diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/lib/factory.js b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/lib/factory.js index 9911152b2af4..6ce9691f7849 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/lib/factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/lib/factory.js @@ -27,6 +27,7 @@ var pow = require( '@stdlib/math/base/special/pow' ); var ln = require( '@stdlib/math/base/special/ln' ); var PINF = require( '@stdlib/constants/float64/pinf' ); var NINF = require( '@stdlib/constants/float64/ninf' ); +var FLOAT64_SMALLEST_NORMAL = require( '@stdlib/constants/float64/smallest-normal' ); // MAIN // @@ -46,7 +47,9 @@ var NINF = require( '@stdlib/constants/float64/ninf' ); * // returns ~-0.936 */ function factory( sigma ) { + var normal; var s2i; + var lns; var s2; if ( isnan( sigma ) || sigma < 0.0 ) { return constantFunction( NaN ); @@ -56,6 +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 logpdf; /** @@ -70,13 +75,32 @@ function factory( sigma ) { * // returns */ function logpdf( x ) { + var lq; + var x2; + var r; + var q; if ( isnan( x ) ) { return NaN; } if ( x < 0.0 || x === PINF ) { return NINF; } - return ln( s2i * x ) - (pow( x, 2.0 ) / ( 2.0 * s2 )); + x2 = pow( x, 2.0 ); + q = s2i * x; + if ( normal && x2 < PINF && q >= FLOAT64_SMALLEST_NORMAL ) { + return ln( q ) - (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. `ln( x/sigma^2 )` is taken directly while that ratio is normal, as subtracting two large logarithms cancels when `x` is close to `sigma^2`... + r = x / sigma; + q = r / sigma; + if ( q >= FLOAT64_SMALLEST_NORMAL && q < PINF ) { + lq = ln( q ); + } else if ( r >= FLOAT64_SMALLEST_NORMAL ) { + lq = ln( r ) - lns; + } else { + lq = ( ln( x ) - lns ) - lns; + } + return lq - ( 0.5 * r * r ); } } diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/lib/main.js index 55cf2c922f76..1ddfed63a4cb 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/lib/main.js +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/lib/main.js @@ -25,6 +25,7 @@ var pow = require( '@stdlib/math/base/special/pow' ); var ln = require( '@stdlib/math/base/special/ln' ); var PINF = require( '@stdlib/constants/float64/pinf' ); var NINF = require( '@stdlib/constants/float64/ninf' ); +var FLOAT64_SMALLEST_NORMAL = require( '@stdlib/constants/float64/smallest-normal' ); // MAIN // @@ -63,7 +64,11 @@ var NINF = require( '@stdlib/constants/float64/ninf' ); */ function logpdf( x, sigma ) { var s2i; + var lq; var s2; + var x2; + var r; + var q; if ( isnan( x ) || isnan( sigma ) || @@ -79,7 +84,27 @@ function logpdf( x, sigma ) { } s2 = pow( sigma, 2.0 ); s2i = 1.0 / s2; - return ln( s2i * x ) - ( 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 ln( q ) - ( 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. `ln( x/sigma^2 )` is taken directly while that ratio is normal, as subtracting two large logarithms cancels when `x` is close to `sigma^2`... + r = x / sigma; + q = r / sigma; + if ( q >= FLOAT64_SMALLEST_NORMAL && q < PINF ) { + lq = ln( q ); + } else if ( r >= FLOAT64_SMALLEST_NORMAL ) { + lq = ln( r ) - ln( sigma ); + } else { + lq = ( ln( x ) - ln( sigma ) ) - ln( sigma ); + } + return lq - ( 0.5 * r * r ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/manifest.json b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/manifest.json index 4b9f8e03256e..f057ca32ddf2 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/manifest.json +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/manifest.json @@ -43,7 +43,8 @@ "@stdlib/math/base/special/pow", "@stdlib/math/base/special/ln", "@stdlib/constants/float64/pinf", - "@stdlib/constants/float64/ninf" + "@stdlib/constants/float64/ninf", + "@stdlib/constants/float64/smallest-normal" ] }, { @@ -63,7 +64,8 @@ "@stdlib/math/base/special/pow", "@stdlib/math/base/special/ln", "@stdlib/constants/float64/pinf", - "@stdlib/constants/float64/ninf" + "@stdlib/constants/float64/ninf", + "@stdlib/constants/float64/smallest-normal" ] }, { @@ -82,7 +84,8 @@ "@stdlib/math/base/special/pow", "@stdlib/math/base/special/ln", "@stdlib/constants/float64/pinf", - "@stdlib/constants/float64/ninf" + "@stdlib/constants/float64/ninf", + "@stdlib/constants/float64/smallest-normal" ] } ] diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/src/main.c