diff --git a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/lib/factory.js b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/lib/factory.js index d98494d35a99..f3c585068694 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/lib/factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/lib/factory.js @@ -23,6 +23,7 @@ var constantFunction = require( '@stdlib/utils/constant-function' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); var erfc = require( '@stdlib/math/base/special/erfc' ); +var erfcx = require( '@stdlib/math/base/special/erfcx' ); var sqrt = require( '@stdlib/math/base/special/sqrt' ); var ln = require( '@stdlib/math/base/special/ln' ); var NINF = require( '@stdlib/constants/float64/ninf' ); @@ -68,6 +69,7 @@ function factory( mu, c ) { * // returns */ function logcdf( x ) { + var w; var z; if ( isnan( x ) ) { return NaN; @@ -75,8 +77,13 @@ function factory( mu, c ) { if ( x < mu ) { return NINF; } - z = sqrt( c / ( 2.0 * ( x-mu ) ) ); - return ln( erfc( z ) ); + w = c / ( 2.0 * ( x-mu ) ); + z = sqrt( w ); + if ( z < 1.0 ) { + return ln( erfc( z ) ); + } + // `erfc(z)` underflows for `z > ~26.5`, so use `ln(erfc(z)) = ln(erfcx(z)) - z^2`: + return ln( erfcx( z ) ) - w; } } diff --git a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/lib/main.js index 0cc35e6377c4..b83ac9c2a1bc 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/lib/main.js +++ b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/lib/main.js @@ -22,6 +22,7 @@ var isnan = require( '@stdlib/math/base/assert/is-nan' ); var erfc = require( '@stdlib/math/base/special/erfc' ); +var erfcx = require( '@stdlib/math/base/special/erfcx' ); var sqrt = require( '@stdlib/math/base/special/sqrt' ); var NINF = require( '@stdlib/constants/float64/ninf' ); var ln = require( '@stdlib/math/base/special/ln' ); @@ -67,6 +68,7 @@ var ln = require( '@stdlib/math/base/special/ln' ); * // returns NaN */ function logcdf( x, mu, c ) { + var w; var z; if ( isnan( x ) || @@ -79,8 +81,13 @@ function logcdf( x, mu, c ) { if ( x < mu ) { return NINF; } - z = sqrt( c / ( 2.0 * ( x-mu ) ) ); - return ln( erfc( z ) ); + w = c / ( 2.0 * ( x-mu ) ); + z = sqrt( w ); + if ( z < 1.0 ) { + return ln( erfc( z ) ); + } + // `erfc(z)` underflows for `z > ~26.5`, so use `ln(erfc(z)) = ln(erfcx(z)) - z^2`: + return ln( erfcx( z ) ) - w; } diff --git a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/manifest.json b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/manifest.json index 6a040775c183..66abbb04ba7d 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/manifest.json +++ b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/manifest.json @@ -41,6 +41,7 @@ "@stdlib/math/base/napi/ternary", "@stdlib/math/base/assert/is-nan", "@stdlib/math/base/special/erfc", + "@stdlib/math/base/special/erfcx", "@stdlib/math/base/special/sqrt", "@stdlib/math/base/special/ln", "@stdlib/constants/float64/ninf" @@ -60,6 +61,7 @@ "dependencies": [ "@stdlib/math/base/assert/is-nan", "@stdlib/math/base/special/erfc", + "@stdlib/math/base/special/erfcx", "@stdlib/math/base/special/sqrt", "@stdlib/math/base/special/ln", "@stdlib/constants/float64/ninf", @@ -80,6 +82,7 @@ "dependencies": [ "@stdlib/math/base/assert/is-nan", "@stdlib/math/base/special/erfc", + "@stdlib/math/base/special/erfcx", "@stdlib/math/base/special/sqrt", "@stdlib/math/base/special/ln", "@stdlib/constants/float64/ninf", diff --git a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/src/main.c index 5b700154492b..47ceb571bc56 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/src/main.c +++ b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/src/main.c @@ -19,6 +19,7 @@ #include "stdlib/stats/base/dists/levy/logcdf.h" #include "stdlib/math/base/assert/is_nan.h" #include "stdlib/math/base/special/erfc.h" +#include "stdlib/math/base/special/erfcx.h" #include "stdlib/math/base/special/sqrt.h" #include "stdlib/constants/float64/ninf.h" #include "stdlib/math/base/special/ln.h" @@ -36,6 +37,7 @@ * // returns ~-0.735 */ double stdlib_base_dists_levy_logcdf( const double x, const double mu, const double c ) { + double w; double z; if ( stdlib_base_is_nan( x ) || @@ -48,6 +50,11 @@ double stdlib_base_dists_levy_logcdf( const double x, const double mu, const dou if ( x < mu ) { return STDLIB_CONSTANT_FLOAT64_NINF; } - z = stdlib_base_sqrt( c / ( 2.0 * ( x-mu ) ) ); - return stdlib_base_ln( stdlib_base_erfc( z ) ); + w = c / ( 2.0 * ( x-mu ) ); + z = stdlib_base_sqrt( w ); + if ( z < 1.0 ) { + return stdlib_base_ln( stdlib_base_erfc( z ) ); + } + // `erfc(z)` underflows for `z > ~26.5`, so use `ln(erfc(z)) = ln(erfcx(z)) - z^2`: + return stdlib_base_ln( stdlib_base_erfcx( z ) ) - w; } diff --git a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/REQUIRE index 98be20b58ed3..06bfe7391215 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/REQUIRE +++ b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/REQUIRE @@ -1,3 +1,3 @@ -Distributions 0.23.8 julia 1.5 JSON 0.21 +SpecialFunctions 0.10.3 diff --git a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/large_variance.json b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/large_variance.json index 84b69fde0224..20e745ca9de8 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/large_variance.json +++ b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/large_variance.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/near_mu.json b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/near_mu.json new file mode 100644 index 000000000000..499c11705dc1 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/near_mu.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/negative_mean.json b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/negative_mean.json index 317fc30f9c97..a0998aa9032a 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/negative_mean.json +++ b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/negative_mean.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/positive_mean.json b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/positive_mean.json index 35f211b6305d..201d8c3d0aa7 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/positive_mean.json +++ b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/positive_mean.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/runner.jl index 4d444f5b1b04..90fbb96b16ab 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/fixtures/julia/runner.jl @@ -16,7 +16,7 @@ # See the License for the specific language governing permissions and # limitations under the License. -import Distributions: logcdf, Levy +import SpecialFunctions: erfc import JSON """ @@ -24,6 +24,8 @@ import JSON Generate fixture data and write to file. +The logarithm of the CDF is evaluated in extended precision from the textbook formula `ln(erfc(sqrt(c / (2*(x-mu)))))`, as `erfc` underflows in double precision close to `mu`. + # Arguments * `x`: input value @@ -41,9 +43,8 @@ julia> gen( x, mu, c, "data.json" ); ``` """ function gen( x, mu, c, name ) - z = Array{Float64}( undef, length(x) ); - for i in eachindex(x) - z[ i ] = logcdf( Levy( mu[i], c[i] ), x[i] ); + z = setprecision( BigFloat, 2048 ) do + Float64.( log.( erfc.( sqrt.( BigFloat.( c ) ./ ( 2 .* ( BigFloat.( x ) .- BigFloat.( mu ) ) ) ) ) ) ) end # Store data to be written to file as a collection: @@ -87,3 +88,9 @@ mu = rand( 1000 ); x = rand( 1000 ) .* 15.0 .+ mu .+ 0.1; c = ( rand( 1000 ) .* 15.0 ) .