refactor: major updates to tests, benchmarks and README file

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Author: prajjwalbajpai

lib/node_modules/@stdlib/lapack/base/dlasv2/README.md

@@ -20,7 +20,37 @@ limitations under the License.
 
 # dlasv2
 
-> Compute singular value decomposition of a 2x2 triangular matrix.
+> Compute the singular value decomposition of a 2x2 upper triangular matrix.
+
+<section class="intro">
+
+The singular value decomposition of a 2x2 upper triangular matrix $ \begin{bmatrix} F & G \\ 0 & H \end{bmatrix}$ is given by -
+
+<!-- <equation class="equation" label="eq:dlasv2_svd" align="center" raw="\left[\begin{array}{rr} \mathrm{CSL} & \mathrm{SNL} \\ -\mathrm{SNL} & \mathrm{CSL} \end{array}\right] \left[\begin{array}{rr} F & G \\ 0 & H \end{array}\right] \left[\begin{array}{rr} \mathrm{CSR} & -\mathrm{SNR} \\ \mathrm{SNR} & \mathrm{CSR} \end{array}\right] = \left[\begin{array}{rr} \mathrm{SSMAX} & 0 \\ 0 & \mathrm{SSMIN} \end{array}\right]" alt="Singular value decomposition of a 2x2 upper triangular matrix."> -->
+
+```math
+\left[\begin{array}{rr}\mathrm{CSL} & \mathrm{SNL} \\
+-\mathrm{SNL} & \mathrm{CSL}\end{array}\right]
+
+\left[\begin{array}{rr}F & G \\
+0 & H\end{array}\right]
+
+\left[\begin{array}{rr}\mathrm{CSR} & -\mathrm{SNR} \\
+\mathrm{SNR} & \mathrm{CSR}\end{array}\right]
+
+=
+
+\left[\begin{array}{rr}\mathrm{SSMAX} & 0 \\
+0 & \mathrm{SSMIN}\end{array}\right]
+```
+
+<!-- </equation> -->
+
+where `CSL`,`SNL`,`CSR`,`SNR` define orthogonal rotations and $\mathrm{SSMAX}^2, \mathrm{SSMIN}^2$ are the eigenvalues of $A^{T}A$.
+
+</section>
+
+<!-- /.intro -->
 
 <section class="usage">
 
@@ -32,22 +62,27 @@ var dlasv2 = require( '@stdlib/lapack/base/dlasv2' );
 
 #### dlasv2( F, G, H, out )
 
-Computes singular value decomposition of a 2x2 triangular matrix.
+Computes the singular value decomposition of a 2x2 upper triangular matrix.
 
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
 var out = new Float64Array( 6 );
 
-out = dlasv2( 2.0, 3.0, 4.0, out );
-// out => <Float64Array>[ 1.5513263285176897, 5.1568776039816795, 0.9664996487646696, 0.25666793515702424, 0.7496781758158659, 0.6618025632357402 ]
+var v = dlasv2( 2.0, 3.0, 4.0, out );
+// returns <Float64Array>[ ~1.5513, ~5.1569, ~0.9665, ~0.2567, ~0.7497, ~0.6618 ]
+
+var bool = ( v === out );
+// returns true
 ```
 
 The function has the following parameters:
 
 -   **F**: the (0,0) element of matrix.
 -   **G**: the (0,1) element of matrix.
 -   **H**: the (1,1) element of matrix.
--   **out**: [`Float64Array`][mdn-float64array] output array containing `SSMIN`, `SSMAX`, `SNR`, `CSR`, `SNL`, and `CSL` respectively.
+-   **out**: [`Float64Array`][@stdlib/array/float64] output array containing `SSMIN`, `SSMAX`, `SNR`, `CSR`, `SNL`, and `CSL` respectively.
+
+On return, `abs(SSMAX)` is the larger singular value, `abs(SSMIN)` is the smaller singular value, and (`CSL`,`SNL`) and (`CSR`,`SNR`) are the left and right singular vectors for `abs(SSMAX)` as described in the decomposition.
 
 Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
 
@@ -63,19 +98,19 @@ var OUT0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
 var OUT1 = new Float64Array( OUT0.buffer, OUT0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
 
 dlasv2( 2.0, 3.0, 4.0, OUT1 );
-// OUT0 => <Float64Array>[ 0.0, 1.5513263285176897, 5.1568776039816795, 0.9664996487646696, 0.25666793515702424, 0.7496781758158659, 0.6618025632357402 ]
+// OUT0 => <Float64Array>[ 0.0, ~1.5513, ~5.1569, ~0.9665, ~0.2567, ~0.7497, ~0.6618 ]
 ```
 
