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use na::{Scalar, Real, DefaultAllocator};

use traits::{Alloc, Dimension, Number};
use aliases::{TMat, TVec};

/// The determinant of the matrix `m`.
pub fn determinant<N: Real, D: Dimension>(m: &TMat<N, D, D>) -> N
    where DefaultAllocator: Alloc<N, D, D> {
    m.determinant()
}

/// The inverse of the matrix `m`.
pub fn inverse<N: Real, D: Dimension>(m: &TMat<N, D, D>) -> TMat<N, D, D>
    where DefaultAllocator: Alloc<N, D, D> {
    m.clone().try_inverse().unwrap_or_else(TMat::<N, D, D>::zeros)
}

/// Component-wise multiplication of two matrices.
pub fn matrix_comp_mult<N: Number, R: Dimension, C: Dimension>(x: &TMat<N, R, C>, y: &TMat<N, R, C>) -> TMat<N, R, C>
    where DefaultAllocator: Alloc<N, R, C> {
    x.component_mul(y)
}

/// Treats the first parameter `c` as a column vector and the second parameter `r` as a row vector and does a linear algebraic matrix multiply `c * r`.
pub fn outer_product<N: Number, R: Dimension, C: Dimension>(c: &TVec<N, R>, r: &TVec<N, C>) -> TMat<N, R, C>
    where DefaultAllocator: Alloc<N, R, C> {
    c * r.transpose()
}

/// The transpose of the matrix `m`.
pub fn transpose<N: Scalar, R: Dimension, C: Dimension>(x: &TMat<N, R, C>) -> TMat<N, C, R>
    where DefaultAllocator: Alloc<N, R, C> {
    x.transpose()
}