diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/lib/factory.js b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/lib/factory.js index fa10fe6ef6c0..05b9baf1fc0b 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/lib/factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/lib/factory.js @@ -25,7 +25,9 @@ var degenerate = require( '@stdlib/stats/base/dists/degenerate/pdf' ).factory; var isnan = require( '@stdlib/math/base/assert/is-nan' ); var exp = require( '@stdlib/math/base/special/exp' ); var pow = require( '@stdlib/math/base/special/pow' ); +var ln = require( '@stdlib/math/base/special/ln' ); var PINF = require( '@stdlib/constants/float64/pinf' ); +var FLOAT64_SMALLEST_NORMAL = require( '@stdlib/constants/float64/smallest-normal' ); // MAIN // @@ -45,7 +47,9 @@ var PINF = require( '@stdlib/constants/float64/pinf' ); * // returns ~0.392 */ function factory( sigma ) { + var normal; var s2i; + var lns; var s2; if ( isnan( sigma ) || sigma < 0.0 ) { return constantFunction( NaN ); @@ -55,6 +59,8 @@ function factory( sigma ) { } s2 = pow( sigma, 2.0 ); s2i = 1.0 / s2; + normal = ( s2 >= FLOAT64_SMALLEST_NORMAL && 2.0 * s2 < PINF ); + lns = ln( sigma ); return pdf; /** @@ -69,13 +75,31 @@ function factory( sigma ) { * // returns */ function pdf( x ) { + var x2; + var r; + var q; if ( isnan( x ) ) { return NaN; } if ( x < 0.0 || x === PINF ) { return 0.0; } - return s2i * x * exp( -pow( x, 2.0 ) / ( 2.0 * s2 ) ); + x2 = pow( x, 2.0 ); + q = s2i * x; + if ( normal && x2 < PINF && q >= FLOAT64_SMALLEST_NORMAL ) { + return q * exp( -x2 / ( 2.0 * s2 ) ); + } + // For `sigma` or `x` far from `1`, forming `sigma^2` or `x^2` overflows or underflows, so evaluate via the ratio `x/sigma` instead... + r = x / sigma; + if ( r === PINF ) { + return 0.0; + } + q = r / sigma; + if ( q < PINF ) { + return q * exp( -0.5 * r * r ); + } + // `x/sigma^2` overflows only for a tiny `sigma`, where the exponential decides the result: + return exp( ( ln( r ) - lns ) - ( 0.5 * r * r ) ); } } diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/lib/main.js index c3e590ea1809..8a9d5237d317 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/lib/main.js +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/lib/main.js @@ -23,7 +23,9 @@ var isnan = require( '@stdlib/math/base/assert/is-nan' ); var exp = require( '@stdlib/math/base/special/exp' ); var pow = require( '@stdlib/math/base/special/pow' ); +var ln = require( '@stdlib/math/base/special/ln' ); var PINF = require( '@stdlib/constants/float64/pinf' ); +var FLOAT64_SMALLEST_NORMAL = require( '@stdlib/constants/float64/smallest-normal' ); // MAIN // @@ -63,6 +65,9 @@ var PINF = require( '@stdlib/constants/float64/pinf' ); function pdf( x, sigma ) { var s2i; var s2; + var x2; + var r; + var q; if ( isnan( x ) || isnan( sigma ) || @@ -78,7 +83,27 @@ function pdf( x, sigma ) { } s2 = pow( sigma, 2.0 ); s2i = 1.0 / s2; - return s2i * x * exp( -pow( x, 2.0 ) / ( 2.0 * s2 ) ); + x2 = pow( x, 2.0 ); + q = s2i * x; + if ( + s2 >= FLOAT64_SMALLEST_NORMAL && + 2.0 * s2 < PINF && + x2 < PINF && + q >= FLOAT64_SMALLEST_NORMAL + ) { + return q * exp( -x2 / ( 2.0 * s2 ) ); + } + // For `sigma` or `x` far from `1`, forming `sigma^2` or `x^2` overflows or underflows, so evaluate via the ratio `x/sigma` instead... + r = x / sigma; + if ( r === PINF ) { + return 0.0; + } + q = r / sigma; + if ( q < PINF ) { + return q * exp( -0.5 * r * r ); + } + // `x/sigma^2` overflows only for a tiny `sigma`, where the exponential decides the result: + return exp( ( ln( r ) - ln( sigma ) ) - ( 0.5 * r * r ) ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/manifest.json b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/manifest.json index 6ef62470ce2d..62ef2d05a46e 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/manifest.json +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/manifest.json @@ -42,7 +42,9 @@ "@stdlib/math/base/assert/is-nan", "@stdlib/math/base/special/exp", "@stdlib/math/base/special/pow", - "@stdlib/constants/float64/pinf" + "@stdlib/constants/float64/pinf", + "@stdlib/constants/float64/smallest-normal", + "@stdlib/math/base/special/ln" ] }, { @@ -61,7 +63,9 @@ "@stdlib/math/base/special/exp", "@stdlib/constants/float64/eps", "@stdlib/math/base/special/pow", - "@stdlib/constants/float64/pinf" + "@stdlib/constants/float64/pinf", + "@stdlib/constants/float64/smallest-normal", + "@stdlib/math/base/special/ln" ] }, { @@ -79,7 +83,9 @@ "@stdlib/math/base/assert/is-nan", "@stdlib/math/base/special/exp", "@stdlib/math/base/special/pow", - "@stdlib/constants/float64/pinf" + "@stdlib/constants/float64/pinf", + "@stdlib/constants/float64/smallest-normal", + "@stdlib/math/base/special/ln" ] } ] diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/src/main.c index 7e5905533c7c..b3beff7bd87f 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/src/main.c +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/src/main.c @@ -20,7 +20,9 @@ #include "stdlib/math/base/assert/is_nan.h" #include "stdlib/math/base/special/exp.h" #include "stdlib/math/base/special/pow.h" +#include "stdlib/math/base/special/ln.h" #include "stdlib/constants/float64/pinf.h" +#include "stdlib/constants/float64/smallest_normal.h" /** * Evaluates the probability density function (PDF) for a Rayleigh distribution with scale parameter `sigma` at a value `x`. @@ -36,6 +38,9 @@ double stdlib_base_dists_rayleigh_pdf( const double x, const double sigma ) { double s2; double s2i; + double x2; + double r; + double q; if ( stdlib_base_is_nan( x ) || stdlib_base_is_nan( sigma ) || @@ -51,5 +56,25 @@ double stdlib_base_dists_rayleigh_pdf( const double x, const double sigma ) { } s2 = stdlib_base_pow( sigma, 2.0 ); s2i = 1.0 / s2; - return s2i * x * stdlib_base_exp( -stdlib_base_pow( x, 2.0 ) / ( 2.0 * s2 ) ); + x2 = stdlib_base_pow( x, 2.0 ); + q = s2i * x; + if ( + s2 >= STDLIB_CONSTANT_FLOAT64_SMALLEST_NORMAL && + 2.0 * s2 < STDLIB_CONSTANT_FLOAT64_PINF && + x2 < STDLIB_CONSTANT_FLOAT64_PINF && + q >= STDLIB_CONSTANT_FLOAT64_SMALLEST_NORMAL + ) { + return q * stdlib_base_exp( -x2 / ( 2.0 * s2 ) ); + } + // For `sigma` or `x` far from `1`, forming `sigma^2` or `x^2` overflows or underflows, so evaluate via the ratio `x/sigma` instead... + r = x / sigma; + if ( r == STDLIB_CONSTANT_FLOAT64_PINF ) { + return 0.0; + } + q = r / sigma; + if ( q < STDLIB_CONSTANT_FLOAT64_PINF ) { + return q * stdlib_base_exp( -0.5 * r * r ); + } + // `x/sigma^2` overflows only for a tiny `sigma`, where the exponential decides the result: + return stdlib_base_exp( ( stdlib_base_ln( r ) - stdlib_base_ln( sigma ) ) - ( 0.5 * r * r ) ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/fixtures/julia/huge_scale.json b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/fixtures/julia/huge_scale.json new file mode 100644 index 000000000000..8a385a461cd3 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/fixtures/julia/huge_scale.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/fixtures/julia/runner.jl index 1290b18d271c..8f3babbd1f84 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/fixtures/julia/runner.jl @@ -61,6 +61,40 @@ function gen( x, sigma, name ) close( outfile ); end +""" + gen_extended( x, sigma, name ) + +Generate fixture data in extended precision and write to file. + +The PDF is evaluated using the textbook formula `x/sigma^2 * exp(-x^2/(2*sigma^2))` in 2048-bit `BigFloat`, as Distributions.jl evaluates it in `Float64`, where `sigma^2` and `x^2` overflow or underflow for scale parameters far from `1`. + +# Arguments + +* `x`: input value +* `sigma`: scale parameter +* `name::AbstractString`: output filename +""" +function gen_extended( x, sigma, name ) + z = setprecision( BigFloat, 2048 ) do + X = BigFloat.( x ); + S = BigFloat.( sigma ); + Float64.