & 3 & 0 \ 0 & 0 & 0 & 3 \end{bmatrix} \]

Matrix negation

• Reference

int mat2Negate(Mat2 *mat, Mat2 *mOut);
int mat3Negate(Mat3 *mat, Mat3 *mOut);
int mat4Negate(Mat4 *mat, Mat4 *mOut);

• Parameters

  • mat: Matrix to negate
  • mOut: A new matrix with the elements negated

• Return Value

  • int: Error code

• Example

nml_t arr[4] = { 1, 3, 2, 4 };
Mat2 mat, result;
mat2Init(arr, &mat);
mat2Negate(&mat, &result);

• Representation \[ \text{-} \text{mat} \quad = \quad \text{result} \]

\[ \text{-} \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \quad \text{=} \quad \begin{bmatrix} -1 & -2 \ -3 & -4 \end{bmatrix} \quad \]