 #### dlasv2.ndarray( F, G, H, out, strideOut, offsetOut )
 
-Computes singular value decomposition of a 2x2 triangular matrix using alternative indexing semantics.
+Computes the singular value decomposition of a 2x2 upper triangular matrix using alternative indexing semantics.
 
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
 var out = new Float64Array( 6 );
 
-out = dlasv2.ndarray( 2.0, 3.0, 4.0, out, 1, 0 );
-// out => <Float64Array>[ 1.5513263285176897, 5.1568776039816795, 0.9664996487646696, 0.25666793515702424, 0.7496781758158659, 0.6618025632357402 ]
+dlasv2.ndarray( 2.0, 3.0, 4.0, out, 1, 0 );
+// out => <Float64Array>[ ~1.5513, ~5.1569, ~0.9665, ~0.2567, ~0.7497, ~0.6618 ]
 ```
 
 The function has the following additional parameters:
@@ -89,10 +124,10 @@ While [`typed array`][mdn-typed-array] views mandate a view offset based on the
 
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
-var out = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] );
+var out = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
 
-out = dlasv2.ndarray( 2.0, 3.0, 4.0, out, 1, 1 );
-// out => <Float64Array>[ 0.0, 1.5513263285176897, 5.1568776039816795, 0.9664996487646696, 0.25666793515702424, 0.7496781758158659, 0.6618025632357402 ]
+dlasv2.ndarray( 2.0, 3.0, 4.0, out, 1, 1 );
+// out => <Float64Array>[ 0.0, ~1.5513, ~5.1569, ~0.9665, ~0.2567, ~0.7497, ~0.6618 ]
 ```
 
 </section>
@@ -121,7 +156,10 @@ var dlasv2 = require( '@stdlib/lapack/base/dlasv2' );
 
