+ Press n or j to go to the next uncovered block, b, p or k for the previous block. +
+ +| 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 | 3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x + | /**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 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';
+
+// MAIN //
+
+var cache = {};
+
+
+// EXPORTS //
+
+module.exports = cache;
+ |
+ Press n or j to go to the next uncovered block, b, p or k for the previous block. +
+ +| 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 | 3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +3x +332x +332x +332x +332x +332x +332x +332x +332x +332x +332x +332x +332x +332x +162x +162x +162x +3x +162x +159x +6037x +6037x +159x +159x +159x +159x +3058x +3058x +3058x +3058x +3058x +159x +162x +162x +162x +332x +332x +3x +3x +3x +3x +3x + | /**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 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 binomcoef = require( '@stdlib/math/base/special/binomcoef' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var ceil = require( '@stdlib/math/base/special/ceil' );
+var cache = require( './cache.js' );
+
+
+// MAIN //
+
+/**
+* Computes polynomial coefficients.
+*
+* ## Notes
+*
+* - Coefficients are computed via a (1,2)-Pascal triangle (i.e., Lucas triangle). For more details, see [Lucas polynomials][oeis-lucas-polynomials] and [Lucas triangle][oeis-lucas-triangle].
+*
+* [oeis-lucas-polynomials]: https://oeis.org/wiki/Lucas_polynomials
+* [oeis-lucas-triangle]: https://oeis.org/wiki/Lucas_triangle
+*
+* @private
+* @param {NonNegativeInteger} n - Lucas polynomial for which to compute coefficients
+* @returns {NonNegativeIntegerArray} polynomial coefficients
+*/
+function coefficients( n ) {
+ var coefs;
+ var half;
+ var high;
+ var low;
+ var p;
+ var a;
+ var b;
+ var m;
+ var i;
+
+ coefs = cache[ n ];
+ if ( coefs === void 0 ) {
+ m = n + 1;
+ coefs = new Array( m );
+ if ( n === 0 ) {
+ coefs[ 0 ] = 2.0;
+ } else {
+ for ( i = 0; i < m; i++ ) {
+ coefs[ i ] = 0.0;
+ }
+ half = n / 2;
+ high = ceil( half );
+ low = floor( half );
+ for ( i = 0; i <= low; i++ ) {
+ p = (2*i) + (n%2);
+ a = 2.0 * binomcoef( high+i-1, low-i-1 );
+ b = binomcoef( high+i-1, low-i );
+ coefs[ p ] += a + b;
+ }
+ }
+ // Memoize the coefficients:
+ cache[ n ] = coefs;
+ }
+ return coefs;
+}
+
+
+// EXPORTS //
+
+module.exports = coefficients;
+ |
+ Press n or j to go to the next uncovered block, b, p or k for the previous block. +
+ +| 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 | 2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +2x +162x +162x +162x +162x +162x +162x +162x +162x +162x +162x +162x +162x +124x +124x +38x +38x +38x +38x +38x +38x +38x +38x +38x +38x +38x +38x +162x +2x +2x +2x +2x +2x + | /**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 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 evalpoly = require( '@stdlib/math/base/tools/evalpoly' ).factory;
+var pow = require( '@stdlib/math/base/special/pow' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var coefficients = require( './coefficients.js' );
+
+
+// MAIN //
+
+/**
+* Returns a function for evaluating a Lucas polynomial.
+*
+* @param {integer} n - Lucas polynomial to evaluate
+* @returns {Function} function for evaluating a Lucas polynomial
+*
+* @example
+* var polyval = factory( 5 );
+*
+* var v = polyval( 1.0 );
+* // returns 11.0
+*
+* v = polyval( 2.0 );
+* // returns 82.0
+*/
+function factory( n ) {
+ var coefs;
+ var an;
+ var f;
+ var s;
+
+ an = abs( n );
+ coefs = coefficients( an );
+
+ f = evalpoly( coefs );
+ s = pow( -1.0, an );
+ if ( n >= 0 || s === 1.0 ) {
+ return f;
+ }
+ return polyval;
+
+ /**
+ * Evaluates a Lucas polynomial.
+ *
+ * @private
+ * @param {number} x - value at which to evaluate a Lucas polynomial
+ * @returns {number} result
+ */
+ function polyval( x ) {
+ return -1.0 * f( x );
+ }
+}
+
+
+// EXPORTS //
+
+module.exports = factory;
+ |
+ Press n or j to go to the next uncovered block, b, p or k for the previous block. +
+ +| File | ++ | Statements | ++ | Branches | ++ | Functions | ++ | Lines | ++ |
|---|---|---|---|---|---|---|---|---|---|
| cache.js | +
+
+ |
+ 100% | +28/28 | +100% | +1/1 | +100% | +0/0 | +100% | +28/28 | +
| coefficients.js | +
+
+ |
+ 100% | +85/85 | +100% | +7/7 | +100% | +1/1 | +100% | +85/85 | +
| factory.js | +
+
+ |
+ 100% | +77/77 | +100% | +6/6 | +100% | +2/2 | +100% | +77/77 | +
| index.js | +
+
+ |
+ 100% | +58/58 | +100% | +1/1 | +100% | +0/0 | +100% | +58/58 | +
| main.js | +
+
+ |
+ 100% | +60/60 | +100% | +4/4 | +100% | +1/1 | +100% | +60/60 | +
+ Press n or j to go to the next uncovered block, b, p or k for the previous block. +
+ +| 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 | 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 + | /** +* @license Apache-2.0 +* +* Copyright (c) 2018 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'; + +/** +* Evaluate a Lucas polynomial. +* +* @module @stdlib/math/base/tools/lucaspoly +* +* @example +* var lucaspoly = require( '@stdlib/math/base/tools/lucaspoly' ); +* +* var v = lucaspoly( 5, 1.0 ); +* // returns 11.0 +* +* @example +* var factory = require( '@stdlib/math/base/tools/lucaspoly' ).factory; +* +* var polyval = factory( 5 ); +* +* var v = polyval( 1.0 ); +* // returns 11.0 +* +* v = polyval( 2.0 ); +* // returns 82.0 +*/ + +// MODULES // + +var setReadOnly = require( '@stdlib/utils/define-nonenumerable-read-only-property' ); +var main = require( './main.js' ); +var factory = require( './factory.js' ); + + +// MAIN // + +setReadOnly( main, 'factory', factory ); + + +// EXPORTS // + +module.exports = main; + |
+ Press n or j to go to the next uncovered block, b, p or k for the previous block. +
+ +| 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 | 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 +161x +161x +161x +161x +161x +161x +161x +161x +161x +161x +85x +85x +76x +161x +1x +1x +1x +1x +1x + | /**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 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 evalpoly = require( '@stdlib/math/base/tools/evalpoly' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var coefficients = require( './coefficients.js' );
+
+
+// MAIN //
+
+/**
+* Evaluates a Lucas polynomial.
+*
+* @param {integer} n - Lucas polynomial to evaluate
+* @param {number} x - value at which to evaluate a Lucas polynomial
+* @returns {number} result
+*
+* @example
+* var v = lucaspoly( 5, 1.0 );
+* // returns 11.0
+*/
+function lucaspoly( n, x ) {
+ var coefs;
+ var an;
+ var v;
+
+ an = abs( n );
+ coefs = coefficients( an );
+
+ v = evalpoly( coefs, x );
+ if ( n >= 0 ) {
+ return v;
+ }
+ return pow( -1.0, an ) * v;
+}
+
+
+// EXPORTS //
+
+module.exports = lucaspoly;
+ |