From 7f7e1c9bb5aca2465d6aee0dcf90431171a2d055 Mon Sep 17 00:00:00 2001 From: Dr Paul Brewer Date: Fri, 10 Jan 2020 03:54:16 -0500 Subject: [PATCH] update edge case behavior; a function with f(l)===0 or f(h)===0 will yield an interval beginning with l or ending with h. --- index.js | 77 ++- package-lock.json | 1540 +++++++++++++++++++++++++++++++++++++++++++++ test/index.js | 250 ++++---- 3 files changed, 1717 insertions(+), 150 deletions(-) create mode 100644 package-lock.json diff --git a/index.js b/index.js index 01b3304..7abd4ef 100644 --- a/index.js +++ b/index.js @@ -1,40 +1,49 @@ /* Copyright 2016 Paul Brewer, Economic & Financial Technology COnsulting LLC */ /* License: MIT https://opensource.org/licenses/MIT */ -module.exports = function(l,h,tol,f){ - 'use strict'; - // returns a two element array giving an inclusive range of zero values of f - // requires strictly everywhere non-descending function f - // use with caution: this code assumes but does and can not check that f is everywhere non-descending - var right=h,left=l,intflag=(tol>=1); - var fl = f(l), fh=f(h); - if ((fl===0) && (fh===0)) return [l,h]; - if (fh=0) return []; - if (fh<=0) return []; - var zleft,zright,mid; - zright=left; - while ((right-zright)>tol){ - mid = (right+zright)/2; - if (intflag) mid = Math.floor(mid); - if (f(mid)>0) - right = mid; - else - zright = mid; +module.exports = function (l, h, tol, f) { + 'use strict'; + // returns a two element array giving an inclusive range of zero values of f + // requires strictly everywhere non-descending function f + // use with caution: this code assumes but does and can not check that f is everywhere non-descending + var right = h, + left = l, + intflag = (tol >= 1); + var fl = f(l), + fh = f(h); + if ((fl === 0) && (fh === 0)) return [l, h]; + if (fh < fl) throw new Error("findZeroRange: requires non-descending function"); + if (fl > 0) return []; + if (fh < 0) return []; + var zleft, zright, mid; + zright = left; + if (fh===0){ + zright = right; + } else { + while ((right - zright) > tol) { + mid = (right + zright) / 2; + if (intflag) mid = Math.floor(mid); + if (f(mid) > 0) + right = mid; + else + zright = mid; } - if (f(zright)<0) - return [zright]; - zleft=zright; - while ((zleft-left)>tol){ - mid = (left+zleft)/2; - if (intflag) mid = Math.floor(mid); - if (f(mid)<0) - left = mid; - else - zleft = mid; + if (f(zright) < 0) + return [zright]; + } + if (fl===0){ + zleft = l; + } else { + zleft = zright; + while ((zleft - left) > tol) { + mid = (left + zleft) / 2; + if (intflag) mid = Math.floor(mid); + if (f(mid) < 0) + left = mid; + else + zleft = mid; } - if (zleft===zright) return [zright]; - return [zleft, zright]; + } + if (zleft === zright) return [zright]; + return [zleft, zright]; }; - - diff --git a/package-lock.json b/package-lock.json new file mode 100644 index 0000000..f548666 --- /dev/null +++ b/package-lock.json @@ -0,0 +1,1540 @@ +{ + "name": "find-zero-range", + "version": "2.0.7", + 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- return function(x){ return slope*Math.floor((x-x0)/divisor); }; +function linearStepF(slope, divisor, x0) { + return function (x) { return slope * Math.floor((x - x0) / divisor); }; } -describe('#findZeroRange ', function(){ - 'use strict'; - describe('linear functions, positive slope ', function(){ - var slopes = [0.00001,0.01,1, 3.45, 10, 74.3, 298, 17345]; - var x0 = [-90,-63.5,-21.1, -10, -5, -0.8765, 0.25, 3.1415926, 7, 45, 123, 456, 948.4321]; - var testgen = function(l,h,tol,mathFuncFunc, testFunc){ - return function(){ - slopes.forEach(function(s){ - x0.forEach(function(z){ - var zeroRange = findZeroRange(l,h,tol,mathFuncFunc(s,z)); - testFunc({ - l:l, - h:h, - tol:tol, - mathFuncFunc:mathFuncFunc, - slope:s, - x0:z, - zeroRange: zeroRange - }); - }); - }); - }; - }; - it('should find an interval with one