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gdiff

Calculate the k-th discrete forward difference of a strided array.

Usage

var gdiff = require( '@stdlib/blas/ext/base/gdiff' );

gdiff( N, k, x, strideX, N1, prepend, strideP, N2, append, strideA, out, strideOut, workspace, strideW )

Calculates the k-th discrete forward difference of a strided array.

var x = [ 2.0, 4.0, 6.0, 8.0, 10.0 ];
var p = [ 1.0 ];
var a = [ 11.0 ];
var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
var w = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];

gdiff( x.length, 1, x, 1, 1, p, 1, 1, a, 1, out, 1, w, 1 );

console.log( out );
// => [ 1.0, 2.0, 2.0, 2.0, 2.0, 1.0 ]

The function has the following parameters:

  • N: number of indexed elements.
  • k: number of times to recursively compute differences.
  • x: input array.
  • strideX: stride length for x.
  • N1: number of indexed elements to prepend.
  • prepend: array containing values to prepend prior to computing differences.
  • strideP: stride length for prepend.
  • N2: number of indexed elements to append.
  • append: array containing values to append prior to computing differences.
  • strideA: stride length for append.
  • out: output array. Must have N + N1 + N2 - k elements.
  • strideOut: stride length for out.
  • workspace: workspace array. Must have N + N1 + N2 - 1 elements.
  • strideW: stride length for workspace.

The N and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute differences of every other element:

var x = [ 2.0, 4.0, 6.0, 8.0, 10.0 ];
var p = [ 1.0 ];
var a = [ 11.0 ];
var out = [ 0.0, 0.0, 0.0, 0.0 ];
var w = [ 0.0, 0.0, 0.0, 0.0 ];

gdiff( 3, 1, x, 2, 1, p, 1, 1, a, 1, out, 1, w, 1 );

console.log( out );
// => [ 1.0, 4.0, 4.0, 1.0 ]

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

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

// Initial array...
var x0 = new Float64Array( [ 2.0, 4.0, 6.0, 8.0, 10.0 ] );

// Create an offset view...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var p = [ 1.0 ];
var a = [ 11.0 ];
var out = [ 0.0, 0.0, 0.0, 0.0, 0.0 ];
var w = [ 0.0, 0.0, 0.0, 0.0, 0.0 ];

gdiff( x1.length, 1, x1, 1, 1, p, 1, 1, a, 1, out, 1, w, 1 );

console.log( out );
// => [ 3.0, 2.0, 2.0, 2.0, 1.0 ]

gdiff.ndarray( N, k, x, strideX, offsetX, N1, prepend, strideP, offsetP, N2, append, strideA, offsetA, out, strideOut, offsetOut, workspace, strideW, offsetW )

Calculates the k-th discrete forward difference of a strided array using alternative indexing semantics.

var x = [ 2.0, 4.0, 6.0, 8.0, 10.0 ];
var p = [ 1.0 ];
var a = [ 11.0 ];
var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
var w = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];

gdiff.ndarray( x.length, 1, x, 1, 0, 1, p, 1, 0, 1, a, 1, 0, out, 1, 0, w, 1, 0 );

console.log( out );
// => [ 1.0, 2.0, 2.0, 2.0, 2.0, 1.0 ]

The function has the following additional parameters:

  • offsetX: starting index for x.
  • offsetP: starting index for prepend.
  • offsetA: starting index for append.
  • offsetOut: starting index for out.
  • offsetW: starting index for workspace.

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 access only the last three elements:

var x = [ 2.0, 4.0, 6.0, 8.0, 10.0 ];
var p = [ 1.0 ];
var a = [ 11.0 ];
var out = [ 0.0, 0.0, 0.0, 0.0 ];
var w = [ 0.0, 0.0, 0.0, 0.0 ];

gdiff.ndarray( 3, 1, x, 1, x.length-3, 1, p, 1, 0, 1, a, 1, 0, out, 1, 0, w, 1, 0 );

console.log( out );
// => [ 5.0, 2.0, 2.0, 1.0 ]

Notes

  • When k <= 1, the workspace array is unused and thus ignored.
  • If N + N1 + N2 <= 1 or k >= N + N1 + N2, both functions return the output array unchanged.

Examples

var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var zeros = require( '@stdlib/array/zeros' );
var gdiff = require( '@stdlib/blas/ext/base/gdiff' );

var x = discreteUniform( 10, -100, 100, {
    'dtype': 'generic'
});
console.log( 'Input array: ', x );

var p = discreteUniform( 2, -100, 100, {
    'dtype': 'generic'
});
console.log( 'Prepend array: ', p );

var a = discreteUniform( 2, -100, 100, {
    'dtype': 'generic'
});
console.log( 'Append array: ', a );

var out = zeros( 10, 'generic' );
var w = zeros( 13, 'generic' );

gdiff( x.length, 4, x, 1, 2, p, 1, 2, a, 1, out, 1, w, 1 );
console.log( 'Output: ', out );