diff --git a/.vscode/settings.json b/.vscode/settings.json index cd97e39..6643ff0 100644 --- a/.vscode/settings.json +++ b/.vscode/settings.json @@ -8,8 +8,8 @@ "editor.formatOnSave": false }, "editor.codeActionsOnSave": { - "source.fixAll": true - }, + "source.fixAll": "explicit" + }, "eslint.validate": ["javascript"], "prettier.useTabs": true, "prettier.jsxSingleQuote": false, diff --git a/dist/bundle.js b/dist/bundle.js index 792e8ca..910059e 100644 --- a/dist/bundle.js +++ b/dist/bundle.js @@ -1,2 +1,2 @@ /*! 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The matrix must be square. Not to be confused with exp(a), which performs element-wise exponentiation.",examples:["expm([[0,2],[0,0]])"],seealso:["exp"]}},45130:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.expm1Docs=void 0,t.expm1Docs={name:"expm1",category:"Arithmetic",syntax:["expm1(x)"],description:"Calculate the value of subtracting 1 from the exponential value.",examples:["expm1(2)","pow(e, 2) - 1","log(expm1(2) + 1)"],seealso:["exp","pow","log"]}},41544:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.fixDocs=void 0,t.fixDocs={name:"fix",category:"Arithmetic",syntax:["fix(x)"],description:"Round a value towards zero. If x is complex, both real and imaginary part are rounded towards zero.",examples:["fix(3.2)","fix(3.8)","fix(-4.2)","fix(-4.8)"],seealso:["ceil","floor","round"]}},35489:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.floorDocs=void 0,t.floorDocs={name:"floor",category:"Arithmetic",syntax:["floor(x)"],description:"Round a value towards minus infinity.If x is complex, both real and imaginary part are rounded towards minus infinity.",examples:["floor(3.2)","floor(3.8)","floor(-4.2)"],seealso:["ceil","fix","round"]}},53045:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.gcdDocs=void 0,t.gcdDocs={name:"gcd",category:"Arithmetic",syntax:["gcd(a, b)","gcd(a, b, c, ...)"],description:"Compute the greatest common divisor.",examples:["gcd(8, 12)","gcd(-4, 6)","gcd(25, 15, -10)"],seealso:["lcm","xgcd"]}},24336:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.hypotDocs=void 0,t.hypotDocs={name:"hypot",category:"Arithmetic",syntax:["hypot(a, b, c, ...)","hypot([a, b, c, ...])"],description:"Calculate the hypotenusa of a list with values. ",examples:["hypot(3, 4)","sqrt(3^2 + 4^2)","hypot(-2)","hypot([3, 4, 5])"],seealso:["abs","norm"]}},32501:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.invmodDocs=void 0,t.invmodDocs={name:"invmod",category:"Arithmetic",syntax:["invmod(a, b)"],description:"Calculate the (modular) multiplicative inverse of a modulo b. Solution to the equation ax ≣ 1 (mod b)",examples:["invmod(8, 12)","invmod(7, 13)","invmod(15151, 15122)"],seealso:["gcd","xgcd"]}},37624:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.lcmDocs=void 0,t.lcmDocs={name:"lcm",category:"Arithmetic",syntax:["lcm(x, y)"],description:"Compute the least common multiple.",examples:["lcm(4, 6)","lcm(6, 21)","lcm(6, 21, 5)"],seealso:["gcd"]}},61855:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.logDocs=void 0,t.logDocs={name:"log",category:"Arithmetic",syntax:["log(x)","log(x, base)"],description:"Compute the logarithm of a value. If no base is provided, the natural logarithm of x is calculated. If base if provided, the logarithm is calculated for the specified base. log(x, base) is defined as log(x) / log(base).",examples:["log(3.5)","a = log(2.4)","exp(a)","10 ^ 4","log(10000, 10)","log(10000) / log(10)","b = log(1024, 2)","2 ^ b"],seealso:["exp","log1p","log2","log10"]}},34072:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.log10Docs=void 0,t.log10Docs={name:"log10",category:"Arithmetic",syntax:["log10(x)"],description:"Compute the 10-base logarithm of a value.",examples:["log10(0.00001)","log10(10000)","10 ^ 4","log(10000) / log(10)","log(10000, 10)"],seealso:["exp","log"]}},88276:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.log1pDocs=void 0,t.log1pDocs={name:"log1p",category:"Arithmetic",syntax:["log1p(x)","log1p(x, base)"],description:"Calculate the logarithm of a `value+1`",examples:["log1p(2.5)","exp(log1p(1.4))","pow(10, 4)","log1p(9999, 10)","log1p(9999) / log(10)"],seealso:["exp","log","log2","log10"]}},15958:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.log2Docs=void 0,t.log2Docs={name:"log2",category:"Arithmetic",syntax:["log2(x)"],description:"Calculate the 2-base of a value. This is the same as calculating `log(x, 2)`.",examples:["log2(0.03125)","log2(16)","log2(16) / log2(2)","pow(2, 4)"],seealso:["exp","log1p","log","log10"]}},62266:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.modDocs=void 0,t.modDocs={name:"mod",category:"Operators",syntax:["x % y","x mod y","mod(x, y)"],description:"Calculates the modulus, the remainder of an integer division.",examples:["7 % 3","11 % 2","10 mod 4","isOdd(x) = x % 2","isOdd(2)","isOdd(3)"],seealso:["divide"]}},13933:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.multiplyDocs=void 0,t.multiplyDocs={name:"multiply",category:"Operators",syntax:["x * y","multiply(x, y)"],description:"multiply two values.",examples:["a = 2.1 * 3.4","a / 3.4","2 * 3 + 4","2 * (3 + 4)","3 * 2.1 km"],seealso:["divide"]}},91896:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.normDocs=void 0,t.normDocs={name:"norm",category:"Arithmetic",syntax:["norm(x)","norm(x, p)"],description:"Calculate the norm of a number, vector or matrix.",examples:["abs(-3.5)","norm(-3.5)","norm(3 - 4i)","norm([1, 2, -3], Infinity)","norm([1, 2, -3], -Infinity)","norm([3, 4], 2)","norm([[1, 2], [3, 4]], 1)",'norm([[1, 2], [3, 4]], "inf")','norm([[1, 2], [3, 4]], "fro")']}},49774:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.nthRootDocs=void 0,t.nthRootDocs={name:"nthRoot",category:"Arithmetic",syntax:["nthRoot(a)","nthRoot(a, root)"],description:'Calculate the nth root of a value. The principal nth root of a positive real number A, is the positive real solution of the equation "x^root = A".',examples:["4 ^ 3","nthRoot(64, 3)","nthRoot(9, 2)","sqrt(9)"],seealso:["nthRoots","pow","sqrt"]}},87676:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.nthRootsDocs=void 0,t.nthRootsDocs={name:"nthRoots",category:"Arithmetic",syntax:["nthRoots(A)","nthRoots(A, root)"],description:'Calculate the nth roots of a value. An nth root of a positive real number A, is a positive real solution of the equation "x^root = A". This function returns an array of complex values.',examples:["nthRoots(1)","nthRoots(1, 3)"],seealso:["sqrt","pow","nthRoot"]}},93817:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.powDocs=void 0,t.powDocs={name:"pow",category:"Operators",syntax:["x ^ y","pow(x, y)"],description:"Calculates the power of x to y, x^y.",examples:["2^3","2*2*2","1 + e ^ (pi * i)","pow([[1, 2], [4, 3]], 2)","pow([[1, 2], [4, 3]], -1)"],seealso:["multiply","nthRoot","nthRoots","sqrt"]}},29441:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.roundDocs=void 0,t.roundDocs={name:"round",category:"Arithmetic",syntax:["round(x)","round(x, n)","round(unit, valuelessUnit)","round(unit, n, valuelessUnit)"],description:"round a value towards the nearest integer.If x is complex, both real and imaginary part are rounded towards the nearest integer. When n is specified, the value is rounded to n decimals.",examples:["round(3.2)","round(3.8)","round(-4.2)","round(-4.8)","round(pi, 3)","round(123.45678, 2)","round(3.241cm, 2, cm)","round([3.2, 3.8, -4.7])"],seealso:["ceil","floor","fix"]}},15623:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.signDocs=void 0,t.signDocs={name:"sign",category:"Arithmetic",syntax:["sign(x)"],description:"Compute the sign of a value. The sign of a value x is 1 when x>1, -1 when x<0, and 0 when x=0.",examples:["sign(3.5)","sign(-4.2)","sign(0)"],seealso:["abs"]}},55098:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.sqrtDocs=void 0,t.sqrtDocs={name:"sqrt",category:"Arithmetic",syntax:["sqrt(x)"],description:"Compute the square root value. If x = y * y, then y is the square root of x.",examples:["sqrt(25)","5 * 5","sqrt(-1)"],seealso:["square","sqrtm","multiply","nthRoot","nthRoots","pow"]}},32180:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.sqrtmDocs=void 0,t.sqrtmDocs={name:"sqrtm",category:"Arithmetic",syntax:["sqrtm(x)"],description:"Calculate the principal square root of a square matrix. The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.",examples:["sqrtm([[33, 24], [48, 57]])"],seealso:["sqrt","abs","square","multiply"]}},37981:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.squareDocs=void 0,t.squareDocs={name:"square",category:"Arithmetic",syntax:["square(x)"],description:"Compute the square of a value. The square of x is x * x.",examples:["square(3)","sqrt(9)","3^2","3 * 3"],seealso:["multiply","pow","sqrt","cube"]}},98940:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.subtractDocs=void 0,t.subtractDocs={name:"subtract",category:"Operators",syntax:["x - y","subtract(x, y)"],description:"subtract two values.",examples:["a = 5.3 - 2","a + 2","2/3 - 1/6","2 * 3 - 3","2.1 km - 500m"],seealso:["add"]}},41589:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.unaryMinusDocs=void 0,t.unaryMinusDocs={name:"unaryMinus",category:"Operators",syntax:["-x","unaryMinus(x)"],description:"Inverse the sign of a value. Converts booleans and strings to numbers.",examples:["-4.5","-(-5.6)",'-"22"'],seealso:["add","subtract","unaryPlus"]}},2293:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.unaryPlusDocs=void 0,t.unaryPlusDocs={name:"unaryPlus",category:"Operators",syntax:["+x","unaryPlus(x)"],description:"Converts booleans and strings to numbers.",examples:["+true",'+"2"'],seealso:["add","subtract","unaryMinus"]}},50773:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.xgcdDocs=void 0,t.xgcdDocs={name:"xgcd",category:"Arithmetic",syntax:["xgcd(a, b)"],description:"Calculate the extended greatest common divisor for two values. The result is an array [d, x, y] with 3 entries, where d is the greatest common divisor, and d = x * a + y * b.",examples:["xgcd(8, 12)","gcd(8, 12)","xgcd(36163, 21199)"],seealso:["gcd","lcm"]}},86375:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.bitAndDocs=void 0,t.bitAndDocs={name:"bitAnd",category:"Bitwise",syntax:["x & y","bitAnd(x, y)"],description:"Bitwise AND operation. Performs the logical AND operation on each pair of the corresponding bits of the two given values by multiplying them. If both bits in the compared position are 1, the bit in the resulting binary representation is 1, otherwise, the result is 0",examples:["5 & 3","bitAnd(53, 131)","[1, 12, 31] & 42"],seealso:["bitNot","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]}},52975:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.bitNotDocs=void 0,t.bitNotDocs={name:"bitNot",category:"Bitwise",syntax:["~x","bitNot(x)"],description:"Bitwise NOT operation. Performs a logical negation on each bit of the given value. Bits that are 0 become 1, and those that are 1 become 0.",examples:["~1","~2","bitNot([2, -3, 4])"],seealso:["bitAnd","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]}},96928:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.bitOrDocs=void 0,t.bitOrDocs={name:"bitOr",category:"Bitwise",syntax:["x | y","bitOr(x, y)"],description:"Bitwise OR operation. Performs the logical inclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if the first bit is 1 or the second bit is 1 or both bits are 1, otherwise, the result is 0.",examples:["5 | 3","bitOr([1, 2, 3], 4)"],seealso:["bitAnd","bitNot","bitXor","leftShift","rightArithShift","rightLogShift"]}},49401:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.bitXorDocs=void 0,t.bitXorDocs={name:"bitXor",category:"Bitwise",syntax:["bitXor(x, y)"],description:"Bitwise XOR operation, exclusive OR. Performs the logical exclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1.",examples:["bitOr(1, 2)","bitXor([2, 3, 4], 4)"],seealso:["bitAnd","bitNot","bitOr","leftShift","rightArithShift","rightLogShift"]}},24989:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.leftShiftDocs=void 0,t.leftShiftDocs={name:"leftShift",category:"Bitwise",syntax:["x << y","leftShift(x, y)"],description:"Bitwise left logical shift of a value x by y number of bits.",examples:["4 << 1","8 >> 1"],seealso:["bitAnd","bitNot","bitOr","bitXor","rightArithShift","rightLogShift"]}},19448:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.rightArithShiftDocs=void 0,t.rightArithShiftDocs={name:"rightArithShift",category:"Bitwise",syntax:["x >> y","rightArithShift(x, y)"],description:"Bitwise right arithmetic shift of a value x by y number of bits.",examples:["8 >> 1","4 << 1","-12 >> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightLogShift"]}},61724:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.rightLogShiftDocs=void 0,t.rightLogShiftDocs={name:"rightLogShift",category:"Bitwise",syntax:["x >>> y","rightLogShift(x, y)"],description:"Bitwise right logical shift of a value x by y number of bits.",examples:["8 >>> 1","4 << 1","-12 >>> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightArithShift"]}},78985:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.bellNumbersDocs=void 0,t.bellNumbersDocs={name:"bellNumbers",category:"Combinatorics",syntax:["bellNumbers(n)"],description:"The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S. `bellNumbers` only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["bellNumbers(3)","bellNumbers(8)"],seealso:["stirlingS2"]}},45823:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.catalanDocs=void 0,t.catalanDocs={name:"catalan",category:"Combinatorics",syntax:["catalan(n)"],description:"The Catalan Numbers enumerate combinatorial structures of many different types. catalan only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["catalan(3)","catalan(8)"],seealso:["bellNumbers"]}},25858:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.compositionDocs=void 0,t.compositionDocs={name:"composition",category:"Combinatorics",syntax:["composition(n, k)"],description:"The composition counts of n into k parts. composition only takes integer arguments. The following condition must be enforced: k <= n.",examples:["composition(5, 3)"],seealso:["combinations"]}},18308:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.stirlingS2Docs=void 0,t.stirlingS2Docs={name:"stirlingS2",category:"Combinatorics",syntax:["stirlingS2(n, k)"],description:"he Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets. `stirlingS2` only takes integer arguments. The following condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) = 1.",examples:["stirlingS2(5, 3)"],seealso:["bellNumbers"]}},58916:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.argDocs=void 0,t.argDocs={name:"arg",category:"Complex",syntax:["arg(x)"],description:"Compute the argument of a complex value. If x = a+bi, the argument is computed as atan2(b, a).",examples:["arg(2 + 2i)","atan2(3, 2)","arg(2 + 3i)"],seealso:["re","im","conj","abs"]}},16652:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.conjDocs=void 0,t.conjDocs={name:"conj",category:"Complex",syntax:["conj(x)"],description:"Compute the complex conjugate of a complex value. If x = a+bi, the complex conjugate is a-bi.",examples:["conj(2 + 3i)","conj(2 - 3i)","conj(-5.2i)"],seealso:["re","im","abs","arg"]}},2313:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.imDocs=void 0,t.imDocs={name:"im",category:"Complex",syntax:["im(x)"],description:"Get the imaginary part of a complex number.",examples:["im(2 + 3i)","re(2 + 3i)","im(-5.2i)","im(2.4)"],seealso:["re","conj","abs","arg"]}},67105:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.reDocs=void 0,t.reDocs={name:"re",category:"Complex",syntax:["re(x)"],description:"Get the real part of a complex number.",examples:["re(2 + 3i)","im(2 + 3i)","re(-5.2i)","re(2.4)"],seealso:["im","conj","abs","arg"]}},52989:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.evaluateDocs=void 0,t.evaluateDocs={name:"evaluate",category:"Expression",syntax:["evaluate(expression)","evaluate(expression, scope)","evaluate([expr1, expr2, expr3, ...])","evaluate([expr1, expr2, expr3, ...], scope)"],description:"Evaluate an expression or an array with expressions.",examples:['evaluate("2 + 3")','evaluate("sqrt(16)")','evaluate("2 inch to cm")','evaluate("sin(x * pi)", { "x": 1/2 })','evaluate(["width=2", "height=4","width*height"])'],seealso:[]}},4452:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.helpDocs=void 0,t.helpDocs={name:"help",category:"Expression",syntax:["help(object)","help(string)"],description:"Display documentation on a function or data type.",examples:["help(sqrt)",'help("complex")'],seealso:[]}},94536:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.distanceDocs=void 0,t.distanceDocs={name:"distance",category:"Geometry",syntax:["distance([x1, y1], [x2, y2])","distance([[x1, y1], [x2, y2]])"],description:"Calculates the Euclidean distance between two points.",examples:["distance([0,0], [4,4])","distance([[0,0], [4,4]])"],seealso:[]}},5957:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.intersectDocs=void 0,t.intersectDocs={name:"intersect",category:"Geometry",syntax:["intersect(expr1, expr2, expr3, expr4)","intersect(expr1, expr2, expr3)"],description:"Computes the intersection point of lines and/or planes.",examples:["intersect([0, 0], [10, 10], [10, 0], [0, 10])","intersect([1, 0, 1], [4, -2, 2], [1, 1, 1, 6])"],seealso:[]}},48089:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.andDocs=void 0,t.andDocs={name:"and",category:"Logical",syntax:["x and y","and(x, y)"],description:"Logical and. Test whether two values are both defined with a nonzero/nonempty value.",examples:["true and false","true and true","2 and 4"],seealso:["not","or","xor"]}},70939:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.notDocs=void 0,t.notDocs={name:"not",category:"Logical",syntax:["not x","not(x)"],description:"Logical not. Flips the boolean value of given argument.",examples:["not true","not false","not 2","not 0"],seealso:["and","or","xor"]}},8206:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.orDocs=void 0,t.orDocs={name:"or",category:"Logical",syntax:["x or y","or(x, y)"],description:"Logical or. Test if at least one value is defined with a nonzero/nonempty value.",examples:["true or false","false or false","0 or 4"],seealso:["not","and","xor"]}},52883:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.xorDocs=void 0,t.xorDocs={name:"xor",category:"Logical",syntax:["x xor y","xor(x, y)"],description:"Logical exclusive or, xor. Test whether one and only one value is defined with a nonzero/nonempty value.",examples:["true xor false","false xor false","true xor true","0 xor 4"],seealso:["not","and","or"]}},47968:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.columnDocs=void 0,t.columnDocs={name:"column",category:"Matrix",syntax:["column(x, index)"],description:"Return a column from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","column(A, 1)","column(A, 2)"],seealso:["row","matrixFromColumns"]}},90945:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.concatDocs=void 0,t.concatDocs={name:"concat",category:"Matrix",syntax:["concat(A, B, C, ...)","concat(A, B, C, ..., dim)"],description:"Concatenate matrices. By default, the matrices are concatenated by the last dimension. The dimension on which to concatenate can be provided as last argument.",examples:["A = [1, 2; 5, 6]","B = [3, 4; 7, 8]","concat(A, B)","concat(A, B, 1)","concat(A, B, 2)"],seealso:["det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},91143:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.countDocs=void 0,t.countDocs={name:"count",category:"Matrix",syntax:["count(x)"],description:"Count the number of elements of a matrix, array or string.",examples:["a = [1, 2; 3, 4; 5, 6]","count(a)","size(a)",'count("hello world")'],seealso:["size"]}},82314:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.crossDocs=void 0,t.crossDocs={name:"cross",category:"Matrix",syntax:["cross(A, B)"],description:"Calculate the cross product for two vectors in three dimensional space.",examples:["cross([1, 1, 0], [0, 1, 1])","cross([3, -3, 1], [4, 9, 2])","cross([2, 3, 4], [5, 6, 7])"],seealso:["multiply","dot"]}},42136:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.ctransposeDocs=void 0,t.ctransposeDocs={name:"ctranspose",category:"Matrix",syntax:["x'","ctranspose(x)"],description:"Complex Conjugate and Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","ctranspose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]}},6319:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.detDocs=void 0,t.detDocs={name:"det",category:"Matrix",syntax:["det(x)"],description:"Calculate the determinant of a matrix",examples:["det([1, 2; 3, 4])","det([-2, 2, 3; -1, 1, 3; 2, 0, -1])"],seealso:["concat","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},92623:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.diagDocs=void 0,t.diagDocs={name:"diag",category:"Matrix",syntax:["diag(x)","diag(x, k)"],description:"Create a diagonal matrix or retrieve the diagonal of a matrix. When x is a vector, a matrix with the vector values on the diagonal will be returned. When x is a matrix, a vector with the diagonal values of the matrix is returned. When k is provided, the k-th diagonal will be filled in or retrieved, if k is positive, the values are placed on the super diagonal. When k is negative, the values are placed on the sub diagonal.",examples:["diag(1:3)","diag(1:3, 1)","a = [1, 2, 3; 4, 5, 6; 7, 8, 9]","diag(a)"],seealso:["concat","det","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},21190:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.diffDocs=void 0,t.diffDocs={name:"diff",category:"Matrix",syntax:["diff(arr)","diff(arr, dim)"],description:["Create a new matrix or array with the difference of the passed matrix or array.","Dim parameter is optional and used to indicant the dimension of the array/matrix to apply the difference","If no dimension parameter is passed it is assumed as dimension 0","Dimension is zero-based in javascript and one-based in the parser","Arrays must be 'rectangular' meaning arrays like [1, 2]","If something is passed as a matrix it will be returned as a matrix but other than that all matrices are converted to arrays"],examples:["A = [1, 2, 4, 7, 0]","diff(A)","diff(A, 1)","B = [[1, 2], [3, 4]]","diff(B)","diff(B, 1)","diff(B, 2)","diff(B, bignumber(2))","diff([[1, 2], matrix([3, 4])], 2)"],seealso:["subtract","partitionSelect"]}},13701:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.dotDocs=void 0,t.dotDocs={name:"dot",category:"Matrix",syntax:["dot(A, B)","A * B"],description:"Calculate the dot product of two vectors. The dot product of A = [a1, a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] is defined as dot(A, B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn",examples:["dot([2, 4, 1], [2, 2, 3])","[2, 4, 1] * [2, 2, 3]"],seealso:["multiply","cross"]}},50786:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.eigsDocs=void 0,t.eigsDocs={name:"eigs",category:"Matrix",syntax:["eigs(x)"],description:"Calculate the eigenvalues and optionally eigenvectors of a square matrix",examples:["eigs([[5, 2.3], [2.3, 1]])","eigs([[1, 2, 3], [4, 5, 6], [7, 8, 9]], { precision: 1e-6, eigenvectors: false }"],seealso:["inv"]}},23086:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.fftDocs=void 0,t.fftDocs={name:"fft",category:"Matrix",syntax:["fft(x)"],description:"Calculate N-dimensional fourier transform",examples:["fft([[1, 0], [1, 0]])"],seealso:["ifft"]}},28230:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.filterDocs=void 0,t.filterDocs={name:"filter",category:"Matrix",syntax:["filter(x, test)"],description:"Filter items in a matrix.",examples:["isPositive(x) = x > 0","filter([6, -2, -1, 4, 3], isPositive)","filter([6, -2, 0, 1, 0], x != 0)"],seealso:["sort","map","forEach"]}},51719:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.flattenDocs=void 0,t.flattenDocs={name:"flatten",category:"Matrix",syntax:["flatten(x)"],description:"Flatten a multi dimensional matrix into a single dimensional matrix.",examples:["a = [1, 2, 3; 4, 5, 6]","size(a)","b = flatten(a)","size(b)"],seealso:["concat","resize","size","squeeze"]}},74417:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.forEachDocs=void 0,t.forEachDocs={name:"forEach",category:"Matrix",syntax:["forEach(x, callback)"],description:"Iterates over all elements of a matrix/array, and executes the given callback function.",examples:["numberOfPets = {}","addPet(n) = numberOfPets[n] = (numberOfPets[n] ? numberOfPets[n]:0 ) + 1;",'forEach(["Dog","Cat","Cat"], addPet)',"numberOfPets"],seealso:["map","sort","filter"]}},40109:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.getMatrixDataTypeDocs=void 0,t.getMatrixDataTypeDocs={name:"getMatrixDataType",category:"Matrix",syntax:["getMatrixDataType(x)"],description:'Find the data type of all elements in a matrix or array, for example "number" if all items are a number and "Complex" if all values are complex numbers. 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The matrix has ones on the diagonal and zeros elsewhere.",examples:["identity(3)","identity(3, 5)","a = [1, 2, 3; 4, 5, 6]","identity(size(a))"],seealso:["concat","det","diag","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},78909:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.ifftDocs=void 0,t.ifftDocs={name:"ifft",category:"Matrix",syntax:["ifft(x)"],description:"Calculate N-dimensional inverse fourier transform",examples:["ifft([[2, 2], [0, 0]])"],seealso:["fft"]}},82849:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.invDocs=void 0,t.invDocs={name:"inv",category:"Matrix",syntax:["inv(x)"],description:"Calculate the inverse of a matrix",examples:["inv([1, 2; 3, 4])","inv(4)","1 / 4"],seealso:["concat","det","diag","identity","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},5568:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.kronDocs=void 0,t.kronDocs={name:"kron",category:"Matrix",syntax:["kron(x, y)"],description:"Calculates the kronecker product of 2 matrices or vectors.",examples:["kron([[1, 0], [0, 1]], [[1, 2], [3, 4]])","kron([1,1], [2,3,4])"],seealso:["multiply","dot","cross"]}},169:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.mapDocs=void 0,t.mapDocs={name:"map",category:"Matrix",syntax:["map(x, callback)"],description:"Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array.",examples:["map([1, 2, 3], square)"],seealso:["filter","forEach"]}},37904:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.matrixFromColumnsDocs=void 0,t.matrixFromColumnsDocs={name:"matrixFromColumns",category:"Matrix",syntax:["matrixFromColumns(...arr)","matrixFromColumns(row1, row2)","matrixFromColumns(row1, row2, row3)"],description:"Create a dense matrix from vectors as individual columns.",examples:["matrixFromColumns([1, 2, 3], [[4],[5],[6]])"],seealso:["matrix","matrixFromRows","matrixFromFunction","zeros"]}},46825:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.matrixFromFunctionDocs=void 0,t.matrixFromFunctionDocs={name:"matrixFromFunction",category:"Matrix",syntax:["matrixFromFunction(size, fn)","matrixFromFunction(size, fn, format)","matrixFromFunction(size, fn, format, datatype)","matrixFromFunction(size, format, fn)","matrixFromFunction(size, format, datatype, fn)"],description:"Create a matrix by evaluating a generating function at each index.",examples:["f(I) = I[1] - I[2]","matrixFromFunction([3,3], f)","g(I) = I[1] - I[2] == 1 ? 