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* @license Apache-2.0
*
* Copyright (c) 2026 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.
*/
/* eslint-disable max-params, max-len */
'use strict';
// MODULES //
var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
var accessors = require( './accessors.js' );
// MAIN //
/**
* Computes the gradient of a strided array using alternative indexing semantics.
*
* ## Notes
*
* - The function supports first-order (i.e., `edgeOrder = 1`) and second-order (i.e., `edgeOrder = 2`) finite-difference approximations at the boundaries.
*
* @param {PositiveInteger} N - number of indexed elements
* @param {PositiveInteger} edgeOrder - approximation order at the boundaries
* @param {NumericArray} x - input array
* @param {integer} strideX - stride length for `x`
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @param {NumericArray} h - spacing array
* @param {integer} strideH - stride length for `h`
* @param {NonNegativeInteger} offsetH - starting index for `h`
* @param {NumericArray} out - output array
* @param {integer} strideOut - stride length for `out`
* @param {NonNegativeInteger} offsetOut - starting index for `out`
* @returns {NumericArray} output array
*
* @example
* var x = [ 0.0, 1.0, 9.0, 36.0, 100.0 ];
* var h = [ 1.0, 2.0, 3.0, 4.0 ];
* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0 ];
*
* ggradient( x.length, 1, x, 1, 0, h, 1, 0, out, 1, 0 );
* // out => [ 1.0, 2.0, 6.0, 12.0, 16.0 ]
*/
function ggradient( N, edgeOrder, x, strideX, offsetX, h, strideH, offsetH, out, strideOut, offsetOut ) {
var prev;
var curr;
var xo;
var ho;
var oo;
var hL;
var hR;
var d1;
var d2;
var ix;
var ih;
var io;
var a;
var b;
var c;
var s;
var i;
if ( N <= 0 || N === 1 ) {
return out;
}
xo = arraylike2object( x );
ho = arraylike2object( h );
oo = arraylike2object( out );
if ( xo.accessorProtocol || ho.accessorProtocol || oo.accessorProtocol ) {
accessors( N, edgeOrder, xo, strideX, offsetX, ho, strideH, offsetH, oo, strideOut, offsetOut );
return out;
}
// Left boundary...
d1 = h[ offsetH ];
if ( edgeOrder >= 2 && N >= 3 ) {
d2 = h[ offsetH + strideH ];
s = d1 + d2;
a = -(d1 + s) / ( d1 * s );
b = s / ( d1 * d2 );
c = -d1 / ( d2 * s );
out[ offsetOut ] = ( a*x[ offsetX ] ) + ( b*x[ offsetX + strideX ] ) + ( c*x[ offsetX + (2*strideX) ] );
} else {
out[ offsetOut ] = ( x[ offsetX + strideX ] - x[ offsetX ] ) / d1;
}
// N=2: right boundary equals left boundary formula (first-order only)...
if ( N === 2 ) {
out[ offsetOut + strideOut ] = ( x[ offsetX + strideX ] - x[ offsetX ] ) / d1;
return out;
}
// Interior points...
ix = offsetX + strideX;
ih = offsetH;
io = offsetOut + strideOut;
prev = x[ offsetX ];
for ( i = 1; i < N-1; i++ ) {
curr = x[ ix ];
hL = h[ ih ];
hR = h[ ih + strideH ];
s = hL + hR;
a = -hR / ( hL * s );
b = (hR - hL) / ( hL * hR );
c = hL / ( hR * s );
out[ io ] = ( a*prev ) + ( b*curr ) + ( c*x[ ix + strideX ] );
prev = curr;
ix += strideX;
ih += strideH;
io += strideOut;
}
// Right boundary...
d2 = h[ ih ];
if ( edgeOrder >= 2 ) {
d1 = h[ ih - strideH ];
s = d1 + d2;
a = d2 / ( d1 * s );
b = -s / ( d1 * d2 );
c = (d2 + s) / ( d2 * s );
out[ io ] = ( a*x[ ix - (2*strideX) ] ) + ( b*prev ) + ( c*x[ ix ] );
} else {
out[ io ] = ( x[ ix ] - prev ) / d2;
}
return out;
}
// EXPORTS //
module.exports = ggradient;
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