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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 | 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 7019x 7019x 1x 1x 7019x 2x 2x 7019x 2x 2x 7014x 7019x 1x 1x 1x 1x 1x | /** * @license Apache-2.0 * * Copyright (c) 2024 The Stdlib Authors. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ 'use strict'; // MODULES // var sinpi = require( '@stdlib/math/base/special/sinpi' ); var cospi =require('@stdlib/math/base/special/cospi'); var isnan = require( '@stdlib/math/base/assert/is-nan' ); var isInfinite = require( '@stdlib/math/base/assert/is-infinite' ); var PI = require( '@stdlib/constants/float64/pi' ); // MAIN // /** * Computes the normalized derivative of cardinal sine of a number. * * ## Method * * For \\( x \neq 0 \\), the normalized derivative of cardinal sine is calculated as * * ```tex * \operatorname{cosc}(x) = \frac{{\operatorname{cos}(\pi x)}-\frac{\operatorname{sin}(\pi x)}{\pi x}}{x}. * ``` * * ## Special Cases * * ```tex * \begin{align*} * \operatorname{cosc}(0) &= 0 & \\ * \operatorname{cosc}(\infty) &= 0 & \\ * \operatorname{cosc}(-\infty) &= 0 & \\ * \operatorname{cosc}(\mathrm{NaN}) &= \mathrm{NaN} * \end{align*} * ``` * * @param {number} x - input value * @returns {number} derivative of cardinal sine * * @example * var v = cosc( 0.5 ); * // returns ~-1.273 * * @example * var v = cosc( -1.2 ); * // returns ~0.544 * * @example * var v = cosc( 0.0 ); * // returns 0.0 * * @example * var v = cosc( NaN ); * // returns NaN */ function cosc( x ) { if ( isnan( x ) ) { return NaN; } if ( isInfinite( x ) ) { return 0.0; } if ( x === 0.0 ) { return 0.0; } return ( cospi( x ) - ( sinpi( x ) / ( PI * x ) ) ) / x ; } // EXPORTS // module.exports = cosc; |