Module compute::linalg

Provides general linear algebra methods and matrix decompositions with a focus on low-dimensional data.

Modules

cholesky	Implements Cholesky decomposition.
lu	Implements LU decomposition and system solving with the decomposition.
substitution	Forward and backward substitution.

Structs

Matrix	Matrix struct.
Vector	A row-major ordering vector struct with various useful methods.

Enums

Axis	Utilities for 3D rotations.
Broadcast

Traits

Dot	A trait for performing matrix products. Follows the behaviour of numpy’s matmul.
Solve

Functions

arange	Generates evenly spaced values within a given interval. Values generated in the half-open interval [start, stop). That is, the stop point is not included.
backward_substitution	Solve a matrix equation of the form Ux=b, where U is an upper triangular matrix. See the Wikipedia page.
broadcast_add
broadcast_div
broadcast_mul
broadcast_sub
cholesky	Computes the Cholesky decomposition of the matrix a using the Cholesky-Banachiewicz algorithm.
cholesky_solve	Solves the system Lx=b, where L is a lower triangular matrix (e.g., a Cholesky decomposed matrix), and b is a one dimensional vector.
col_to_row_major	Convert a 1D matrix from column-major ordering into row-major ordering.
design	Create a design matrix from a given matrix.
diag
diag_matrix	Create a diagonal matrix with the given elements along the elements.
dot	Calculates the dot product of two equal-length vectors. When the feature “blas” is enabled, uses ddot from BLAS. Otherwise, uses a length-8 unrolled loop.
forward_substitution	Solve a matrix equation of the form Lx=b, where L is a lower triangular matrix. See the Wikipedia page.
inf_norm	Calculates the infinity norm of a matrix. That is, it sums the absolute values along each row, and then returns the largest of these values.
invert_matrix	Given an n by n matrix, invert it. The resulting matrix is returned as a flattened array.
is_design	Checks whether a 1D array is a valid design matrix, given its number of rows.
is_matrix	Checks whether a 1D array is a valid matrix representation given the number of rows.
is_positive_definite	Checks whether a 1d array is a valid positive definite matrix.
is_square	Checks whether a 1D array is a valid square matrix.
is_symmetric	Checks whether a 1D array is a valid symmetric matrix.
linspace	Generates evenly spaced values within a given interval, with a set number of points. Both the start and stop points are included.
lu	Computes the pivoted LU decomposition of a square matrix. For some matrix A, this decomposition is A = PLU. The resulting matrix has U in its upper triangle and L in its lower triangle. The unit diagonal elements of L are not stored. The pivot indices representing the permutation matrix P is also returned.
lu_solve	Solve the linear system Ax = b given a LU decomposed matrix A. The first argument should be a tuple, where the first element is the LU decomposed matrix and the second element is the pivots P.
matmatadd
matmatdiv
matmatmul
matmatsub
matmul	Multiply two matrices together, optionally transposing one or both of them.
matmul_blocked	Performs blocked matrix multiplication with block size bsize. See the API for the matmul.
norm	Calculates the norm of a vector.
rotation_matrix_ccw	Returns a 3D counter-clockwise rotation matrix along the axis axis (either X, Y, or Z) with a given angle in radians.
rotation_matrix_cw	Returns a 3D clockwise rotation matrix along the axis axis (either X, Y, or Z) with a given angle in radians.
row_to_col_major	Convert a 1D matrix from row-major ordering into column-major ordering.
solve	Solve the linear system Ax = b.
solve_sys	Solves a system of linear scalar equations. a must represent a square matrix.
sum	Calculates the sum of a vector.
svadd	Implements a loop-unrolled version of the + function to be applied element-wise between a scalar and a vector (in that order).
svdiv	Implements a loop-unrolled version of the / function to be applied element-wise between a scalar and a vector (in that order).
svmul	Implements a loop-unrolled version of the `
svsub	Implements a loop-unrolled version of the `
toeplitz	Given a vector of length n, creates n stacked duplicates, resulting in a square Toeplitz matrix. This function also assumes evenness. That is, x_i = x_{-i}.
transpose	Transpose a matrix.
vabs	Implements a loop-unrolled version of the abs function to be applied element-wise to a vector.
vacos	Implements a loop-unrolled version of the acos function to be applied element-wise to a vector.
vacosh	Implements a loop-unrolled version of the acosh function to be applied element-wise to a vector.