point', - testgen(-1000,1000,0.00001,linearF,function(t){ - assert.strictEqual(t.zeroRange.length, 1); - })); - it('should find the zero to tol of 0.000001', - testgen(-1000,1000,0.000001,linearF,function(t){ - t.zeroRange[0].should.be.approximately(t.x0,t.tol); - })); - it('should find an approximate zero to tol 1 and be an integer', - testgen(-1000,1000,1,linearF,function(t){ - assert.strictEqual(t.zeroRange[0],Math.floor(t.zeroRange[0])); - t.zeroRange[0].should.be.approximately(t.x0,t.tol); - })); - it('should return [] when the search range is too low', function(){ - findZeroRange(0,100,0.001,linearF(1,1000)).should.eql([]); - }); - it('should return [] when the search range is too high', function(){ - findZeroRange(2000,3000,0.001,linearF(1,1000)).should.eql([]); - }); +describe('#findZeroRange ', function () { + 'use strict'; + describe('linear functions, positive slope ', function () { + var slopes = [0.00001, 0.001, 0.01, 1, 3.45, 10, 74.3, 298, 17345]; + var x0 = [-1000, -90, -63.5, -21.1, -10, -5, -0.8765, 0.25, 3.1415926, 7, 45, 123, 456, 948.4321, 1000]; + var testgen = function (l, h, tol, mathFuncFunc, testFunc) { + return function () { + slopes.forEach(function (s) { + x0.forEach(function (z) { + var zeroRange = findZeroRange(l, h, tol, mathFuncFunc(s, z)); + testFunc({ + l: l, + h: h, + tol: tol, + mathFuncFunc: mathFuncFunc, + slope: s, + x0: z, + zeroRange: zeroRange + }); + }); + }); + }; + }; + it('should find an interval with one point', + testgen(-1000, 1000, 0.00001, linearF, function (t) { + assert.strictEqual(t.zeroRange.length, 1); + })); + it('should find the zero to tol of 0.000001', + testgen(-1000, 1000, 0.000001, linearF, function (t) { + t.zeroRange[0].should.be.approximately(t.x0, t.tol); + })); + it('should find an approximate zero to tol 1 and be an integer', + testgen(-1000, 1000, 1, linearF, function (t) { + assert.strictEqual(t.zeroRange[0], Math.floor(t.zeroRange[0])); + t.zeroRange[0].should.be.approximately(t.x0, t.tol); + })); + it('should return [] when the search range is too low', function () { + findZeroRange(0, 100, 0.001, linearF(1, 1000)).should.eql([]); }); + it('should return [] when the search range is too high', function () { + findZeroRange(2000, 3000, 0.001, linearF(1, 1000)).should.eql([]); + }); + }); - describe('linear function, negative slope', function(){ - it('should throw when the function is decreasing', function(){ - var decreasing = function(){ - var rng = findZeroRange(0,100,0.001,linearF(-1,50)); - }; - decreasing.should.throw(); - }); + describe('linear function, negative slope', function () { + it('should throw when the function is decreasing', function () { + var decreasing = function () { + var rng = findZeroRange(0, 100, 0.001, linearF(-1, 50)); + }; + decreasing.should.throw(); }); + }); - describe('non-zero constant function', function(){ - it('should return [] for negative constant function', function(){ - findZeroRange(0,100,0.01,function(x){ return -5;}).should.eql([]); - }); - it('should return [] fpr positive constant function', function(){ - findZeroRange(0,100,0.01,function(x){ return 42;}).should.eql([]); - }); + describe('non-zero constant function', function () { + it('should return [] for negative constant function', function () { + findZeroRange(0, 100, 0.01, function (x) { return -5; }).should.eql([]); }); - - describe('zero constant function ', function(){ - it('should return [l,h] as zero range', function(){ - findZeroRange(0,100,0.01,function(x){ return 0; }).should.eql([0,100]); - findZeroRange(-232,147,1,function(x){ return 0; }).should.eql([-232,147]); - }); + it('should return [] fpr positive constant function', function () { + findZeroRange(0, 100, 0.01, function (x) { return 42; }).should.eql([]); }); + }); - describe('linear step functions, positive slope', function(){ - var slopes = [0.00001,0.01,1, 3.45, 10, 74.3, 