From 4313949bdfca1063da33b9818a31a2362a0e87c1 Mon Sep 17 00:00:00 2001 From: Abhist17 Date: Sun, 4 Oct 2026 01:36:39 +0530 Subject: [PATCH] fix: avoid cancellation near the edges of the support in `stats/base/dists/cosine/pdf` `1 + cos(pi*z)` cancels as `z` approaches -1 or 1, and the density was `0` there although it is positive. Use `1 + cos(pi*z) = 2*cos(pi*z/2)^2`. The fixtures are now generated from the textbook formula in extended precision, with `x` inside the support: `positive_mean.json` held only out-of-support points, so its test checked nothing. --- .../base/dists/cosine/pdf/lib/factory.js | 6 +++- .../stats/base/dists/cosine/pdf/lib/main.js | 6 +++- .../stats/base/dists/cosine/pdf/src/main.c | 5 ++- .../cosine/pdf/test/fixtures/julia/REQUIRE | 1 - .../cosine/pdf/test/fixtures/julia/edges.json | 1 + .../test/fixtures/julia/large_variance.json | 2 +- .../test/fixtures/julia/negative_mean.json | 2 +- .../test/fixtures/julia/positive_mean.json | 2 +- .../cosine/pdf/test/fixtures/julia/runner.jl | 34 ++++++++++++------- .../dists/cosine/pdf/test/test.factory.js | 30 ++++++++++++++-- .../base/dists/cosine/pdf/test/test.native.js | 28 +++++++++++++-- .../base/dists/cosine/pdf/test/test.pdf.js | 28 +++++++++++++-- 12 files changed, 116 insertions(+), 29 deletions(-) create mode 100644 lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/edges.json diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/lib/factory.js b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/lib/factory.js index a1c520ea277a..8aa519358c0b 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/lib/factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/lib/factory.js @@ -64,6 +64,7 @@ function factory( mu, s ) { * // returns */ function pdf( x ) { + var c; var z; if ( isnan( x ) ) { return NaN; @@ -75,7 +76,10 @@ function factory( mu, s ) { return 0.0; } z = ( x - mu ) / s; - return ( 1.0 + cospi( z ) ) / ( 2.0 * s ); + + // `1 + cos(pi*z)` cancels near the edges of the support (`z = -1` and `z = 1`); `1 + cos(pi*z) = 2*cos(pi*z/2)^2` has no subtraction: + c = cospi( z / 2.0 ); + return ( c * c ) / s; } } diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/lib/main.js index bb693ba2f904..c825c1e14224 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/lib/main.js +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/lib/main.js @@ -69,6 +69,7 @@ var PINF = require( '@stdlib/constants/float64/pinf' ); * // returns Infinity */ function pdf( x, mu, s ) { + var c; var z; if ( isnan( x ) || @@ -88,7 +89,10 @@ function pdf( x, mu, s ) { return 0.0; } z = ( x - mu ) / s; - return ( 1.0 + cospi( z ) ) / ( 2.0 * s ); + + // `1 + cos(pi*z)` cancels near the edges of the support (`z = -1` and `z = 1`); `1 + cos(pi*z) = 2*cos(pi*z/2)^2` has no subtraction: + c = cospi( z / 2.0 ); + return ( c * c ) / s; } diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/src/main.c index df6182708ea8..dcd5482fa45f 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/src/main.c +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/src/main.c @@ -52,5 +52,8 @@ double stdlib_base_dists_cosine_pdf( const double x, const double mu, const doub return 0.0; } const double p = ( x - mu ) / s; - return ( 1.0 + stdlib_base_cospi( p ) ) / ( 2.0 * s ); + + // `1 + cos(pi*z)` cancels near the edges of the support (`z = -1` and `z = 1`); `1 + cos(pi*z) = 2*cos(pi*z/2)^2` has no subtraction: + const double c = stdlib_base_cospi( p / 2.0 ); + return ( c * c ) / s; } diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/REQUIRE index 98be20b58ed3..308c3be89c85 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/REQUIRE +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/REQUIRE @@ -1,3 +1,2 @@ -Distributions 0.23.8 julia 1.5 JSON 0.21 diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/edges.json b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/edges.json new file mode 100644 index 000000000000..143b05b08bfa --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/edges.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/large_variance.json b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/large_variance.json index 3d77c531d603..4696ee6c535f 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/large_variance.json +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/large_variance.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/negative_mean.json b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/negative_mean.json index 68035d61643c..140e65560f8a 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/negative_mean.json +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/negative_mean.