4 : 0",'matrixFromFunction([100, 100], "sparse", g)',"matrixFromFunction([5], random)"],seealso:["matrix","matrixFromRows","matrixFromColumns","zeros"]}},26388:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.matrixFromRowsDocs=void 0,t.matrixFromRowsDocs={name:"matrixFromRows",category:"Matrix",syntax:["matrixFromRows(...arr)","matrixFromRows(row1, row2)","matrixFromRows(row1, row2, row3)"],description:"Create a dense matrix from vectors as individual rows.",examples:["matrixFromRows([1, 2, 3], [[4],[5],[6]])"],seealso:["matrix","matrixFromColumns","matrixFromFunction","zeros"]}},84898:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.onesDocs=void 0,t.onesDocs={name:"ones",category:"Matrix",syntax:["ones(m)","ones(m, n)","ones(m, n, p, ...)","ones([m])","ones([m, n])","ones([m, n, p, ...])"],description:"Create a matrix containing ones.",examples:["ones(3)","ones(3, 5)","ones([2,3]) * 4.5","a = [1, 2, 3; 4, 5, 6]","ones(size(a))"],seealso:["concat","det","diag","identity","inv","range","size","squeeze","subset","trace","transpose","zeros"]}},18226:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.partitionSelectDocs=void 0,t.partitionSelectDocs={name:"partitionSelect",category:"Matrix",syntax:["partitionSelect(x, k)","partitionSelect(x, k, compare)"],description:"Partition-based selection of an array or 1D matrix. Will find the kth smallest value, and mutates the input array. Uses Quickselect.",examples:["partitionSelect([5, 10, 1], 2)",'partitionSelect(["C", "B", "A", "D"], 1, compareText)',"arr = [5, 2, 1]","partitionSelect(arr, 0) # returns 1, arr is now: [1, 2, 5]","arr","partitionSelect(arr, 1, 'desc') # returns 2, arr is now: [5, 2, 1]","arr"],seealso:["sort"]}},65506:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.pinvDocs=void 0,t.pinvDocs={name:"pinv",category:"Matrix",syntax:["pinv(x)"],description:"Calculate the Moore–Penrose inverse of a matrix",examples:["pinv([1, 2; 3, 4])","pinv([[1, 0], [0, 1], [0, 1]])","pinv(4)"],seealso:["inv"]}},29960:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.rangeDocs=void 0,t.rangeDocs={name:"range",category:"Type",syntax:["start:end","start:step:end","range(start, end)","range(start, end, step)","range(string)"],description:"Create a range. Lower bound of the range is included, upper bound is excluded.",examples:["1:5","3:-1:-3","range(3, 7)","range(0, 12, 2)",'range("4:10")',"range(1m, 1m, 3m)","a = [1, 2, 3, 4; 5, 6, 7, 8]","a[1:2, 1:2]"],seealso:["concat","det","diag","identity","inv","ones","size","squeeze","subset","trace","transpose","zeros"]}},96753:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.reshapeDocs=void 0,t.reshapeDocs={name:"reshape",category:"Matrix",syntax:["reshape(x, sizes)"],description:"Reshape a multi dimensional array to fit the specified dimensions.",examples:["reshape([1, 2, 3, 4, 5, 6], [2, 3])","reshape([[1, 2], [3, 4]], [1, 4])","reshape([[1, 2], [3, 4]], [4])","reshape([1, 2, 3, 4], [-1, 2])"],seealso:["size","squeeze","resize"]}},63246:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.resizeDocs=void 0,t.resizeDocs={name:"resize",category:"Matrix",syntax:["resize(x, size)","resize(x, size, defaultValue)"],description:"Resize a matrix.",examples:["resize([1,2,3,4,5], [3])","resize([1,2,3], [5])","resize([1,2,3], [5], -1)","resize(2, [2, 3])",'resize("hello", [8], "!")'],seealso:["size","subset","squeeze","reshape"]}},46146:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.rotateDocs=void 0,t.rotateDocs={name:"rotate",category:"Matrix",syntax:["rotate(w, theta)","rotate(w, theta, v)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotate([1, 0], pi / 2)",'rotate(matrix([1, 0]), unit("35deg"))','rotate([1, 0, 0], unit("90deg"), [0, 0, 1])','rotate(matrix([1, 0, 0]), unit("90deg"), matrix([0, 0, 1]))'],seealso:["matrix","rotationMatrix"]}},21462:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.rotationMatrixDocs=void 0,t.rotationMatrixDocs={name:"rotationMatrix",category:"Matrix",syntax:["rotationMatrix(theta)","rotationMatrix(theta, v)","rotationMatrix(theta, v, format)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotationMatrix(pi / 2)",'rotationMatrix(unit("45deg"), [0, 0, 1])','rotationMatrix(1, matrix([0, 0, 1]), "sparse")'],seealso:["cos","sin"]}},99019:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.rowDocs=void 0,t.rowDocs={name:"row",category:"Matrix",syntax:["row(x, index)"],description:"Return a row from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","row(A, 1)","row(A, 2)"],seealso:["column","matrixFromRows"]}},26271:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.sizeDocs=void 0,t.sizeDocs={name:"size",category:"Matrix",syntax:["size(x)"],description:"Calculate the size of a matrix.",examples:["size(2.3)",'size("hello world")',"a = [1, 2; 3, 4; 5, 6]","size(a)","size(1:6)"],seealso:["concat","count","det","diag","identity","inv","ones","range","squeeze","subset","trace","transpose","zeros"]}},78498:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.sortDocs=void 0,t.sortDocs={name:"sort",category:"Matrix",syntax:["sort(x)","sort(x, compare)"],description:'Sort the items in a matrix. Compare can be a string "asc", "desc", "natural", or a custom sort function.',examples:["sort([5, 10, 1])",'sort(["C", "B", "A", "D"], "natural")',"sortByLength(a, b) = size(a)[1] - size(b)[1]",'sort(["Langdon", "Tom", "Sara"], sortByLength)','sort(["10", "1", "2"], "natural")'],seealso:["map","filter","forEach"]}},88969:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.squeezeDocs=void 0,t.squeezeDocs={name:"squeeze",category:"Matrix",syntax:["squeeze(x)"],description:"Remove inner and outer singleton dimensions from a matrix.",examples:["a = zeros(3,2,1)","size(squeeze(a))","b = zeros(1,1,3)","size(squeeze(b))"],seealso:["concat","det","diag","identity","inv","ones","range","size","subset","trace","transpose","zeros"]}},16186:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.subsetDocs=void 0,t.subsetDocs={name:"subset",category:"Matrix",syntax:["value(index)","value(index) = replacement","subset(value, [index])","subset(value, [index], replacement)"],description:"Get or set a subset of the entries of a matrix or characters of a string. Indexes are one-based. There should be one index specification for each dimension of the target. Each specification can be a single index, a list of indices, or a range in colon notation `l:u`. In a range, both the lower bound l and upper bound u are included; and if a bound is omitted it defaults to the most extreme valid value. The cartesian product of the indices specified in each dimension determines the target of the operation.",examples:["d = [1, 2; 3, 4]","e = []","e[1, 1:2] = [5, 6]","e[2, :] = [7, 8]","f = d * e","f[2, 1]","f[:, 1]","f[[1,2], [1,3]] = [9, 10; 11, 12]","f"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","trace","transpose","zeros"]}},45592:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.traceDocs=void 0,t.traceDocs={name:"trace",category:"Matrix",syntax:["trace(A)"],description:"Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.",examples:["A = [1, 2, 3; -1, 2, 3; 2, 0, 3]","trace(A)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","transpose","zeros"]}},79091:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.transposeDocs=void 0,t.transposeDocs={name:"transpose",category:"Matrix",syntax:["x'","transpose(x)"],description:"Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","transpose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]}},81421:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.zerosDocs=void 0,t.zerosDocs={name:"zeros",category:"Matrix",syntax:["zeros(m)","zeros(m, n)","zeros(m, n, p, ...)","zeros([m])","zeros([m, n])","zeros([m, n, p, ...])"],description:"Create a matrix containing zeros.",examples:["zeros(3)","zeros(3, 5)","a = [1, 2, 3; 4, 5, 6]","zeros(size(a))"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose"]}},14124:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.solveODEDocs=void 0,t.solveODEDocs={name:"solveODE",category:"Numeric",syntax:["solveODE(func, tspan, y0)","solveODE(func, tspan, y0, options)"],description:"Numerical Integration of Ordinary Differential Equations.",examples:["f(t,y) = y","tspan = [0, 4]","solveODE(f, tspan, 1)","solveODE(f, tspan, [1, 2])",'solveODE(f, tspan, 1, { method:"RK23", maxStep:0.1 })'],seealso:["derivative","simplifyCore"]}},55021:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.combinationsDocs=void 0,t.combinationsDocs={name:"combinations",category:"Probability",syntax:["combinations(n, k)"],description:"Compute the number of combinations of n items taken k at a time",examples:["combinations(7, 5)"],seealso:["combinationsWithRep","permutations","factorial"]}},62280:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.combinationsWithRepDocs=void 0,t.combinationsWithRepDocs={name:"combinationsWithRep",category:"Probability",syntax:["combinationsWithRep(n, k)"],description:"Compute the number of combinations of n items taken k at a time with replacements.",examples:["combinationsWithRep(7, 5)"],seealso:["combinations","permutations","factorial"]}},65101:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.factorialDocs=void 0,t.factorialDocs={name:"factorial",category:"Probability",syntax:["n!","factorial(n)"],description:"Compute the factorial of a value",examples:["5!","5 * 4 * 3 * 2 * 1","3!"],seealso:["combinations","combinationsWithRep","permutations","gamma"]}},84386:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.gammaDocs=void 0,t.gammaDocs={name:"gamma",category:"Probability",syntax:["gamma(n)"],description:"Compute the gamma function. For small values, the Lanczos approximation is used, and for large values the extended Stirling approximation.",examples:["gamma(4)","3!","gamma(1/2)","sqrt(pi)"],seealso:["factorial"]}},54018:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.kldivergenceDocs=void 0,t.kldivergenceDocs={name:"kldivergence",category:"Probability",syntax:["kldivergence(x, y)"],description:"Calculate the Kullback-Leibler (KL) divergence between two distributions.",examples:["kldivergence([0.7,0.5,0.4], [0.2,0.9,0.5])"],seealso:[]}},24595:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.lgammaDocs=void 0,t.lgammaDocs={name:"lgamma",category:"Probability",syntax:["lgamma(n)"],description:"Logarithm of the gamma function for real, positive numbers and complex numbers, using Lanczos approximation for numbers and Stirling series for complex numbers.",examples:["lgamma(4)","lgamma(1/2)","lgamma(i)","lgamma(complex(1.1, 2))"],seealso:["gamma"]}},9224:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.multinomialDocs=void 0,t.multinomialDocs={name:"multinomial",category:"Probability",syntax:["multinomial(A)"],description:"Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai > 0.",examples:["multinomial([1, 2, 1])"],seealso:["combinations","factorial"]}},51009:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.permutationsDocs=void 0,t.permutationsDocs={name:"permutations",category:"Probability",syntax:["permutations(n)","permutations(n, k)"],description:"Compute the number of permutations of n items taken k at a time",examples:["permutations(5)","permutations(5, 3)"],seealso:["combinations","combinationsWithRep","factorial"]}},43162:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.pickRandomDocs=void 0,t.pickRandomDocs={name:"pickRandom",category:"Probability",syntax:["pickRandom(array)","pickRandom(array, number)","pickRandom(array, weights)","pickRandom(array, number, weights)","pickRandom(array, weights, number)"],description:"Pick a random entry from a given array.",examples:["pickRandom(0:10)","pickRandom([1, 3, 1, 6])","pickRandom([1, 3, 1, 6], 2)","pickRandom([1, 3, 1, 6], [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], 2, [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], [2, 3, 2, 1], 2)"],seealso:["random","randomInt"]}},38127:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.randomDocs=void 0,t.randomDocs={name:"random",category:"Probability",syntax:["random()","random(max)","random(min, max)","random(size)","random(size, max)","random(size, min, max)"],description:"Return a random number.",examples:["random()","random(10, 20)","random([2, 3])"],seealso:["pickRandom","randomInt"]}},27752:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.randomIntDocs=void 0,t.randomIntDocs={name:"randomInt",category:"Probability",syntax:["randomInt(max)","randomInt(min, max)","randomInt(size)","randomInt(size, max)","randomInt(size, min, max)"],description:"Return a random integer number",examples:["randomInt(10, 20)","randomInt([2, 3], 10)"],seealso:["pickRandom","random"]}},72758:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.compareDocs=void 0,t.compareDocs={name:"compare",category:"Relational",syntax:["compare(x, y)"],description:"Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compare(2, 3)","compare(3, 2)","compare(2, 2)","compare(5cm, 40mm)","compare(2, [1, 2, 3])"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compareNatural","compareText"]}},94609:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.compareNaturalDocs=void 0,t.compareNaturalDocs={name:"compareNatural",category:"Relational",syntax:["compareNatural(x, y)"],description:"Compare two values of any type in a deterministic, natural way. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compareNatural(2, 3)","compareNatural(3, 2)","compareNatural(2, 2)","compareNatural(5cm, 40mm)",'compareNatural("2", "10")',"compareNatural(2 + 3i, 2 + 4i)","compareNatural([1, 2, 4], [1, 2, 3])","compareNatural([1, 5], [1, 2, 3])","compareNatural([1, 2], [1, 2])","compareNatural({a: 2}, {a: 4})"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare","compareText"]}},35851:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.compareTextDocs=void 0,t.compareTextDocs={name:"compareText",category:"Relational",syntax:["compareText(x, y)"],description:"Compare two strings lexically. Comparison is case sensitive. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:['compareText("B", "A")','compareText("A", "B")','compareText("A", "A")','compareText("2", "10")','compare("2", "10")',"compare(2, 10)",'compareNatural("2", "10")','compareText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural"]}},70339:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.deepEqualDocs=void 0,t.deepEqualDocs={name:"deepEqual",category:"Relational",syntax:["deepEqual(x, y)"],description:"Check equality of two matrices element wise. Returns true if the size of both matrices is equal and when and each of the elements are equal.",examples:["deepEqual([1,3,4], [1,3,4])","deepEqual([1,3,4], [1,3])"],seealso:["equal","unequal","smaller","larger","smallerEq","largerEq","compare"]}},82245:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.equalDocs=void 0,t.equalDocs={name:"equal",category:"Relational",syntax:["x == y","equal(x, y)"],description:"Check equality of two values. Returns true if the values are equal, and false if not.",examples:["2+2 == 3","2+2 == 4","a = 3.2","b = 6-2.8","a == b","50cm == 0.5m"],seealso:["unequal","smaller","larger","smallerEq","largerEq","compare","deepEqual","equalText"]}},81057:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.equalTextDocs=void 0,t.equalTextDocs={name:"equalText",category:"Relational",syntax:["equalText(x, y)"],description:"Check equality of two strings. Comparison is case sensitive. Returns true if the values are equal, and false if not.",examples:['equalText("Hello", "Hello")','equalText("a", "A")','equal("2e3", "2000")','equalText("2e3", "2000")','equalText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural","compareText","equal"]}},74947:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.largerDocs=void 0,t.largerDocs={name:"larger",category:"Relational",syntax:["x > y","larger(x, y)"],description:"Check if value x is larger than y. Returns true if x is larger than y, and false if not.",examples:["2 > 3","5 > 2*2","a = 3.3","b = 6-2.8","(a > b)","(b < a)","5 cm > 2 inch"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare"]}},59460:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.largerEqDocs=void 0,t.largerEqDocs={name:"largerEq",category:"Relational",syntax:["x >= y","largerEq(x, y)"],description:"Check if value x is larger or equal to y. Returns true if x is larger or equal to y, and false if not.",examples:["2 >= 1+1","2 > 1+1","a = 3.2","b = 6-2.8","(a >= b)"],seealso:["equal","unequal","smallerEq","smaller","compare"]}},59181:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.smallerDocs=void 0,t.smallerDocs={name:"smaller",category:"Relational",syntax:["x < y","smaller(x, y)"],description:"Check if value x is smaller than value y. Returns true if x is smaller than y, and false if not.",examples:["2 < 3","5 < 2*2","a = 3.3","b = 6-2.8","(a < b)","5 cm < 2 inch"],seealso:["equal","unequal","larger","smallerEq","largerEq","compare"]}},60020:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.smallerEqDocs=void 0,t.smallerEqDocs={name:"smallerEq",category:"Relational",syntax:["x <= y","smallerEq(x, y)"],description:"Check if value x is smaller or equal to value y. Returns true if x is smaller than y, and false if not.",examples:["2 <= 1+1","2 < 1+1","a = 3.2","b = 6-2.8","(a <= b)"],seealso:["equal","unequal","larger","smaller","largerEq","compare"]}},30482:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.unequalDocs=void 0,t.unequalDocs={name:"unequal",category:"Relational",syntax:["x != y","unequal(x, y)"],description:"Check unequality of two values. Returns true if the values are unequal, and false if they are equal.",examples:["2+2 != 3","2+2 != 4","a = 3.2","b = 6-2.8","a != b","50cm != 0.5m","5 cm != 2 inch"],seealso:["equal","smaller","larger","smallerEq","largerEq","compare","deepEqual"]}},69001:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setCartesianDocs=void 0,t.setCartesianDocs={name:"setCartesian",category:"Set",syntax:["setCartesian(set1, set2)"],description:"Create the cartesian product of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays and the values will be sorted in ascending order before the operation.",examples:["setCartesian([1, 2], [3, 4])"],seealso:["setUnion","setIntersect","setDifference","setPowerset"]}},73554:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setDifferenceDocs=void 0,t.setDifferenceDocs={name:"setDifference",category:"Set",syntax:["setDifference(set1, set2)"],description:"Create the difference of two (multi)sets: every element of set1, that is not the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setDifference([1, 2, 3, 4], [3, 4, 5, 6])","setDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setSymDifference"]}},19619:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setDistinctDocs=void 0,t.setDistinctDocs={name:"setDistinct",category:"Set",syntax:["setDistinct(set)"],description:"Collect the distinct elements of a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setDistinct([1, 1, 1, 2, 2, 3])"],seealso:["setMultiplicity"]}},59441:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setIntersectDocs=void 0,t.setIntersectDocs={name:"setIntersect",category:"Set",syntax:["setIntersect(set1, set2)"],description:"Create the intersection of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIntersect([1, 2, 3, 4], [3, 4, 5, 6])","setIntersect([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setDifference"]}},68419:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setIsSubsetDocs=void 0,t.setIsSubsetDocs={name:"setIsSubset",category:"Set",syntax:["setIsSubset(set1, set2)"],description:"Check whether a (multi)set is a subset of another (multi)set: every element of set1 is the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIsSubset([1, 2], [3, 4, 5, 6])","setIsSubset([3, 4], [3, 4, 5, 6])"],seealso:["setUnion","setIntersect","setDifference"]}},63004:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setMultiplicityDocs=void 0,t.setMultiplicityDocs={name:"setMultiplicity",category:"Set",syntax:["setMultiplicity(element, set)"],description:"Count the multiplicity of an element in a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setMultiplicity(1, [1, 2, 2, 4])","setMultiplicity(2, [1, 2, 2, 4])"],seealso:["setDistinct","setSize"]}},67519:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setPowersetDocs=void 0,t.setPowersetDocs={name:"setPowerset",category:"Set",syntax:["setPowerset(set)"],description:"Create the powerset of a (multi)set: the powerset contains very possible subsets of a (multi)set. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setPowerset([1, 2, 3])"],seealso:["setCartesian"]}},83900:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setSizeDocs=void 0,t.setSizeDocs={name:"setSize",category:"Set",syntax:["setSize(set)","setSize(set, unique)"],description:'Count the number of elements of a (multi)set. When the second parameter "unique" is true, count only the unique values. A multi-dimension array will be converted to a single-dimension array before the operation.',examples:["setSize([1, 2, 2, 4])","setSize([1, 2, 2, 4], true)"],seealso:["setUnion","setIntersect","setDifference"]}},64323:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setSymDifferenceDocs=void 0,t.setSymDifferenceDocs={name:"setSymDifference",category:"Set",syntax:["setSymDifference(set1, set2)"],description:"Create the symmetric difference of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setSymDifference([1, 2, 3, 4], [3, 4, 5, 6])","setSymDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setDifference"]}},91979:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setUnionDocs=void 0,t.setUnionDocs={name:"setUnion",category:"Set",syntax:["setUnion(set1, set2)"],description:"Create the union of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setUnion([1, 2, 3, 4], [3, 4, 5, 6])","setUnion([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setIntersect","setDifference"]}},75220:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.freqzDocs=void 0,t.freqzDocs={name:"freqz",category:"Signal",syntax:["freqz(b, a)","freqz(b, a, w)"],description:"Calculates the frequency response of a filter given its numerator and denominator coefficients.",examples:["freqz([1, 2], [1, 2, 3])","freqz([1, 2], [1, 2, 3], [0, 1])","freqz([1, 2], [1, 2, 3], 512)"],seealso:[]}},60498:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.zpk2tfDocs=void 0,t.zpk2tfDocs={name:"zpk2tf",category:"Signal",syntax:["zpk2tf(z, p, k)"],description:"Compute the transfer function of a zero-pole-gain model.",examples:["zpk2tf([1, 2], [-1, -2], 1)","zpk2tf([1, 2], [-1, -2])","zpk2tf([1 - 3i, 2 + 2i], [-1, -2])"],seealso:[]}},31566:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.erfDocs=void 0,t.erfDocs={name:"erf",category:"Special",syntax:["erf(x)"],description:"Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x",examples:["erf(0.2)","erf(-0.5)","erf(4)"],seealso:[]}},65125:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.zetaDocs=void 0,t.zetaDocs={name:"zeta",category:"Special",syntax:["zeta(s)"],description:"Compute the Riemann Zeta Function using an infinite series and Riemanns Functional Equation for the entire complex plane",examples:["zeta(0.2)","zeta(-0.5)","zeta(4)"],seealso:[]}},25321:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.corrDocs=void 0,t.corrDocs={name:"corr",category:"Statistics",syntax:["corr(A,B)"],description:"Compute the correlation coefficient of a two list with values, For matrices, the matrix correlation coefficient is calculated.",examples:["corr([2, 4, 6, 8],[1, 2, 3, 6])","corr(matrix([[1, 2.2, 3, 4.8, 5], [1, 2, 3, 4, 5]]), matrix([[4, 5.3, 6.6, 7, 8], [1, 2, 3, 4, 5]]))"],seealso:["max","mean","min","median","min","prod","std","sum"]}},78950:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.cumSumDocs=void 0,t.cumSumDocs={name:"cumsum",category:"Statistics",syntax:["cumsum(a, b, c, ...)","cumsum(A)"],description:"Compute the cumulative sum of all values.",examples:["cumsum(2, 3, 4, 1)","cumsum([2, 3, 4, 1])","cumsum([1, 2; 3, 4])","cumsum([1, 2; 3, 4], 1)","cumsum([1, 2; 3, 4], 2)"],seealso:["max","mean","median","min","prod","std","sum","variance"]}},79579:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.madDocs=void 0,t.madDocs={name:"mad",category:"Statistics",syntax:["mad(a, b, c, ...)","mad(A)"],description:"Compute the median absolute deviation of a matrix or a list with values. The median absolute deviation is defined as the median of the absolute deviations from the median.",examples:["mad(10, 20, 30)","mad([1, 2, 3])"],seealso:["mean","median","std","abs"]}},43606:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.maxDocs=void 0,t.maxDocs={name:"max",category:"Statistics",syntax:["max(a, b, c, ...)","max(A)","max(A, dimension)"],description:"Compute the maximum value of a list of values.",examples:["max(2, 3, 4, 1)","max([2, 3, 4, 1])","max([2, 5; 4, 3])","max([2, 5; 4, 3], 1)","max([2, 5; 4, 3], 2)","max(2.7, 7.1, -4.5, 2.0, 4.1)","min(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["mean","median","min","prod","std","sum","variance"]}},70878:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.meanDocs=void 0,t.meanDocs={name:"mean",category:"Statistics",syntax:["mean(a, b, c, ...)","mean(A)","mean(A, dimension)"],description:"Compute the arithmetic mean of a list of values.",examples:["mean(2, 3, 4, 1)","mean([2, 3, 4, 1])","mean([2, 5; 4, 3])","mean([2, 5; 4, 3], 1)","mean([2, 5; 4, 3], 2)","mean([1.0, 2.7, 3.2, 4.0])"],seealso:["max","median","min","prod","std","sum","variance"]}},52797:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.medianDocs=void 0,t.medianDocs={name:"median",category:"Statistics",syntax:["median(a, b, c, ...)","median(A)"],description:"Compute the median of all values. The values are sorted and the middle value is returned. In case of an even number of values, the average of the two middle values is returned.",examples:["median(5, 2, 7)","median([3, -1, 5, 7])"],seealso:["max","mean","min","prod","std","sum","variance","quantileSeq"]}},90759:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.minDocs=void 0,t.minDocs={name:"min",category:"Statistics",syntax:["min(a, b, c, ...)","min(A)","min(A, dimension)"],description:"Compute the minimum value of a list of values.",examples:["min(2, 3, 4, 1)","min([2, 3, 4, 1])","min([2, 5; 4, 3])","min([2, 5; 4, 3], 1)","min([2, 5; 4, 3], 2)","min(2.7, 7.1, -4.5, 2.0, 4.1)","max(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["max","mean","median","prod","std","sum","variance"]}},27894:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.modeDocs=void 0,t.modeDocs={name:"mode",category:"Statistics",syntax:["mode(a, b, c, ...)","mode(A)","mode(A, a, b, B, c, ...)"],description:"Computes the mode of all values as an array. In case mode being more than one, multiple values are returned in an array.",examples:["mode(2, 1, 4, 3, 1)","mode([1, 2.7, 3.2, 4, 2.7])","mode(1, 4, 6, 1, 6)"],seealso:["max","mean","min","median","prod","std","sum","variance"]}},97291:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.prodDocs=void 0,t.prodDocs={name:"prod",category:"Statistics",syntax:["prod(a, b, c, ...)","prod(A)"],description:"Compute the product of all values.",examples:["prod(2, 3, 4)","prod([2, 3, 4])","prod([2, 5; 4, 3])"],seealso:["max","mean","min","median","min","std","sum","variance"]}},94453:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.quantileSeqDocs=void 0,t.quantileSeqDocs={name:"quantileSeq",category:"Statistics",syntax:["quantileSeq(A, prob[, sorted])","quantileSeq(A, [prob1, prob2, ...][, sorted])","quantileSeq(A, N[, sorted])"],description:"Compute the prob order quantile of a matrix or a list with values. 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t){const t=document.createElement("li");t.innerHTML=n,n===e&&(t.className="active"),s.append(t)}r.append(i,s);const c=r.querySelector(".select"),u=r.querySelector(".caret"),l=r.querySelector(".menu"),d=r.querySelectorAll(".menu li"),p=r.querySelector(".selected");c.addEventListener("click",(()=>{c.classList.toggle("select-clicked"),u.classList.toggle("caret-rotate"),l.classList.toggle("menu-open")}));let f=e;return s.addEventListener("click",(e=>{if("LI"===e.target.tagName){const t=e.target;p.innerText=t.innerText,f=t.innerText,d.forEach((e=>{e.classList.remove("active")})),t.classList.add("active"),c.classList.remove("select-clicked"),u.classList.remove("caret-rotate"),l.classList.remove("menu-open")}})),{UI:r,getSelectedOption:function(){return f}}}function E(e,t,n,r){const i=document.createElement("input");return i.type="text",i.name=e,i.placeholder=t,i.className=n,i.addEventListener("keypress",r),i}_.id="hypothesis-testing-container";const A=document.querySelector("nav #nav-button"),j=document.querySelector("aside");function T(e){j.contains(e.target)||A.contains(e.target)||j.classList.contains("hidden")||(j.classList.add("hidden"),window.removeEventListener("click",T))}A.onclick=()=>{j.classList.toggle("hidden"),window.addEventListener("click",T)};const F=document.querySelector("main").innerHTML,B=document.querySelector("header img"),R=document.querySelector("main"),q=document.querySelectorAll("aside button");function k(e){if(e){let t=e.firstChild;for(;t;)t.remove(),t=e.firstChild}}B.onclick=()=>{k(R),R.innerHTML=F},q.forEach((e=>{e.addEventListener("click",(()=>{k(R)}))})),q[0].addEventListener("click",(function(){const e=document.createElement("h2");e.textContent="# Frequency Distribution Table (Ungrouped)";const n=document.createElement("div");n.innerHTML="

