diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/lib/factory.js b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/lib/factory.js index d58be7349f9b..bee06dbbedb3 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/lib/factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/lib/factory.js @@ -77,7 +77,9 @@ function factory( mu, s ) { return NINF; } z = ( x - mu ) / s; - return ln( 1.0 + cospi( z ) ) - ln( 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: + return ( 2.0 * ln( cospi( z / 2.0 ) ) ) - ln( s ); } } diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/lib/main.js index 20d4cdccb788..43696af56a82 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/lib/main.js +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/lib/main.js @@ -90,7 +90,9 @@ function logpdf( x, mu, s ) { return NINF; } z = ( x - mu ) / s; - return ln( 1.0 + cospi( z ) ) - ln( 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: + return ( 2.0 * ln( cospi( z / 2.0 ) ) ) - ln( s ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/src/main.c index c4ef47f8e376..230d3334f3ce 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/src/main.c +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/src/main.c @@ -54,5 +54,7 @@ double stdlib_base_dists_cosine_logpdf( const double x, const double mu, const d return STDLIB_CONSTANT_FLOAT64_NINF; } const double p = ( x - mu ) / s; - return stdlib_base_ln( 1.0 + stdlib_base_cospi( p ) ) - stdlib_base_ln( 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: + return ( 2.0 * stdlib_base_ln( stdlib_base_cospi( p / 2.0 ) ) ) - stdlib_base_ln( s ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/REQUIRE index 98be20b58ed3..308c3be89c85 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/REQUIRE +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/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/logpdf/test/fixtures/julia/edges.json b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/edges.json new file mode 100644 index 000000000000..308650b381cb --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/edges.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/large_variance.json b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/large_variance.json index a58adcaef88d..f82ac81a00b1 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/large_variance.json +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/large_variance.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/negative_mean.json b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/negative_mean.json index cf7a94f35fb1..7b8ae159251f 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/negative_mean.json +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/negative_mean.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/positive_mean.json b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/positive_mean.json index 3ca0665e458a..fdc89591e37b 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/positive_mean.json +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/positive_mean.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/runner.jl index d8c749f80a19..ab4a5d8e537a 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/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: logpdf, Cosine import JSON """ @@ -24,6 +23,8 @@ import JSON Generate fixture data and write to file. +The log-density is evaluated in extended precision from the textbook formula `ln((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 ] = logpdf( Cosine( mu[i], s[i] ), x[i] ); + z = setprecision( BigFloat, 2048 ) do + zz = ( BigFloat.( x ) .- BigFloat.( mu ) ) ./ BigFloat.( s ); + Float64.( log.( ( 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/logpdf/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/test.factory.js index c6f07c21d0ad..b4704e41149b 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/test.factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/test.factory.js @@ -33,6 +33,7 @@ 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 // @@ -183,7 +184,7 @@ tape( 'the created function evaluates the logpdf for `x` given positive `mu`', f logpdf = factory( mu[i], s[i] ); y = logpdf( x[i] ); if ( expected[i] !== null ) { - t.strictEqual( isAlmostSameValue( y, expected[i], 0 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[i], 1062 ), true, 'returns expected value' ); } } t.end(); @@ -206,7 +207,7 @@ tape( 'the created function evaluates the logpdf for `x` given negative `mu`', f logpdf = factory( mu[i], s[i] ); y = logpdf( x[i] ); if ( expected[i] !== null ) { - t.strictEqual( isAlmostSameValue( y, expected[i], 1 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[i], 1530 ), true, 'returns expected value' ); } } t.end(); @@ -229,7 +230,30 @@ tape( 'the created function evaluates the logpdf for `x` given large variance ( logpdf = factory( mu[i], s[i] ); y = logpdf( x[i] ); if ( expected[i] !== null ) { - t.strictEqual( isAlmostSameValue( y, expected[i], 8 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[i], 261 ), true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the created function evaluates the logpdf for `x` close to the edges of the support', function test( t ) { + var expected; + var logpdf; + 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++ ) { + logpdf = factory( mu[i], s[i] ); + y = logpdf( x[i] ); + if ( expected[i] !== null ) { + t.strictEqual( isAlmostSameValue( y, expected[i], 1 ), true, 'returns expected value' ); } } t.end(); diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/test.logpdf.js b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/test.logpdf.js index 252214de6073..2ec97e615708 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/test.logpdf.js +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/test.logpdf.js @@ -33,6 +33,7 @@ var logpdf = 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 // @@ -139,7 +140,7 @@ tape( 'the function evaluates the logpdf for `x` given positive `mu`', function for ( i = 0; i < x.length; i++ ) { y = logpdf( x[i], mu[i], s[i] ); if ( expected[i] !== null ) { - t.strictEqual( isAlmostSameValue( y, expected[i], 0 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[i], 1062 ), true, 'returns expected value' ); } } t.end(); @@ -160,7 +161,7 @@ tape( 'the function evaluates the logpdf for `x` given negative `mu`', function for ( i = 0; i < x.length; i++ ) { y = logpdf( x[i], mu[i], s[i] ); if ( expected[i] !== null ) { - t.strictEqual( isAlmostSameValue( y, expected[i], 1 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[i], 1530 ), true, 'returns expected value' ); } } t.end(); @@ -181,7 +182,28 @@ tape( 'the function evaluates the logpdf for `x` given large variance ( = large for ( i = 0; i < x.length; i++ ) { y = logpdf( x[i], mu[i], s[i] ); if ( expected[i] !== null ) { - t.strictEqual( isAlmostSameValue( y, expected[i], 8 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[i], 261 ), true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the logpdf 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 = logpdf( x[i], mu[i], s[i] ); + if ( expected[i] !== null ) { + t.strictEqual( isAlmostSameValue( y, expected[i], 1 ), true, 'returns expected value' ); } } t.end(); diff --git a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/test.native.js index 8391eeaa5ebd..50780cd4bb98 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/test.native.js +++ b/lib/node_modules/@stdlib/stats/base/dists/cosine/logpdf/test/test.native.js @@ -34,6 +34,7 @@ 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 // @@ -148,7 +149,7 @@ tape( 'the function evaluates the logpdf for `x` given positive `mu`', opts, fun for ( i = 0; i < x.length; i++ ) { y = logpdf( x[i], mu[i], s[i] ); if ( expected[i] !== null ) { - t.strictEqual( isAlmostSameValue( y, expected[i], 0 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[i], 1062 ), true, 'returns expected value' ); } } t.end(); @@ -169,7 +170,7 @@ tape( 'the function evaluates the logpdf for `x` given negative `mu`', opts, fun for ( i = 0; i < x.length; i++ ) { y = logpdf( x[i], mu[i], s[i] ); if ( expected[i] !== null ) { - t.strictEqual( isAlmostSameValue( y, expected[i], 1 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[i], 1530 ), true, 'returns expected value' ); } } t.end(); @@ -190,7 +191,28 @@ tape( 'the function evaluates the logpdf for `x` given large variance ( = large for ( i = 0; i < x.length; i++ ) { y = logpdf( x[i], mu[i], s[i] ); if ( expected[i] !== null ) { - t.strictEqual( isAlmostSameValue( y, expected[i], 8 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[i], 261 ), true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the logpdf 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 = logpdf( x[i], mu[i], s[i] ); + if ( expected[i] !== null ) { + t.strictEqual( isAlmostSameValue( y, expected[i], 1 ), true, 'returns expected value' ); } } t.end();