matrix type

[gingerBill]

New type: matrix[R, C]T

Supports:

• multiplication a * b
  • multiplication between matrices and arrays
  • matrix[A, B]T * matrix[B, C]T == matrix[A, C]T
  • matrix[N, M]T * [M]T== matrix[N, 1]T or [N]T
  • [N]T * matrix[N, M]T == matrix[1, M]T or [M]T
• component-wise operations (if the element type supports it)
  • +, -, &, |, ~, &~, <<, >>
  • No support for: /, %, %%
• matrix indexing: m[i, j]
  • Mirrors other type usages: type on the left, usage on the right
• column-major array indexing m[j][i] == m[i, j]
• Element types of integers, floats, complex numbers
  • No support for booleans, quaternions, nor any compound type
• Compound literals, written row-major (to aid reading/writing) but stored column-major (performance):

m := matrix[2, 4]f32{
	1, 3, 5, 7, 
	2, 4, 6, 8,
}

Internal layout:

• Column-major layout: matrix[R, C]T == [C][R]T
• High alignment properties to allow for (SIMD) vectorization
• Zero padding (alignment rules compensation for this)
  • Compromise of third-party libraries over performance benefits
• Limited to a maximum of 16 elements (rows*columns), and a minimum of 1 element

Built-in Procedures (compiler-level)

• tranpose(m)
• outer_product(a, b)
• hadamard_product(m)
• matrix_flatten(m) (converts matrix into a flattened array (array of columns)
• conj(m)

Built-in Procedures (library-level) (for square matrices)

• determinant(m)
• adjugate(m)
• inverse(m)
• inverse_transpose(m)
• hermitian_adjoint(m)
• matrix_trace(m)
• matrix_minor(m)