dlassq

Return an updated sum of squares represented in scaled form.

This routine returns the values $s_{textrm{out}}$ and $\textrm{ss}_{\textrm{out}}$ such that

where $x_i = X_{(i-1) \cdot \textrm{sx}}$ and $\textrm{sx}$ is the stride of X. The value of $\textrm{ss}_{\textrm{in}}$ is assumed to be nonnegative.

Installation

npm install @stdlib/lapack-base-dlassq

Usage

var dlassq = require( '@stdlib/lapack-base-dlassq' );

dlassq( N, X, strideX, scale, sumsq )

Returns an updated sum of squares represented in scaled form.

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

var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );

var out = dlassq( 4, X, 1, 1.0, 0.0 );
// returns <Float64Array>[ 1.0, 30.0 ]

The function has the following parameters:

• N: number of indexed elements.
• X: input Float64Array.
• strideX: stride length for X.
• scale: scaling factor.
• sumsq: basic sum of squares from which output is factored out.

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( [ 0.0, 1.0, 2.0, 3.0, 4.0 ] );

// Create an offset view:
var X1 = new Float64Array( X0.buffer, X0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

// Compute the sum of squares:
var out = dlassq( X1.length, X1, 1, 1.0, 0.0 );
// returns <Float64Array>[ 1.0, 30.0 ]

The returned Float64Array contains an updated scale factor and an updated sum of squares, respectively.

dlassq.ndarray( N, X, sx, ox, scale, sumsq, out, so, oo )

Returns an updated sum of squares represented in scaled form using alternative indexing semantics.

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

var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
var out = new Float64Array( [ 0.0, 0.0 ] );

dlassq.ndarray( 4, X, 1, 0, 1.0, 0.0, out, 1, 0 );
// out => <Float64Array>[ 1.0, 30.0 ]

The function has the following additional parameters:

• ox: starting index for X.
• out: output Float64Array.
• so: stride length for out.
• oo: starting index for out.

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,

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

var X = new Float64Array( [ 1.0, 0.0, 2.0, 0.0, 3.0, 0.0, 4.0 ] );
var out = new Float64Array( [ 0.0, 0.0, 999.9, 0.0, 999.9 ] );

dlassq.ndarray( 4, X, 2, 0, 1.0, 0.0, out, 2, 1 );
// out => <Float64Array>[ 0.0, 1.0, 999.9, 30.0, 999.9 ]

Notes

• dlassq() corresponds to the LAPACK function dlassq.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var dlassq = require( '@stdlib/lapack-base-dlassq' );

var X = discreteUniform( 10, -10, 10, {
    'dtype': 'float64'
});
console.log( X );

var out = dlassq( X.length, X, 1, 1.0, 0.0 );
console.log( out );

C APIs

Usage

TODO

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Examples

TODO

References

• Blue, James L. 1978. "A Portable Fortran Program to Find the Euclidean Norm of a Vector." ACM Transactions on Mathematical Software 4 (1). New York, NY, USA: Association for Computing Machinery: 15–23. doi:10.1145/355769.355771.
• Anderson, Edward. 2017. "Algorithm 978: Safe Scaling in the Level 1 BLAS." ACM Transactions on Mathematical Software 44 (1). New York, NY, USA: Association for Computing Machinery: 1–28. doi:10.1145/3061665.

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.

Community

License

See LICENSE.

Copyright

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