README.md

Chebyshev Series

Evaluate a Chebyshev series using single-precision floating-point arithmetic.

A Chebyshev series in a variable x can be expressed as

$$\sum_{i=0}^{n} c_i T_i(x/2)$$

where c_n, c_{n-1}, ..., c_0 are constants and T_i are Chebyshev polynomials of the first kind.

Usage

var chebyshevSeriesf = require( '@stdlib/math/base/tools/chebyshev-seriesf' );

chebyshevSeriesf( x, c )

Evaluates a Chebyshev series having coefficients c at a value x.

var Float32Array = require( '@stdlib/array/float32' );

var v = chebyshevSeriesf( 1.0, new Float32Array( [ 1.0, 0.5 ] ) );
// returns 0.75

The function evaluates Chebyshev polynomials at x/2.

chebyshevSeriesf.factory( c )

Uses code generation to in-line coefficients and return a function for evaluating a Chebyshev series using single-precision floating-point arithmetic.

var Float32Array = require( '@stdlib/array/float32' );

var evaluate = chebyshevSeriesf.factory( new Float32Array( [ 1.0, 0.5 ] ) );

// 0.5 * T_0(0.5) + 1.0 * T_1(0.5)
var v = evaluate( 1.0 );
// returns 0.75

The returned function evaluates Chebyshev polynomials at x/2.

Notes

• The value at which to evaluate a Chebyshev series is expected to reside on the interval [-2, 2].
• The coefficients c must be ordered in descending degree.
• For hot code paths in which coefficients are invariant, a compiled function will be more performant than chebyshevSeriesf().
• While code generation can boost performance, its use may be problematic in browser contexts enforcing a strict content security policy (CSP). If running in or targeting an environment with a CSP, avoid using code generation.

Examples

var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var uniform = require( '@stdlib/random/array/uniform' );
var logEachMap = require( '@stdlib/console/log-each-map' );
var chebyshevSeriesf = require( '@stdlib/math/base/tools/chebyshev-seriesf' );

// Create an array of random coefficients:
var coef = discreteUniform( 10, -100, 100, {
    'dtype': 'float32'
});

// Evaluate the series at random values using the direct function:
var v = uniform( 100, -2.0, 2.0, {
    'dtype': 'float32'
});
var i;
for ( i = 0; i < v.length; i++ ) {
    console.log( 'f(%0.4f) = %0.4f', v[ i ], chebyshevSeriesf( v[ i ], coef ) );
}

// Generate a chebyshev series evaluation function:
var evaluate = chebyshevSeriesf.factory( coef );
var x = uniform( 100, -2.0, 2.0, {
    'dtype': 'float32'
});
logEachMap( 'f(%0.4f) = %0.4f', x, evaluate );