feat: add `stats/base/dists/halfnormal/entropy` by bhargava-d16 · Pull Request #9753 · stdlib-js/stdlib

bhargava-d16 · 2026-01-14T22:18:21Z

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Progresses #9416

Description

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This pull request:

This PR adds implementation of entropy calculation for half-normal distribution.

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This pull request has the following related issues:

[RFC]: Tracking issue for complete implementation of @stdlib/stats/base/dists/halfnormal package #9416

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Read, understood, and followed the contributing guidelines.

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I consulted ChatGPT to verify mathematical formulation of half-normal entropy function and to confirm expected numerical values

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stdlib-bot · 2026-01-14T22:21:08Z

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/halfnormal/entropy	$\color{green}164/164$ $\color{green}+0.00%$	$\color{green}8/8$ $\color{green}+0.00%$	$\color{green}2/2$ $\color{green}+0.00%$	$\color{green}164/164$ $\color{green}+0.00%$

The above coverage report was generated for the changes in this PR.

Planeshifter

Thanks for this PR! Left initial comment.

Planeshifter · 2026-01-14T23:32:10Z

+// returns ~2.6238370975295946
+```
+
+If provided `sigma < 0`, the function returns `NaN`.


The documentation says sigma < 0 but the implementation in lib/main.js checks sigma <= 0.0. This should be updated to sigma <= 0 to match the implementation behavior (sigma=0 also returns NaN).

Note: docs/repl.txt correctly uses σ ≤ 0.

Planeshifter · 2026-01-14T23:32:11Z

+
+```c
+double out = stdlib_base_dists_halfnormal_entropy( 1.0 );
+// returns ~0.726


The expected output value ~0.726 is incorrect. For sigma=1.0, the entropy should be ~1.0143991850954939 (as shown correctly in the JavaScript examples above).

double out = stdlib_base_dists_halfnormal_entropy( 1.0 ); // returns ~1.014

Planeshifter · 2026-01-14T23:32:12Z

+*
+* ## Notes
+*
+* -   If provided `σ < 0`, the function returns `NaN`.


The documentation says σ < 0 but the implementation checks σ <= 0. This should be updated to σ ≤ 0 to match the implementation behavior (sigma=0 also returns NaN).

Note: docs/repl.txt correctly uses σ ≤ 0.

Planeshifter · 2026-01-15T01:56:51Z

+var y = entropy( 1.0 );
+// returns ~1.0143991850954939
+
+y = entropy( 5.0 );
+// returns ~2.6238370975295946


Suggested change

var y = entropy( 1.0 );

// returns ~1.0143991850954939

y = entropy( 5.0 );

// returns ~2.6238370975295946

var y = entropy( 1.0 );

// returns ~1.014

y = entropy( 5.0 );

// returns ~2.624

--- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: passed - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: passed - task: lint_license_headers status: passed ---

Planeshifter · 2026-01-16T05:16:28Z

@@ -0,0 +1,26 @@
+{{alias}}( σ )


The file should start with a leading blank line before {{alias}}.

Suggested change

{{alias}}( σ )

{{alias}}( σ )

Planeshifter · 2026-01-16T05:16:30Z

+* var v = entropy( 1.0 );
+* // returns ~1.0143991850954939
+*
+* @example
+* var v = entropy( 5.0 );
+* // returns ~2.6238370975295946


Same as the repl.txt - the example return values should use short approximations instead of full precision. Reference packages (e.g., rayleigh/entropy) use // returns ~3.139 rather than the full value.

Suggested change

* var v = entropy( 1.0 );

* // returns ~1.0143991850954939

*

* @example

* var v = entropy( 5.0 );

* // returns ~2.6238370975295946

* var v = entropy( 1.0 );

* // returns ~1.014

*

* @example

* var v = entropy( 5.0 );

* // returns ~2.624

Planeshifter · 2026-01-16T05:16:32Z

+	for ( i = 0; i < expected.length; i++ ) {
+		y = entropy( sigma[ i ] );
+		if ( y === expected[ i ] ) {
+			t.strictEqual(y, expected[ i ], 'sigma: '+sigma[i]+', y: '+y+', expected: '+expected[i]);


Missing space after t.strictEqual( - should be t.strictEqual( y, with a space after the opening parenthesis, matching stdlib's spacing convention.

