Trait totsu_core::solver::LinAlg

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pub trait LinAlg {
    type F: Float;
    type Sl: SliceLike<F = Self::F> + ?Sized;

    fn norm(x: &Self::Sl) -> Self::F;
    fn copy(x: &Self::Sl, y: &mut Self::Sl);
    fn scale(alpha: Self::F, x: &mut Self::Sl);
    fn add(alpha: Self::F, x: &Self::Sl, y: &mut Self::Sl);
    fn adds(s: Self::F, y: &mut Self::Sl);
    fn abssum(x: &Self::Sl, incx: usize) -> Self::F;
    fn transform_di(
        alpha: Self::F,
        mat: &Self::Sl,
        x: &Self::Sl,
        beta: Self::F,
        y: &mut Self::Sl
    );
}

Expand description

Linear algebra trait.

Required Associated Types§

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type F: Float

Floating point data type used as scalars.

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type Sl: SliceLike<F = Self::F> + ?Sized

Data type of slice of F used as vectors.

Required Methods§

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fn norm(x: &Self::Sl) -> Self::F

Calculates 2-norm (or euclidean norm) \(\|x\|_2=\sqrt{\sum_i x_i^2}\).

Returns the calculated norm.

x is a vector \(x\).

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fn copy(x: &Self::Sl, y: &mut Self::Sl)

Copies from a vector to another vector.

x is a slice to copy.
y is a slice being copied to. x and y shall have the same length.

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fn scale(alpha: Self::F, x: &mut Self::Sl)

Calculates \(\alpha x\).

alpha is a scalar \(\alpha\).
x is a vector \(x\) before entry, \(\alpha x\) on exit.

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fn add(alpha: Self::F, x: &Self::Sl, y: &mut Self::Sl)

Calculates \(\alpha x + y\).

alpha is a scalar \(\alpha\).
x is a vector \(x\).
y is a vector \(y\) before entry, \(\alpha x + y\) on exit. x and y shall have the same length.

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fn adds(s: Self::F, y: &mut Self::Sl)

Calculates \(s\mathbb{1} + y\).

s is a scalar \(s\).
y is a vector \(y\) before entry, \(s\mathbb{1} + y\) on exit.

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fn abssum(x: &Self::Sl, incx: usize) -> Self::F

Calculates 1-norm (or sum of absolute values) \(\|x\|_1=\sum_i |x_i|\).

Returns the calculated norm.

x is a vector \(x\).
incx is spacing between elements of x

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fn transform_di(
    alpha: Self::F,
    mat: &Self::Sl,
    x: &Self::Sl,
    beta: Self::F,
    y: &mut Self::Sl
)

Calculates \(\alpha D x + \beta y\), where \(D={\bf diag}(d)\) is a diagonal matrix.

alpha is a scalar \(\alpha\).
mat is a diagonal vector \(d\) of \(D\).
x is a vector \(x\).
beta is a scalar \(\beta\).
y is a vector \(y\) before entry, \(\alpha D x + \beta y\) on exit. mat, x and y shall have the same length.