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/positive_mean.json b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/positive_mean.json index 981df36f6b03..3af24f008c11 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/positive_mean.json +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/positive_mean.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/runner.jl index bb28173c6a9f..e702ec272ced 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/fixtures/julia/runner.jl @@ -16,7 +16,6 @@ # See the License for the specific language governing permissions and # limitations under the License. -import Distributions: pdf, Cosine import JSON """ @@ -24,6 +23,8 @@ import JSON Generate fixture data and write to file. +The density is evaluated in extended precision from the textbook formula `(1 + cos(pi*z)) / (2s)`, with `z = (x-mu)/s`. + # Arguments * `x`: input value @@ -41,9 +42,9 @@ julia> gen( x, mu, s, "data.json" ); ``` """ function gen( x, mu, s, name ) - z = Array{Float64}( undef, length(x) ); - for i in eachindex(x) - z[ i ] = pdf( Cosine( mu[i], s[i] ), x[i] ); + z = setprecision( BigFloat, 2048 ) do + zz = ( BigFloat.( x ) .- BigFloat.( mu ) ) ./ BigFloat.( s ); + Float64.( ( 1 .+ cos.( BigFloat( pi ) .* zz ) ) ./ ( 2 .* BigFloat.( s ) ) ) end # Store data to be written to file as a collection: @@ -70,20 +71,27 @@ file = @__FILE__; # Extract the directory in which this file resides: dir = dirname( file ); -# Negative mean: -x = rand( 1000 ) .* 10.0 .- 20.0; +# Negative mean (`x` inside the support): mu = rand( 1000 ) .* -10.0; -s = rand( 1000 ) .* 5.0; +s = ( rand( 1000 ) .* 5.0 ) .+ 0.1; +x = mu .+ ( s .* ( ( rand( 1000 ) .* 2.0 ) .- 1.0 ) ); gen( x, mu, s, "negative_mean.json" ); -# Positive mean: -x = rand( 1000 ) .* 10.0 .- 20.0; +# Positive mean (`x` inside the support): mu = rand( 1000 ) .* 10.0; -s = rand( 1000 ) .* 5.0; +s = ( rand( 1000 ) .* 5.0 ) .+ 0.1; +x = mu .+ ( s .* ( ( rand( 1000 ) .* 2.0 ) .- 1.0 ) ); gen( x, mu, s, "positive_mean.json" ); -# Large variance: -x = rand( 1000 ) .* 5.0; +# Large variance (`x` inside the support): mu = rand( 1000 ); -s = rand( 1000 ) .* 20.0; +s = ( rand( 1000 ) .* 20.0 ) .+ 1.0; +x = mu .+ ( s .* ( ( rand( 1000 ) .* 2.0 ) .- 1.0 ) ); gen( x, mu, s, "large_variance.json" ); + +# Close to the edges of the support (`mu = 0` and `s` a power of two, so that `z = x/s` is exact and the test measures the error from `1 + cos(pi*z)`): +s = repeat( [ 0.5, 1.0, 2.0, 4.0 ], 250 ); +d = exp10.( range( -15.0, stop = -1.0, length = 500 ) ); +x = s .* vcat( 1.0 .- d, -1.0 .+ d ); +mu = zeros( 1000 ); +gen( x, mu, s, "edges.json" ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/test.factory.js index 524d8c341fac..e653bc77fe2b 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/test.factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/test.factory.js @@ -34,6 +34,7 @@ var factory = require( './../lib/factory.js' ); var positiveMean = require( './fixtures/julia/positive_mean.json' ); var negativeMean = require( './fixtures/julia/negative_mean.json' ); var largeVariance = require( './fixtures/julia/large_variance.json' ); +var edges = require( './fixtures/julia/edges.json' ); // TESTS // @@ -184,7 +185,7 @@ tape( 'the created function evaluates the pdf for `x` given positive `mu`', func pdf = factory( mu[i], s[i] ); y = pdf( x[i] ); if ( expected[i] !== null && !( expected[i] === 0.0 && y < EPS ) ) { - t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 255 ), true, 'returns expected value' ); } } t.end(); @@ -207,7 +208,7 @@ tape( 'the created function evaluates the pdf for `x` given negative `mu`', func pdf = factory( mu[i], s[i] ); y = pdf( x[i] ); if ( expected[i] !== null && !( expected[i] === 0.0 && y < EPS ) ) { - t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1742 ), true, 'returns expected value' ); } } t.end(); @@ -230,7 +231,30 @@ tape( 'the created function evaluates the pdf for `x` given large variance ( = l pdf = factory( mu[i], s[i] ); y = pdf( x[i] ); if ( expected[i] !== null ) { - t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 370 ), true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the created function evaluates the pdf for `x` close to the edges of the support', function test( t ) { + var expected; + var pdf; + var mu; + var s; + var x; + var y; + var i; + + expected = edges.expected; + x = edges.x; + mu = edges.mu; + s = edges.s; + for ( i = 0; i < x.length; i++ ) { + pdf = factory( mu[i], s[i] ); + y = pdf( x[i] ); + if ( expected[i] !