Struct num_dual::StaticMat[−][src]

pub struct StaticMat<T, const M: usize, const N: usize>(_);
Expand description

A statically allocated MxN matrix. The struct is used in the vector (hyper) dual numbers and provides utilities for the calculation of Jacobians.

Implementations

Derive a vector of dual numbers.

let v = StaticVec::new_vec([4.0, 3.0]).map(DualVec64::<2>::from_re).derive();
let n = (v[0].powi(2) + v[1].powi(2)).sqrt();
assert_eq!(n.re, 5.0);
assert_relative_eq!(n.eps[0], 0.8);
assert_relative_eq!(n.eps[1], 0.6);

Extract the Jacobian from a vector of Dual numbers.

let xy = StaticVec::new_vec([5.0, 3.0]).map(DualVec64::<2>::from).derive();
let j = StaticVec::new_vec([xy[0] * xy[1].powi(3), xy[0].powi(2) * xy[1]]).jacobian();
assert_eq!(j[(0,0)], 27.0);     // y³
assert_eq!(j[(0,1)], 135.0);    // 3xy²
assert_eq!(j[(1,0)], 30.0);     // 2xy
assert_eq!(j[(1,1)], 25.0);     // x²

Derive a vector of second order dual numbers.

let v = StaticVec::new_vec([4.0, 3.0]).map(Dual2Vec64::<2>::from_re).derive();
let n = (v[0].powi(2) + v[1].powi(2)).sqrt();
assert_eq!(n.re, 5.0);
assert_relative_eq!(n.v1[0], 0.8);
assert_relative_eq!(n.v1[1], 0.6);
assert_relative_eq!(n.v2[(0,0)], 0.072);
assert_relative_eq!(n.v2[(0,1)], -0.096);
assert_relative_eq!(n.v2[(1,0)], -0.096);
assert_relative_eq!(n.v2[(1,1)], 0.128);

Derive a vector of hyper dual numbers w.r.t. to the first set of variables.

Derive a vector of hyper dual numbers w.r.t. to the second set of variables.

let x = HyperDualVec64::<1, 2>::from_re(2.0).derive1();
let v = StaticVec::new_vec([2.0, 3.0]).map(HyperDualVec64::<1, 2>::from_re).derive2();
let n = (x.powi(2)*v[0].powi(2) + v[1].powi(2)).sqrt();
assert_eq!(n.re, 5.0);
assert_relative_eq!(n.eps1[0], 1.6);
assert_relative_eq!(n.eps2[0], 1.6);
assert_relative_eq!(n.eps2[1], 0.6);
assert_relative_eq!(n.eps1eps2[(0,0)], 1.088);
assert_relative_eq!(n.eps1eps2[(0,1)], -0.192);

Create a new StaticMat from an array of arrays.

Return a reference to the raw data in the StaticMat.

Create a new StaticVec from an array.

Return a reference to the raw data in the StaticVec.

Create a NxN unity matrix.

sum over all elements in the vector.

Calculate the Euclidian norm of the vector

Apply a function elementwise to all elements of the matrix and return a new matrix with the results.

Apply a function elementwise to all elements of the matrix and a second matrix. Return a new matrix with the results.

Iterate over all matrix elements.

Perform a matrix-matrix multiplication.

use num_dual::StaticMat;
let a = StaticMat::new([[1, 2], [3, 4]]);
let b = StaticMat::new([[2, 1], [4, 3]]);
let x = a.matmul(&b);
assert_eq!(x[(0,0)], 10);
assert_eq!(x[(0,1)], 7);
assert_eq!(x[(1,0)], 22);
assert_eq!(x[(1,1)], 15);

Perform a matrix-matrix multiplication in which the first matrix is transposed.

use num_dual::StaticVec;
let a = StaticVec::new_vec([1, 2]);
let b = StaticVec::new_vec([2, 1]);
let x = a.transpose_matmul(&b);
assert_eq!(x[(0,0)], 2);
assert_eq!(x[(0,1)], 1);
assert_eq!(x[(1,0)], 4);
assert_eq!(x[(1,1)], 2);

Perform a matrix-matrix multiplication in which the second matrix is transposed.

use num_dual::{StaticMat, StaticVec};
let a = StaticMat::new([[1, 2], [3, 4]]);
let b = StaticVec::new_vec([2, 1]);
let x = a.matmul_transpose(&b);
assert_eq!(x[(0, 0)], 4);
assert_eq!(x[(1, 0)], 10);

Transpose the matrix.

Return a new vector containing the first M elements of self.

Return a new vector containing the last M elements of self.

Calculate the dot product of two vectors.

use num_dual::StaticVec;
let a = StaticVec::new_vec([1, 2, 3, 4]);
let b = StaticVec::new_vec([2, 1, 4, 3]);
assert_eq!(a.dot(&b), 28);

multiply each matrix element with f in place.

Trait Implementations

The resulting type after applying the + operator.

Performs the + operation. Read more

The resulting type after applying the + operator.

Performs the + operation. Read more

Performs the += operation. Read more

Performs the += operation. Read more

Returns a copy of the value. Read more

Performs copy-assignment from source. Read more

Formats the value using the given formatter. Read more

Formats the value using the given formatter. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

Performs the /= operation. Read more

Performs the /= operation. Read more

The returned type after indexing.

Performs the indexing (container[index]) operation. Read more

Performs the mutable indexing (container[index]) operation. Read more

The resulting type after applying the * operator.

Performs the * operation. Read more

The resulting type after applying the * operator.

Performs the * operation. Read more

Performs the *= operation. Read more

Performs the *= operation. Read more

The resulting type after applying the - operator.

Performs the unary - operation. Read more

Returns the multiplicative identity element of Self, 1. Read more

Sets self to the multiplicative identity element of Self, 1.

Returns true if self is equal to the multiplicative identity. Read more

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

The resulting type after applying the % operator.

Performs the % operation. Read more

The resulting type after applying the % operator.

Performs the % operation. Read more

Performs the %= operation. Read more

Performs the %= operation. Read more

The resulting type after applying the - operator.

Performs the - operation. Read more

The resulting type after applying the - operator.

Performs the - operation. Read more

Performs the -= operation. Read more

Performs the -= operation. Read more

Returns the additive identity element of Self, 0. Read more

Returns true if self is equal to the additive identity.

Sets self to the additive identity element of Self, 0.

Auto Trait Implementations

Blanket Implementations

Gets the TypeId of self. Read more

Immutably borrows from an owned value. Read more

Mutably borrows from an owned value. Read more

Performs the conversion.

Performs the conversion.

The resulting type after obtaining ownership.

Creates owned data from borrowed data, usually by cloning. Read more

🔬 This is a nightly-only experimental API. (toowned_clone_into)

Uses borrowed data to replace owned data, usually by cloning. Read more

Converts the given value to a String. Read more

The type returned in the event of a conversion error.

Performs the conversion.

The type returned in the event of a conversion error.

Performs the conversion.