Important characteristics of a large mass of data can be readily assessed by grouping the data into different classes and then determining the number of observations that fall in each of the classes.

",n.innerHTML+="

Such an arrangement in tabular form is called a frequency distribution

";const r=document.createElement("form");r.id="frq-dist-u-form",function(e){const n=document.createElement("label");n.textContent="Data Set (e.g. 1,2,3):";const r=document.createElement("input");r.type="text",r.name="dataset",r.placeholder="1,2,3",n.appendChild(r),r.addEventListener("keypress",s);const i=document.createElement("label");i.textContent="Number of Classes:";const c=document.createElement("input");c.type="text",c.name="numClasses",c.placeholder="1 - 999",c.maxLength="3",i.appendChild(c),i.appendChild(c),c.addEventListener("keypress",o),r.setAttribute("required",!0),c.setAttribute("required",!0);const u=document.createElement("button");u.textContent="Show Frequency Distribution",u.type="submit";const l=document.createElement("p");l.textContent="All* fields are required",l.style.display="none",l.style.color="red",l.style.textAlign="center",u.addEventListener("click",(e=>{e.preventDefault(),k(a),r.value&&c.value?(function(e,n){const r=t()(e,n),i=document.createElement("p");i.textContent="Data Set (Sorted): ",i.id="data-set-display";const o=e.sort();for(let t=0;t{const t=document.createElement("th");t.textContent=e,c.appendChild(t)}));for(let e=0;e{t.insertCell().textContent=r[n][e]}))}a.append(s,i)}(r.value.split(",").filter((e=>""!==e.trim())).map(Number),Number(c.value)),l.style.display="none",c.value="",r.value=""):l.style.display="block"})),e.append(n,i,u,l)}(r);const c=document.createElement("div");c.innerHTML="

✏️ How It Works

",c.innerHTML+="

From the data entered, the calculator computes for the class width (range / class number) rounded up to the nearest whole number. (range = min - max)

",c.innerHTML+="Using the computed class width, the calculator now computes for the class intervals of the data. Starting with the lowest value in the data set which will be used as base for the lower class interval, the calculator will add a value of (class width - 1) to get the higher class interval. The value of class width will be added to the following class intervals.",c.innerHTML+="

\n  const maxClassInterval = Math.min(...dataSet) + ((classWidth * classNumber) - 1);\n  for (let i = Math.min(...dataSet); i <= maxClassInterval; i += classWidth) {\n    classInterval.push({ min: i, max: i + (classWidth - 1) });\n  }\n  

",c.innerHTML+="The calculator proceeds to computing the class boundaries by subtracting 0.5 to the lower value of class intervals and adding 0.5 to the higher value of class intervals.",c.innerHTML+="

\n  classBoundaries = classInterval.map((classInt) => ({\n    min: classInt.min - 0.5,\n    max: classInt.max + 0.5,\n  }));\n  

",c.innerHTML+="Class mark is computed by adding the lower and higher value of the corresponding interval and dividing them to 2",c.innerHTML+="

\n  classMark = fTable.classInterval.map((classInt) => (classInt.min + classInt.max) / 2);\n  

",c.innerHTML+="The calculator computes the frequency of values within each class interval by tallying the number of data points that fall into each interval.",c.innerHTML+="

\n  classFrequency = [];\n  for (let i = 0; i < classNumber; i += 1) {\n    classFrequency.push(0);\n    for (let j = 0; j < dataSet.length; j += 1) {\n      if (dataSet[j] >= classInterval[i].min && dataSet[j] <= classInterval[i].max) {\n        classFrequency[i] += 1;\n      }\n    }\n  }\n  

",c.innerHTML+="The relative frequency for each class interval is calculated by dividing the corresponding class frequency by the total number of data points in the dataset, resulting in a proportional value for each interval. The resulting value that has any fractional part of the number will have a maximum of three decimal places.",c.innerHTML+="

\n  fTable.relativeFrequency = fTable.classFrequency.map((frequency) => (\n    Number((frequency / dataSet.length).toFixed(3))\n  ));\n  

",i.append(e,n,r,a,c)})),q[1].addEventListener("click",(function(){const e=document.createElement("h2");e.textContent="# Symmetry and Skewness";const t=document.createElement("div");t.innerHTML="

Symmetric: if distribution can be folded along a vertical axis so that the two sides coincide.

",t.innerHTML+="

Skewed: a distribution that lacks symmetry with respect to vertical axis.

";const n=document.createElement("form");n.id="skewness-form",function(e){const t=document.createElement("label");t.textContent="Data Set (e.g. 1,2,3):";const n=document.createElement("input");n.type="text",n.name="dataset",n.placeholder="1,2,3",t.appendChild(n),n.addEventListener("keypress",d);const r=document.createElement("label"),i=document.createElement("input");i.type="checkbox",i.name="population",i.checked=!0,r.appendChild(i),r.appendChild(document.createTextNode(" Population"));const a=document.createElement("label"),o=document.createElement("input");o.type="checkbox",o.name="sample",a.appendChild(o),a.appendChild(document.createTextNode(" Sample"));const s=[i,o];s.forEach((e=>{e.addEventListener("change",(e=>{s.forEach((t=>{t.checked||t===e.target?t!==e.target&&(t.checked=!1):t.checked=!0}))}))}));const u=document.createElement("button");u.textContent="Show Symmetry and Skewness",u.type="submit";const p=document.createElement("p");p.textContent="All* fields are required",p.style.display="none",p.style.color="red",p.style.textAlign="center",u.addEventListener("click",(e=>{if(e.preventDefault(),k(l),n.value){p.style.display="none";const e=i.checked?"population":"sample";!function(e,t){const n=e.value.split(",").filter((e=>""!==e.trim())).map(Number),r=(0,c.calculateSkewness)(n,t),i=(0,c.getSymmetry)(r),a=document.createElement("p");a.textContent="Data Set (Sorted): ",a.id="data-set-display";const o=n.sort();for(let e=0;e✏️ How It Works",r.innerHTML+="

The skewness of a dataset is calculated using the following formula:

",r.innerHTML+="

Skewness = 3(Mean−Median) / Standard Deviation

",r.innerHTML+="

Where:

",r.innerHTML+="

- Mean is the mean (average) of the dataset.

",r.innerHTML+="

- Median is the median of the dataset.

",r.innerHTML+="

- Standard Deviation is the standard deviation of the dataset.

",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function calculateSkewness(data, type = 'population') {\n    const skewness = (3 * (getMean(data) - getMedian(data))) / getStandardDeviation(data, type);\n    return skewness;\n  }\n  

",r.innerHTML+="

The formula essentially measures the asymmetry of the dataset. If the skewness is:

",r.innerHTML+="

- Positive: The data distribution is skewed to the right (positively skewe

",r.innerHTML+="

- Negative: The data distribution is skewed to the left (negatively skewed).

",r.innerHTML+="

- The data distribution is symmetric (normally skewed).

",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function getSymmetry(skewness) {\n    if (skewness > 0) return 'positively skewed';\n    if (skewness < 0) return 'negatively skewed';\n    return 'normally skewed'; // === 0\n  }\n  

",u.append(e,t,n,l,r)})),q[2].addEventListener("click",(function(){const e=document.createElement("h2");e.textContent="# Simple Correlation Coefficient";const t=document.createElement("div");t.innerHTML="

It is also called as Pearson's correlation or Product moment correlation coefficient

",t.innerHTML+="

It measures the nature and strength between two variables of the quantitative type

";const n=document.createElement("form");n.id="simple-corre-form",function(e){const t=document.createElement("label");t.textContent="X Data Set (e.g. 1,2,3):";const n=document.createElement("input");n.type="text",n.name="dataset",n.placeholder="1,2,3",t.appendChild(n),n.addEventListener("keypress",y);const r=document.createElement("label");r.textContent="Y Data Set (e.g. 1,2,3):";const i=document.createElement("input");i.type="text",i.name="dataset",i.placeholder="1,2,3",r.appendChild(i),i.addEventListener("keypress",y);const a=document.createElement("label");a.textContent="X Label:",a.className="data-label";const o=document.createElement("input");o.type="text",o.name="x-label",o.value="X",a.appendChild(o);const s=document.createElement("label");s.textContent="Y Label:",s.className="data-label";const c=document.createElement("input");c.type="text",c.name="y-label",c.value="Y",s.appendChild(c),n.setAttribute("required",!0),i.setAttribute("required",!0);const u=document.createElement("button");u.textContent="Show Simple Correlation Coefficient",u.type="submit";const l=document.createElement("p");l.textContent="All* fields are required",l.style.display="none",l.style.color="red",l.style.textAlign="center",u.addEventListener("click",(e=>{e.preventDefault(),k(m),n.value&&i.value?(function(e,t,n){const r=(0,p.calculateSimpleCorrelation)(e,t),i=(0,p.getFinalLabel)(r),a=document.createElement("p");a.textContent=`Result: ${r}, ${i}`;const o=document.createElement("table"),s=o.insertRow();n.forEach((e=>{const t=document.createElement("th");t.textContent=e,s.appendChild(t)}));let c=0,u=0,l=0,d=0,f=0;for(let n=0;n""!==e.trim())).map(Number),i.value.split(",").filter((e=>""!==e.trim())).map(Number),[o.value,c.value,"X²","Y²","XY"]),l.style.display="none",n.value="",i.value="",o.value="X",c.value="Y"):l.style.display="block"})),e.append(a,t,s,r,u,l)}(n);const r=document.createElement("div");r.innerHTML="

✏️ How It Works

",r.innerHTML+="

To interpret the correlation coefficient:

",r.innerHTML+="The calculator uses a labeling function that categorizes the coefficient based on its value. A coefficient of 0 is labeled 'no relation,' while a coefficient of 1 or -1 indicates a 'perfect correlation.' For other coefficients, the label reflects both the nature (positive or negative) and strength (weak, moderate, strong) of the correlation.",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function getFinalLabel(value) {\n    if (value === 0) return 'no relation';\n    if (value === 1 || value === -1) return 'perfect correlation';\n    return 'getNature(value) getStrength(value) correlation';\n  }\n  

",r.innerHTML+="

To calculate the correlation coefficient:

",r.innerHTML+="The correlation calculation involves various steps, including obtaining sums, products, and squared values of data points from two datasets. The size of the datasets (n) is considered. Applying the Pearson correlation formula, which involves covariance and standard deviations, yields the correlation coefficient. The final result is limited to three decimal points.",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function calculateSimpleCorrelation(xData, yData) {\n    const summationX = xData.reduce((acc, val) => acc + val, 0);\n    const summationY = yData.reduce((acc, val) => acc + val, 0);\n  \n    const xyData = []; const xSquaredData = []; const\n      ySquaredData = [];\n    for (let i = 0; i < xData.length; i += 1) {\n      xyData[i] = xData[i] * yData[i];\n      xSquaredData[i] = xData[i] ** 2;\n      ySquaredData[i] = yData[i] ** 2;\n    }\n  \n    const summationXY = xyData.reduce((acc, val) => acc + val, 0);\n    const summationXSquared = xSquaredData.reduce((acc, val) => acc + val, 0);\n    const summationYSquared = ySquaredData.reduce((acc, val) => acc + val, 0);\n    const n = xData.length;\n  \n    const xSquaredDividedByN = summationX ** 2 / n;\n    const ySquaredDividedByN = summationY ** 2 / n;\n  \n    const denominator = Math.sqrt(\n      (summationXSquared - xSquaredDividedByN) * (summationYSquared - ySquaredDividedByN),\n    );\n    const numerator = summationXY - ((summationX * summationY) / n);\n    const simpleCorrelation = numerator / denominator;\n    return limitDecimalPoints(simpleCorrelation, 3);\n  }\n  

",f.append(e,t,n,m,r)})),q[3].addEventListener("click",(function(){const e=document.createElement("h2");e.textContent="# Spearman Rank Correlation Coefficient";const t=document.createElement("div");t.innerHTML="

The Spearman rank correlation coefficient, is a statistical measure that assesses the strength and direction of the monotonic relationship between two variables. It is a non-parametric measure, meaning it doesn't rely on the distribution of the data, making it suitable for both continuous and ordinal data.",t.innerHTML+="

It measures the nature and strength between two variables of the quantitative type

",t.innerHTML+="

Note: when inserting ordinal data (not a number but a label), type them in order, (for example: University,Secondary,Preparatory,Nursery,Illiterate) and type the corresponding value for each of the values on the second variable input (Y Data Set)

