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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.
*/
'use strict';
// VARIABLES //
var M = 5;
// MAIN //
/**
* Computes the integral of a double-precision floating-point strided array using the trapezoidal rule and alternative indexing semantics.
*
* ## Notes
*
* - The function computes an approximation of the integral using the trapezoidal rule whose accuracy depends on the sample point spacing and the smoothness of the underlying function.
*
* @param {NonNegativeInteger} N - number of indexed elements
* @param {Float64Array} x - first input array
* @param {integer} strideX - stride length for `x`
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @param {Float64Array} y - second input array
* @param {integer} strideY - stride length for `y`
* @param {NonNegativeInteger} offsetY - starting index for `y`
* @returns {number} integral approximation
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var x = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] );
* var y = new Float64Array( [ 0.0, 1.0, 4.0, 9.0 ] );
*
* var out = dtrapezoid( x.length, x, 1, 0, y, 1, 0 );
* // returns 9.5
*/
function dtrapezoid( N, x, strideX, offsetX, y, strideY, offsetY ) {
var sum;
var x0;
var x1;
var y0;
var y1;
var ix;
var iy;
var m;
var i;
sum = 0.0;
if ( N <= 1 ) {
return sum;
}
ix = offsetX;
iy = offsetY;
// Use unrolled loops if both strides are equal to `1`...
if ( strideX === 1 && strideY === 1 ) {
m = ( N-1 ) % M;
// If we have a remainder, run a clean-up loop...
if ( m > 0 ) {
for ( i = 0; i < m; i++ ) {
sum += ( x[ ix+1 ] - x[ ix ] ) * ( y[ iy ] + y[ iy+1 ] );
ix += 1;
iy += 1;
}
}
if ( N-1 < M ) {
return sum * 0.5;
}
for ( i = m; i < N-1; i += M ) {
sum += ( ( x[ix+1]-x[ix] ) * ( y[iy]+y[iy+1] ) ) +
( ( x[ix+2]-x[ix+1] ) * ( y[iy+1]+y[iy+2] ) ) +
( ( x[ix+3]-x[ix+2] ) * ( y[iy+2]+y[iy+3] ) ) +
( ( x[ix+4]-x[ix+3] ) * ( y[iy+3]+y[iy+4] ) ) +
( ( x[ix+5]-x[ix+4] ) * ( y[iy+4]+y[iy+5] ) );
ix += M;
iy += M;
}
return sum * 0.5;
}
x0 = x[ ix ];
y0 = y[ iy ];
for ( i = 1; i < N; i++ ) {
ix += strideX;
iy += strideY;
x1 = x[ ix ];
y1 = y[ iy ];
sum += ( x1-x0 ) * ( y1+y0 );
x0 = x1;
y0 = y1;
}
return sum * 0.5;
}
// EXPORTS //
module.exports = dtrapezoid;
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