+ 1.0; gen( x, mu, c, "large_variance.json" ); + +# Close to `mu`: +mu = ( rand( 1000 ) .* 20.0 ) .- 10.0; +x = mu .+ exp10.( range( -15.0, stop = 0.0, length = 1000 ) ); +c = ( rand( 1000 ) .* 5.0 ) .+ 0.1; +gen( x, mu, c, "near_mu.json" ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/test.factory.js index 8a4f584282e0..64563cb107b3 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/test.factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/test.factory.js @@ -31,6 +31,7 @@ var factory = require( './../lib/factory.js' ); // FIXTURES // var positiveMean = require( './fixtures/julia/positive_mean.json' ); +var nearMu = require( './fixtures/julia/near_mu.json' ); var negativeMean = require( './fixtures/julia/negative_mean.json' ); var largeVariance = require( './fixtures/julia/large_variance.json' ); @@ -168,7 +169,7 @@ tape( 'the created function evaluates the logcdf for `x` given positive `mu`', f for ( i = 0; i < x.length; i++ ) { logcdf = factory( mu[i], c[i] ); y = logcdf( x[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 3 ), true, 'returns expected value' ); } t.end(); }); @@ -189,7 +190,7 @@ tape( 'the created function evaluates the logcdf for `x` given negative `mu`', f for ( i = 0; i < x.length; i++ ) { logcdf = factory( mu[i], c[i] ); y = logcdf( x[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 3 ), true, 'returns expected value' ); } t.end(); }); @@ -210,7 +211,49 @@ tape( 'the created function evaluates the logcdf for `x` given large variance ( for ( i = 0; i < x.length; i++ ) { logcdf = factory( mu[i], c[i] ); y = logcdf( x[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 3 ), true, 'returns expected value' ); } t.end(); }); + +tape( 'the created function evaluates the logcdf for `x` close to `mu`', function test( t ) { + var expected; + var logcdf; + var mu; + var c; + var i; + var x; + var y; + + expected = nearMu.expected; + x = nearMu.x; + mu = nearMu.mu; + c = nearMu.c; + for ( i = 0; i < x.length; i++ ) { + logcdf = factory( mu[i], c[i] ); + y = logcdf( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the created function evaluates the logcdf for `x` very close to `mu`', function test( t ) { + var logcdf; + var y; + + logcdf = factory( 0.0, 1.0 ); + y = logcdf( 1.0e-20 ); + t.strictEqual( isAlmostSameValue( y, -5.0e19, 0 ), true, 'returns expected value' ); + + y = logcdf( 1.0e-200 ); + t.strictEqual( isAlmostSameValue( y, -5.0e199, 0 ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided `x` equal to `mu`, the created function returns `-infinity`', function test( t ) { + var logcdf = factory( 2.0, 1.0 ); + var y = logcdf( 2.0 ); + t.strictEqual( y, NINF, 'returns expected value' ); + t.end(); +}); diff --git a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/test.logcdf.js b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/test.logcdf.js index 80e4283735f5..1b10ee9023f5 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/test.logcdf.js +++ b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/test.logcdf.js @@ -31,6 +31,7 @@ var logcdf = require( './../lib' ); // FIXTURES // var positiveMean = require( './fixtures/julia/positive_mean.json' ); +var nearMu = require( './fixtures/julia/near_mu.json' ); var negativeMean = require( './fixtures/julia/negative_mean.json' ); var largeVariance = require( './fixtures/julia/large_variance.json' ); @@ -116,7 +117,7 @@ tape( 'the function evaluates the logcdf for `x` given positive `mu`', function c = positiveMean.c; for ( i = 0; i < x.length; i++ ) { y = logcdf( x[i], mu[i], c[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 3 ), true, 'returns expected value' ); } t.end(); }); @@ -135,7 +136,7 @@ tape( 'the function evaluates the logcdf for `x` given