";const n=document.createElement("form");n.id="spearman-rank-form",function(e){const t=document.createElement("label");t.textContent="X Data Set (e.g. 1,2,3):";const n=document.createElement("input");n.type="text",n.name="dataset",n.placeholder="1,2,3",t.appendChild(n),n.addEventListener("keypress",b);const r=document.createElement("label");r.textContent="Y Data Set (e.g. 1,2,3):";const i=document.createElement("input");i.type="text",i.name="dataset",i.placeholder="1,2,3",r.appendChild(i),i.addEventListener("keypress",b);const a=document.createElement("label");a.textContent="X Label:",a.className="data-label";const o=document.createElement("input");o.type="text",o.name="x-label",o.value="X",a.appendChild(o);const s=document.createElement("label");s.textContent="Y Label:",s.className="data-label";const c=document.createElement("input");c.type="text",c.name="y-label",c.value="Y",s.appendChild(c),n.setAttribute("required",!0),i.setAttribute("required",!0);const u=document.createElement("button");u.textContent="Show Spearman Rank Correlation Coefficient",u.type="submit";const l=document.createElement("p");l.textContent="All* fields are required",l.style.display="none",l.style.color="red",l.style.textAlign="center",u.addEventListener("click",(e=>{if(e.preventDefault(),k(g),n.value&&i.value){let e=n.value.split(",").filter((e=>""!==e.trim()));e=e.map((e=>{const t=Number(e.trim());return isNaN(t)?e.trim():t}));let t=i.value.split(",").filter((e=>""!==e.trim()));t=t.map((e=>{const t=Number(e.trim());return isNaN(t)?e.trim():t})),function(e,t,n){console.log(e);const r=(0,v.spearmanRank)(e,t),i=r.computedValue,a=(0,p.getFinalLabel)(i),o=document.createElement("p");o.textContent=`Result: ${i}, ${a}`;const s=document.createElement("table"),c=s.insertRow(),u=(0,v.hasDuplicates)(e)||(0,v.hasDuplicates)(t);if(!1===u?(n.push("Rank X"),n.push("Rank Y"),n.push("di"),n.push("di²"),n.forEach((e=>{const t=document.createElement("th");t.textContent=e,c.appendChild(t)}))):(n.push("Rank X"),n.push("Rank Y"),n.push("Rx-MRx"),n.push("Ry-MRy"),n.push("(Rx-MRx)*(Ry-MRy)"),n.push("(Rx-MRx)²"),n.push("(Ry-MRy)²"),n.forEach((e=>{const t=document.createElement("th");t.textContent=e,c.appendChild(t)}))),!1===u){const n=r.xRankData,i=r.yRankData,a=r.diData,o=r.diSquaredData,c=r.diSquaredSummation;for(let r=0;r✏️ How It Works",r.innerHTML+="

To interpret the correlation coefficient:

",r.innerHTML+="The calculator uses a labeling function that categorizes the coefficient based on its value. A coefficient of 0 is labeled 'no relation,' while a coefficient of 1 or -1 indicates a 'perfect correlation.' For other coefficients, the label reflects both the nature (positive or negative) and strength (weak, moderate, strong) of the correlation.",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function getFinalLabel(value) {\n    if (value === 0) return 'no relation';\n    if (value === 1 || value === -1) return 'perfect correlation';\n    return 'getNature(value) getStrength(value) correlation';\n  }\n  

",r.innerHTML+="

To rank the data:

",r.innerHTML+="

This function rank is designed to assign ranks to an array of data points, with a distinction made between cases where the data contains duplicates and where it does not. The function first creates an array of objects, each containing the original value and its index. Depending on whether the data is composed of strings or numerical values, it either maintains the original order for strings or sorts the array in descending order for numerical values. When duplicates are present, the function calculates average ranks for sets of identical values and assigns these ranks to all occurrences. The function then maps the calculated ranks back to the original order of the data using the stored indices, providing a final array of ranked data. This approach ensures accurate ranking, making the function suitable for scenarios where the presence of duplicate values needs to be appropriately considered.

",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function rank(data) {\n    let dataObjects = [];\n    for (let i = 0; i < data.length; i++) {\n      dataObjects.push({value: data[i], index: i});\n    }\n  \n    let rankData = [];\n    let mainSortedData = [];\n    if (typeof data[0] === 'string'){\n      mainSortedData = dataObjects;\n    } else {\n      mainSortedData = [...dataObjects].sort((a, b) => b.value - a.value);\n    }\n    //inserted two dumies para hindi sya malito sa variable i.\n    mainSortedData.push({value: undefined, index: undefined});\n    mainSortedData.push({value: undefined, index: undefined});\n    const dataArray = [], duplicateRank = []; \n    \n    for (let i = 0; i < data.length; i++) {\n      if (mainSortedData[i].value === mainSortedData[i+1].value){\n        let duplicate = mainSortedData[i].value;\n        duplicateRank.push(i + 1);\n        for (let j = i + 1; j < data.length; j++) {\n          if (duplicate === mainSortedData[j].value) {\n            duplicateRank.push(j + 1);\n          }\n        }\n  \n        i += duplicateRank.length;\n      }\n      \n  \n      if (duplicateRank.length > 0){\n        const sum = duplicateRank.reduce((acc, val) => acc + val, 0);\n        const n = duplicateRank.length;\n        let average = sum/n;\n  \n        for (let i = 0; i < duplicateRank.length; i++) {\n          duplicateRank[i] = average;\n        }\n  \n        const len = duplicateRank.length;\n  \n        for (let i = 0; i < len; i++) {\n          rankData.push(duplicateRank.pop());\n        }\n      }\n  \n  \n      if (mainSortedData[i].value !== mainSortedData[i+1].value && i < data.length) {\n        rankData.push(i + 1);\n        dataArray.push(mainSortedData[i].value);\n      } else if (mainSortedData[i].value === mainSortedData[i+1].value) {\n        i--;\n      }\n    }\n    \n    let rankedData = [];\n    for (let h = 0; h < data.length; h++) {\n      rankedData[mainSortedData[h].index] = rankData[h];\n    }\n    return rankedData;\n  }\n  

",r.innerHTML+="

To calculate the spearman rank correlation coefficient:

",r.innerHTML+="The provided JavaScript function calculates the Spearman rank correlation coefficient for two sets of data points, considering the presence of duplicates. In the absence of duplicates, it ranks the data, computes differences between corresponding ranks, and applies the Spearman formula to obtain the correlation coefficient. Additional information, including ranked data, differences, and squared differences, is returned. In the presence of duplicates, the function calculates mean ranks and performs modified Spearman calculations, returning a variety of intermediate results such as mean ranks, differences from mean ranks, and products of differences. The function limits the computed Spearman rank to three decimal places and provides a comprehensive set of outputs for both scenarios to aid in result interpretation and debugging.",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function spearmanRank(xData, yData) {\n    const duplicatesChecker = hasDuplicates(xData) || hasDuplicates(yData);\n  \n    const n = xData.length;\n    if (duplicatesChecker === false){\n      const xRankData = rank(xData); const yRankData = rank(yData); const diData = [];\n  \n      for (let i = 0; i < n; i += 1) {\n        diData[i] = xRankData[i] - yRankData[i];\n      }\n      const diSquaredData = diData.map((num) => num ** 2);\n      const diSquaredSummation = diSquaredData.reduce((acc, val) => acc + val, 0);\n      const spearmanRank = 1 - ((6 * diSquaredSummation) / (n * ((n ** 2) - 1)));\n  \n      return {\n        computedValue: limitDecimalPoints(spearmanRank, 3), \n        xRankData: xRankData, \n        yRankData: yRankData,\n        diData: diData,\n        diSquaredData: diSquaredData,\n        diSquaredSummation: diSquaredSummation,\n      };\n    } else {\n      const xRankData = rank(xData); const yRankData = rank(yData);\n      const MRx = xRankData.reduce((acc, val) => acc + val, 0) / n;\n      const MRy = yRankData.reduce((acc, val) => acc + val, 0) / n;\n      let RxMinusMrxData = []; RyMinusMryData = []; ProductData = []; RxMinusMRxRaiseTo2Data = []; RyMinusMRyRaiseTo2Data = [];\n      for (let i = 0; i < n; i++) {\n        RxMinusMrxData[i] = xRankData[i] - MRx;\n        RyMinusMryData[i] = yRankData[i] - MRy;\n        ProductData[i] = RxMinusMrxData[i] * RyMinusMryData[i];\n        RxMinusMRxRaiseTo2Data[i] = RxMinusMrxData[i] ** 2;\n        RyMinusMRyRaiseTo2Data[i] = RyMinusMryData[i] ** 2;\n      }\n  \n      const SummationOfProductData = ProductData.reduce((acc, val) => acc + val, 0);\n      const SummationOfRxMinusMRxRaiseTo2Data = RxMinusMRxRaiseTo2Data.reduce((acc, val) => acc + val, 0);\n      const SummationOfRyMinusMRyRaiseTo2Data = RyMinusMRyRaiseTo2Data.reduce((acc, val) => acc + val, 0);\n  \n      const spearmanRank = SummationOfProductData / (Math.sqrt(SummationOfRxMinusMRxRaiseTo2Data * SummationOfRyMinusMRyRaiseTo2Data))\n  \n      return {\n        computedValue: limitDecimalPoints(spearmanRank, 3), \n        xRankData: xRankData, \n        yRankData: yRankData,\n        MRx: MRx,\n        MRy: MRy,\n        RxMinusMrxData: RxMinusMrxData,\n        RyMinusMryData: RyMinusMryData,\n        ProductData: ProductData,\n        RxMinusMRxRaiseTo2Data: RxMinusMRxRaiseTo2Data,\n        RyMinusMRyRaiseTo2Data: RyMinusMRyRaiseTo2Data,\n        SummationOfProductData: SummationOfProductData,\n        SummationOfRxMinusMRxRaiseTo2Data: SummationOfRxMinusMRxRaiseTo2Data,\n        SummationOfRyMinusMRyRaiseTo2Data: SummationOfRyMinusMRyRaiseTo2Data\n      };\n    }\n  }\n  

",h.append(e,t,n,g,r)})),q[4].addEventListener("click",(function(){const e=document.createElement("h2");e.textContent="# Linear Regression";const t=document.createElement("div");t.innerHTML="

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to the observed data. The goal is to find the best-fitting line that minimizes the sum of squared differences between the observed values and the values predicted by the model.

",t.innerHTML+="

In a simple linear regression, there is one dependent variable and one independent variable, and the relationship is represented by the equation: Y = a + bX

";const n=document.createElement("form");n.id="linear-regression-form",function(e){const t=document.createElement("label");t.textContent="X Data Set (e.g. 1,2,3):";const n=document.createElement("input");n.type="text",n.name="dataset",n.placeholder="1,2,3",t.appendChild(n),n.addEventListener("keypress",w);const r=document.createElement("label");r.textContent="Y Data Set (e.g. 1,2,3):";const i=document.createElement("input");i.type="text",i.name="dataset",i.placeholder="1,2,3",r.appendChild(i),i.addEventListener("keypress",w);const a=document.createElement("label");a.textContent="X Label:",a.className="data-label";const o=document.createElement("input");o.type="text",o.name="x-label",o.value="X",a.appendChild(o);const s=document.createElement("label");s.textContent="Y Label:",s.className="data-label";const c=document.createElement("input");c.type="text",c.name="y-label",c.value="Y",s.appendChild(c);const u=document.createElement("label");u.textContent="Give value/s of x to predict the corresponding y:",u.className="data-label";const l=document.createElement("input");l.type="text",l.name="y-label",l.placeholder="1,2,3",u.appendChild(l),n.setAttribute("required",!0),i.setAttribute("required",!0),l.setAttribute("required",!0);const d=document.createElement("button");d.textContent="Show Linear Regression Analysis",d.type="submit";const p=document.createElement("p");p.textContent="All* fields are required",p.style.display="none",p.style.color="red",p.style.textAlign="center",d.addEventListener("click",(e=>{if(e.preventDefault(),k(M),n.value&&i.value&&l.value){let e=n.value.split(",").filter((e=>""!==e.trim()));e=e.map((e=>{const t=Number(e.trim());return isNaN(t)?e.trim():t}));let t=i.value.split(",").filter((e=>""!==e.trim()));t=t.map((e=>{const t=Number(e.trim());return isNaN(t)?e.trim():t}));let r=l.value.split(",").filter((e=>""!==e.trim()));r=r.map((e=>{const t=Number(e.trim());return isNaN(t)?e.trim():t})),function(e,t,n,r){const i=(0,D.linearRegression)(e,t),a=i.a,o=i.b,s=`Y = ${a} ${1===Math.sign(o)?"+":-1===Math.sign(o)?"-":"0"} ${o}x`,c=document.createElement("p");c.textContent=`Linear Equation: ${s}`;const u=document.createElement("table"),l=u.insertRow();r.push("xy"),r.push("x²"),r.push("y²"),r.forEach((e=>{const t=document.createElement("th");t.textContent=e,l.appendChild(t)}));for(let n=0;n✏️ How It Works",r.innerHTML+="

To interpret the linear regression:

",r.innerHTML+="The calculator uses a linear regression function which conducts simple linear regression on given arrays of x and y data points. The function calculates the coefficients of the linear regression equation (Y = a + bX) by computing various summations and intermediate results. It employs arrays to store products, squares, and sums during the calculation process. The resulting object returned by the function includes the calculated coefficients (a and b), intermediate arrays, means of x and y, and summations.",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function linearRegression(xData, yData) {\n    const summationX = xData.reduce((acc, val) => acc + val, 0);\n    const summationY = yData.reduce((acc, val) => acc + val, 0);\n  \n    const xyData = []; const xSquaredData = []; const\n      ySquaredData = [];\n    for (let i = 0; i < xData.length; i += 1) {\n      xyData[i] = xData[i] * yData[i];\n      xSquaredData[i] = xData[i] ** 2;\n      ySquaredData[i] = yData[i] ** 2;\n    }\n  \n    const summationXY = xyData.reduce((acc, val) => acc + val, 0);\n    const summationXSquared = xSquaredData.reduce((acc, val) => acc + val, 0);\n    const summationYSquared = ySquaredData.reduce((acc, val) => acc + val, 0);\n    const n = xData.length;\n  \n    const xMean = limitDecimalPoints(summationX/n,3);\n    const yMean = limitDecimalPoints(summationY/n,3);\n  \n    const b = limitDecimalPoints((summationXY - ((summationX*summationY)/n))/(summationXSquared - ((summationX ** 2)/n)), 3);\n    const a = limitDecimalPoints(yMean - (b * xMean), 3);\n    return {\n      a: a,\n      b: b,\n      xyData: xyData,\n      xSquaredData: xSquaredData,\n      ySquaredData: ySquaredData,\n      xMean: xMean,\n      yMean: yMean,\n      summationX: summationX,\n      summationY: summationY,\n      summationXY: summationXY,\n      summationXSquared: summationXSquared,\n      summationYSquared: summationYSquared\n    };\n  }\n  

",N.append(e,t,n,M,r)})),q[6].addEventListener("click",(function(){const e=document.createElement("h2");e.textContent="# Hypothesis Testing";const t=document.createElement("div");t.innerHTML="

Hypothesis testing is a way for researchers to figure out if the differences they see in data are likely real or just due to random chance. It involves making educated guesses, called hypotheses, and then using statistical methods to check if the data supports or contradicts these guesses. The process helps determine if observed effects are genuine or could have happened by random fluctuations.

",t.innerHTML+="

It involves formulating a null hypothesis (Ho), representing a default assumption of no effect, and an alternative hypothesis (H1) or (Ha), suggesting a significant difference or effect.

";const n=document.createElement("form");n.id="hypothesis-testing-form",function(e){const t=document.createElement("label");t.textContent="Claim: ",t.className="displayInline";const n=C("μ",["μ","p"],"parameter"),r=C("≤",["≤","=","≥",">","≠","<"],"operator"),i=E("valueReference","100","displayInline",P);t.appendChild(n.UI),t.appendChild(r.UI),t.appendChild(i);const a=document.createElement("label");a.textContent="Sample size (n): ",a.className="displayInline";const o=E("sampleSize","30","displayInline",P);a.appendChild(o);const s=document.createElement("label");s.textContent="Sample mean (x̄): ",s.className="displayInline";const c=E("sampleMean","45","displayInline",P);s.appendChild(c);const u=document.createElement("label");u.textContent="Population mean (μ): ",u.className="displayInline";const l=E("populationMean","55","displayInline",P);u.appendChild(l);const d=document.createElement("label");d.textContent="Standard Deviation (s): ",d.className="displayInline";const p=E("standardDeviation","10","displayInline",P);d.appendChild(p);const f=document.createElement("label");f.textContent="Alpha (a): ",f.className="displayInline";const m=C("0.05",["0.05","0.01","0.10"],"alpha");f.appendChild(m.UI);const y=document.createElement("button");y.textContent="Show Hypothesis Testing Computation",y.type="submit";const v=document.createElement("p");v.textContent="All* fields are required",v.style.display="none",v.style.color="red",v.style.textAlign="center";const h=[i,o,c,l,p];y.addEventListener("click",(e=>{e.preventDefault(),k(_);let t=!0;for(let e of h)if(""===e.value||isNaN(Number(e.value.trim()))){t=!1;break}t?(function(e,t,n,r,i,a,o,s){const c=(0,O.hypothesisTesting)(e,t,n,r,i,a,o,s),u=document.createElement("p");u.innerHTML=`Conclusion: "${c.conclusion}"`;const l=document.createElement("p");l.innerHTML="Computed Values:";let d=document.createElement("p"),p=document.createElement("p");c.claim===c.nullHypo?(d.innerHTML=`Null Hypothesis (Ho): ${e} ${c.nullHypo.operator} ${c.nullHypo.valueReference} (Claim)`,p.innerHTML=`Alternative Hypothesis (Ha): ${e} ${c.altHypo.operator} ${c.altHypo.valueReference}`):(d.innerHTML=`Null Hypothesis (Ho): ${e} ${c.nullHypo.operator} ${c.nullHypo.valueReference}`,p.innerHTML=`Alternative Hypothesis (Ha): ${e} ${c.altHypo.operator} ${c.altHypo.valueReference} (Claim)`);const f=document.createElement("p");f.innerHTML=`Value of computed Z-Score: ${c.z}`;const m=document.createElement("p");m.innerHTML=`Corresponding value of z-score on Z-table: ${c.zc} `;const y=document.createElement("p");y.innerHTML=`Tail Orientation: ${c.tailOrientation} test`;const v=document.createElement("p");v.innerHTML=`P Value: ${c.PValue} `,_.append(u,l,d,p,f,m,y,v)}(n.getSelectedOption(),r.getSelectedOption(),Number(i.value.trim()),Number(o.value.trim()),Number(c.value.trim()),Number(l.value.trim()),Number(p.value.trim()),Number(m.getSelectedOption().trim())),v.style.display="none"):v.style.display="block"})),e.append(t,a,s,u,d,f,y,v)}(n);const r=document.createElement("div");r.innerHTML="

✏️ How It Works

",r.innerHTML+="

To interpret hypothesis testing:

",r.innerHTML+="The calculator uses a hypothesis testing function for conducting hypothesis tests on a sample mean. The function takes parameters such as the operator (<, >, =) for the null hypothesis, a reference value, sample size, sample mean, standard deviation, and significance level (alpha). It constructs null and alternative hypotheses, determines the tail orientation of the test, calculates the test statistic (z), converts it to a cumulative probability (zc), and computes the p-value based on the tail orientation. The function then decides whether to reject the null hypothesis based on the p-value and significance level. Finally, it generates a conclusion statement, indicating whether there is enough evidence to reject or support the null hypothesis. The results, including hypotheses, test statistics, p-value, and the conclusion, are returned in an object.",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function hypothesisTesting(operator, valueReference, n, sampleMean, sd, alpha) {\n    let nullHypo, altHypo, claim, tailOrientation;\n    if (nullHypoOperators.includes(operator)){\n      nullHypo = {operator: operator, valueReference: valueReference};\n      if (operator === '≤'){\n        altHypo = {operator: '>', valueReference: valueReference};\n        tailOrientation = 'right-tailed';\n      } else if (operator === '≥'){\n        altHypo = {operator: '<', valueReference: valueReference};\n        tailOrientation = 'left-tailed';\n      } else if (operator === '='){\n        altHypo = {operator: '≠', valueReference: valueReference};\n        tailOrientation = 'two-tailed';\n      }\n      claim = nullHypo;\n    } else if (altHypoOperators.includes(operator)) {\n      altHypo = {operator: operator, valueReference: valueReference};\n      if (operator === '>'){\n        tailOrientation = 'right-tailed';\n        nullHypo = {operator: '≤', valueReference: valueReference}\n      } else if (operator === '<'){\n        tailOrientation = 'left-tailed';\n        nullHypo = {operator: '≥', valueReference: valueReference}\n      } else if (operator === '≠'){\n        tailOrientation = 'two-tailed';\n        nullHypo = {operator: '=', valueReference: valueReference}\n      }\n      claim = altHypo;\n    }\n    const populationMean = valueReference;\n    const z = limitDecimalPoints(((sampleMean - populationMean) / (sd / Math.sqrt(n))), 2);\n    const zc = limitDecimalPoints((stats.erf(z / Math.sqrt(2)) / 2 + 0.5), 4);\n  \n    let PValue;\n    if (tailOrientation === 'left-tailed'){\n      PValue = zc;\n    } else if (tailOrientation === 'right-tailed'){\n      PValue = limitDecimalPoints((1 - zc), 4);\n    } else if (tailOrientation === 'two-tailed'){\n      PValue = limitDecimalPoints((2 * zc), 4);\n    } \n  \n    let rejectNullHypothesis = false;\n    if (PValue <= alpha){\n      rejectNullHypothesis = true;\n    } else {\n      rejectNullHypothesis = false;\n    }\n  \n    let conclusion = ''; \n    if (claim === nullHypo){\n      if (rejectNullHypothesis){\n        conclusion = `At the {alpha * 100}% level of significance, There is enough evidence to reject the claim.`;\n      } else {\n        conclusion = `At the {alpha * 100}% level of significance, There is not enough evidence to reject the claim.`;\n      }\n    } else {\n      if (rejectNullHypothesis){\n        conclusion = `At the {alpha * 100}% level of significance, There is enough evidence to support the claim.`;\n      } else {\n        conclusion = `At the {alpha * 100}% level of significance, There is not enough evidence to support the claim.`;\n      }\n    }\n  \n    return {\n      nullHypo: nullHypo, \n      altHypo: altHypo,\n      claim: claim,\n      tailOrientation: tailOrientation,\n      z: z,\n      zc: zc,\n      PValue: PValue,\n      conclusion: conclusion\n    };\n  }\n  