== null && !( expected[i] === 0.0 && y < EPS ) ) { + t.strictEqual( isAlmostSameValue( y, expected[ i ], 3 ), true, 'returns expected value' ); } } t.end(); diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/test.native.js index d29b03682819..49069aaa8bd4 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/test.native.js +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/test.native.js @@ -35,6 +35,7 @@ var tryRequire = require( '@stdlib/utils/try-require' ); var positiveMean = require( './fixtures/julia/positive_mean.json' ); var negativeMean = require( './fixtures/julia/negative_mean.json' ); var largeVariance = require( './fixtures/julia/large_variance.json' ); +var edges = require( './fixtures/julia/edges.json' ); // VARIABLES // @@ -149,7 +150,7 @@ tape( 'the function evaluates the pdf for `x` given positive `mu`', opts, functi for ( i = 0; i < x.length; i++ ) { y = pdf( x[i], mu[i], s[i] ); if ( expected[i] !== null && !( expected[i] === 0.0 && y < EPS ) ) { - t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 255 ), true, 'returns expected value' ); } } t.end(); @@ -170,7 +171,7 @@ tape( 'the function evaluates the pdf for `x` given negative `mu`', opts, functi for ( i = 0; i < x.length; i++ ) { y = pdf( x[i], mu[i], s[i] ); if ( expected[i] !== null && !( expected[i] === 0.0 && y < EPS ) ) { - t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1742 ), true, 'returns expected value' ); } } t.end(); @@ -191,7 +192,28 @@ tape( 'the function evaluates the pdf for `x` given large variance ( = large `s` for ( i = 0; i < x.length; i++ ) { y = pdf( x[i], mu[i], s[i] ); if ( expected[i] !== null ) { - t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 370 ), true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the pdf for `x` close to the edges of the support', opts, function test( t ) { + var expected; + var mu; + var x; + var s; + var y; + var i; + + expected = edges.expected; + x = edges.x; + mu = edges.mu; + s = edges.s; + for ( i = 0; i < x.length; i++ ) { + y = pdf( x[i], mu[i], s[i] ); + if ( expected[i] !== null && !( expected[i] === 0.0 && y < EPS ) ) { + t.strictEqual( isAlmostSameValue( y, expected[ i ], 3 ), true, 'returns expected value' ); } } t.end(); diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/test.pdf.js b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/test.pdf.js index 5c47459ae45f..c33caa81393a 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/test.pdf.js +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/pdf/test/test.pdf.js @@ -34,6 +34,7 @@ var pdf = require( './../lib' ); var positiveMean = require( './fixtures/julia/positive_mean.json' ); var negativeMean = require( './fixtures/julia/negative_mean.json' ); var largeVariance = require( './fixtures/julia/large_variance.json' ); +var edges = require( './fixtures/julia/edges.json' ); // TESTS // @@ -140,7 +141,7 @@ tape( 'the function evaluates the pdf for `x` given positive `mu`', function tes for ( i = 0; i < x.length; i++ ) { y = pdf( x[i], mu[i], s[i] ); if ( expected[i] !== null && !( expected[i] === 0.0 && y < EPS ) ) { - t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 255 ), true, 'returns expected value' ); } } t.end(); @@ -161,7 +162,7 @@ tape( 'the function evaluates the pdf for `x` given negative `mu`', function tes for ( i = 0; i < x.length; i++ ) { y = pdf( x[i], mu[i], s[i] ); if ( expected[i] !== null && !( expected[i] === 0.0 && y < EPS ) ) { - t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1742 ), true, 'returns expected value' ); } } t.end(); @@ -182,7 +183,28 @@ tape( 'the function evaluates the pdf for `x` given large variance ( = large `s` for ( i = 0; i < x.length; i++ ) { y = pdf( x[i], mu[i], s[i] ); if ( expected[i] !== null ) { - t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 370 ), true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the pdf for `x` close to the edges of the support', function test( t ) { + var expected; + var mu; + var x; + var s; + var y; + var i; + + expected = edges.expected; + x = edges.x; + mu = edges.mu; + s = edges.s; + for ( i = 0; i < x.length; i++ ) { + y = pdf( x[i], mu[i], s[i] ); + if ( expected[i] !== null && !( expected[i] === 0.0 && y < EPS ) ) { + t.strictEqual( isAlmostSameValue( y, expected[ i ], 3 ), true, 'returns expected value' ); } } t.end();