diff --git a/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/lib/factory.js b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/lib/factory.js index 231e8d2d6f25..cfdf70ec7e65 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/lib/factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/lib/factory.js @@ -21,9 +21,7 @@ // MODULES // var constantFunction = require( '@stdlib/utils/constant-function' ); -var signum = require( '@stdlib/math/base/special/signum' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); -var abs = require( '@stdlib/math/base/special/abs' ); var ln = require( '@stdlib/math/base/special/ln' ); @@ -69,7 +67,11 @@ function factory( mu, b ) { if ( isnan( p ) || p < 0.0 || p > 1.0 ) { return NaN; } - return mu - ( b * signum( p-0.5 ) * ln( 1.0 - (2.0 * abs( p-0.5 )) ) ); + // Work with the tail probability (`p` or `1-p`, which is exact for `p >= 0.5`) rather than `1 - 2|p-0.5|`, which rounds away the low-order bits of a small `p`: + if ( p < 0.5 ) { + return mu + ( b * ln( 2.0*p ) ); + } + return mu - ( b * ln( 2.0*(1.0-p) ) ); } } diff --git a/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/lib/main.js index 20d250b27048..e49e7a294149 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/lib/main.js +++ b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/lib/main.js @@ -20,9 +20,7 @@ // MODULES // -var signum = require( '@stdlib/math/base/special/signum' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); -var abs = require( '@stdlib/math/base/special/abs' ); var ln = require( '@stdlib/math/base/special/ln' ); @@ -80,7 +78,11 @@ function quantile( p, mu, b ) { ) { return NaN; } - return mu - ( b * signum( p-0.5 ) * ln( 1.0 - ( 2.0 * abs( p-0.5 ) ) ) ); + // Work with the tail probability (`p` or `1-p`, which is exact for `p >= 0.5`) rather than `1 - 2|p-0.5|`, which rounds away the low-order bits of a small `p`: + if ( p < 0.5 ) { + return mu + ( b * ln( 2.0*p ) ); + } + return mu - ( b * ln( 2.0*(1.0-p) ) ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/manifest.json b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/manifest.json index b47be193613d..901953c4e553 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/manifest.json +++ b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/manifest.json @@ -39,9 +39,7 @@ "libpath": [], "dependencies": [ "@stdlib/math/base/napi/ternary", - "@stdlib/math/base/special/signum", "@stdlib/math/base/assert/is-nan", - "@stdlib/math/base/special/abs", "@stdlib/math/base/special/ln" ] }, @@ -57,9 +55,7 @@ "libraries": [], "libpath": [], "dependencies": [ - "@stdlib/math/base/special/signum", "@stdlib/math/base/assert/is-nan", - "@stdlib/math/base/special/abs", "@stdlib/constants/float64/eps", "@stdlib/math/base/special/ln" ] @@ -76,9 +72,7 @@ "libraries": [], "libpath": [], "dependencies": [ - "@stdlib/math/base/special/signum", "@stdlib/math/base/assert/is-nan", - "@stdlib/math/base/special/abs", "@stdlib/math/base/special/ln" ] } diff --git a/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/src/main.c index 1cb81bd06ff0..d5f2eb945e66 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/src/main.c +++ b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/src/main.c @@ -17,9 +17,7 @@ */ #include "stdlib/stats/base/dists/laplace/quantile.h" -#include "stdlib/math/base/special/signum.h" #include "stdlib/math/base/assert/is_nan.h" -#include "stdlib/math/base/special/abs.h" #include "stdlib/math/base/special/ln.h" /** @@ -45,5 +43,9 @@ double stdlib_base_dists_laplace_quantile( const double p, const double mu, cons ) { return 0.0/0.0; // NaN } - return mu - ( b * stdlib_base_signum( p-0.5 ) * stdlib_base_ln( 1.0 - ( 2.0 * stdlib_base_abs( p-0.5 ) ) ) ); + // Work with the tail probability (`p` or `1-p`, which is exact for `p >= 0.5`) rather than `1 - 2|p-0.5|`, which rounds away the low-order bits of a small `p`: + if ( p < 0.5 ) { + return mu + ( b * stdlib_base_ln( 2.0*p ) ); + } + return mu - ( b * stdlib_base_ln( 2.0*(1.0-p) ) ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/test/fixtures/julia/runner.jl index 684158542625..4554e1a57e13 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/test/fixtures/julia/runner.jl @@ -64,6 +64,42 @@ function gen( p, mu, b, name ) close( outfile ); end +""" + gen_tails( p, mu, b, name ) + +Generate fixture data for the tails in extended precision and write to file. In double precision, `1 - 2|p-0.5|` rounds away the low-order bits of a small `p` (all of them for `p < 2^-54`), so the reference value is computed from the textbook formula `mu - b*sign(p-0.5)*ln(1 - 2|p-0.5|)` at 2048 bits. + +# Arguments + +* `p`: input value +* `mu`: location parameter +* `b`: scale parameter +* `name::AbstractString`: output filename +""" +function gen_tails( p, mu, b, name ) + z = setprecision( BigFloat, 2048 ) do + q = BigFloat.