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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';
// MAIN //
/**
* Computes the gradient of a strided array using alternative indexing semantics and accessor arrays.
*
* ## Notes
*
* - The function supports first-order (i.e., `edgeOrder = 1`) and second-order (i.e., `edgeOrder = 2`) finite-difference approximations at the boundaries.
*
* @private
* @param {PositiveInteger} N - number of indexed elements
* @param {PositiveInteger} edgeOrder - approximation order at the boundaries
* @param {Object} x - input array object
* @param {Collection} x.data - input array data
* @param {Array<Function>} x.accessors - array element accessors
* @param {integer} strideX - stride length for `x`
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @param {Object} h - spacing array object
* @param {Collection} h.data - spacing array data
* @param {Array<Function>} h.accessors - array element accessors
* @param {integer} strideH - stride length for `h`
* @param {NonNegativeInteger} offsetH - starting index for `h`
* @param {Object} out - output array object
* @param {Collection} out.data - output array data
* @param {Array<Function>} out.accessors - array element accessors
* @param {integer} strideOut - stride length for `out`
* @param {NonNegativeInteger} offsetOut - starting index for `out`
* @returns {Object} output array object
*
* @example
* var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
* var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
*
* 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, arraylike2object( toAccessorArray( x ) ), 1, 0, arraylike2object( toAccessorArray( h ) ), 1, 0, arraylike2object( toAccessorArray( out ) ), 1, 0 );
*
* console.log( 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 xbuf;
var hbuf;
var obuf;
var xget;
var hget;
var oset;
var prev;
var curr;
var hL;
var hR;
var d1;
var d2;
var ix;
var ih;
var io;
var a;
var b;
var c;
var s;
var i;
// Cache references to array data and accessors:
xbuf = x.data;
hbuf = h.data;
obuf = out.data;
xget = x.accessors[ 0 ];
hget = h.accessors[ 0 ];
oset = out.accessors[ 1 ];
// Left boundary...
d1 = hget( hbuf, offsetH );
if ( edgeOrder >= 2 && N >= 3 ) {
d2 = hget( hbuf, offsetH + strideH );
s = d1 + d2;
a = -(d1 + s) / ( d1 * s );
b = s / ( d1 * d2 );
c = -d1 / ( d2 * s );
oset( obuf, offsetOut, ( a*xget( xbuf, offsetX ) ) + ( b*xget( xbuf, offsetX + strideX ) ) + ( c*xget( xbuf, offsetX + (2*strideX) ) ) );
} else {
oset( obuf, offsetOut, ( xget( xbuf, offsetX + strideX ) - xget( xbuf, offsetX ) ) / d1 );
}
// N=2: right boundary equals left boundary formula (first-order only)...
if ( N === 2 ) {
oset( obuf, offsetOut + strideOut, ( xget( xbuf, offsetX + strideX ) - xget( xbuf, offsetX ) ) / d1 );
return out;
}
// Interior points...
ix = offsetX + strideX;
ih = offsetH;
io = offsetOut + strideOut;
prev = xget( xbuf, offsetX );
for ( i = 1; i < N-1; i++ ) {
curr = xget( xbuf, ix );
hL = hget( hbuf, ih );
hR = hget( hbuf, ih + strideH );
s = hL + hR;
a = -hR / ( hL * s );
b = (hR - hL) / ( hL * hR );
c = hL / ( hR * s );
oset( obuf, io, ( a*prev ) + ( b*curr ) + ( c*xget( xbuf, ix + strideX ) ) );
prev = curr;
ix += strideX;
ih += strideH;
io += strideOut;
}
// Right boundary...
d2 = hget( hbuf, ih );
if ( edgeOrder >= 2 ) {
d1 = hget( hbuf, ih - strideH );
s = d1 + d2;
a = d2 / ( d1 * s );
b = -s / ( d1 * d2 );
c = (d2 + s) / ( d2 * s );
oset( obuf, io, ( a*xget( xbuf, ix - (2*strideX) ) ) + ( b*prev ) + ( c*xget( xbuf, ix ) ) );
} else {
oset( obuf, io, ( xget( xbuf, ix ) - prev ) / d2 );
}
return out;
}
// EXPORTS //
module.exports = ggradient;
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