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The matrix must be square. Not to be confused with exp(a), which performs element-wise exponentiation.",examples:["expm([[0,2],[0,0]])"],seealso:["exp"]}},45130:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.expm1Docs=void 0,t.expm1Docs={name:"expm1",category:"Arithmetic",syntax:["expm1(x)"],description:"Calculate the value of subtracting 1 from the exponential value.",examples:["expm1(2)","pow(e, 2) - 1","log(expm1(2) + 1)"],seealso:["exp","pow","log"]}},41544:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.fixDocs=void 0,t.fixDocs={name:"fix",category:"Arithmetic",syntax:["fix(x)"],description:"Round a value towards zero. If x is complex, both real and imaginary part are rounded towards zero.",examples:["fix(3.2)","fix(3.8)","fix(-4.2)","fix(-4.8)"],seealso:["ceil","floor","round"]}},35489:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.floorDocs=void 0,t.floorDocs={name:"floor",category:"Arithmetic",syntax:["floor(x)"],description:"Round a value towards minus infinity.If x is complex, both real and imaginary part are rounded towards minus infinity.",examples:["floor(3.2)","floor(3.8)","floor(-4.2)"],seealso:["ceil","fix","round"]}},53045:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.gcdDocs=void 0,t.gcdDocs={name:"gcd",category:"Arithmetic",syntax:["gcd(a, b)","gcd(a, b, c, ...)"],description:"Compute the greatest common divisor.",examples:["gcd(8, 12)","gcd(-4, 6)","gcd(25, 15, -10)"],seealso:["lcm","xgcd"]}},24336:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.hypotDocs=void 0,t.hypotDocs={name:"hypot",category:"Arithmetic",syntax:["hypot(a, b, c, ...)","hypot([a, b, c, ...])"],description:"Calculate the hypotenusa of a list with values. ",examples:["hypot(3, 4)","sqrt(3^2 + 4^2)","hypot(-2)","hypot([3, 4, 5])"],seealso:["abs","norm"]}},32501:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.invmodDocs=void 0,t.invmodDocs={name:"invmod",category:"Arithmetic",syntax:["invmod(a, b)"],description:"Calculate the (modular) multiplicative inverse of a modulo b. Solution to the equation ax ≣ 1 (mod b)",examples:["invmod(8, 12)","invmod(7, 13)","invmod(15151, 15122)"],seealso:["gcd","xgcd"]}},37624:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.lcmDocs=void 0,t.lcmDocs={name:"lcm",category:"Arithmetic",syntax:["lcm(x, y)"],description:"Compute the least common multiple.",examples:["lcm(4, 6)","lcm(6, 21)","lcm(6, 21, 5)"],seealso:["gcd"]}},61855:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.logDocs=void 0,t.logDocs={name:"log",category:"Arithmetic",syntax:["log(x)","log(x, base)"],description:"Compute the logarithm of a value. If no base is provided, the natural logarithm of x is calculated. If base if provided, the logarithm is calculated for the specified base. log(x, base) is defined as log(x) / log(base).",examples:["log(3.5)","a = log(2.4)","exp(a)","10 ^ 4","log(10000, 10)","log(10000) / log(10)","b = log(1024, 2)","2 ^ b"],seealso:["exp","log1p","log2","log10"]}},34072:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.log10Docs=void 0,t.log10Docs={name:"log10",category:"Arithmetic",syntax:["log10(x)"],description:"Compute the 10-base logarithm of a value.",examples:["log10(0.00001)","log10(10000)","10 ^ 4","log(10000) / log(10)","log(10000, 10)"],seealso:["exp","log"]}},88276:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.log1pDocs=void 0,t.log1pDocs={name:"log1p",category:"Arithmetic",syntax:["log1p(x)","log1p(x, base)"],description:"Calculate the logarithm of a `value+1`",examples:["log1p(2.5)","exp(log1p(1.4))","pow(10, 4)","log1p(9999, 10)","log1p(9999) / log(10)"],seealso:["exp","log","log2","log10"]}},15958:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.log2Docs=void 0,t.log2Docs={name:"log2",category:"Arithmetic",syntax:["log2(x)"],description:"Calculate the 2-base of a value. This is the same as calculating `log(x, 2)`.",examples:["log2(0.03125)","log2(16)","log2(16) / log2(2)","pow(2, 4)"],seealso:["exp","log1p","log","log10"]}},62266:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.modDocs=void 0,t.modDocs={name:"mod",category:"Operators",syntax:["x % y","x mod y","mod(x, y)"],description:"Calculates the modulus, the remainder of an integer division.",examples:["7 % 3","11 % 2","10 mod 4","isOdd(x) = x % 2","isOdd(2)","isOdd(3)"],seealso:["divide"]}},13933:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.multiplyDocs=void 0,t.multiplyDocs={name:"multiply",category:"Operators",syntax:["x * y","multiply(x, y)"],description:"multiply two values.",examples:["a = 2.1 * 3.4","a / 3.4","2 * 3 + 4","2 * (3 + 4)","3 * 2.1 km"],seealso:["divide"]}},91896:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.normDocs=void 0,t.normDocs={name:"norm",category:"Arithmetic",syntax:["norm(x)","norm(x, p)"],description:"Calculate the norm of a number, vector or matrix.",examples:["abs(-3.5)","norm(-3.5)","norm(3 - 4i)","norm([1, 2, -3], Infinity)","norm([1, 2, -3], -Infinity)","norm([3, 4], 2)","norm([[1, 2], [3, 4]], 1)",'norm([[1, 2], [3, 4]], "inf")','norm([[1, 2], [3, 4]], "fro")']}},49774:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.nthRootDocs=void 0,t.nthRootDocs={name:"nthRoot",category:"Arithmetic",syntax:["nthRoot(a)","nthRoot(a, root)"],description:'Calculate the nth root of a value. The principal nth root of a positive real number A, is the positive real solution of the equation "x^root = A".',examples:["4 ^ 3","nthRoot(64, 3)","nthRoot(9, 2)","sqrt(9)"],seealso:["nthRoots","pow","sqrt"]}},87676:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.nthRootsDocs=void 0,t.nthRootsDocs={name:"nthRoots",category:"Arithmetic",syntax:["nthRoots(A)","nthRoots(A, root)"],description:'Calculate the nth roots of a value. An nth root of a positive real number A, is a positive real solution of the equation "x^root = A". This function returns an array of complex values.',examples:["nthRoots(1)","nthRoots(1, 3)"],seealso:["sqrt","pow","nthRoot"]}},93817:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.powDocs=void 0,t.powDocs={name:"pow",category:"Operators",syntax:["x ^ y","pow(x, y)"],description:"Calculates the power of x to y, x^y.",examples:["2^3","2*2*2","1 + e ^ (pi * i)","pow([[1, 2], [4, 3]], 2)","pow([[1, 2], [4, 3]], -1)"],seealso:["multiply","nthRoot","nthRoots","sqrt"]}},29441:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.roundDocs=void 0,t.roundDocs={name:"round",category:"Arithmetic",syntax:["round(x)","round(x, n)","round(unit, valuelessUnit)","round(unit, n, valuelessUnit)"],description:"round a value towards the nearest integer.If x is complex, both real and imaginary part are rounded towards the nearest integer. When n is specified, the value is rounded to n decimals.",examples:["round(3.2)","round(3.8)","round(-4.2)","round(-4.8)","round(pi, 3)","round(123.45678, 2)","round(3.241cm, 2, cm)","round([3.2, 3.8, -4.7])"],seealso:["ceil","floor","fix"]}},15623:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.signDocs=void 0,t.signDocs={name:"sign",category:"Arithmetic",syntax:["sign(x)"],description:"Compute the sign of a value. The sign of a value x is 1 when x>1, -1 when x<0, and 0 when x=0.",examples:["sign(3.5)","sign(-4.2)","sign(0)"],seealso:["abs"]}},55098:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.sqrtDocs=void 0,t.sqrtDocs={name:"sqrt",category:"Arithmetic",syntax:["sqrt(x)"],description:"Compute the square root value. If x = y * y, then y is the square root of x.",examples:["sqrt(25)","5 * 5","sqrt(-1)"],seealso:["square","sqrtm","multiply","nthRoot","nthRoots","pow"]}},32180:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.sqrtmDocs=void 0,t.sqrtmDocs={name:"sqrtm",category:"Arithmetic",syntax:["sqrtm(x)"],description:"Calculate the principal square root of a square matrix. The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.",examples:["sqrtm([[33, 24], [48, 57]])"],seealso:["sqrt","abs","square","multiply"]}},37981:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.squareDocs=void 0,t.squareDocs={name:"square",category:"Arithmetic",syntax:["square(x)"],description:"Compute the square of a value. The square of x is x * x.",examples:["square(3)","sqrt(9)","3^2","3 * 3"],seealso:["multiply","pow","sqrt","cube"]}},98940:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.subtractDocs=void 0,t.subtractDocs={name:"subtract",category:"Operators",syntax:["x - y","subtract(x, y)"],description:"subtract two values.",examples:["a = 5.3 - 2","a + 2","2/3 - 1/6","2 * 3 - 3","2.1 km - 500m"],seealso:["add"]}},41589:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.unaryMinusDocs=void 0,t.unaryMinusDocs={name:"unaryMinus",category:"Operators",syntax:["-x","unaryMinus(x)"],description:"Inverse the sign of a value. Converts booleans and strings to numbers.",examples:["-4.5","-(-5.6)",'-"22"'],seealso:["add","subtract","unaryPlus"]}},2293:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.unaryPlusDocs=void 0,t.unaryPlusDocs={name:"unaryPlus",category:"Operators",syntax:["+x","unaryPlus(x)"],description:"Converts booleans and strings to numbers.",examples:["+true",'+"2"'],seealso:["add","subtract","unaryMinus"]}},50773:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.xgcdDocs=void 0,t.xgcdDocs={name:"xgcd",category:"Arithmetic",syntax:["xgcd(a, b)"],description:"Calculate the extended greatest common divisor for two values. The result is an array [d, x, y] with 3 entries, where d is the greatest common divisor, and d = x * a + y * b.",examples:["xgcd(8, 12)","gcd(8, 12)","xgcd(36163, 21199)"],seealso:["gcd","lcm"]}},86375:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.bitAndDocs=void 0,t.bitAndDocs={name:"bitAnd",category:"Bitwise",syntax:["x & y","bitAnd(x, y)"],description:"Bitwise AND operation. Performs the logical AND operation on each pair of the corresponding bits of the two given values by multiplying them. If both bits in the compared position are 1, the bit in the resulting binary representation is 1, otherwise, the result is 0",examples:["5 & 3","bitAnd(53, 131)","[1, 12, 31] & 42"],seealso:["bitNot","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]}},52975:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.bitNotDocs=void 0,t.bitNotDocs={name:"bitNot",category:"Bitwise",syntax:["~x","bitNot(x)"],description:"Bitwise NOT operation. Performs a logical negation on each bit of the given value. Bits that are 0 become 1, and those that are 1 become 0.",examples:["~1","~2","bitNot([2, -3, 4])"],seealso:["bitAnd","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]}},96928:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.bitOrDocs=void 0,t.bitOrDocs={name:"bitOr",category:"Bitwise",syntax:["x | y","bitOr(x, y)"],description:"Bitwise OR operation. Performs the logical inclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if the first bit is 1 or the second bit is 1 or both bits are 1, otherwise, the result is 0.",examples:["5 | 3","bitOr([1, 2, 3], 4)"],seealso:["bitAnd","bitNot","bitXor","leftShift","rightArithShift","rightLogShift"]}},49401:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.bitXorDocs=void 0,t.bitXorDocs={name:"bitXor",category:"Bitwise",syntax:["bitXor(x, y)"],description:"Bitwise XOR operation, exclusive OR. Performs the logical exclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1.",examples:["bitOr(1, 2)","bitXor([2, 3, 4], 4)"],seealso:["bitAnd","bitNot","bitOr","leftShift","rightArithShift","rightLogShift"]}},24989:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.leftShiftDocs=void 0,t.leftShiftDocs={name:"leftShift",category:"Bitwise",syntax:["x << y","leftShift(x, y)"],description:"Bitwise left logical shift of a value x by y number of bits.",examples:["4 << 1","8 >> 1"],seealso:["bitAnd","bitNot","bitOr","bitXor","rightArithShift","rightLogShift"]}},19448:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.rightArithShiftDocs=void 0,t.rightArithShiftDocs={name:"rightArithShift",category:"Bitwise",syntax:["x >> y","rightArithShift(x, y)"],description:"Bitwise right arithmetic shift of a value x by y number of bits.",examples:["8 >> 1","4 << 1","-12 >> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightLogShift"]}},61724:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.rightLogShiftDocs=void 0,t.rightLogShiftDocs={name:"rightLogShift",category:"Bitwise",syntax:["x >>> y","rightLogShift(x, y)"],description:"Bitwise right logical shift of a value x by y number of bits.",examples:["8 >>> 1","4 << 1","-12 >>> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightArithShift"]}},78985:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.bellNumbersDocs=void 0,t.bellNumbersDocs={name:"bellNumbers",category:"Combinatorics",syntax:["bellNumbers(n)"],description:"The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S. `bellNumbers` only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["bellNumbers(3)","bellNumbers(8)"],seealso:["stirlingS2"]}},45823:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.catalanDocs=void 0,t.catalanDocs={name:"catalan",category:"Combinatorics",syntax:["catalan(n)"],description:"The Catalan Numbers enumerate combinatorial structures of many different types. catalan only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["catalan(3)","catalan(8)"],seealso:["bellNumbers"]}},25858:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.compositionDocs=void 0,t.compositionDocs={name:"composition",category:"Combinatorics",syntax:["composition(n, k)"],description:"The composition counts of n into k parts. composition only takes integer arguments. The following condition must be enforced: k <= n.",examples:["composition(5, 3)"],seealso:["combinations"]}},18308:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.stirlingS2Docs=void 0,t.stirlingS2Docs={name:"stirlingS2",category:"Combinatorics",syntax:["stirlingS2(n, k)"],description:"he Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets. `stirlingS2` only takes integer arguments. The following condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) = 1.",examples:["stirlingS2(5, 3)"],seealso:["bellNumbers"]}},58916:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.argDocs=void 0,t.argDocs={name:"arg",category:"Complex",syntax:["arg(x)"],description:"Compute the argument of a complex value. If x = a+bi, the argument is computed as atan2(b, a).",examples:["arg(2 + 2i)","atan2(3, 2)","arg(2 + 3i)"],seealso:["re","im","conj","abs"]}},16652:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.conjDocs=void 0,t.conjDocs={name:"conj",category:"Complex",syntax:["conj(x)"],description:"Compute the complex conjugate of a complex value. If x = a+bi, the complex conjugate is a-bi.",examples:["conj(2 + 3i)","conj(2 - 3i)","conj(-5.2i)"],seealso:["re","im","abs","arg"]}},2313:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.imDocs=void 0,t.imDocs={name:"im",category:"Complex",syntax:["im(x)"],description:"Get the imaginary part of a complex number.",examples:["im(2 + 3i)","re(2 + 3i)","im(-5.2i)","im(2.4)"],seealso:["re","conj","abs","arg"]}},67105:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.reDocs=void 0,t.reDocs={name:"re",category:"Complex",syntax:["re(x)"],description:"Get the real part of a complex number.",examples:["re(2 + 3i)","im(2 + 3i)","re(-5.2i)","re(2.4)"],seealso:["im","conj","abs","arg"]}},52989:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.evaluateDocs=void 0,t.evaluateDocs={name:"evaluate",category:"Expression",syntax:["evaluate(expression)","evaluate(expression, scope)","evaluate([expr1, expr2, expr3, ...])","evaluate([expr1, expr2, expr3, ...], scope)"],description:"Evaluate an expression or an array with expressions.",examples:['evaluate("2 + 3")','evaluate("sqrt(16)")','evaluate("2 inch to cm")','evaluate("sin(x * pi)", { "x": 1/2 })','evaluate(["width=2", "height=4","width*height"])'],seealso:[]}},4452:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.helpDocs=void 0,t.helpDocs={name:"help",category:"Expression",syntax:["help(object)","help(string)"],description:"Display documentation on a function or data type.",examples:["help(sqrt)",'help("complex")'],seealso:[]}},94536:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.distanceDocs=void 0,t.distanceDocs={name:"distance",category:"Geometry",syntax:["distance([x1, y1], [x2, y2])","distance([[x1, y1], [x2, y2]])"],description:"Calculates the Euclidean distance between two points.",examples:["distance([0,0], [4,4])","distance([[0,0], [4,4]])"],seealso:[]}},5957:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.intersectDocs=void 0,t.intersectDocs={name:"intersect",category:"Geometry",syntax:["intersect(expr1, expr2, expr3, expr4)","intersect(expr1, expr2, expr3)"],description:"Computes the intersection point of lines and/or planes.",examples:["intersect([0, 0], [10, 10], [10, 0], [0, 10])","intersect([1, 0, 1], [4, -2, 2], [1, 1, 1, 6])"],seealso:[]}},48089:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.andDocs=void 0,t.andDocs={name:"and",category:"Logical",syntax:["x and y","and(x, y)"],description:"Logical and. Test whether two values are both defined with a nonzero/nonempty value.",examples:["true and false","true and true","2 and 4"],seealso:["not","or","xor"]}},70939:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.notDocs=void 0,t.notDocs={name:"not",category:"Logical",syntax:["not x","not(x)"],description:"Logical not. Flips the boolean value of given argument.",examples:["not true","not false","not 2","not 0"],seealso:["and","or","xor"]}},8206:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.orDocs=void 0,t.orDocs={name:"or",category:"Logical",syntax:["x or y","or(x, y)"],description:"Logical or. Test if at least one value is defined with a nonzero/nonempty value.",examples:["true or false","false or false","0 or 4"],seealso:["not","and","xor"]}},52883:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.xorDocs=void 0,t.xorDocs={name:"xor",category:"Logical",syntax:["x xor y","xor(x, y)"],description:"Logical exclusive or, xor. Test whether one and only one value is defined with a nonzero/nonempty value.",examples:["true xor false","false xor false","true xor true","0 xor 4"],seealso:["not","and","or"]}},47968:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.columnDocs=void 0,t.columnDocs={name:"column",category:"Matrix",syntax:["column(x, index)"],description:"Return a column from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","column(A, 1)","column(A, 2)"],seealso:["row","matrixFromColumns"]}},90945:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.concatDocs=void 0,t.concatDocs={name:"concat",category:"Matrix",syntax:["concat(A, B, C, ...)","concat(A, B, C, ..., dim)"],description:"Concatenate matrices. By default, the matrices are concatenated by the last dimension. The dimension on which to concatenate can be provided as last argument.",examples:["A = [1, 2; 5, 6]","B = [3, 4; 7, 8]","concat(A, B)","concat(A, B, 1)","concat(A, B, 2)"],seealso:["det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},91143:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.countDocs=void 0,t.countDocs={name:"count",category:"Matrix",syntax:["count(x)"],description:"Count the number of elements of a matrix, array or string.",examples:["a = [1, 2; 3, 4; 5, 6]","count(a)","size(a)",'count("hello world")'],seealso:["size"]}},82314:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.crossDocs=void 0,t.crossDocs={name:"cross",category:"Matrix",syntax:["cross(A, B)"],description:"Calculate the cross product for two vectors in three dimensional space.",examples:["cross([1, 1, 0], [0, 1, 1])","cross([3, -3, 1], [4, 9, 2])","cross([2, 3, 4], [5, 6, 7])"],seealso:["multiply","dot"]}},42136:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.ctransposeDocs=void 0,t.ctransposeDocs={name:"ctranspose",category:"Matrix",syntax:["x'","ctranspose(x)"],description:"Complex Conjugate and Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","ctranspose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]}},6319:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.detDocs=void 0,t.detDocs={name:"det",category:"Matrix",syntax:["det(x)"],description:"Calculate the determinant of a matrix",examples:["det([1, 2; 3, 4])","det([-2, 2, 3; -1, 1, 3; 2, 0, -1])"],seealso:["concat","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},92623:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.diagDocs=void 0,t.diagDocs={name:"diag",category:"Matrix",syntax:["diag(x)","diag(x, k)"],description:"Create a diagonal matrix or retrieve the diagonal of a matrix. When x is a vector, a matrix with the vector values on the diagonal will be returned. When x is a matrix, a vector with the diagonal values of the matrix is returned. When k is provided, the k-th diagonal will be filled in or retrieved, if k is positive, the values are placed on the super diagonal. When k is negative, the values are placed on the sub diagonal.",examples:["diag(1:3)","diag(1:3, 1)","a = [1, 2, 3; 4, 5, 6; 7, 8, 9]","diag(a)"],seealso:["concat","det","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},21190:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.diffDocs=void 0,t.diffDocs={name:"diff",category:"Matrix",syntax:["diff(arr)","diff(arr, dim)"],description:["Create a new matrix or array with the difference of the passed matrix or array.","Dim parameter is optional and used to indicant the dimension of the array/matrix to apply the difference","If no dimension parameter is passed it is assumed as dimension 0","Dimension is zero-based in javascript and one-based in the parser","Arrays must be 'rectangular' meaning arrays like [1, 2]","If something is passed as a matrix it will be returned as a matrix but other than that all matrices are converted to arrays"],examples:["A = [1, 2, 4, 7, 0]","diff(A)","diff(A, 1)","B = [[1, 2], [3, 4]]","diff(B)","diff(B, 1)","diff(B, 2)","diff(B, bignumber(2))","diff([[1, 2], matrix([3, 4])], 2)"],seealso:["subtract","partitionSelect"]}},13701:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.dotDocs=void 0,t.dotDocs={name:"dot",category:"Matrix",syntax:["dot(A, B)","A * B"],description:"Calculate the dot product of two vectors. The dot product of A = [a1, a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] is defined as dot(A, B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn",examples:["dot([2, 4, 1], [2, 2, 3])","[2, 4, 1] * [2, 2, 3]"],seealso:["multiply","cross"]}},50786:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.eigsDocs=void 0,t.eigsDocs={name:"eigs",category:"Matrix",syntax:["eigs(x)"],description:"Calculate the eigenvalues and optionally eigenvectors of a square matrix",examples:["eigs([[5, 2.3], [2.3, 1]])","eigs([[1, 2, 3], [4, 5, 6], [7, 8, 9]], { precision: 1e-6, eigenvectors: false }"],seealso:["inv"]}},23086:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.fftDocs=void 0,t.fftDocs={name:"fft",category:"Matrix",syntax:["fft(x)"],description:"Calculate N-dimensional fourier transform",examples:["fft([[1, 0], [1, 0]])"],seealso:["ifft"]}},28230:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.filterDocs=void 0,t.filterDocs={name:"filter",category:"Matrix",syntax:["filter(x, test)"],description:"Filter items in a matrix.",examples:["isPositive(x) = x > 0","filter([6, -2, -1, 4, 3], isPositive)","filter([6, -2, 0, 1, 0], x != 0)"],seealso:["sort","map","forEach"]}},51719:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.flattenDocs=void 0,t.flattenDocs={name:"flatten",category:"Matrix",syntax:["flatten(x)"],description:"Flatten a multi dimensional matrix into a single dimensional matrix.",examples:["a = [1, 2, 3; 4, 5, 6]","size(a)","b = flatten(a)","size(b)"],seealso:["concat","resize","size","squeeze"]}},74417:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.forEachDocs=void 0,t.forEachDocs={name:"forEach",category:"Matrix",syntax:["forEach(x, callback)"],description:"Iterates over all elements of a matrix/array, and executes the given callback function.",examples:["numberOfPets = {}","addPet(n) = numberOfPets[n] = (numberOfPets[n] ? numberOfPets[n]:0 ) + 1;",'forEach(["Dog","Cat","Cat"], addPet)',"numberOfPets"],seealso:["map","sort","filter"]}},40109:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.getMatrixDataTypeDocs=void 0,t.getMatrixDataTypeDocs={name:"getMatrixDataType",category:"Matrix",syntax:["getMatrixDataType(x)"],description:'Find the data type of all elements in a matrix or array, for example "number" if all items are a number and "Complex" if all values are complex numbers. 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The matrix has ones on the diagonal and zeros elsewhere.",examples:["identity(3)","identity(3, 5)","a = [1, 2, 3; 4, 5, 6]","identity(size(a))"],seealso:["concat","det","diag","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},78909:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.ifftDocs=void 0,t.ifftDocs={name:"ifft",category:"Matrix",syntax:["ifft(x)"],description:"Calculate N-dimensional inverse fourier transform",examples:["ifft([[2, 2], [0, 0]])"],seealso:["fft"]}},82849:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.invDocs=void 0,t.invDocs={name:"inv",category:"Matrix",syntax:["inv(x)"],description:"Calculate the inverse of a matrix",examples:["inv([1, 2; 3, 4])","inv(4)","1 / 4"],seealso:["concat","det","diag","identity","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},5568:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.kronDocs=void 0,t.kronDocs={name:"kron",category:"Matrix",syntax:["kron(x, y)"],description:"Calculates the kronecker product of 2 matrices or vectors.",examples:["kron([[1, 0], [0, 1]], [[1, 2], [3, 4]])","kron([1,1], [2,3,4])"],seealso:["multiply","dot","cross"]}},169:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.mapDocs=void 0,t.mapDocs={name:"map",category:"Matrix",syntax:["map(x, callback)"],description:"Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array.",examples:["map([1, 2, 3], square)"],seealso:["filter","forEach"]}},37904:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.matrixFromColumnsDocs=void 0,t.matrixFromColumnsDocs={name:"matrixFromColumns",category:"Matrix",syntax:["matrixFromColumns(...arr)","matrixFromColumns(row1, row2)","matrixFromColumns(row1, row2, row3)"],description:"Create a dense matrix from vectors as individual columns.",examples:["matrixFromColumns([1, 2, 3], [[4],[5],[6]])"],seealso:["matrix","matrixFromRows","matrixFromFunction","zeros"]}},46825:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.matrixFromFunctionDocs=void 0,t.matrixFromFunctionDocs={name:"matrixFromFunction",category:"Matrix",syntax:["matrixFromFunction(size, fn)","matrixFromFunction(size, fn, format)","matrixFromFunction(size, fn, format, datatype)","matrixFromFunction(size, format, fn)","matrixFromFunction(size, format, datatype, fn)"],description:"Create a matrix by evaluating a generating function at each index.",examples:["f(I) = I[1] - I[2]","matrixFromFunction([3,3], f)","g(I) = I[1] - I[2] == 1 ? 