( p ); + Float64.( BigFloat.( mu ) .- ( BigFloat.( b ) .* sign.( q .- 0.5 ) .* log.( 1 .- ( 2 .* abs.( q .- 0.5 ) ) ) ) ) + end + + # Store data to be written to file as a collection: + data = Dict([ + ("p", p), + ("mu", mu), + ("b", b), + ("expected", z) + ]); + + # Based on the script directory, create an output filepath: + filepath = joinpath( dir, name ); + + # Write the data to the output filepath as JSON: + outfile = open( filepath, "w" ); + write( outfile, JSON.json(data) ); + write( outfile, "\n" ); + close( outfile ); +end + # Get the filename: file = @__FILE__; @@ -87,3 +123,9 @@ p = rand( 1000 ); mu = rand( 1000 ); b = rand( 1000 ) .* 20.0; gen( p, mu, b, "large_variance.json" ); + +# Tails (`p` and `1-p` log-spaced; `mu = 0`, so that the result does not also measure the rounding of `mu + ...`): +p = vcat( exp10.( range( -300.0, stop = -1.0, length = 500 ) ), 1.0 .- exp10.( range( -16.0, stop = -1.0, length = 500 ) ) ); +mu = zeros( 1000 ); +b = ( rand( 1000 ) .* 5.0 ) .+ 0.1; +gen_tails( p, mu, b, "tails.json" ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/test/fixtures/julia/tails.json b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/test/fixtures/julia/tails.json new file mode 100644 index 000000000000..e1637724f449 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/test/fixtures/julia/tails.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/test/test.factory.js index b40b63c4b7de..d16194bbf261 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/test/test.factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/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 tails = require( './fixtures/julia/tails.json' ); // TESTS // @@ -197,3 +198,26 @@ tape( 'the created function evaluates the quantile function at `p` given large v } t.end(); }); + +tape( 'the created function evaluates the quantile function at `p` in the tails (`p` or `1-p` close to `0`)', function test( t ) { + var expected; + var quantile; + var mu; + var b; + var i; + var p; + var y; + + expected = tails.expected; + p = tails.p; + mu = tails.mu; + b = tails.b; + for ( i = 0; i < p.length; i++ ) { + quantile = factory( mu[i], b[i] ); + y = quantile( p[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/laplace/quantile/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/test/test.native.js index 69a964e53593..6f3035a9fda8 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/test/test.native.js +++ b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/test/test.native.js @@ -42,6 +42,7 @@ var opts = { 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 tails = require( './fixtures/julia/tails.json' ); // TESTS // @@ -162,3 +163,24 @@ tape( 'the function evaluates the quantile function at `p` given large variance } t.end(); }); + +tape( 'the function evaluates the quantile function at `p` in the tails (`p` or `1-p` close to `0`)', opts, function test( t ) { + var expected; + var mu; + var b; + var i; + var p; + var y; + + expected = tails.expected; + p = tails.p; + mu = tails.mu; + b = tails.b; + for ( i = 0; i < p.length; i++ ) { + y = quantile( p[i], mu[i], b[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/laplace/quantile/test/test.quantile.js b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/test/test.quantile.js index 000dbca6a8a7..4a7df2de7e14 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/test/test.quantile.js +++ b/lib/node_modules/@stdlib/stats/base/dists/laplace/quantile/test/test.quantile.js @@ -33,6 +33,7 @@ var quantile = 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 tails = require( './fixtures/julia/tails.json' ); // TESTS // @@ -153,3 +154,24 @@ tape( 'the function evaluates the quantile function at `p` given large variance } t.end(); }); + +tape( 'the function evaluates the quantile function at `p` in the tails (`p` or `1-p` close to `0`)', function test( t ) { + var expected; + var mu; + var b; + var i; + var p; + var y; + + expected = tails.expected; + p = tails.p; + mu = tails.mu; + b = tails.b; + for ( i = 0; i < p.length; i++ ) { + y = quantile( p[i], mu[i], b[i] ); + if ( expected[i] !== null ) { + t.strictEqual( isAlmostSameValue( y, expected[i], 1 ), true, 'returns expected value' ); + } + } + t.end(); +});