# Algebra¶

## Extrapolation¶

colour

 Extrapolator([interpolator, method, left, ...]) Extrapolate the 1-D function of given interpolator.

## Interpolation¶

colour

 KernelInterpolator(x, y[, window, kernel, ...]) Kernel based interpolation of a 1-D function. NearestNeighbourInterpolator(*args, **kwargs) A nearest-neighbour interpolator. LinearInterpolator(x, y[, dtype]) Interpolate linearly a 1-D function. NullInterpolator(x, y[, absolute_tolerance, ...]) Perform 1-D function null interpolation, i.e. a call within given tolerances will return existing $$y$$ variable values and default if outside tolerances. PchipInterpolator(x, y, *args, **kwargs) Interpolate a 1-D function using Piecewise Cubic Hermite Interpolating Polynomial interpolation. SpragueInterpolator(x, y[, dtype]) Construct a fifth-order polynomial that passes through $$y$$ dependent variable.
 lagrange_coefficients(r[, n]) Compute the Lagrange Coefficients at given point $$r$$ for degree $$n$$. TABLE_INTERPOLATION_METHODS Supported table interpolation methods. table_interpolation(V_xyz, table[, method]) Perform interpolation of given $$V_{xyz}$$ values using given interpolation table.

Interpolation Kernels

colour

 Return the nearest-neighbour kernel evaluated at given samples. Return the linear kernel evaluated at given samples. kernel_sinc(x[, a]) Return the sinc kernel evaluated at given samples. kernel_lanczos(x[, a]) Return the lanczos kernel evaluated at given samples. kernel_cardinal_spline(x[, a, b]) Return the cardinal spline kernel evaluated at given samples.

Ancillary Objects

colour.algebra

 table_interpolation_trilinear(V_xyz, table) Perform the trilinear interpolation of given $$V_{xyz}$$ values using given interpolation table. table_interpolation_tetrahedral(V_xyz, table) Perform the tetrahedral interpolation of given $$V_{xyz}$$ values using given interpolation table.

## Coordinates¶

colour.algebra

 Transform given cartesian coordinates array $$xyz$$ to spherical coordinates array $$\rho\theta\phi$$ (radial distance, inclination or elevation and azimuth). Transform given spherical coordinates array $$\rho\theta\phi$$ (radial distance, inclination or elevation and azimuth) to cartesian coordinates array $$xyz$$. Transform given cartesian coordinates array $$xy$$ to polar coordinates array $$\rho\phi$$ (radial coordinate, angular coordinate). Transform given polar coordinates array $$\rho\phi$$ (radial coordinate, angular coordinate) to cartesian coordinates array $$xy$$. Transform given cartesian coordinates array $$xyz$$ to cylindrical coordinates array $$\rho\phi z$$ (radial distance, azimuth and height). Transform given cylindrical coordinates array $$\rho\phi z$$ (radial distance, azimuth and height) to cartesian coordinates array $$xyz$$.

## Geometry¶

colour.algebra

 Normalise given vector $$a$$. Return the Euclidean distance between point array $$a$$ and point array $$b$$. Return the Manhattan (or City-Block) distance between point array $$a$$ and point array $$b$$. extend_line_segment(a, b[, distance]) Extend the line segment defined by point arrays $$a$$ and $$b$$ by given distance and return the new end point. intersect_line_segments(l_1, l_2) Compute $$l_1$$ line segments intersections with $$l_2$$ line segments. ellipse_coefficients_general_form(coefficients) Return the general form ellipse coefficients from given canonical form ellipse coefficients. ellipse_coefficients_canonical_form(coefficients) Return the canonical form ellipse coefficients from given general form ellipse coefficients. point_at_angle_on_ellipse(phi, coefficients) Return the coordinates of the point at angle $$\phi$$ in degrees on the ellipse with given canonical form coefficients. ELLIPSE_FITTING_METHODS Supported ellipse fitting methods. ellipse_fitting(a[, method]) Return the coefficients of the implicit second-order polynomial/quadratic curve that fits given point array $$a$$ using given method.

Ancillary Objects

colour.algebra

 Define the specification for intersection of line segments $$l_1$$ and $$l_2$$ returned by colour.algebra.intersect_line_segments() definition. Return the coefficients of the implicit second-order polynomial/quadratic curve that fits given point array $$a$$ using Halir and Flusser (1998) method.

## Random¶

colour.algebra

 random_triplet_generator(size[, limits, ...]) Return a generator yielding random triplets.

## Regression¶

colour.algebra

 Compute the least-squares mapping from dependent variable $$y$$ to independent variable $$x$$ using Moore-Penrose inverse.

## Common¶

colour.algebra

 Return whether Colour safe / symmetrical power function is enabled. set_spow_enable(enable) Set Colour safe / symmetrical power function enabled state. spow_enable(enable) Define a context manager and decorator temporarily setting Colour safe / symmetrical power function enabled state. spow(a, p) Raise given array $$a$$ to the power $$p$$ as follows: $$sign(a) * |a|^p$$. normalise_maximum(a[, axis, factor, clip]) Normalise given array $$a$$ values by $$a$$ maximum value and optionally clip them between. vector_dot(m, v) Perform the dot product of the matrix array $$m$$ with the vector array $$v$$. matrix_dot(a, b) Perform the dot product of the matrix array $$a$$ with the matrix array $$b$$. linear_conversion(a, old_range, new_range) Perform a simple linear conversion of given array $$a$$ between the old and new ranges. linstep_function(x[, a, b, clip]) Perform a simple linear interpolation between given array $$a$$ and array $$b$$ using $$x$$ array. lerp(x[, a, b, clip]) Perform a simple linear interpolation between given array $$a$$ and array $$b$$ using $$x$$ array. smoothstep_function(x[, a, b, clip]) Evaluate the smoothstep sigmoid-like function on array $$x$$. smooth(x[, a, b, clip]) Evaluate the smoothstep sigmoid-like function on array $$x$$. Return whether $$a$$ array is an identity matrix.