dcityblock

Compute the city block (Manhattan) distance between two double-precision floating-point strided arrays.

The city block distance (also known as the Manhattan or taxicab distance) is defined as

where a_i and b_i are the ith components of vectors A and B, respectively.

Installation

npm install @stdlib/stats-strided-distances-dcityblock

Usage

var dcityblock = require( '@stdlib/stats-strided-distances-dcityblock' );

dcityblock( N, x, strideX, y, strideY )

Computes the city block (Manhattan) distance between two double-precision floating-point strided arrays.

var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 4.0, 2.0, -3.0, 5.0, -1.0 ] );
var y = new Float64Array( [ 2.0, 6.0, -1.0, -4.0, 8.0 ] );

var z = dcityblock( x.length, x, 1, y, 1 );
// returns 26.0

The function has the following parameters:

• N: number of indexed elements.
• x: input Float64Array.
• strideX: stride length of x.
• y: input Float64Array.
• strideY: stride length of y.

The N and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to calculate the city block (Manhattan) distance between every other element in x and the first N elements of y in reverse order,

var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );

var z = dcityblock( 3, x, 2, y, -1 );
// returns 6.0

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

var Float64Array = require( '@stdlib/array-float64' );

// Initial arrays...
var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y0 = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element

var z = dcityblock( 3, x1, 1, y1, 1 );
// returns 24.0

dcityblock.ndarray( N, x, strideX, offsetX, y, strideY, offsetY )

Computes the city block (Manhattan) distance between two double-precision floating-point strided arrays using alternative indexing semantics.

var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 4.0, 2.0, -3.0, 5.0, -1.0 ] );
var y = new Float64Array( [ 2.0, 6.0, -1.0, -4.0, 8.0 ] );

var z = dcityblock.ndarray( x.length, x, 1, 0, y, 1, 0 );
// returns 26.0

The function has the following additional parameters:

• offsetX: starting index for x.
• offsetY: starting index for y.

While typed array views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example, to calculate the city block (Manhattan) distance between every other element in x starting from the second element with the last 3 elements in y in reverse order

var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

var z = dcityblock.ndarray( 3, x, 2, 1, y, -1, y.length-1 );
// returns 21.0

Notes

• If N <= 0, both functions return NaN.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var dcityblock = require( '@stdlib/stats-strided-distances-dcityblock' );

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 10, 0, 100, opts );
console.log( x );

var y = discreteUniform( x.length, 0, 10, opts );
console.log( y );

var out = dcityblock.ndarray( x.length, x, 1, 0, y, -1, y.length-1 );
console.log( out );

C APIs

Usage

#include "stdlib/stats/strided/distances/dcityblock.h"

stdlib_strided_dcityblock( N, *X, strideX, *Y, strideY )

Computes the city block (Manhattan) distance between two double-precision floating-point strided arrays.

const double x[] = { 4.0, 2.0, -3.0, 5.0, -1.0 };
const double y[] = { 2.0, 6.0, -1.0, -4.0, 8.0 };

double v = stdlib_strided_dcityblock( 5, x, 1, y, 1 );
// returns 26.0

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• X: [in] double* first input array.
• strideX: [in] CBLAS_INT stride length of X.
• Y: [in] double* second input array.
• strideY: [in] CBLAS_INT stride length of Y.

double stdlib_strided_dcityblock( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const double *Y, const CBLAS_INT strideY );

stdlib_strided_dcityblock_ndarray( N, *X, strideX, offsetX, *Y, strideY, offsetY )

Computes the city block (Manhattan) distance between two double-precision floating-point strided arrays using alternative indexing semantics.

const double x[] = { 4.0, 2.0, -3.0, 5.0, -1.0 };
const double y[] = { 2.0, 6.0, -1.0, -4.0, 8.0 };

double v = stdlib_strided_dcityblock_ndarray( 5, x, -1, 4, y, -1, 4 );
// returns 26.0

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• X: [in] double* first input array.
• strideX: [in] CBLAS_INT stride length of X.
• offsetX: [in] CBLAS_INT starting index for X.
• Y: [in] double* second input array.
• strideY: [in] CBLAS_INT stride length of Y.
• offsetY: [in] CBLAS_INT starting index for Y.

double stdlib_strided_dcityblock_ndarray( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const double *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY );

Examples

#include "stdlib/stats/strided/distances/dcityblock.h"
#include <stdio.h>

int main( void ) {
    // Create strided arrays:
    const double x[] = { 1.0, -2.0, 3.0, -4.0, 5.0, -6.0, 7.0, -8.0 };
    const double y[] = { 1.0, -2.0, 3.0, -4.0, 5.0, -6.0, 7.0, -8.0 };

    // Specify the number of elements:
    const int N = 8;

    // Specify strides:
    const int strideX = 1;
    const int strideY = -1;

    // Compute the city block (Manhattan) distance between `x` and `y`:
    double d = stdlib_strided_dcityblock( N, x, strideX, y, strideY );

    // Print the result:
    printf( "City block (Manhattan) distance: %lf\n", d );

    // Compute the city block (Manhattan) distance between `x` and `y` with offsets:
    d = stdlib_strided_dcityblock_ndarray( N, x, strideX, 0, y, strideY, N-1 );

    // Print the result:
    printf( "City block (Manhattan) distance: %lf\n", d );
}

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

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License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.