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logspace

Return a new ndarray filled with logarithmically spaced values over a specified interval along one or more ndarray dimensions.

Installation

npm install @stdlib/blas-ext-logspace

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var logspace = require( '@stdlib/blas-ext-logspace' );

logspace( shape, base, start, stop[, endpoint][, options] )

Returns a new ndarray filled with logarithmically spaced values over a specified interval along one or more ndarray dimensions.

var x = logspace( [ 4 ], 10.0, 0.0, 3.0 );
// returns <ndarray>[ 1.0, 10.0, 100.0, 1000.0 ]

The function has the following parameters:

• shape: array shape.
• base: base of the logarithmic scale. May be either a number or an ndarray having a real-valued or "generic" data type. If provided an ndarray, the value must have a shape which is broadcast-compatible with the complement of the shape defined by options.dims. For example, given the input shape [2, 3, 4] and options.dims=[0], a base ndarray must have a shape which is broadcast-compatible with the shape [3, 4]. Similarly, when performing the operation over all elements in a provided input shape, a base ndarray must be a zero-dimensional ndarray.
• start: exponent of the starting value, where the starting value is given by base^start. May be either a number, a complex number, or an ndarray having a numeric or "generic" data type. If provided an ndarray, the value must have a shape which is broadcast-compatible with the complement of the shape defined by options.dims. For example, given the input shape [2, 3, 4] and options.dims=[0], a start ndarray must have a shape which is broadcast-compatible with the shape [3, 4]. Similarly, when performing the operation over all elements in a provided input shape, a start ndarray must be a zero-dimensional ndarray.
• stop: exponent of the final value, where the final value is given by base^stop. May be either a number, a complex number, or an ndarray having a numeric or "generic" data type. If provided an ndarray, the value must have a shape which is broadcast-compatible with the complement of the shape defined by options.dims. For example, given the input shape [2, 3, 4] and options.dims=[0], a stop ndarray must have a shape which is broadcast-compatible with the shape [3, 4]. Similarly, when performing the operation over all elements in a provided input shape, a stop ndarray must be a zero-dimensional ndarray.
• endpoint: specifies whether to include the base^stop value when writing values to the output ndarray (optional). May be either a boolean or an ndarray having a boolean or "generic" data type. If provided an ndarray, the value must have a shape which is broadcast-compatible with the complement of the shape defined by options.dims. For example, given the input shape [2, 3, 4] and options.dims=[0], an endpoint ndarray must have a shape which is broadcast-compatible with the shape [3, 4]. Similarly, when performing the operation over all elements in a provided input shape, an endpoint ndarray must be a zero-dimensional ndarray. Default: true.
• options: function options (optional).

The function accepts the following options:

• dims: list of dimensions over which to perform operation. If not provided, the function generates logarithmically spaced values along the last dimension. Default: [-1].
• dtype: output ndarray data type. If both start and stop are real-valued, the output array data type may be any floating-point data type or "generic". However, if either start or stop are complex-valued, the output array data type must be a complex floating-point data type or "generic". If a data type is provided, start and stop are cast to the specified data type. If a data type is not provided, the default output array data type is determined by applying type promotion rules to the base, start, and stop data types.
• order: specifies whether an ndarray is 'row-major' (C-style) or 'column-major' (Fortran-style). If base, start, stop, and endpoint are scalar values, the default order is 'row-major'. If base, start, stop, and/or endpoint arrays have the same memory layout, the default order is the same layout. Otherwise, the default order is 'row-major'.
• mode: specifies how to handle indices which exceed array dimensions (see ndarray). Default: 'throw'.
• submode: a mode array which specifies for each dimension how to handle subscripts which exceed array dimensions (see ndarray). If provided fewer modes than dimensions, the function recycles modes using modulo arithmetic. Default: [ options.mode ].

By default, the function always includes the base^stop value in the list of values written to an output ndarray. To exclude the base^stop value, provide an endpoint argument.

var x = logspace( [ 4 ], 10.0, 0.0, 4.0, false );
// returns <ndarray>[ 1.0, 10.0, 100.0, 1000.0 ]

When provided scalar or zero-dimensional ndarray base, start, stop, and endpoint arguments, the values are broadcast across all elements in the shape defined by the complement of those dimensions specified by options.dims. To specify separate sub-array configurations, provide non-zero-dimensional ndarray arguments.

var array = require( '@stdlib/ndarray-array' );
var BooleanArray = require( '@stdlib/array-bool' );

var start = array( [ 0.0, 3.0 ] );
var end = array( [ 2.0, 6.0 ] );
var endpoint = array( new BooleanArray( [ true, false ] ) );

var x = logspace( [ 2, 3 ], 10.0, start, end, endpoint );
// returns <ndarray>[ [ 1.0, 10.0, 100.0 ], [ 1000.0, 10000.0, 100000.0 ] ]

By default, the function generates logarithmically spaced values along the last dimension of an output ndarray. To perform the operation over specific dimensions, provide a dims option.

var x = logspace( [ 2, 2 ], 10.0, 0.0, 3.0, {
    'dims': [ 0, 1 ]
});
// returns <ndarray>[ [ 1.0, 10.0 ], [ 100.0, 1000.0 ] ]

To specify the output ndarray data type, provide a dtype option.

var x = logspace( [ 4 ], 10.0, 0.0, 3.0, {
    'dtype': 'float32'
});
// returns <ndarray>[ 1.0, 10.0, 100.0, 1000.0 ]

logspace.assign( out, base, start, stop[, endpoint][, options] )

