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dcanberra

Compute the Canberra distance between two double-precision floating-point strided arrays.

The Canberra distance is a weighted version of the Manhattan distance where each dimension's contribution is normalized by the sum of the absolute coordinate values. It is defined as

$$D(\mathbf{A}, \mathbf{B}) = \sum_{i=0}^{N-1} \frac{\left| a_{i} - b_{i} \right|}{\left| a_{i} \right| + \left| b_{i} \right|}$$

where a_i and b_i are the ith components of vectors A and B, respectively. When both a_i and b_i are zero, the contribution to the sum is treated as zero.

Usage

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

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

Computes the Canberra 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 = dcanberra( x.length, x, 1, y, 1 );
// returns ~3.333

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 Canberra 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 = dcanberra( 3, x, 2, y, -1 );
// returns ~1.167

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 = dcanberra( 3, x1, 1, y1, 1 );
// returns ~1.738

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

Computes the Canberra 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 = dcanberra.ndarray( x.length, x, 1, 0, y, 1, 0 );
// returns ~3.333

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 Canberra 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 = dcanberra.ndarray( 3, x, 2, 1, y, -1, y.length-1 );
// returns ~1.431

Notes

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

Examples

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

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

C APIs

Usage

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

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

Computes the Canberra 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_dcanberra( 5, x, 1, y, 1 );
// returns ~3.333

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

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

Computes the Canberra 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_dcanberra_ndarray( 5, x, -1, 4, y, -1, 4 );
// returns ~3.333

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_dcanberra_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/dcanberra.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 Canberra distance between `x` and `y`:
    double d = stdlib_strided_dcanberra( N, x, strideX, y, strideY );

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

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

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