index cfa6d9962357..93cc14a7862c 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/src/main.c +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/src/main.c @@ -22,6 +22,7 @@ #include "stdlib/math/base/special/ln.h" #include "stdlib/constants/float64/pinf.h" #include "stdlib/constants/float64/ninf.h" +#include "stdlib/constants/float64/smallest_normal.h" /** * Evaluates the natural logarithm of the probability density function (PDF) for a Rayleigh distribution with scale parameter `sigma` at a value `x`. @@ -36,7 +37,11 @@ */ double stdlib_base_dists_rayleigh_logpdf( const double x, const double sigma ) { double s2i; + double lq; double s2; + double x2; + double r; + double q; if ( stdlib_base_is_nan( x ) || stdlib_base_is_nan( sigma ) || @@ -52,5 +57,25 @@ double stdlib_base_dists_rayleigh_logpdf( const double x, const double sigma ) { } s2 = stdlib_base_pow( sigma, 2.0 ); s2i = 1.0 / s2; - return stdlib_base_ln( s2i * x ) - 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 stdlib_base_ln( q ) - 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. `ln( x/sigma^2 )` is taken directly while that ratio is normal, as subtracting two large logarithms cancels when `x` is close to `sigma^2`... + r = x / sigma; + q = r / sigma; + if ( q >= STDLIB_CONSTANT_FLOAT64_SMALLEST_NORMAL && q < STDLIB_CONSTANT_FLOAT64_PINF ) { + lq = stdlib_base_ln( q ); + } else if ( r >= STDLIB_CONSTANT_FLOAT64_SMALLEST_NORMAL ) { + lq = stdlib_base_ln( r ) - stdlib_base_ln( sigma ); + } else { + lq = ( stdlib_base_ln( x ) - stdlib_base_ln( sigma ) ) - stdlib_base_ln( sigma ); + } + return lq - ( 0.5 * r * r ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/huge_scale.json b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/huge_scale.json new file mode 100644 index 000000000000..cc0ff4ebb70f --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/huge_scale.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/large_scale.json b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/large_scale.json index 182a33050892..56f715ec04d3 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/large_scale.json +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/large_scale.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/medium_scale.json b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/medium_scale.json index f1fcf1176404..c5a07d6120cf 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/medium_scale.json +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/medium_scale.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/runner.jl index 2b0119b35a08..cbde1d224b24 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/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, Rayleigh import JSON """ @@ -39,9 +38,11 @@ julia> gen( x, sigma, \"data.json\" ); ``` """ function gen( x, sigma, name ) - z = Array{Float64}( undef, length(x) ); - for i in eachindex(x) - z[ i ] = logpdf( Rayleigh( sigma[i] ), x[i] ); + # The log PDF is evaluated in extended precision using the textbook formula `ln(x/sigma^2) - x^2/(2*sigma^2)`, as forming `sigma^2` or `x^2` in double precision overflows or underflows for scale parameters far from `1`... + z = setprecision( BigFloat, 2048 ) do + X = BigFloat.( x ); + S = BigFloat.( sigma ); + Float64.( log.( X ./ ( S .^ 2 ) ) .- ( ( X .^ 2 ) ./ ( 2 .* ( S .^ 2 ) ) ) ); end # Store data to be written to file as a collection: @@ -81,3 +82,13 @@ 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 ) .* 4.0 ) .- 3.0 ); +gen( x, sigma, "tiny_scale.json" ); + +# Huge scale parameter (`sigma^2` overflows): +sigma = exp10.( ( rand( 1000 ) .* 45.0 ) .+ 155.0 ); +x = sigma .* exp10.( ( rand( 1000 ) .* 4.0 ) .- 3.0 ); +gen( x, sigma, "huge_scale.json" ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/small_scale.json b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/small_scale.json index 6e57e7b4f33a..279ad52e070e 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/small_scale.json +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/small_scale.