4 : 0",'matrixFromFunction([100, 100], "sparse", g)',"matrixFromFunction([5], random)"],seealso:["matrix","matrixFromRows","matrixFromColumns","zeros"]}},26388:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.matrixFromRowsDocs=void 0,t.matrixFromRowsDocs={name:"matrixFromRows",category:"Matrix",syntax:["matrixFromRows(...arr)","matrixFromRows(row1, row2)","matrixFromRows(row1, row2, row3)"],description:"Create a dense matrix from vectors as individual rows.",examples:["matrixFromRows([1, 2, 3], [[4],[5],[6]])"],seealso:["matrix","matrixFromColumns","matrixFromFunction","zeros"]}},84898:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.onesDocs=void 0,t.onesDocs={name:"ones",category:"Matrix",syntax:["ones(m)","ones(m, n)","ones(m, n, p, ...)","ones([m])","ones([m, n])","ones([m, n, p, ...])"],description:"Create a matrix containing ones.",examples:["ones(3)","ones(3, 5)","ones([2,3]) * 4.5","a = [1, 2, 3; 4, 5, 6]","ones(size(a))"],seealso:["concat","det","diag","identity","inv","range","size","squeeze","subset","trace","transpose","zeros"]}},18226:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.partitionSelectDocs=void 0,t.partitionSelectDocs={name:"partitionSelect",category:"Matrix",syntax:["partitionSelect(x, k)","partitionSelect(x, k, compare)"],description:"Partition-based selection of an array or 1D matrix. Will find the kth smallest value, and mutates the input array. Uses Quickselect.",examples:["partitionSelect([5, 10, 1], 2)",'partitionSelect(["C", "B", "A", "D"], 1, compareText)',"arr = [5, 2, 1]","partitionSelect(arr, 0) # returns 1, arr is now: [1, 2, 5]","arr","partitionSelect(arr, 1, 'desc') # returns 2, arr is now: [5, 2, 1]","arr"],seealso:["sort"]}},65506:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.pinvDocs=void 0,t.pinvDocs={name:"pinv",category:"Matrix",syntax:["pinv(x)"],description:"Calculate the Moore–Penrose inverse of a matrix",examples:["pinv([1, 2; 3, 4])","pinv([[1, 0], [0, 1], [0, 1]])","pinv(4)"],seealso:["inv"]}},29960:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.rangeDocs=void 0,t.rangeDocs={name:"range",category:"Type",syntax:["start:end","start:step:end","range(start, end)","range(start, end, step)","range(string)"],description:"Create a range. Lower bound of the range is included, upper bound is excluded.",examples:["1:5","3:-1:-3","range(3, 7)","range(0, 12, 2)",'range("4:10")',"range(1m, 1m, 3m)","a = [1, 2, 3, 4; 5, 6, 7, 8]","a[1:2, 1:2]"],seealso:["concat","det","diag","identity","inv","ones","size","squeeze","subset","trace","transpose","zeros"]}},96753:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.reshapeDocs=void 0,t.reshapeDocs={name:"reshape",category:"Matrix",syntax:["reshape(x, sizes)"],description:"Reshape a multi dimensional array to fit the specified dimensions.",examples:["reshape([1, 2, 3, 4, 5, 6], [2, 3])","reshape([[1, 2], [3, 4]], [1, 4])","reshape([[1, 2], [3, 4]], [4])","reshape([1, 2, 3, 4], [-1, 2])"],seealso:["size","squeeze","resize"]}},63246:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.resizeDocs=void 0,t.resizeDocs={name:"resize",category:"Matrix",syntax:["resize(x, size)","resize(x, size, defaultValue)"],description:"Resize a matrix.",examples:["resize([1,2,3,4,5], [3])","resize([1,2,3], [5])","resize([1,2,3], [5], -1)","resize(2, [2, 3])",'resize("hello", [8], "!")'],seealso:["size","subset","squeeze","reshape"]}},46146:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.rotateDocs=void 0,t.rotateDocs={name:"rotate",category:"Matrix",syntax:["rotate(w, theta)","rotate(w, theta, v)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotate([1, 0], pi / 2)",'rotate(matrix([1, 0]), unit("35deg"))','rotate([1, 0, 0], unit("90deg"), [0, 0, 1])','rotate(matrix([1, 0, 0]), unit("90deg"), matrix([0, 0, 1]))'],seealso:["matrix","rotationMatrix"]}},21462:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.rotationMatrixDocs=void 0,t.rotationMatrixDocs={name:"rotationMatrix",category:"Matrix",syntax:["rotationMatrix(theta)","rotationMatrix(theta, v)","rotationMatrix(theta, v, format)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotationMatrix(pi / 2)",'rotationMatrix(unit("45deg"), [0, 0, 1])','rotationMatrix(1, matrix([0, 0, 1]), "sparse")'],seealso:["cos","sin"]}},99019:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.rowDocs=void 0,t.rowDocs={name:"row",category:"Matrix",syntax:["row(x, index)"],description:"Return a row from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","row(A, 1)","row(A, 2)"],seealso:["column","matrixFromRows"]}},26271:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.sizeDocs=void 0,t.sizeDocs={name:"size",category:"Matrix",syntax:["size(x)"],description:"Calculate the size of a matrix.",examples:["size(2.3)",'size("hello world")',"a = [1, 2; 3, 4; 5, 6]","size(a)","size(1:6)"],seealso:["concat","count","det","diag","identity","inv","ones","range","squeeze","subset","trace","transpose","zeros"]}},78498:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.sortDocs=void 0,t.sortDocs={name:"sort",category:"Matrix",syntax:["sort(x)","sort(x, compare)"],description:'Sort the items in a matrix. Compare can be a string "asc", "desc", "natural", or a custom sort function.',examples:["sort([5, 10, 1])",'sort(["C", "B", "A", "D"], "natural")',"sortByLength(a, b) = size(a)[1] - size(b)[1]",'sort(["Langdon", "Tom", "Sara"], sortByLength)','sort(["10", "1", "2"], "natural")'],seealso:["map","filter","forEach"]}},88969:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.squeezeDocs=void 0,t.squeezeDocs={name:"squeeze",category:"Matrix",syntax:["squeeze(x)"],description:"Remove inner and outer singleton dimensions from a matrix.",examples:["a = zeros(3,2,1)","size(squeeze(a))","b = zeros(1,1,3)","size(squeeze(b))"],seealso:["concat","det","diag","identity","inv","ones","range","size","subset","trace","transpose","zeros"]}},16186:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.subsetDocs=void 0,t.subsetDocs={name:"subset",category:"Matrix",syntax:["value(index)","value(index) = replacement","subset(value, [index])","subset(value, [index], replacement)"],description:"Get or set a subset of the entries of a matrix or characters of a string. Indexes are one-based. There should be one index specification for each dimension of the target. Each specification can be a single index, a list of indices, or a range in colon notation `l:u`. In a range, both the lower bound l and upper bound u are included; and if a bound is omitted it defaults to the most extreme valid value. The cartesian product of the indices specified in each dimension determines the target of the operation.",examples:["d = [1, 2; 3, 4]","e = []","e[1, 1:2] = [5, 6]","e[2, :] = [7, 8]","f = d * e","f[2, 1]","f[:, 1]","f[[1,2], [1,3]] = [9, 10; 11, 12]","f"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","trace","transpose","zeros"]}},45592:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.traceDocs=void 0,t.traceDocs={name:"trace",category:"Matrix",syntax:["trace(A)"],description:"Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.",examples:["A = [1, 2, 3; -1, 2, 3; 2, 0, 3]","trace(A)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","transpose","zeros"]}},79091:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.transposeDocs=void 0,t.transposeDocs={name:"transpose",category:"Matrix",syntax:["x'","transpose(x)"],description:"Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","transpose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]}},81421:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.zerosDocs=void 0,t.zerosDocs={name:"zeros",category:"Matrix",syntax:["zeros(m)","zeros(m, n)","zeros(m, n, p, ...)","zeros([m])","zeros([m, n])","zeros([m, n, p, ...])"],description:"Create a matrix containing zeros.",examples:["zeros(3)","zeros(3, 5)","a = [1, 2, 3; 4, 5, 6]","zeros(size(a))"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose"]}},14124:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.solveODEDocs=void 0,t.solveODEDocs={name:"solveODE",category:"Numeric",syntax:["solveODE(func, tspan, y0)","solveODE(func, tspan, y0, options)"],description:"Numerical Integration of Ordinary Differential Equations.",examples:["f(t,y) = y","tspan = [0, 4]","solveODE(f, tspan, 1)","solveODE(f, tspan, [1, 2])",'solveODE(f, tspan, 1, { method:"RK23", maxStep:0.1 })'],seealso:["derivative","simplifyCore"]}},55021:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.combinationsDocs=void 0,t.combinationsDocs={name:"combinations",category:"Probability",syntax:["combinations(n, k)"],description:"Compute the number of combinations of n items taken k at a time",examples:["combinations(7, 5)"],seealso:["combinationsWithRep","permutations","factorial"]}},62280:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.combinationsWithRepDocs=void 0,t.combinationsWithRepDocs={name:"combinationsWithRep",category:"Probability",syntax:["combinationsWithRep(n, k)"],description:"Compute the number of combinations of n items taken k at a time with replacements.",examples:["combinationsWithRep(7, 5)"],seealso:["combinations","permutations","factorial"]}},65101:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.factorialDocs=void 0,t.factorialDocs={name:"factorial",category:"Probability",syntax:["n!","factorial(n)"],description:"Compute the factorial of a value",examples:["5!","5 * 4 * 3 * 2 * 1","3!"],seealso:["combinations","combinationsWithRep","permutations","gamma"]}},84386:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.gammaDocs=void 0,t.gammaDocs={name:"gamma",category:"Probability",syntax:["gamma(n)"],description:"Compute the gamma function. For small values, the Lanczos approximation is used, and for large values the extended Stirling approximation.",examples:["gamma(4)","3!","gamma(1/2)","sqrt(pi)"],seealso:["factorial"]}},54018:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.kldivergenceDocs=void 0,t.kldivergenceDocs={name:"kldivergence",category:"Probability",syntax:["kldivergence(x, y)"],description:"Calculate the Kullback-Leibler (KL) divergence between two distributions.",examples:["kldivergence([0.7,0.5,0.4], [0.2,0.9,0.5])"],seealso:[]}},24595:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.lgammaDocs=void 0,t.lgammaDocs={name:"lgamma",category:"Probability",syntax:["lgamma(n)"],description:"Logarithm of the gamma function for real, positive numbers and complex numbers, using Lanczos approximation for numbers and Stirling series for complex numbers.",examples:["lgamma(4)","lgamma(1/2)","lgamma(i)","lgamma(complex(1.1, 2))"],seealso:["gamma"]}},9224:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.multinomialDocs=void 0,t.multinomialDocs={name:"multinomial",category:"Probability",syntax:["multinomial(A)"],description:"Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai > 0.",examples:["multinomial([1, 2, 1])"],seealso:["combinations","factorial"]}},51009:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.permutationsDocs=void 0,t.permutationsDocs={name:"permutations",category:"Probability",syntax:["permutations(n)","permutations(n, k)"],description:"Compute the number of permutations of n items taken k at a time",examples:["permutations(5)","permutations(5, 3)"],seealso:["combinations","combinationsWithRep","factorial"]}},43162:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.pickRandomDocs=void 0,t.pickRandomDocs={name:"pickRandom",category:"Probability",syntax:["pickRandom(array)","pickRandom(array, number)","pickRandom(array, weights)","pickRandom(array, number, weights)","pickRandom(array, weights, number)"],description:"Pick a random entry from a given array.",examples:["pickRandom(0:10)","pickRandom([1, 3, 1, 6])","pickRandom([1, 3, 1, 6], 2)","pickRandom([1, 3, 1, 6], [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], 2, [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], [2, 3, 2, 1], 2)"],seealso:["random","randomInt"]}},38127:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.randomDocs=void 0,t.randomDocs={name:"random",category:"Probability",syntax:["random()","random(max)","random(min, max)","random(size)","random(size, max)","random(size, min, max)"],description:"Return a random number.",examples:["random()","random(10, 20)","random([2, 3])"],seealso:["pickRandom","randomInt"]}},27752:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.randomIntDocs=void 0,t.randomIntDocs={name:"randomInt",category:"Probability",syntax:["randomInt(max)","randomInt(min, max)","randomInt(size)","randomInt(size, max)","randomInt(size, min, max)"],description:"Return a random integer number",examples:["randomInt(10, 20)","randomInt([2, 3], 10)"],seealso:["pickRandom","random"]}},72758:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.compareDocs=void 0,t.compareDocs={name:"compare",category:"Relational",syntax:["compare(x, y)"],description:"Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compare(2, 3)","compare(3, 2)","compare(2, 2)","compare(5cm, 40mm)","compare(2, [1, 2, 3])"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compareNatural","compareText"]}},94609:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.compareNaturalDocs=void 0,t.compareNaturalDocs={name:"compareNatural",category:"Relational",syntax:["compareNatural(x, y)"],description:"Compare two values of any type in a deterministic, natural way. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compareNatural(2, 3)","compareNatural(3, 2)","compareNatural(2, 2)","compareNatural(5cm, 40mm)",'compareNatural("2", "10")',"compareNatural(2 + 3i, 2 + 4i)","compareNatural([1, 2, 4], [1, 2, 3])","compareNatural([1, 5], [1, 2, 3])","compareNatural([1, 2], [1, 2])","compareNatural({a: 2}, {a: 4})"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare","compareText"]}},35851:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.compareTextDocs=void 0,t.compareTextDocs={name:"compareText",category:"Relational",syntax:["compareText(x, y)"],description:"Compare two strings lexically. Comparison is case sensitive. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:['compareText("B", "A")','compareText("A", "B")','compareText("A", "A")','compareText("2", "10")','compare("2", "10")',"compare(2, 10)",'compareNatural("2", "10")','compareText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural"]}},70339:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.deepEqualDocs=void 0,t.deepEqualDocs={name:"deepEqual",category:"Relational",syntax:["deepEqual(x, y)"],description:"Check equality of two matrices element wise. Returns true if the size of both matrices is equal and when and each of the elements are equal.",examples:["deepEqual([1,3,4], [1,3,4])","deepEqual([1,3,4], [1,3])"],seealso:["equal","unequal","smaller","larger","smallerEq","largerEq","compare"]}},82245:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.equalDocs=void 0,t.equalDocs={name:"equal",category:"Relational",syntax:["x == y","equal(x, y)"],description:"Check equality of two values. Returns true if the values are equal, and false if not.",examples:["2+2 == 3","2+2 == 4","a = 3.2","b = 6-2.8","a == b","50cm == 0.5m"],seealso:["unequal","smaller","larger","smallerEq","largerEq","compare","deepEqual","equalText"]}},81057:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.equalTextDocs=void 0,t.equalTextDocs={name:"equalText",category:"Relational",syntax:["equalText(x, y)"],description:"Check equality of two strings. Comparison is case sensitive. Returns true if the values are equal, and false if not.",examples:['equalText("Hello", "Hello")','equalText("a", "A")','equal("2e3", "2000")','equalText("2e3", "2000")','equalText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural","compareText","equal"]}},74947:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.largerDocs=void 0,t.largerDocs={name:"larger",category:"Relational",syntax:["x > y","larger(x, y)"],description:"Check if value x is larger than y. Returns true if x is larger than y, and false if not.",examples:["2 > 3","5 > 2*2","a = 3.3","b = 6-2.8","(a > b)","(b < a)","5 cm > 2 inch"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare"]}},59460:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.largerEqDocs=void 0,t.largerEqDocs={name:"largerEq",category:"Relational",syntax:["x >= y","largerEq(x, y)"],description:"Check if value x is larger or equal to y. Returns true if x is larger or equal to y, and false if not.",examples:["2 >= 1+1","2 > 1+1","a = 3.2","b = 6-2.8","(a >= b)"],seealso:["equal","unequal","smallerEq","smaller","compare"]}},59181:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.smallerDocs=void 0,t.smallerDocs={name:"smaller",category:"Relational",syntax:["x < y","smaller(x, y)"],description:"Check if value x is smaller than value y. Returns true if x is smaller than y, and false if not.",examples:["2 < 3","5 < 2*2","a = 3.3","b = 6-2.8","(a < b)","5 cm < 2 inch"],seealso:["equal","unequal","larger","smallerEq","largerEq","compare"]}},60020:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.smallerEqDocs=void 0,t.smallerEqDocs={name:"smallerEq",category:"Relational",syntax:["x <= y","smallerEq(x, y)"],description:"Check if value x is smaller or equal to value y. Returns true if x is smaller than y, and false if not.",examples:["2 <= 1+1","2 < 1+1","a = 3.2","b = 6-2.8","(a <= b)"],seealso:["equal","unequal","larger","smaller","largerEq","compare"]}},30482:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.unequalDocs=void 0,t.unequalDocs={name:"unequal",category:"Relational",syntax:["x != y","unequal(x, y)"],description:"Check unequality of two values. Returns true if the values are unequal, and false if they are equal.",examples:["2+2 != 3","2+2 != 4","a = 3.2","b = 6-2.8","a != b","50cm != 0.5m","5 cm != 2 inch"],seealso:["equal","smaller","larger","smallerEq","largerEq","compare","deepEqual"]}},69001:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setCartesianDocs=void 0,t.setCartesianDocs={name:"setCartesian",category:"Set",syntax:["setCartesian(set1, set2)"],description:"Create the cartesian product of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays and the values will be sorted in ascending order before the operation.",examples:["setCartesian([1, 2], [3, 4])"],seealso:["setUnion","setIntersect","setDifference","setPowerset"]}},73554:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setDifferenceDocs=void 0,t.setDifferenceDocs={name:"setDifference",category:"Set",syntax:["setDifference(set1, set2)"],description:"Create the difference of two (multi)sets: every element of set1, that is not the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setDifference([1, 2, 3, 4], [3, 4, 5, 6])","setDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setSymDifference"]}},19619:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setDistinctDocs=void 0,t.setDistinctDocs={name:"setDistinct",category:"Set",syntax:["setDistinct(set)"],description:"Collect the distinct elements of a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setDistinct([1, 1, 1, 2, 2, 3])"],seealso:["setMultiplicity"]}},59441:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setIntersectDocs=void 0,t.setIntersectDocs={name:"setIntersect",category:"Set",syntax:["setIntersect(set1, set2)"],description:"Create the intersection of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIntersect([1, 2, 3, 4], [3, 4, 5, 6])","setIntersect([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setDifference"]}},68419:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setIsSubsetDocs=void 0,t.setIsSubsetDocs={name:"setIsSubset",category:"Set",syntax:["setIsSubset(set1, set2)"],description:"Check whether a (multi)set is a subset of another (multi)set: every element of set1 is the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIsSubset([1, 2], [3, 4, 5, 6])","setIsSubset([3, 4], [3, 4, 5, 6])"],seealso:["setUnion","setIntersect","setDifference"]}},63004:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setMultiplicityDocs=void 0,t.setMultiplicityDocs={name:"setMultiplicity",category:"Set",syntax:["setMultiplicity(element, set)"],description:"Count the multiplicity of an element in a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setMultiplicity(1, [1, 2, 2, 4])","setMultiplicity(2, [1, 2, 2, 4])"],seealso:["setDistinct","setSize"]}},67519:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setPowersetDocs=void 0,t.setPowersetDocs={name:"setPowerset",category:"Set",syntax:["setPowerset(set)"],description:"Create the powerset of a (multi)set: the powerset contains very possible subsets of a (multi)set. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setPowerset([1, 2, 3])"],seealso:["setCartesian"]}},83900:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setSizeDocs=void 0,t.setSizeDocs={name:"setSize",category:"Set",syntax:["setSize(set)","setSize(set, unique)"],description:'Count the number of elements of a (multi)set. When the second parameter "unique" is true, count only the unique values. A multi-dimension array will be converted to a single-dimension array before the operation.',examples:["setSize([1, 2, 2, 4])","setSize([1, 2, 2, 4], true)"],seealso:["setUnion","setIntersect","setDifference"]}},64323:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setSymDifferenceDocs=void 0,t.setSymDifferenceDocs={name:"setSymDifference",category:"Set",syntax:["setSymDifference(set1, set2)"],description:"Create the symmetric difference of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setSymDifference([1, 2, 3, 4], [3, 4, 5, 6])","setSymDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setDifference"]}},91979:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setUnionDocs=void 0,t.setUnionDocs={name:"setUnion",category:"Set",syntax:["setUnion(set1, set2)"],description:"Create the union of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setUnion([1, 2, 3, 4], [3, 4, 5, 6])","setUnion([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setIntersect","setDifference"]}},75220:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.freqzDocs=void 0,t.freqzDocs={name:"freqz",category:"Signal",syntax:["freqz(b, a)","freqz(b, a, w)"],description:"Calculates the frequency response of a filter given its numerator and denominator coefficients.",examples:["freqz([1, 2], [1, 2, 3])","freqz([1, 2], [1, 2, 3], [0, 1])","freqz([1, 2], [1, 2, 3], 512)"],seealso:[]}},60498:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.zpk2tfDocs=void 0,t.zpk2tfDocs={name:"zpk2tf",category:"Signal",syntax:["zpk2tf(z, p, k)"],description:"Compute the transfer function of a zero-pole-gain model.",examples:["zpk2tf([1, 2], [-1, -2], 1)","zpk2tf([1, 2], [-1, -2])","zpk2tf([1 - 3i, 2 + 2i], [-1, -2])"],seealso:[]}},31566:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.erfDocs=void 0,t.erfDocs={name:"erf",category:"Special",syntax:["erf(x)"],description:"Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x",examples:["erf(0.2)","erf(-0.5)","erf(4)"],seealso:[]}},65125:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.zetaDocs=void 0,t.zetaDocs={name:"zeta",category:"Special",syntax:["zeta(s)"],description:"Compute the Riemann Zeta Function using an infinite series and Riemanns Functional Equation for the entire complex plane",examples:["zeta(0.2)","zeta(-0.5)","zeta(4)"],seealso:[]}},25321:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.corrDocs=void 0,t.corrDocs={name:"corr",category:"Statistics",syntax:["corr(A,B)"],description:"Compute the correlation coefficient of a two list with values, For matrices, the matrix correlation coefficient is calculated.",examples:["corr([2, 4, 6, 8],[1, 2, 3, 6])","corr(matrix([[1, 2.2, 3, 4.8, 5], [1, 2, 3, 4, 5]]), matrix([[4, 5.3, 6.6, 7, 8], [1, 2, 3, 4, 5]]))"],seealso:["max","mean","min","median","min","prod","std","sum"]}},78950:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.cumSumDocs=void 0,t.cumSumDocs={name:"cumsum",category:"Statistics",syntax:["cumsum(a, b, c, ...)","cumsum(A)"],description:"Compute the cumulative sum of all values.",examples:["cumsum(2, 3, 4, 1)","cumsum([2, 3, 4, 1])","cumsum([1, 2; 3, 4])","cumsum([1, 2; 3, 4], 1)","cumsum([1, 2; 3, 4], 2)"],seealso:["max","mean","median","min","prod","std","sum","variance"]}},79579:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.madDocs=void 0,t.madDocs={name:"mad",category:"Statistics",syntax:["mad(a, b, c, ...)","mad(A)"],description:"Compute the median absolute deviation of a matrix or a list with values. The median absolute deviation is defined as the median of the absolute deviations from the median.",examples:["mad(10, 20, 30)","mad([1, 2, 3])"],seealso:["mean","median","std","abs"]}},43606:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.maxDocs=void 0,t.maxDocs={name:"max",category:"Statistics",syntax:["max(a, b, c, ...)","max(A)","max(A, dimension)"],description:"Compute the maximum value of a list of values.",examples:["max(2, 3, 4, 1)","max([2, 3, 4, 1])","max([2, 5; 4, 3])","max([2, 5; 4, 3], 1)","max([2, 5; 4, 3], 2)","max(2.7, 7.1, -4.5, 2.0, 4.1)","min(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["mean","median","min","prod","std","sum","variance"]}},70878:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.meanDocs=void 0,t.meanDocs={name:"mean",category:"Statistics",syntax:["mean(a, b, c, ...)","mean(A)","mean(A, dimension)"],description:"Compute the arithmetic mean of a list of values.",examples:["mean(2, 3, 4, 1)","mean([2, 3, 4, 1])","mean([2, 5; 4, 3])","mean([2, 5; 4, 3], 1)","mean([2, 5; 4, 3], 2)","mean([1.0, 2.7, 3.2, 4.0])"],seealso:["max","median","min","prod","std","sum","variance"]}},52797:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.medianDocs=void 0,t.medianDocs={name:"median",category:"Statistics",syntax:["median(a, b, c, ...)","median(A)"],description:"Compute the median of all values. The values are sorted and the middle value is returned. In case of an even number of values, the average of the two middle values is returned.",examples:["median(5, 2, 7)","median([3, -1, 5, 7])"],seealso:["max","mean","min","prod","std","sum","variance","quantileSeq"]}},90759:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.minDocs=void 0,t.minDocs={name:"min",category:"Statistics",syntax:["min(a, b, c, ...)","min(A)","min(A, dimension)"],description:"Compute the minimum value of a list of values.",examples:["min(2, 3, 4, 1)","min([2, 3, 4, 1])","min([2, 5; 4, 3])","min([2, 5; 4, 3], 1)","min([2, 5; 4, 3], 2)","min(2.7, 7.1, -4.5, 2.0, 4.1)","max(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["max","mean","median","prod","std","sum","variance"]}},27894:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.modeDocs=void 0,t.modeDocs={name:"mode",category:"Statistics",syntax:["mode(a, b, c, ...)","mode(A)","mode(A, a, b, B, c, ...)"],description:"Computes the mode of all values as an array. In case mode being more than one, multiple values are returned in an array.",examples:["mode(2, 1, 4, 3, 1)","mode([1, 2.7, 3.2, 4, 2.7])","mode(1, 4, 6, 1, 6)"],seealso:["max","mean","min","median","prod","std","sum","variance"]}},97291:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.prodDocs=void 0,t.prodDocs={name:"prod",category:"Statistics",syntax:["prod(a, b, c, ...)","prod(A)"],description:"Compute the product of all values.",examples:["prod(2, 3, 4)","prod([2, 3, 4])","prod([2, 5; 4, 3])"],seealso:["max","mean","min","median","min","std","sum","variance"]}},94453:(e,t)=>{"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.quantileSeqDocs=void 0,t.quantileSeqDocs={name:"quantileSeq",category:"Statistics",syntax:["quantileSeq(A, prob[, sorted])","quantileSeq(A, [prob1, prob2, ...][, sorted])","quantileSeq(A, N[, sorted])"],description:"Compute the prob order quantile of a matrix or a list with values. 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t){const t=document.createElement("li");t.innerHTML=n,n===e&&(t.className="active"),s.append(t)}r.append(i,s);const c=r.querySelector(".select"),u=r.querySelector(".caret"),l=r.querySelector(".menu"),d=r.querySelectorAll(".menu li"),p=r.querySelector(".selected");c.addEventListener("click",(()=>{c.classList.toggle("select-clicked"),u.classList.toggle("caret-rotate"),l.classList.toggle("menu-open")}));let f=e;return s.addEventListener("click",(e=>{if("LI"===e.target.tagName){const t=e.target;p.innerText=t.innerText,f=t.innerText,d.forEach((e=>{e.classList.remove("active")})),t.classList.add("active"),c.classList.remove("select-clicked"),u.classList.remove("caret-rotate"),l.classList.remove("menu-open")}})),{UI:r,getSelectedOption:function(){return f}}}function E(e,t,n,r){const i=document.createElement("input");return i.type="text",i.name=e,i.placeholder=t,i.className=n,i.addEventListener("keypress",r),i}_.id="hypothesis-testing-container";const A=document.querySelector("nav #nav-button"),j=document.querySelector("aside");function T(e){j.contains(e.target)||A.contains(e.target)||j.classList.contains("hidden")||(j.classList.add("hidden"),window.removeEventListener("click",T))}A.onclick=()=>{j.classList.toggle("hidden"),window.addEventListener("click",T)};const F=document.querySelector("main").innerHTML,B=document.querySelector("header img"),R=document.querySelector("main"),q=document.querySelectorAll("aside button");function k(e){if(e){let t=e.firstChild;for(;t;)t.remove(),t=e.firstChild}}B.onclick=()=>{k(R),R.innerHTML=F},q.forEach((e=>{e.addEventListener("click",(()=>{k(R)}))})),q[0].addEventListener("click",(function(){const e=document.createElement("h2");e.textContent="# Frequency Distribution Table (Ungrouped)";const n=document.createElement("div");n.innerHTML="