Fills an ndarray with logarithmically spaced values over a specified interval along one or more ndarray dimensions.

var zeros = require( '@stdlib/ndarray-zeros' );

var x = zeros( [ 4 ] );
// returns <ndarray>

var out = logspace.assign( x, 10.0, 0.0, 3.0 );
// returns <ndarray>[ 1.0, 10.0, 100.0, 1000.0 ]

var bool = ( x === out );
// returns true

The function has the following parameters:

• out: output ndarray. Must have a floating-point or "generic" data type.
• base: base of the logarithmic scale. May be either a number or an ndarray having a real-valued or "generic" data type. If provided an ndarray, the value must have a shape which is broadcast-compatible with the complement of the shape defined by options.dims. For example, given the input shape [2, 3, 4] and options.dims=[0], a base ndarray must have a shape which is broadcast-compatible with the shape [3, 4]. Similarly, when performing the operation over all elements in a provided output ndarray, a base ndarray must be a zero-dimensional ndarray.
• start: exponent of the starting value, where the starting value is given by base^start. May be either a number, a complex number, or an ndarray having a numeric or "generic" data type. If provided an ndarray, the value must have a shape which is broadcast-compatible with the complement of the shape defined by options.dims. For example, given the input shape [2, 3, 4] and options.dims=[0], a start ndarray must have a shape which is broadcast-compatible with the shape [3, 4]. Similarly, when performing the operation over all elements in a provided output ndarray, a start ndarray must be a zero-dimensional ndarray.
• stop: exponent of the final value, where the final value is given by base^stop. May be either a number, a complex number, or an ndarray having a numeric or "generic" data type. If provided an ndarray, the value must have a shape which is broadcast-compatible with the complement of the shape defined by options.dims. For example, given the input shape [2, 3, 4] and options.dims=[0], a stop ndarray must have a shape which is broadcast-compatible with the shape [3, 4]. Similarly, when performing the operation over all elements in a provided output ndarray, a stop ndarray must be a zero-dimensional ndarray.
• endpoint: specifies whether to include the base^stop value when writing values to the output ndarray (optional). May be either a boolean or an ndarray having a boolean or "generic" data type. If provided an ndarray, the value must have a shape which is broadcast-compatible with the complement of the shape defined by options.dims. For example, given the input shape [2, 3, 4] and options.dims=[0], an endpoint ndarray must have a shape which is broadcast-compatible with the shape [3, 4]. Similarly, when performing the operation over all elements in a provided output ndarray, an endpoint ndarray must be a zero-dimensional ndarray. Default: true.
• options: function options (optional).

The function accepts the following options:

• dims: list of dimensions over which to perform operation. If not provided, the function generates logarithmically spaced values along the last dimension. Default: [-1].

Notes

• Let M be the number of logarithmically spaced values to be written along one or more ndarray dimensions. The spacing between the exponents is thus given by

  Δ = (stop-start)/(M-1)
  

  and the generated values are equal to base^(start+Δ*i) for i = 0, 1, ..., M-1.

• If an output ndarray has a single element and the function is supposed to include the base^stop value, the set of values written to an output ndarray only includes the base^stop value, but not the base^start value.

• Otherwise, when an output ndarray has a single element and the function is not supposed to include the base^stop value, the set of values written to an output ndarray only includes the base^start value, but not the base^stop value.

• For a real-valued output ndarray, if start is less than stop, the exponents are generated in ascending order, and, if start is greater than stop, the exponents are generated in descending order.

• When an output ndarray contains at least two values and the function is supposed to include the base^stop value, the set of values written to an output ndarray is guaranteed to include the base^start and base^stop values. Beware, however, that values between base^start and base^stop are subject to floating-point rounding errors.

• When writing to a complex floating-point output ndarray, real-valued start and stop values are treated as complex numbers having a real component equaling the provided value and having an imaginary component equaling zero.

• When generating logarithmically spaced complex floating-point numbers, generated values follow a logarithmic spiral in the complex plane, where imaginary components of start and stop control phase rotation.

• The base of the logarithmic scale must be real-valued, even when writing to a complex floating-point output ndarray.

• Both start and stop are cast to the data type of the output ndarray.

• The function iterates over ndarray elements according to the memory layout of an output ndarray. Accordingly, performance degradation is possible when operating over multiple dimensions of a large non-contiguous multi-dimensional output ndarray. In such scenarios, one may want to copy an output ndarray to contiguous memory before filling with logarithmically spaced values.

Examples

var ndarray2array = require( '@stdlib/ndarray-to-array' );
var array = require( '@stdlib/ndarray-array' );
var logspace = require( '@stdlib/blas-ext-logspace' );

// Create two vectors defining exponent bounds:
var start = array( [ 0.0, 1.0, 2.0, 3.0, 4.0 ] );
var end = array( [ 4.0, 5.0, 6.0, 7.0, 8.0 ] );

// Create a grid:
var out = logspace( [ 5, 5 ], 2.0, start, end, true );
console.log( ndarray2array( out ) );

// Generate logarithmically spaced values over multiple dimensions:
out = logspace( [ 5, 5 ], 2.0, 0.0, 24.0, true, {
    'dims': [ 0, 1 ]
});
console.log( ndarray2array( out ) );

// Generate logarithmically spaced values over multiple dimensions in column-major order:
out = logspace( [ 5, 5 ], 2.0, 0.0, 24.0, true, {
    'dims': [ 0, 1 ],
    'order': 'column-major'
});
console.log( ndarray2array( out ) );

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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

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