negative `mu`', function c = negativeMean.c; for ( i = 0; i < x.length; i++ ) { y = logcdf( x[i], mu[i], c[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 3 ), true, 'returns expected value' ); } t.end(); }); @@ -154,7 +155,44 @@ tape( 'the function evaluates the logcdf for `x` given large variance ( = large c = largeVariance.c; for ( i = 0; i < x.length; i++ ) { y = logcdf( x[i], mu[i], c[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 3 ), true, 'returns expected value' ); } t.end(); }); + +tape( 'the function evaluates the logcdf for `x` close to `mu`', function test( t ) { + var expected; + var mu; + var c; + var i; + var x; + var y; + + expected = nearMu.expected; + x = nearMu.x; + mu = nearMu.mu; + c = nearMu.c; + for ( i = 0; i < x.length; i++ ) { + y = logcdf( x[i], mu[i], c[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the logcdf for `x` very close to `mu`', function test( t ) { + var y; + + y = logcdf( 1.0e-20, 0.0, 1.0 ); + t.strictEqual( isAlmostSameValue( y, -5.0e19, 0 ), true, 'returns expected value' ); + + y = logcdf( 1.0e-200, 0.0, 1.0 ); + t.strictEqual( isAlmostSameValue( y, -5.0e199, 0 ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided `x` equal to `mu`, the function returns `-infinity`', function test( t ) { + var y = logcdf( 2.0, 2.0, 1.0 ); + t.strictEqual( y, NINF, 'returns expected value' ); + t.end(); +}); diff --git a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/test.native.js index 6bf85155d12a..b134c9724033 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/test.native.js +++ b/lib/node_modules/@stdlib/stats/base/dists/levy/logcdf/test/test.native.js @@ -40,6 +40,7 @@ var opts = { // FIXTURES // var positiveMean = require( './fixtures/julia/positive_mean.json' ); +var nearMu = require( './fixtures/julia/near_mu.json' ); var negativeMean = require( './fixtures/julia/negative_mean.json' ); var largeVariance = require( './fixtures/julia/large_variance.json' ); @@ -125,7 +126,7 @@ tape( 'the function evaluates the logcdf for `x` given positive `mu`', opts, fun c = positiveMean.c; for ( i = 0; i < x.length; i++ ) { y = logcdf( x[i], mu[i], c[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 3 ), true, 'returns expected value' ); } t.end(); }); @@ -144,7 +145,7 @@ tape( 'the function evaluates the logcdf for `x` given negative `mu`', opts, fun c = negativeMean.c; for ( i = 0; i < x.length; i++ ) { y = logcdf( x[i], mu[i], c[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 3 ), true, 'returns expected value' ); } t.end(); }); @@ -163,7 +164,44 @@ tape( 'the function evaluates the logcdf for `x` given large variance ( = large c = largeVariance.c; for ( i = 0; i < x.length; i++ ) { y = logcdf( x[i], mu[i], c[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 3 ), true, 'returns expected value' ); } t.end(); }); + +tape( 'the function evaluates the logcdf for `x` close to `mu`', opts, function test( t ) { + var expected; + var mu; + var c; + var i; + var x; + var y; + + expected = nearMu.expected; + x = nearMu.x; + mu = nearMu.mu; + c = nearMu.c; + for ( i = 0; i < x.length; i++ ) { + y = logcdf( x[i], mu[i], c[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the logcdf for `x` very close to `mu`', opts, function test( t ) { + var y; + + y = logcdf( 1.0e-20, 0.0, 1.0 ); + t.strictEqual( isAlmostSameValue( y, -5.0e19, 0 ), true, 'returns expected value' ); + + y = logcdf( 1.0e-200, 0.0, 1.0 ); + t.strictEqual( isAlmostSameValue( y, -5.0e199, 0 ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided `x` equal to `mu`, the function returns `-infinity`', opts, function test( t ) { + var y = logcdf( 2.0, 2.0, 1.0 ); + t.strictEqual( y, NINF, 'returns expected value' ); + t.end(); +});