vadd	Implements a loop-unrolled version of the + function to be applied element-wise to two vectors.
vadd_mut	Implements a loop-unrolled version of the += function to be applied element-wise to two vectors.
vandermonde	Given some length m data x, create an nth order Vandermonde matrix.
vasin	Implements a loop-unrolled version of the asin function to be applied element-wise to a vector.
vasinh	Implements a loop-unrolled version of the asinh function to be applied element-wise to a vector.
vatan	Implements a loop-unrolled version of the atan function to be applied element-wise to a vector.
vatanh	Implements a loop-unrolled version of the atanh function to be applied element-wise to a vector.
vcbrt	Implements a loop-unrolled version of the cbrt function to be applied element-wise to a vector.
vceil	Implements a loop-unrolled version of the ceil function to be applied element-wise to a vector.
vcos	Implements a loop-unrolled version of the cos function to be applied element-wise to a vector.
vcosh	Implements a loop-unrolled version of the cosh function to be applied element-wise to a vector.
vdiv	Implements a loop-unrolled version of the / function to be applied element-wise to two vectors.
vdiv_mut	Implements a loop-unrolled version of the /= function to be applied element-wise to two vectors.
vexp	Implements a loop-unrolled version of the exp function to be applied element-wise to a vector.
vexp2	Implements a loop-unrolled version of the exp2 function to be applied element-wise to a vector.
vexpm1	Implements a loop-unrolled version of the exp_m1 function to be applied element-wise to a vector.
vfloor	Implements a loop-unrolled version of the floor function to be applied element-wise to a vector.
vln	Implements a loop-unrolled version of the ln function to be applied element-wise to a vector.
vln1p	Implements a loop-unrolled version of the ln_1p function to be applied element-wise to a vector.
vlog2	Implements a loop-unrolled version of the log2 function to be applied element-wise to a vector.
vlog10	Implements a loop-unrolled version of the log10 function to be applied element-wise to a vector.
vmul	Implements a loop-unrolled version of the `
vmul_mut	Implements a loop-unrolled version of the *= function to be applied element-wise to two vectors.
vpowf	Implements a loop-unrolled version of the powf function to be applied element-wise to a vector.
vpowi	Implements a loop-unrolled version of the powi function to be applied element-wise to a vector.
vrecip	Implements a loop-unrolled version of the recip function to be applied element-wise to a vector.
vround	Implements a loop-unrolled version of the round function to be applied element-wise to a vector.
vsadd	Implements a loop-unrolled version of the + function to be applied element-wise between a vector and a scalar (in that order).
vsadd_mut	Implements a loop-unrolled version of the += function to be applied element-wise between a vector and a scalar (in that order).
vsdiv	Implements a loop-unrolled version of the / function to be applied element-wise between a vector and a scalar (in that order).
vsdiv_mut	Implements a loop-unrolled version of the /= function to be applied element-wise between a vector and a scalar (in that order).
vsignum	Implements a loop-unrolled version of the signum function to be applied element-wise to a vector.
vsin	Implements a loop-unrolled version of the sin function to be applied element-wise to a vector.
vsinh	Implements a loop-unrolled version of the sinh function to be applied element-wise to a vector.
vsmul	Implements a loop-unrolled version of the `
vsmul_mut	Implements a loop-unrolled version of the *= function to be applied element-wise between a vector and a scalar (in that order).
vsqrt	Implements a loop-unrolled version of the sqrt function to be applied element-wise to a vector.
vssub	Implements a loop-unrolled version of the `
vssub_mut	Implements a loop-unrolled version of the -= function to be applied element-wise between a vector and a scalar (in that order).
vsub	Implements a loop-unrolled version of the `
vsub_mut	Implements a loop-unrolled version of the -= function to be applied element-wise to two vectors.
vtan	Implements a loop-unrolled version of the tan function to be applied element-wise to a vector.
vtanh	Implements a loop-unrolled version of the tanh function to be applied element-wise to a vector.
vtodegrees	Implements a loop-unrolled version of the to_degrees function to be applied element-wise to a vector.
vtoradians	Implements a loop-unrolled version of the to_radians function to be applied element-wise to a vector.
xtx	Given a matrix X with k rows, return X transpose times X, which is a symmetric matrix.