Suggested change

t.strictEqual(y, expected[ i ], 'sigma: '+sigma[i]+', y: '+y+', expected: '+expected[i]);

t.strictEqual( y, expected[ i ], 'sigma: '+sigma[i]+', y: '+y+', expected: '+expected[i] );

Planeshifter · 2026-01-16T05:16:33Z

+		} else {
+			delta = abs( y - expected[ i ] );
+			tol = 40.0 * EPS * abs( expected[ i ] );
+			t.ok(delta <= tol, 'within tolerance. sigma: '+sigma[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.');


Missing space after t.ok( - should be t.ok( delta with a space after the opening parenthesis.

Suggested change

t.ok(delta <= tol, 'within tolerance. sigma: '+sigma[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.');

t.ok( delta <= tol, 'within tolerance. sigma: '+sigma[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );

Planeshifter · 2026-01-16T05:16:34Z

+		} else {
+			delta = abs( y - expected[ i ] );
+			tol = 40.0 * EPS * abs( expected[ i ] );
+			t.ok(delta <= tol, 'within tolerance. sigma: '+sigma[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.');


Missing space after t.ok( - should be t.ok( delta with a space after the opening parenthesis.

Suggested change

t.ok(delta <= tol, 'within tolerance. sigma: '+sigma[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.');

t.ok( delta <= tol, 'within tolerance. sigma: '+sigma[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );

Planeshifter · 2026-01-16T05:22:19Z

+    > var v = {{alias}}( 1.0 )
+    ~1.0143991850954939
+    > v = {{alias}}( 5.0 )
+    ~2.6238370975295946


The example output values should use short approximations instead of full precision. Looking at other stdlib repl.txt files (e.g., rayleigh/entropy), they use formats like ~3.34 and ~2.446 rather than ~1.0143991850954939.

Suggested change

> var v = {{alias}}( 1.0 )

~1.0143991850954939

> v = {{alias}}( 5.0 )

~2.6238370975295946

> var v = {{alias}}( 1.0 )

~1.014

> v = {{alias}}( 5.0 )

~2.624

Planeshifter · 2026-01-16T05:23:15Z

+* var v = entropy( 1.0 );
+* // returns ~1.0143991850954939
+*
+* v = entropy( 5.0 );
+* // returns ~2.6238370975295946


Suggested change

* var v = entropy( 1.0 );

* // returns ~1.0143991850954939

*

* v = entropy( 5.0 );

* // returns ~2.6238370975295946

* var v = entropy( 1.0 );

* // returns ~1.014

*

* v = entropy( 5.0 );

* // returns ~2.624

Planeshifter · 2026-01-16T05:23:31Z

+* var v = entropy( 1.0 );
+* // returns ~1.0143991850954939
+*
+* @example
+* var v = entropy( 5.0 );
+* // returns ~2.6238370975295946


Suggested change

* var v = entropy( 1.0 );

* // returns ~1.0143991850954939

*

* @example

* var v = entropy( 5.0 );

* // returns ~2.6238370975295946

* var v = entropy( 1.0 );

* // returns ~1.014

*

* @example

* var v = entropy( 5.0 );

* // returns ~2.624

Planeshifter · 2026-01-16T05:23:48Z

+* var v = entropy( 1.0 );
+* // returns ~1.0143991850954939
+*
+* @example
+* var v = entropy( 5.0 );
+* // returns ~2.6238370975295946


Suggested change

* var v = entropy( 1.0 );

* // returns ~1.0143991850954939

*

* @example

* var v = entropy( 5.0 );

* // returns ~2.6238370975295946

* var v = entropy( 1.0 );

* // returns ~1.014

*

* @example

* var v = entropy( 5.0 );

* // returns ~2.624

Planeshifter · 2026-01-16T05:24:07Z

+* double y = stdlib_base_dists_halfnormal_entropy( 1.0 );
+* // returns ~1.0143991850954939


Suggested change

* double y = stdlib_base_dists_halfnormal_entropy( 1.0 );

* // returns ~1.0143991850954939

* double y = stdlib_base_dists_halfnormal_entropy( 1.0 );

* // returns ~1.014

--- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: passed - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: missing_dependencies - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: passed - task: lint_license_headers status: passed ---

--- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed ---

--- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: missing_dependencies - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed ---

bhargava-d16 · 2026-01-16T18:51:08Z

Changes applied as requested @Planeshifter. Thanks for the review !

bhargava-d16 · 2026-01-21T02:50:43Z

@Planeshifter I have made the requested changes.Please let me know if it needs further improvements

Signed-off-by: Philipp Burckhardt <pburckhardt@outlook.com>

Planeshifter

Let's land this one; thank you!