Important characteristics of a large mass of data can be readily assessed by grouping the data into different classes and then determining the number of observations that fall in each of the classes.

",n.innerHTML+="

Such an arrangement in tabular form is called a frequency distribution

";const r=document.createElement("form");r.id="frq-dist-u-form",function(e){const n=document.createElement("label");n.textContent="Data Set (e.g. 1,2,3):";const r=document.createElement("input");r.type="text",r.name="dataset",r.placeholder="1,2,3",n.appendChild(r),r.addEventListener("keypress",s);const i=document.createElement("label");i.textContent="Number of Classes:";const c=document.createElement("input");c.type="text",c.name="numClasses",c.placeholder="1 - 999",c.maxLength="3",i.appendChild(c),i.appendChild(c),c.addEventListener("keypress",o),r.setAttribute("required",!0),c.setAttribute("required",!0);const u=document.createElement("button");u.textContent="Show Frequency Distribution",u.type="submit";const l=document.createElement("p");l.textContent="All* fields are required",l.style.display="none",l.style.color="red",l.style.textAlign="center",u.addEventListener("click",(e=>{e.preventDefault(),k(a),r.value&&c.value?(function(e,n){const r=t()(e,n),i=document.createElement("p");i.textContent="Data Set (Sorted): ",i.id="data-set-display";const o=e.sort();for(let t=0;t{const t=document.createElement("th");t.textContent=e,c.appendChild(t)}));for(let e=0;e{t.insertCell().textContent=r[n][e]}))}a.append(s,i)}(r.value.split(",").filter((e=>""!==e.trim())).map(Number),Number(c.value)),l.style.display="none",c.value="",r.value=""):l.style.display="block"})),e.append(n,i,u,l)}(r);const c=document.createElement("div");c.innerHTML="

✏️ How It Works

",c.innerHTML+="

From the data entered, the calculator computes for the class width (range / class number) rounded up to the nearest whole number. (range = min - max)

",c.innerHTML+="Using the computed class width, the calculator now computes for the class intervals of the data. Starting with the lowest value in the data set which will be used as base for the lower class interval, the calculator will add a value of (class width - 1) to get the higher class interval. The value of class width will be added to the following class intervals.",c.innerHTML+="

\n  const maxClassInterval = Math.min(...dataSet) + ((classWidth * classNumber) - 1);\n  for (let i = Math.min(...dataSet); i <= maxClassInterval; i += classWidth) {\n    classInterval.push({ min: i, max: i + (classWidth - 1) });\n  }\n  

",c.innerHTML+="The calculator proceeds to computing the class boundaries by subtracting 0.5 to the lower value of class intervals and adding 0.5 to the higher value of class intervals.",c.innerHTML+="

\n  classBoundaries = classInterval.map((classInt) => ({\n    min: classInt.min - 0.5,\n    max: classInt.max + 0.5,\n  }));\n  

",c.innerHTML+="Class mark is computed by adding the lower and higher value of the corresponding interval and dividing them to 2",c.innerHTML+="

\n  classMark = fTable.classInterval.map((classInt) => (classInt.min + classInt.max) / 2);\n  

",c.innerHTML+="The calculator computes the frequency of values within each class interval by tallying the number of data points that fall into each interval.",c.innerHTML+="

\n  classFrequency = [];\n  for (let i = 0; i < classNumber; i += 1) {\n    classFrequency.push(0);\n    for (let j = 0; j < dataSet.length; j += 1) {\n      if (dataSet[j] >= classInterval[i].min && dataSet[j] <= classInterval[i].max) {\n        classFrequency[i] += 1;\n      }\n    }\n  }\n  

",c.innerHTML+="The relative frequency for each class interval is calculated by dividing the corresponding class frequency by the total number of data points in the dataset, resulting in a proportional value for each interval. The resulting value that has any fractional part of the number will have a maximum of three decimal places.",c.innerHTML+="

\n  fTable.relativeFrequency = fTable.classFrequency.map((frequency) => (\n    Number((frequency / dataSet.length).toFixed(3))\n  ));\n  

",i.append(e,n,r,a,c)})),q[1].addEventListener("click",(function(){const e=document.createElement("h2");e.textContent="# Symmetry and Skewness";const t=document.createElement("div");t.innerHTML="

Symmetric: if distribution can be folded along a vertical axis so that the two sides coincide.

",t.innerHTML+="

Skewed: a distribution that lacks symmetry with respect to vertical axis.

";const n=document.createElement("form");n.id="skewness-form",function(e){const t=document.createElement("label");t.textContent="Data Set (e.g. 1,2,3):";const n=document.createElement("input");n.type="text",n.name="dataset",n.placeholder="1,2,3",t.appendChild(n),n.addEventListener("keypress",d);const r=document.createElement("label"),i=document.createElement("input");i.type="checkbox",i.name="population",i.checked=!0,r.appendChild(i),r.appendChild(document.createTextNode(" Population"));const a=document.createElement("label"),o=document.createElement("input");o.type="checkbox",o.name="sample",a.appendChild(o),a.appendChild(document.createTextNode(" Sample"));const s=[i,o];s.forEach((e=>{e.addEventListener("change",(e=>{s.forEach((t=>{t.checked||t===e.target?t!==e.target&&(t.checked=!1):t.checked=!0}))}))}));const u=document.createElement("button");u.textContent="Show Symmetry and Skewness",u.type="submit";const p=document.createElement("p");p.textContent="All* fields are required",p.style.display="none",p.style.color="red",p.style.textAlign="center",u.addEventListener("click",(e=>{if(e.preventDefault(),k(l),n.value){p.style.display="none";const e=i.checked?"population":"sample";!function(e,t){const n=e.value.split(",").filter((e=>""!==e.trim())).map(Number),r=(0,c.calculateSkewness)(n,t),i=(0,c.getSymmetry)(r),a=document.createElement("p");a.textContent="Data Set (Sorted): ",a.id="data-set-display";const o=n.sort();for(let e=0;e✏️ How It Works",r.innerHTML+="

The skewness of a dataset is calculated using the following formula:

",r.innerHTML+="

Skewness = 3(Mean−Median) / Standard Deviation

",r.innerHTML+="

Where:

",r.innerHTML+="

- Mean is the mean (average) of the dataset.

",r.innerHTML+="

- Median is the median of the dataset.

",r.innerHTML+="

- Standard Deviation is the standard deviation of the dataset.

",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function calculateSkewness(data, type = 'population') {\n    const skewness = (3 * (getMean(data) - getMedian(data))) / getStandardDeviation(data, type);\n    return skewness;\n  }\n  

",r.innerHTML+="

The formula essentially measures the asymmetry of the dataset. If the skewness is:

",r.innerHTML+="

- Positive: The data distribution is skewed to the right (positively skewe

",r.innerHTML+="

- Negative: The data distribution is skewed to the left (negatively skewed).

",r.innerHTML+="

- The data distribution is symmetric (normally skewed).

",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function getSymmetry(skewness) {\n    if (skewness > 0) return 'positively skewed';\n    if (skewness < 0) return 'negatively skewed';\n    return 'normally skewed'; // === 0\n  }\n  

",u.append(e,t,n,l,r)})),q[2].addEventListener("click",(function(){const e=document.createElement("h2");e.textContent="# Simple Correlation Coefficient";const t=document.createElement("div");t.innerHTML="

It is also called as Pearson's correlation or Product moment correlation coefficient

",t.innerHTML+="

It measures the nature and strength between two variables of the quantitative type

";const n=document.createElement("form");n.id="simple-corre-form",function(e){const t=document.createElement("label");t.textContent="X Data Set (e.g. 1,2,3):";const n=document.createElement("input");n.type="text",n.name="dataset",n.placeholder="1,2,3",t.appendChild(n),n.addEventListener("keypress",y);const r=document.createElement("label");r.textContent="Y Data Set (e.g. 1,2,3):";const i=document.createElement("input");i.type="text",i.name="dataset",i.placeholder="1,2,3",r.appendChild(i),i.addEventListener("keypress",y);const a=document.createElement("label");a.textContent="X Label:",a.className="data-label";const o=document.createElement("input");o.type="text",o.name="x-label",o.value="X",a.appendChild(o);const s=document.createElement("label");s.textContent="Y Label:",s.className="data-label";const c=document.createElement("input");c.type="text",c.name="y-label",c.value="Y",s.appendChild(c),n.setAttribute("required",!0),i.setAttribute("required",!0);const u=document.createElement("button");u.textContent="Show Simple Correlation Coefficient",u.type="submit";const l=document.createElement("p");l.textContent="All* fields are required",l.style.display="none",l.style.color="red",l.style.textAlign="center",u.addEventListener("click",(e=>{e.preventDefault(),k(m),n.value&&i.value?(function(e,t,n){const r=(0,p.calculateSimpleCorrelation)(e,t),i=(0,p.getFinalLabel)(r),a=document.createElement("p");a.textContent=`Result: ${r}, ${i}`;const o=document.createElement("table"),s=o.insertRow();n.forEach((e=>{const t=document.createElement("th");t.textContent=e,s.appendChild(t)}));let c=0,u=0,l=0,d=0,f=0;for(let n=0;n""!==e.trim())).map(Number),i.value.split(",").filter((e=>""!==e.trim())).map(Number),[o.value,c.value,"X²","Y²","XY"]),l.style.display="none",n.value="",i.value="",o.value="X",c.value="Y"):l.style.display="block"})),e.append(a,t,s,r,u,l)}(n);const r=document.createElement("div");r.innerHTML="

✏️ How It Works

",r.innerHTML+="

To interpret the correlation coefficient:

",r.innerHTML+="The calculator uses a labeling function that categorizes the coefficient based on its value. A coefficient of 0 is labeled 'no relation,' while a coefficient of 1 or -1 indicates a 'perfect correlation.' For other coefficients, the label reflects both the nature (positive or negative) and strength (weak, moderate, strong) of the correlation.",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function getFinalLabel(value) {\n    if (value === 0) return 'no relation';\n    if (value === 1 || value === -1) return 'perfect correlation';\n    return 'getNature(value) getStrength(value) correlation';\n  }\n  

",r.innerHTML+="

To calculate the correlation coefficient:

",r.innerHTML+="The correlation calculation involves various steps, including obtaining sums, products, and squared values of data points from two datasets. The size of the datasets (n) is considered. Applying the Pearson correlation formula, which involves covariance and standard deviations, yields the correlation coefficient. The final result is limited to three decimal points.",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function calculateSimpleCorrelation(xData, yData) {\n    const summationX = xData.reduce((acc, val) => acc + val, 0);\n    const summationY = yData.reduce((acc, val) => acc + val, 0);\n  \n    const xyData = []; const xSquaredData = []; const\n      ySquaredData = [];\n    for (let i = 0; i < xData.length; i += 1) {\n      xyData[i] = xData[i] * yData[i];\n      xSquaredData[i] = xData[i] ** 2;\n      ySquaredData[i] = yData[i] ** 2;\n    }\n  \n    const summationXY = xyData.reduce((acc, val) => acc + val, 0);\n    const summationXSquared = xSquaredData.reduce((acc, val) => acc + val, 0);\n    const summationYSquared = ySquaredData.reduce((acc, val) => acc + val, 0);\n    const n = xData.length;\n  \n    const xSquaredDividedByN = summationX ** 2 / n;\n    const ySquaredDividedByN = summationY ** 2 / n;\n  \n    const denominator = Math.sqrt(\n      (summationXSquared - xSquaredDividedByN) * (summationYSquared - ySquaredDividedByN),\n    );\n    const numerator = summationXY - ((summationX * summationY) / n);\n    const simpleCorrelation = numerator / denominator;\n    return limitDecimalPoints(simpleCorrelation, 3);\n  }\n  

",f.append(e,t,n,m,r)})),q[3].addEventListener("click",(function(){const e=document.createElement("h2");e.textContent="# Spearman Rank Correlation Coefficient";const t=document.createElement("div");t.innerHTML="

The Spearman rank correlation coefficient, is a statistical measure that assesses the strength and direction of the monotonic relationship between two variables. It is a non-parametric measure, meaning it doesn't rely on the distribution of the data, making it suitable for both continuous and ordinal data.",t.innerHTML+="

It measures the nature and strength between two variables of the quantitative type

",t.innerHTML+="

Note: when inserting ordinal data (not a number but a label), type them in order, (for example: University,Secondary,Preparatory,Nursery,Illiterate) and type the corresponding value for each of the values on the second variable input (Y Data Set)

";const n=document.createElement("form");n.id="spearman-rank-form",function(e){const t=document.createElement("label");t.textContent="X Data Set (e.g. 1,2,3):";const n=document.createElement("input");n.type="text",n.name="dataset",n.placeholder="1,2,3",t.appendChild(n),n.addEventListener("keypress",b);const r=document.createElement("label");r.textContent="Y Data Set (e.g. 1,2,3):";const i=document.createElement("input");i.type="text",i.name="dataset",i.placeholder="1,2,3",r.appendChild(i),i.addEventListener("keypress",b);const a=document.createElement("label");a.textContent="X Label:",a.className="data-label";const o=document.createElement("input");o.type="text",o.name="x-label",o.value="X",a.appendChild(o);const s=document.createElement("label");s.textContent="Y Label:",s.className="data-label";const c=document.createElement("input");c.type="text",c.name="y-label",c.value="Y",s.appendChild(c),n.setAttribute("required",!0),i.setAttribute("required",!0);const u=document.createElement("button");u.textContent="Show Spearman Rank Correlation Coefficient",u.type="submit";const l=document.createElement("p");l.textContent="All* fields are required",l.style.display="none",l.style.color="red",l.style.textAlign="center",u.addEventListener("click",(e=>{if(e.preventDefault(),k(g),n.value&&i.value){let e=n.value.split(",").filter((e=>""!==e.trim()));e=e.map((e=>{const t=Number(e.trim());return isNaN(t)?e.trim():t}));let t=i.value.split(",").filter((e=>""!==e.trim()));t=t.map((e=>{const t=Number(e.trim());return isNaN(t)?e.trim():t})),function(e,t,n){console.log(e);const r=(0,v.spearmanRank)(e,t),i=r.computedValue,a=(0,p.getFinalLabel)(i),o=document.createElement("p");o.textContent=`Result: ${i}, ${a}`;const s=document.createElement("table"),c=s.insertRow(),u=(0,v.hasDuplicates)(e)||(0,v.hasDuplicates)(t);if(!1===u?(n.push("Rank X"),n.push("Rank Y"),n.push("di"),n.push("di²"),n.forEach((e=>{const t=document.createElement("th");t.textContent=e,c.appendChild(t)}))):(n.push("Rank X"),n.push("Rank Y"),n.push("Rx-MRx"),n.push("Ry-MRy"),n.push("(Rx-MRx)*(Ry-MRy)"),n.push("(Rx-MRx)²"),n.push("(Ry-MRy)²"),n.forEach((e=>{const t=document.createElement("th");t.textContent=e,c.appendChild(t)}))),!1===u){const n=r.xRankData,i=r.yRankData,a=r.diData,o=r.diSquaredData,c=r.diSquaredSummation;for(let r=0;r✏️ How It Works",r.innerHTML+="

To interpret the correlation coefficient:

",r.innerHTML+="The calculator uses a labeling function that categorizes the coefficient based on its value. A coefficient of 0 is labeled 'no relation,' while a coefficient of 1 or -1 indicates a 'perfect correlation.' For other coefficients, the label reflects both the nature (positive or negative) and strength (weak, moderate, strong) of the correlation.",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function getFinalLabel(value) {\n    if (value === 0) return 'no relation';\n    if (value === 1 || value === -1) return 'perfect correlation';\n    return 'getNature(value) getStrength(value) correlation';\n  }\n  

",r.innerHTML+="

To rank the data:

",r.innerHTML+="

This function rank is designed to assign ranks to an array of data points, with a distinction made between cases where the data contains duplicates and where it does not. The function first creates an array of objects, each containing the original value and its index. Depending on whether the data is composed of strings or numerical values, it either maintains the original order for strings or sorts the array in descending order for numerical values. When duplicates are present, the function calculates average ranks for sets of identical values and assigns these ranks to all occurrences. The function then maps the calculated ranks back to the original order of the data using the stored indices, providing a final array of ranked data. This approach ensures accurate ranking, making the function suitable for scenarios where the presence of duplicate values needs to be appropriately considered.