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/tiny_scale.json b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/tiny_scale.json new file mode 100644 index 000000000000..1a70742bf867 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/fixtures/julia/tiny_scale.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/test.factory.js index 45414efd15ff..3453eda49a31 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/test.factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/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' ); @@ -187,3 +189,45 @@ tape( 'the created function evaluates the logpdf for `x` given large scale param } t.end(); }); + +tape( 'the created function evaluates the logpdf for `x` given tiny scale parameter `sigma`', function test( t ) { + var expected; + var logpdf; + var sigma; + var i; + var x; + var y; + + expected = tinyScale.expected; + x = tinyScale.x; + sigma = tinyScale.sigma; + for ( i = 0; i < x.length; i++ ) { + logpdf = factory( sigma[i] ); + y = logpdf( 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 logpdf for `x` given huge scale parameter `sigma`', function test( t ) { + var expected; + var logpdf; + var sigma; + var i; + var x; + var y; + + expected = hugeScale.expected; + x = hugeScale.x; + sigma = hugeScale.sigma; + for ( i = 0; i < x.length; i++ ) { + logpdf = factory( sigma[i] ); + y = logpdf( 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/logpdf/test/test.logpdf.js b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/test.logpdf.js index 7d8e3542e592..8bfb2b160033 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/test.logpdf.js +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/test.logpdf.js @@ -33,6 +33,8 @@ var logpdf = 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' ); @@ -180,3 +182,57 @@ tape( 'the function evaluates the logpdf for `x` given large scale parameter `si } t.end(); }); + +tape( 'the function evaluates the logpdf for `x` given tiny scale parameter `sigma`', function test( t ) { + var expected; + var delta; + var sigma; + var tol; + var i; + var x; + var y; + + expected = tinyScale.expected; + x = tinyScale.x; + sigma = tinyScale.sigma; + for ( i = 0; i < x.length; i++ ) { + y = logpdf( x[i], sigma[i] ); + if ( expected[i] !== null ) { + if ( y === expected[i] ) { + t.strictEqual( y, expected[i], 'x: '+x[i]+', sigma: '+sigma[i]+', y: '+y+', expected: '+expected[i] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 3.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. sigma: '+sigma[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); + } + } + } + t.end(); +}); + +tape( 'the function evaluates the logpdf for `x` given huge scale parameter `sigma`', function test( t ) { + var expected; + var delta; + var sigma; + var tol; + var i; + var x; + var y; + + expected = hugeScale.expected; + x = hugeScale.x; + sigma = hugeScale.sigma; + for ( i = 0; i < x.length; i++ ) { + y = logpdf( x[i], sigma[i] ); + if ( expected[i] !== null ) { + if ( y === expected[i] ) { + t.strictEqual( y, expected[i], 'x: '+x[i]+', sigma: '+sigma[i]+', y: '+y+', expected: '+expected[i] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 3.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. sigma: '+sigma[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); + } + } + } + t.end(); +}); diff --git a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/test.native.js index 39fdfceb97a6..c429e2c77724 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/test/test.native.js +++ b/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logpdf/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' ); @@ -164,3 +166,41 @@ tape( 'the function evaluates the logpdf for `x` given large scale parameter `si } t.end(); }); + +tape( 'the function evaluates the logpdf 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 = logpdf( 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 logpdf 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 = logpdf( x[i], sigma[i] ); + if ( expected[i] !== null ) { + t.strictEqual( isAlmostSameValue( y, expected[i], 2 ), true, 'returns expected value' ); + } + } + t.end(); +});