 var out = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
 
-out = dlasv2( 2.0, 3.0, 4.0, out );
+dlasv2( 1.0, 1e6, 2.0, out );
+console.log( out );
+
+dlasv2.ndarray( 1.0, 1e6, 2.0, out, 1, 0 );
 console.log( out );
 ```
 
@@ -215,7 +253,7 @@ TODO
 
 [lapack-dlasv2]: https://www.netlib.org/lapack/explore-html/d8/da7/group__lasv2_ga96f9f244300d82921950e2c393b4b20f.html#ga96f9f244300d82921950e2c393b4b20f
 
-[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
+[@stdlib/array/float64]: https://stdlib.io/docs/api/latest/@stdlib/array/float64
 
 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
 

lib/node_modules/@stdlib/lapack/base/dlasv2/benchmark/benchmark.js

@@ -21,72 +21,40 @@
 // MODULES //
 
 var bench = require( '@stdlib/bench' );
-var uniform = require( '@stdlib/random/array/uniform' );
+var uniform = require( '@stdlib/random/base/uniform' );
+var Float64Array = require( '@stdlib/array/float64' );
+var format = require( '@stdlib/string/format' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var pkg = require( './../package.json' ).name;
 var dlasv2 = require( './../lib/dlasv2.js' );
 
 
-// VARIABLES //
+// MAIN //
 
-var options = {
-	'dtype': 'float64'
-};
+bench( format( '%s', pkg ), function benchmark( b ) {
+	var out;
+	var f;
+	var g;
+	var h;
+	var i;
 
+	out = new Float64Array( 6 );
 
-// FUNCTIONS //
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		f = uniform( -10.0, 10.0 );
+		g = uniform( -10.0, 10.0 );
+		h = uniform( -10.0, 10.0 );
 
-/**
-* Creates a benchmark function.
-*
-* @private
-* @returns {Function} benchmark function
-*/
-function createBenchmark( ) {
-	var out = uniform( 6, 0.0, 100.0, options );
-	return benchmark;
-
-	function benchmark( b ) {
-		var d;
-		var i;
-
-		b.tic();
-		for ( i = 0; i < b.iterations; i++ ) {
-			d = dlasv2( out[ 0 ], out[ 2 ], out[ 1 ], out );
-			if ( isnan( d[ i%out.length ] ) ) {
-				b.fail( 'should not return NaN' );
-			}
-		}
-		b.toc();
-		if ( isnan( d[ i%out.length ] ) ) {
+		dlasv2( f, g, h, out );
+		if ( isnan( out[ i%out.length ] ) ) {
 			b.fail( 'should not return NaN' );
 		}
-		b.pass( 'benchmark finished' );
-		b.end();
 	}
-}
-
-
-// MAIN //
-
-/**
-* Main execution sequence.
-*
-* @private
-*/
-function main() {
-	var min;
-	var max;
-	var f;
-	var i;
-
-	min = 1; // 10^min
-	max = 6; // 10^max
-
-	for ( i = min; i <= max; i++ ) {
-		f = createBenchmark();
-		bench( pkg, f );
+	b.toc();
+	if ( isnan( out[ i%out.length ] ) ) {
+		b.fail( 'should not return NaN' );
 	}
-}
-
-main();
+	b.pass( 'benchmark finished' );
+	b.end();
+});

lib/node_modules/@stdlib/lapack/base/dlasv2/benchmark/benchmark.ndarray.js

@@ -21,72 +21,40 @@
 // MODULES //
 
 var bench = require( '@stdlib/bench' );
-var uniform = require( '@stdlib/random/array/uniform' );
+var uniform = require( '@stdlib/random/base/uniform' );
+var Float64Array = require( '@stdlib/array/float64' );
+var format = require( '@stdlib/string/format' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var pkg = require( './../package.json' ).name;
 var dlasv2 = require( './../lib/ndarray.js' );
 
 
-// VARIABLES //
+// MAIN //
 
-var options = {
-	'dtype': 'float64'
-};
+bench( format( '%s', pkg ), function benchmark( b ) {
+	var out;
+	var f;
+	var g;
+	var h;
+	var i;
 
+	out = new Float64Array( 6 );
 
-// FUNCTIONS //
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		f = uniform( -10.0, 10.0 );
+		g = uniform( -10.0, 10.0 );
+		h = uniform( -10.0, 10.0 );
 
-/**
-* Creates a benchmark function.
-*
-* @private
-* @returns {Function} benchmark function
-*/
-function createBenchmark( ) {
-	var out = uniform( 6, 0.0, 100.0, options );
-	return benchmark;
-
-	function benchmark( b ) {
-		var d;
-		var i;
-
-		b.tic();
-		for ( i = 0; i < b.iterations; i++ ) {
-			d = dlasv2( out[ 0 ], out[ 2 ], out[ 1 ], out, 1, 0 );
-			if ( isnan( d[ i%out.length ] ) ) {
-				b.fail( 'should not return NaN' );
-			}
-		}
-		b.toc();
-		if ( isnan( d[ i%out.length ] ) ) {
+		dlasv2( f, g, h, out, 1, 0 );
+		if ( isnan( out[ i%out.length ] ) ) {
 			b.fail( 'should not return NaN' );
 		}
-		b.pass( 'benchmark finished' );
-		b.end();
 	}
-}
-
-
-// MAIN //
-
-/**
-* Main execution sequence.
-*
-* @private
-*/
-function main() {
-	var min;
-	var max;
-	var f;
-	var i;
-
-	min = 1; // 10^min
-	max = 6; // 10^max
-
-	for ( i = min; i <= max; i++ ) {
-		f = createBenchmark();
-		bench( pkg+':ndarray', f );
+	b.toc();
+	if ( isnan( out[ i%out.length ] ) ) {
+		b.fail( 'should not return NaN' );
 	}
-}
-
-main();
+	b.pass( 'benchmark finished' );
+	b.end();
+});