",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function rank(data) {\n    let dataObjects = [];\n    for (let i = 0; i < data.length; i++) {\n      dataObjects.push({value: data[i], index: i});\n    }\n  \n    let rankData = [];\n    let mainSortedData = [];\n    if (typeof data[0] === 'string'){\n      mainSortedData = dataObjects;\n    } else {\n      mainSortedData = [...dataObjects].sort((a, b) => b.value - a.value);\n    }\n    //inserted two dumies para hindi sya malito sa variable i.\n    mainSortedData.push({value: undefined, index: undefined});\n    mainSortedData.push({value: undefined, index: undefined});\n    const dataArray = [], duplicateRank = []; \n    \n    for (let i = 0; i < data.length; i++) {\n      if (mainSortedData[i].value === mainSortedData[i+1].value){\n        let duplicate = mainSortedData[i].value;\n        duplicateRank.push(i + 1);\n        for (let j = i + 1; j < data.length; j++) {\n          if (duplicate === mainSortedData[j].value) {\n            duplicateRank.push(j + 1);\n          }\n        }\n  \n        i += duplicateRank.length;\n      }\n      \n  \n      if (duplicateRank.length > 0){\n        const sum = duplicateRank.reduce((acc, val) => acc + val, 0);\n        const n = duplicateRank.length;\n        let average = sum/n;\n  \n        for (let i = 0; i < duplicateRank.length; i++) {\n          duplicateRank[i] = average;\n        }\n  \n        const len = duplicateRank.length;\n  \n        for (let i = 0; i < len; i++) {\n          rankData.push(duplicateRank.pop());\n        }\n      }\n  \n  \n      if (mainSortedData[i].value !== mainSortedData[i+1].value && i < data.length) {\n        rankData.push(i + 1);\n        dataArray.push(mainSortedData[i].value);\n      } else if (mainSortedData[i].value === mainSortedData[i+1].value) {\n        i--;\n      }\n    }\n    \n    let rankedData = [];\n    for (let h = 0; h < data.length; h++) {\n      rankedData[mainSortedData[h].index] = rankData[h];\n    }\n    return rankedData;\n  }\n  

",r.innerHTML+="

To calculate the spearman rank correlation coefficient:

",r.innerHTML+="The provided JavaScript function calculates the Spearman rank correlation coefficient for two sets of data points, considering the presence of duplicates. In the absence of duplicates, it ranks the data, computes differences between corresponding ranks, and applies the Spearman formula to obtain the correlation coefficient. Additional information, including ranked data, differences, and squared differences, is returned. In the presence of duplicates, the function calculates mean ranks and performs modified Spearman calculations, returning a variety of intermediate results such as mean ranks, differences from mean ranks, and products of differences. The function limits the computed Spearman rank to three decimal places and provides a comprehensive set of outputs for both scenarios to aid in result interpretation and debugging.",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function spearmanRank(xData, yData) {\n    const duplicatesChecker = hasDuplicates(xData) || hasDuplicates(yData);\n  \n    const n = xData.length;\n    if (duplicatesChecker === false){\n      const xRankData = rank(xData); const yRankData = rank(yData); const diData = [];\n  \n      for (let i = 0; i < n; i += 1) {\n        diData[i] = xRankData[i] - yRankData[i];\n      }\n      const diSquaredData = diData.map((num) => num ** 2);\n      const diSquaredSummation = diSquaredData.reduce((acc, val) => acc + val, 0);\n      const spearmanRank = 1 - ((6 * diSquaredSummation) / (n * ((n ** 2) - 1)));\n  \n      return {\n        computedValue: limitDecimalPoints(spearmanRank, 3), \n        xRankData: xRankData, \n        yRankData: yRankData,\n        diData: diData,\n        diSquaredData: diSquaredData,\n        diSquaredSummation: diSquaredSummation,\n      };\n    } else {\n      const xRankData = rank(xData); const yRankData = rank(yData);\n      const MRx = xRankData.reduce((acc, val) => acc + val, 0) / n;\n      const MRy = yRankData.reduce((acc, val) => acc + val, 0) / n;\n      let RxMinusMrxData = []; RyMinusMryData = []; ProductData = []; RxMinusMRxRaiseTo2Data = []; RyMinusMRyRaiseTo2Data = [];\n      for (let i = 0; i < n; i++) {\n        RxMinusMrxData[i] = xRankData[i] - MRx;\n        RyMinusMryData[i] = yRankData[i] - MRy;\n        ProductData[i] = RxMinusMrxData[i] * RyMinusMryData[i];\n        RxMinusMRxRaiseTo2Data[i] = RxMinusMrxData[i] ** 2;\n        RyMinusMRyRaiseTo2Data[i] = RyMinusMryData[i] ** 2;\n      }\n  \n      const SummationOfProductData = ProductData.reduce((acc, val) => acc + val, 0);\n      const SummationOfRxMinusMRxRaiseTo2Data = RxMinusMRxRaiseTo2Data.reduce((acc, val) => acc + val, 0);\n      const SummationOfRyMinusMRyRaiseTo2Data = RyMinusMRyRaiseTo2Data.reduce((acc, val) => acc + val, 0);\n  \n      const spearmanRank = SummationOfProductData / (Math.sqrt(SummationOfRxMinusMRxRaiseTo2Data * SummationOfRyMinusMRyRaiseTo2Data))\n  \n      return {\n        computedValue: limitDecimalPoints(spearmanRank, 3), \n        xRankData: xRankData, \n        yRankData: yRankData,\n        MRx: MRx,\n        MRy: MRy,\n        RxMinusMrxData: RxMinusMrxData,\n        RyMinusMryData: RyMinusMryData,\n        ProductData: ProductData,\n        RxMinusMRxRaiseTo2Data: RxMinusMRxRaiseTo2Data,\n        RyMinusMRyRaiseTo2Data: RyMinusMRyRaiseTo2Data,\n        SummationOfProductData: SummationOfProductData,\n        SummationOfRxMinusMRxRaiseTo2Data: SummationOfRxMinusMRxRaiseTo2Data,\n        SummationOfRyMinusMRyRaiseTo2Data: SummationOfRyMinusMRyRaiseTo2Data\n      };\n    }\n  }\n  

",h.append(e,t,n,g,r)})),q[4].addEventListener("click",(function(){const e=document.createElement("h2");e.textContent="# Linear Regression";const t=document.createElement("div");t.innerHTML="

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to the observed data. The goal is to find the best-fitting line that minimizes the sum of squared differences between the observed values and the values predicted by the model.

",t.innerHTML+="

In a simple linear regression, there is one dependent variable and one independent variable, and the relationship is represented by the equation: Y = a + bX

";const n=document.createElement("form");n.id="linear-regression-form",function(e){const t=document.createElement("label");t.textContent="X Data Set (e.g. 1,2,3):";const n=document.createElement("input");n.type="text",n.name="dataset",n.placeholder="1,2,3",t.appendChild(n),n.addEventListener("keypress",w);const r=document.createElement("label");r.textContent="Y Data Set (e.g. 1,2,3):";const i=document.createElement("input");i.type="text",i.name="dataset",i.placeholder="1,2,3",r.appendChild(i),i.addEventListener("keypress",w);const a=document.createElement("label");a.textContent="X Label:",a.className="data-label";const o=document.createElement("input");o.type="text",o.name="x-label",o.value="X",a.appendChild(o);const s=document.createElement("label");s.textContent="Y Label:",s.className="data-label";const c=document.createElement("input");c.type="text",c.name="y-label",c.value="Y",s.appendChild(c);const u=document.createElement("label");u.textContent="Give value/s of x to predict the corresponding y:",u.className="data-label";const l=document.createElement("input");l.type="text",l.name="y-label",l.placeholder="1,2,3",u.appendChild(l),n.setAttribute("required",!0),i.setAttribute("required",!0),l.setAttribute("required",!0);const d=document.createElement("button");d.textContent="Show Linear Regression Analysis",d.type="submit";const p=document.createElement("p");p.textContent="All* fields are required",p.style.display="none",p.style.color="red",p.style.textAlign="center",d.addEventListener("click",(e=>{if(e.preventDefault(),k(M),n.value&&i.value&&l.value){let e=n.value.split(",").filter((e=>""!==e.trim()));e=e.map((e=>{const t=Number(e.trim());return isNaN(t)?e.trim():t}));let t=i.value.split(",").filter((e=>""!==e.trim()));t=t.map((e=>{const t=Number(e.trim());return isNaN(t)?e.trim():t}));let r=l.value.split(",").filter((e=>""!==e.trim()));r=r.map((e=>{const t=Number(e.trim());return isNaN(t)?e.trim():t})),function(e,t,n,r){const i=(0,D.linearRegression)(e,t),a=i.a,o=i.b,s=`Y = ${a} ${1===Math.sign(o)?"+":-1===Math.sign(o)?"-":"0"} ${Math.abs(o)}x`,c=document.createElement("p");c.textContent=`Linear Equation: ${s}`;const u=document.createElement("table"),l=u.insertRow();r.push("xy"),r.push("x²"),r.push("y²"),r.forEach((e=>{const t=document.createElement("th");t.textContent=e,l.appendChild(t)}));for(let n=0;n✏️ How It Works",r.innerHTML+="

To interpret the linear regression:

",r.innerHTML+="The calculator uses a linear regression function which conducts simple linear regression on given arrays of x and y data points. The function calculates the coefficients of the linear regression equation (Y = a + bX) by computing various summations and intermediate results. It employs arrays to store products, squares, and sums during the calculation process. The resulting object returned by the function includes the calculated coefficients (a and b), intermediate arrays, means of x and y, and summations.",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function linearRegression(xData, yData) {\n    const summationX = xData.reduce((acc, val) => acc + val, 0);\n    const summationY = yData.reduce((acc, val) => acc + val, 0);\n  \n    const xyData = []; const xSquaredData = []; const\n      ySquaredData = [];\n    for (let i = 0; i < xData.length; i += 1) {\n      xyData[i] = xData[i] * yData[i];\n      xSquaredData[i] = xData[i] ** 2;\n      ySquaredData[i] = yData[i] ** 2;\n    }\n  \n    const summationXY = xyData.reduce((acc, val) => acc + val, 0);\n    const summationXSquared = xSquaredData.reduce((acc, val) => acc + val, 0);\n    const summationYSquared = ySquaredData.reduce((acc, val) => acc + val, 0);\n    const n = xData.length;\n  \n    const xMean = limitDecimalPoints(summationX/n,3);\n    const yMean = limitDecimalPoints(summationY/n,3);\n  \n    const b = limitDecimalPoints((summationXY - ((summationX*summationY)/n))/(summationXSquared - ((summationX ** 2)/n)), 3);\n    const a = limitDecimalPoints(yMean - (b * xMean), 3);\n    return {\n      a: a,\n      b: b,\n      xyData: xyData,\n      xSquaredData: xSquaredData,\n      ySquaredData: ySquaredData,\n      xMean: xMean,\n      yMean: yMean,\n      summationX: summationX,\n      summationY: summationY,\n      summationXY: summationXY,\n      summationXSquared: summationXSquared,\n      summationYSquared: summationYSquared\n    };\n  }\n  

",N.append(e,t,n,M,r)})),q[6].addEventListener("click",(function(){const e=document.createElement("h2");e.textContent="# Hypothesis Testing";const t=document.createElement("div");t.innerHTML="

Hypothesis testing is a way for researchers to figure out if the differences they see in data are likely real or just due to random chance. It involves making educated guesses, called hypotheses, and then using statistical methods to check if the data supports or contradicts these guesses. The process helps determine if observed effects are genuine or could have happened by random fluctuations.

",t.innerHTML+="

It involves formulating a null hypothesis (Ho), representing a default assumption of no effect, and an alternative hypothesis (H1) or (Ha), suggesting a significant difference or effect.

";const n=document.createElement("form");n.id="hypothesis-testing-form",function(e){const t=document.createElement("label");t.textContent="Claim: ",t.className="displayInline";const n=C("μ",["μ","p"],"parameter"),r=C("≤",["≤","=","≥",">","≠","<"],"operator"),i=E("valueReference","100","displayInline",P);t.appendChild(n.UI),t.appendChild(r.UI),t.appendChild(i);const a=document.createElement("label");a.textContent="Sample size (n): ",a.className="displayInline";const o=E("sampleSize","30","displayInline",P);a.appendChild(o);const s=document.createElement("label");s.textContent="Sample mean (x̄): ",s.className="displayInline";const c=E("sampleMean","45","displayInline",P);s.appendChild(c);const u=document.createElement("label");u.textContent="Population mean (μ): ",u.className="displayInline";const l=E("populationMean","55","displayInline",P);u.appendChild(l);const d=document.createElement("label");d.textContent="Standard Deviation (s): ",d.className="displayInline";const p=E("standardDeviation","10","displayInline",P);d.appendChild(p);const f=document.createElement("label");f.textContent="Alpha (a): ",f.className="displayInline";const m=C("0.05",["0.05","0.01","0.10"],"alpha");f.appendChild(m.UI);const y=document.createElement("button");y.textContent="Show Hypothesis Testing Computation",y.type="submit";const v=document.createElement("p");v.textContent="All* fields are required",v.style.display="none",v.style.color="red",v.style.textAlign="center";const h=[i,o,c,l,p];y.addEventListener("click",(e=>{e.preventDefault(),k(_);let t=!0;for(let e of h)if(""===e.value||isNaN(Number(e.value.trim()))){t=!1;break}t?(function(e,t,n,r,i,a,o,s){const c=(0,O.hypothesisTesting)(e,t,n,r,i,a,o,s),u=document.createElement("p");u.innerHTML=`Conclusion: "${c.conclusion}"`;const l=document.createElement("p");l.innerHTML="Computed Values:";let d=document.createElement("p"),p=document.createElement("p");c.claim===c.nullHypo?(d.innerHTML=`Null Hypothesis (Ho): ${e} ${c.nullHypo.operator} ${c.nullHypo.valueReference} (Claim)`,p.innerHTML=`Alternative Hypothesis (Ha): ${e} ${c.altHypo.operator} ${c.altHypo.valueReference}`):(d.innerHTML=`Null Hypothesis (Ho): ${e} ${c.nullHypo.operator} ${c.nullHypo.valueReference}`,p.innerHTML=`Alternative Hypothesis (Ha): ${e} ${c.altHypo.operator} ${c.altHypo.valueReference} (Claim)`);const f=document.createElement("p");f.innerHTML=`Value of computed Z-Score: ${c.z}`;const m=document.createElement("p");m.innerHTML=`Corresponding value of z-score on Z-table: ${c.zc} `;const y=document.createElement("p");y.innerHTML=`Tail Orientation: ${c.tailOrientation} test`;const v=document.createElement("p");v.innerHTML=`P Value: ${c.PValue} `,_.append(u,l,d,p,f,m,y,v)}(n.getSelectedOption(),r.getSelectedOption(),Number(i.value.trim()),Number(o.value.trim()),Number(c.value.trim()),Number(l.value.trim()),Number(p.value.trim()),Number(m.getSelectedOption().trim())),v.style.display="none"):v.style.display="block"})),e.append(t,a,s,u,d,f,y,v)}(n);const r=document.createElement("div");r.innerHTML="

✏️ How It Works

",r.innerHTML+="

To interpret hypothesis testing:

",r.innerHTML+="The calculator uses a hypothesis testing function for conducting hypothesis tests on a sample mean. The function takes parameters such as the operator (<, >, =) for the null hypothesis, a reference value, sample size, sample mean, standard deviation, and significance level (alpha). It constructs null and alternative hypotheses, determines the tail orientation of the test, calculates the test statistic (z), converts it to a cumulative probability (zc), and computes the p-value based on the tail orientation. The function then decides whether to reject the null hypothesis based on the p-value and significance level. Finally, it generates a conclusion statement, indicating whether there is enough evidence to reject or support the null hypothesis. The results, including hypotheses, test statistics, p-value, and the conclusion, are returned in an object.",r.innerHTML+="

Expressed in javascript:

",r.innerHTML+="

\n  function hypothesisTesting(operator, valueReference, n, sampleMean, sd, alpha) {\n    let nullHypo, altHypo, claim, tailOrientation;\n    if (nullHypoOperators.includes(operator)){\n      nullHypo = {operator: operator, valueReference: valueReference};\n      if (operator === '≤'){\n        altHypo = {operator: '>', valueReference: valueReference};\n        tailOrientation = 'right-tailed';\n      } else if (operator === '≥'){\n        altHypo = {operator: '<', valueReference: valueReference};\n        tailOrientation = 'left-tailed';\n      } else if (operator === '='){\n        altHypo = {operator: '≠', valueReference: valueReference};\n        tailOrientation = 'two-tailed';\n      }\n      claim = nullHypo;\n    } else if (altHypoOperators.includes(operator)) {\n      altHypo = {operator: operator, valueReference: valueReference};\n      if (operator === '>'){\n        tailOrientation = 'right-tailed';\n        nullHypo = {operator: '≤', valueReference: valueReference}\n      } else if (operator === '<'){\n        tailOrientation = 'left-tailed';\n        nullHypo = {operator: '≥', valueReference: valueReference}\n      } else if (operator === '≠'){\n        tailOrientation = 'two-tailed';\n        nullHypo = {operator: '=', valueReference: valueReference}\n      }\n      claim = altHypo;\n    }\n    const populationMean = valueReference;\n    const z = limitDecimalPoints(((sampleMean - populationMean) / (sd / Math.sqrt(n))), 2);\n    const zc = limitDecimalPoints((stats.erf(z / Math.sqrt(2)) / 2 + 0.5), 4);\n  \n    let PValue;\n    if (tailOrientation === 'left-tailed'){\n      PValue = zc;\n    } else if (tailOrientation === 'right-tailed'){\n      PValue = limitDecimalPoints((1 - zc), 4);\n    } else if (tailOrientation === 'two-tailed'){\n      PValue = limitDecimalPoints((2 * zc), 4);\n    } \n  \n    let rejectNullHypothesis = false;\n    if (PValue <= alpha){\n      rejectNullHypothesis = true;\n    } else {\n      rejectNullHypothesis = false;\n    }\n  \n    let conclusion = ''; \n    if (claim === nullHypo){\n      if (rejectNullHypothesis){\n        conclusion = `At the {alpha * 100}% level of significance, There is enough evidence to reject the claim.`;\n      } else {\n        conclusion = `At the {alpha * 100}% level of significance, There is not enough evidence to reject the claim.`;\n      }\n    } else {\n      if (rejectNullHypothesis){\n        conclusion = `At the {alpha * 100}% level of significance, There is enough evidence to support the claim.`;\n      } else {\n        conclusion = `At the {alpha * 100}% level of significance, There is not enough evidence to support the claim.`;\n      }\n    }\n  \n    return {\n      nullHypo: nullHypo, \n      altHypo: altHypo,\n      claim: claim,\n      tailOrientation: tailOrientation,\n      z: z,\n      zc: zc,\n      PValue: PValue,\n      conclusion: conclusion\n    };\n  }\n  

",S.append(e,t,n,_,r)}))})()})(); \ No newline at end of file diff --git a/src/hypothesis-testing.js b/src/hypothesis-testing.js index 7a1b261..55c2ee3 100644 --- a/src/hypothesis-testing.js +++ b/src/hypothesis-testing.js @@ -32,7 +32,7 @@ function hypothesisTesting(parameter, operator, valueReference, n, sampleMean, p } claim = altHypo; } - const z = limitDecimalPoints(((sampleMean - populationMean) / (sd / Math.sqrt(n))), 2); + const z = limitDecimalPoints(((sampleMean - populationMean) / (sd / limitDecimalPoints(Math.sqrt(n), 3))), 2); const zc = limitDecimalPoints((stats.erf(z / Math.sqrt(2)) / 2 + 0.5), 4); let PValue; diff --git a/src/ui-linear-regression.js b/src/ui-linear-regression.js index 321bf48..63d7400 100644 --- a/src/ui-linear-regression.js +++ b/src/ui-linear-regression.js @@ -22,7 +22,7 @@ function displayResults(x, y, givendata, labels) { const a = linearRegValues.a; const b = linearRegValues.b; let sign = Math.sign(b) === 1 ? '+' : Math.sign(b) === -1 ? '-' : '0'; - const mainEquation = `Y = ${a} ${sign} ${b}x`; + const mainEquation = `Y = ${a} ${sign} ${Math.abs(b)}x`; const p = document.createElement('p'); p.textContent = `Linear Equation: ${mainEquation}`;