298, 17345]; - var divisors = [0.1,0.3333,0.5,1,2,5,7,13,17,25,101,243,412,542]; - var x0 = [-90,-63.5,-21.1, -10, -5, -0.8765, 0.25, 3.1415926, 7, 45, 123, 456]; - var testgen = function(l,h,tol,testFunc){ - return function(){ - slopes.forEach(function(s){ - divisors.forEach(function(d){ - x0.forEach(function(z){ - var zeroRange = findZeroRange(l,h,tol,linearStepF(s,d,z)); - testFunc({ - l:l, - h:h, - tol:tol, - slope:s, - divisor:d, - x0:z, - x1:z+d, - zeroRange: zeroRange - }); - }); - }); - }); - }; - }; - it('with tol 0.000001 should find an interval with distinct endpoints', - testgen(-1000,1000,0.00001,function(t){ - assert.ok(t.zeroRange.length===2); - assert.ok(t.zeroRange[0]1){ - assert.strictEqual(t.zeroRange.length, 2); - assert.strictEqual(t.zeroRange[0],Math.floor(t.zeroRange[0])); - assert.strictEqual(t.zeroRange[1],Math.floor(t.zeroRange[1])); - t.zeroRange[0].should.be.approximately(t.x0,t.tol); - t.zeroRange[1].should.be.approximately(t.x1,t.tol); - } else { - assert.strictEqual(t.zeroRange.length,1); - assert.strictEqual(t.zeroRange[0],Math.floor(t.zeroRange[0])); - t.zeroRange[0].should.be.approximately(t.x0,t.tol); - } - })); + describe('zero constant function ', function () { + it('should return [l,h] as zero range', function () { + findZeroRange(0, 100, 0.01, function (x) { return 0; }).should.eql([0, 100]); + findZeroRange(-232, 147, 1, function (x) { return 0; }).should.eql([-232, 147]); }); - + }); + describe('linear step functions, positive slope', function () { + var slopes = [0.00001, 0.01, 1, 3.45, 10, 74.3, 298, 17345]; + var divisors = [0.1, 0.3333, 0.5, 1, 2, 5, 7, 13, 17, 25, 101, 243, 412, 542,600,700,800,900]; + var x0 = [-500,-400,-300,-200,-90, -63.5, -21.1, -10, -5, -0.8765, 0.25, 3.1415926, 7, 45, 123, 456]; + var testgen = function (l, h, tol, testFunc) { + return function () { + slopes.forEach(function (s) { + divisors.forEach(function (d) { + x0.forEach(function (z) { + var zeroRange = findZeroRange(l, h, tol, linearStepF(s, d, z)); + testFunc({ + l: l, + h: h, + tol: tol, + slope: s, + divisor: d, + x0: Math.min(h,Math.max(l,z)), + x1: Math.min(h,Math.max(l,z + d)), + zeroRange: zeroRange + }); + }); + }); + }); + }; + }; + it('with tol 0.000001 should find an interval with distinct endpoints', + testgen(-1000, 1000, 0.00001, function (t) { + assert.ok(t.zeroRange.length === 2); + assert.ok(t.zeroRange[0] < t.zeroRange[1]); + })); + it('should find the range to tol of 0.000001', + testgen(-1000, 1000, 0.000001, function (t) { + t.zeroRange[0].should.be.approximately(t.x0, t.tol); + t.zeroRange[1].should.be.approximately(t.x1, t.tol); + })); + it('with tol 1 should find an approximate zero or zeros as appropriate and be integer(s)', + testgen(-1000, 1000, 1, function (t) { + if (t.divisor > 1) { + assert.strictEqual(t.zeroRange.length, 2); + assert.strictEqual(t.zeroRange[0], Math.floor(t.zeroRange[0])); + assert.strictEqual(t.zeroRange[1], Math.floor(t.zeroRange[1])); + t.zeroRange[0].should.be.approximately(t.x0, t.tol); + t.zeroRange[1].should.be.approximately(t.x1, t.tol); + } else { + assert.strictEqual(t.zeroRange.length, 1); + assert.strictEqual(t.zeroRange[0], Math.floor(t.zeroRange[0])); + t.zeroRange[0].should.be.approximately(t.x0, t.tol); + } + })); + it('should find exact answers to integer problems with tol=1', testgen(-1000,1000,1,function(t){ + if ( + (Math.floor(t.divisor)===t.divisor) && + (Math.floor(t.x0)===t.x0) && + (Math.floor(t.x1)===t.x1) && + (t.x1>t.x0) + ){ + try { + if (t.divisor===1){ + t.zeroRange.length.should.equal(1); + t.zeroRange[0].should.equal(t.x0); + } else if (t.divisor>1){ + t.zeroRange.length.should.equal(2); + t.zeroRange[0].should.equal(t.x0); + if (t.x1===t.h) t.zeroRange[1].should.equal(t.h); + else t.zeroRange[1].should.equal(t.x1-1); + } + } catch(e){ console.log(e); console.log(t); throw e;} + } + })); + }); });