( ( X ./ ( S .^ 2 ) ) .* exp.( .-( X .^ 2 ) ./ ( 2 .* ( S .^ 2 ) ) ) ); + end + + # Store data to be written to file as a collection: + data = Dict([ + ("x", x), + ("sigma", sigma), + ("expected", z) + ]); + + # Write the data to the output filepath as JSON: + outfile = open( joinpath( dir, name ), "w" ); + write( outfile, JSON.json(data) ); + write( outfile, "\n" ); + close( outfile ); +end + # Get the filename: file = @__FILE__; @@ -81,3 +115,13 @@ gen( x, sigma, "medium_scale.json" ); x = rand( 1000 ) .* 20.0; sigma = rand( 1000 ) .* 5.0; gen( x, sigma, "small_scale.json" ); + +# Tiny scale parameter (`sigma^2` underflows): +sigma = exp10.( ( rand( 1000 ) .* 45.0 ) .- 200.0 ); +x = sigma .* exp10.( ( rand( 1000 ) .* 3.0 ) .- 3.0 ); +gen_extended( x, sigma, "tiny_scale.json" ); + +# Huge scale parameter (`sigma^2` overflows): +sigma = exp10.( ( rand( 1000 ) .* 45.0 ) .+ 155.0 ); +x = sigma .* exp10.( ( rand( 1000 ) .* 3.0 ) .- 3.0 ); +gen_extended( x, sigma, "huge_scale.json" ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/fixtures/julia/tiny_scale.json b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/fixtures/julia/tiny_scale.json new file mode 100644 index 000000000000..0df9f6d88fda --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/fixtures/julia/tiny_scale.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/test.factory.js index c0e4475d81c3..b0dd0e04f2aa 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/test.factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/test.factory.js @@ -32,6 +32,8 @@ var factory = require( './../lib/factory.js' ); var smallScale = require( './fixtures/julia/small_scale.json' ); var mediumScale = require( './fixtures/julia/medium_scale.json' ); +var tinyScale = require( './fixtures/julia/tiny_scale.json' ); +var hugeScale = require( './fixtures/julia/huge_scale.json' ); var largeScale = require( './fixtures/julia/large_scale.json' ); @@ -86,6 +88,20 @@ tape( 'if provided a valid `sigma`, the function returns a function which return t.end(); }); +tape( 'the created function returns `0` when `x/sigma` overflows', function test( t ) { + var pdf; + var y; + + pdf = factory( 1.0e-10 ); + y = pdf( 1.0e300 ); + t.strictEqual( y, 0.0, 'returns expected value' ); + + pdf = factory( 1.0e-300 ); + y = pdf( 1.0e308 ); + t.strictEqual( y, 0.0, 'returns expected value' ); + t.end(); +}); + tape( 'if provided a negative `sigma`, the created function always returns `NaN`', function test( t ) { var pdf; var y; @@ -187,3 +203,45 @@ tape( 'the created function evaluates the pdf for `x` given large scale paramete } t.end(); }); + +tape( 'the created function evaluates the pdf for `x` given tiny scale parameter `sigma`', function test( t ) { + var expected; + var sigma; + var pdf; + var i; + var x; + var y; + + expected = tinyScale.expected; + x = tinyScale.x; + sigma = tinyScale.sigma; + for ( i = 0; i < x.length; i++ ) { + pdf = factory( sigma[i] ); + y = pdf( x[i] ); + if ( expected[i] !== null ) { + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the created function evaluates the pdf for `x` given huge scale parameter `sigma`', function test( t ) { + var expected; + var sigma; + var pdf; + var i; + var x; + var y; + + expected = hugeScale.expected; + x = hugeScale.x; + sigma = hugeScale.sigma; + for ( i = 0; i < x.length; i++ ) { + pdf = factory( sigma[i] ); + y = pdf( x[i] ); + if ( expected[i] !