stdlib-bot · 2026-01-22T05:46:44Z

PR Commit Message

feat: add `stats/base/dists/halfnormal/entropy`

PR-URL: https://github.com/stdlib-js/stdlib/pull/9753
Ref: https://github.com/stdlib-js/stdlib/issues/9416

Co-authored-by: Philipp Burckhardt <pburckhardt@outlook.com>
Reviewed-by: Philipp Burckhardt <pburckhardt@outlook.com>
Signed-off-by: Philipp Burckhardt <pburckhardt@outlook.com>

Please review the above commit message and make any necessary adjustments.

kgryte · 2026-01-24T09:03:41Z

+	if ( isnan( sigma ) || sigma <= 0.0 ) {
+		return NaN;
+	}
+	return 0.5 + ln( sigma ) + ln( SQRT_HALF_PI ) + ( 0.5 * GAMMA );


@bhargava-d16 Can you explain how you derived this formula? It doesn't match Wikipedia (ref: https://en.wikipedia.org/wiki/Half-normal_distribution), so I am curious as to its derivation.

cc @Planeshifter

And in fact, when tested against SciPy, all tests fail.

The initial formulation followed the structure used for related scale distributions (e.g. Rayleigh), where the entropy contains an E[ln X] and thus a gamma/2 contribution.

However, explicitly expanding the half-normal log-density shows that the entropy depends only on a second-moment term E[X **2] and no logarithmic expectation remains after simplification.

I will update the implementation to use the simplified closed-form expression 0.5 + ln(sigma) + ln(sqrt(pi/2))

Please let me know if there are any additional changes or checks you’d recommend.

@bhargava-d16 Sorry. I am not sure I follow. Would you mind providing the mathematical derivation of the entropy for a half-normal distribution?

@bhargava-d16 Please do not bother submitting a PR, as I went through and fixed the entire implementation. The implementation now returns the same results as SciPy.

Starting from the definition of differential entropy
(Ref: https://en.wikipedia.org/wiki/Differential_entropy),

H(X) = -∫ f(x) ln f(x) dx,

where the integral is over [0, infinity) since the half-normal distribution
is supported on x ≥ 0.

For a half-normal distribution with scale parameter sigma > 0, the
probability density function is
(Ref: https://en.wikipedia.org/wiki/Half-normal_distribution)

f(x) = sqrt(2)/(sigmasqrt(pi)) * exp(-x^2/(2sigma^2)), x ≥ 0.

Taking the logarithm on both sides,

ln f(x) = ln(sqrt(2)/(sigmasqrt(pi))) - x^2/(2sigma^2).

Substituting into the entropy definition and splitting terms gives

H(X) = -ln(sqrt(2)/(sigmasqrt(pi))) + E[X^2]/(2sigma^2).

For a half-normal random variable X = |Z| with
Z ~ N(0, sigma^2), we have X^2 = Z^2, and hence

E[X^2] = Var(Z) + (E[Z])^2 = sigma^2.

Therefore the second term evaluates to 1/2, and combining terms yields

H(X) = 0.5 + ln(sigma) + 0.5*ln(pi/2)
= 0.5 + ln(sigma) + ln(sqrt(pi/2))

Thank you for the implementation.Out of curiosity, purely for learning purposes, whether the derivation I shared earlier was correct or if there were any differences with the approach you ended with.

PR-URL: stdlib-js#9753 Ref: stdlib-js#9416 Co-authored-by: Philipp Burckhardt <pburckhardt@outlook.com> Reviewed-by: Philipp Burckhardt <pburckhardt@outlook.com> Signed-off-by: Philipp Burckhardt <pburckhardt@outlook.com>

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chore: minor clean-up

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Comment thread lib/node_modules/@stdlib/stats/base/dists/halfnormal/entropy/README.md Outdated

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Signed-off-by: Philipp Burckhardt <pburckhardt@outlook.com>

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	t.strictEqual(y, expected[ i ], 'sigma: '+sigma[i]+', y: '+y+', expected: '+expected[i]);
	t.strictEqual( y, expected[ i ], 'sigma: '+sigma[i]+', y: '+y+', expected: '+expected[i] );

	t.ok(delta <= tol, 'within tolerance. sigma: '+sigma[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.');
	t.ok( delta <= tol, 'within tolerance. sigma: '+sigma[i]+'. y: '+y+'. E: '+expected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );

		* double y = stdlib_base_dists_halfnormal_entropy( 1.0 );
		* // returns ~1.0143991850954939

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