== null ) { + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + } + t.end(); +}); diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/test.native.js index 4201206e8b44..76fa874447e7 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/test.native.js +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/test.native.js @@ -33,6 +33,8 @@ var NINF = require( '@stdlib/constants/float64/ninf' ); var smallScale = require( './fixtures/julia/small_scale.json' ); var mediumScale = require( './fixtures/julia/medium_scale.json' ); +var tinyScale = require( './fixtures/julia/tiny_scale.json' ); +var hugeScale = require( './fixtures/julia/huge_scale.json' ); var largeScale = require( './fixtures/julia/large_scale.json' ); @@ -66,6 +68,17 @@ tape( 'if provided `+infinity` for `x` and a valid `sigma`, the function returns t.end(); }); +tape( 'the function returns `0` when `x/sigma` overflows', opts, function test( t ) { + var y; + + y = pdf( 1.0e300, 1.0e-10 ); + t.strictEqual( y, 0.0, 'returns expected value' ); + + y = pdf( 1.0e308, 1.0e-300 ); + t.strictEqual( y, 0.0, 'returns expected value' ); + t.end(); +}); + tape( 'if provided `-infinity` for `x` and a valid `sigma`, the function returns `0`', opts, function test( t ) { var y = pdf( NINF, 1.0 ); t.strictEqual( y, 0.0, 'returns expected value' ); @@ -164,3 +177,41 @@ tape( 'the function evaluates the pdf for `x` given large scale parameter `sigma } t.end(); }); + +tape( 'the function evaluates the pdf for `x` given tiny scale parameter `sigma`', opts, function test( t ) { + var expected; + var sigma; + var i; + var x; + var y; + + expected = tinyScale.expected; + x = tinyScale.x; + sigma = tinyScale.sigma; + for ( i = 0; i < x.length; i++ ) { + y = pdf( x[i], sigma[i] ); + if ( expected[i] !== null ) { + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the pdf for `x` given huge scale parameter `sigma`', opts, function test( t ) { + var expected; + var sigma; + var i; + var x; + var y; + + expected = hugeScale.expected; + x = hugeScale.x; + sigma = hugeScale.sigma; + for ( i = 0; i < x.length; i++ ) { + y = pdf( x[i], sigma[i] ); + if ( expected[i] !== null ) { + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + } + t.end(); +}); diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/test.pdf.js b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/test.pdf.js index 06d7a2941992..3e6aa98e69bf 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/test.pdf.js +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/test/test.pdf.js @@ -32,6 +32,8 @@ var pdf = require( './../lib' ); var smallScale = require( './fixtures/julia/small_scale.json' ); var mediumScale = require( './fixtures/julia/medium_scale.json' ); +var tinyScale = require( './fixtures/julia/tiny_scale.json' ); +var hugeScale = require( './fixtures/julia/huge_scale.json' ); var largeScale = require( './fixtures/julia/large_scale.json' ); @@ -57,6 +59,17 @@ tape( 'if provided `+infinity` for `x` and a valid `sigma`, the function returns t.end(); }); +tape( 'the function returns `0` when `x/sigma` overflows', function test( t ) { + var y; + + y = pdf( 1.0e300, 1.0e-10 ); + t.strictEqual( y, 0.0, 'returns expected value' ); + + y = pdf( 1.0e308, 1.0e-300 ); + t.strictEqual( y, 0.0, 'returns expected value' ); + t.end(); +}); + tape( 'if provided `-infinity` for `x` and a valid `sigma`, the function returns `0`', function test( t ) { var y = pdf( NINF, 1.0 ); t.strictEqual( y, 0.0, 'returns expected value' ); @@ -155,3 +168,41 @@ tape( 'the function evaluates the pdf for `x` given large scale parameter `sigma } t.end(); }); + +tape( 'the function evaluates the pdf for `x` given tiny scale parameter `sigma`', function test( t ) { + var expected; + var sigma; + var i; + var x; + var y; + + expected = tinyScale.expected; + x = tinyScale.x; + sigma = tinyScale.sigma; + for ( i = 0; i < x.length; i++ ) { + y = pdf( x[i], sigma[i] ); + if ( expected[i] !== null ) { + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the pdf for `x` given huge scale parameter `sigma`', function test( t ) { + var expected; + var sigma; + var i; + var x; + var y; + + expected = hugeScale.expected; + x = hugeScale.x; + sigma = hugeScale.sigma; + for ( i = 0; i < x.length; i++ ) { + y = pdf( x[i], sigma[i] ); + if ( expected[i] !== null ) { + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + } + t.end(); +});