| 1 |
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| 2 |
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| 3 | const deepMap = require('../../utils/collection/deepMap')
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| 4 |
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| 5 | function factory (type, config, load, typed) {
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| 6 | const latex = require('../../utils/latex')
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| 7 |
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| 8 | /**
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| 9 | * Calculate the value of subtracting 1 from the exponential value.
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| 10 | * For matrices, the function is evaluated element wise.
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| 11 | *
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| 12 | * Syntax:
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| 13 | *
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| 14 | * math.expm1(x)
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| 15 | *
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| 16 | * Examples:
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| 17 | *
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| 18 | * math.expm1(2) // returns number 6.38905609893065
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| 19 | * math.pow(math.e, 2) - 1 // returns number 6.3890560989306495
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| 20 | * math.log(math.expm1(2) + 1) // returns number 2
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| 21 | *
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| 22 | * math.expm1([1, 2, 3])
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| 23 | * // returns Array [
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| 24 | * // 1.718281828459045,
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| 25 | * // 6.3890560989306495,
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| 26 | * // 19.085536923187668
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| 27 | * // ]
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| 28 | *
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| 29 | * See also:
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| 30 | *
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| 31 | * exp, log, pow
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| 32 | *
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| 33 | * @param {number | BigNumber | Complex | Array | Matrix} x A number or matrix to apply expm1
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| 34 | * @return {number | BigNumber | Complex | Array | Matrix} Exponent of `x`
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| 35 | */
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| 36 | const expm1 = typed('expm1', {
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| 37 | 'number': Math.expm1 || _expm1,
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| 38 |
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| 39 | 'Complex': function (x) {
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| 40 | const r = Math.exp(x.re)
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| 41 | return new type.Complex(
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| 42 | r * Math.cos(x.im) - 1,
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| 43 | r * Math.sin(x.im)
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| 44 | )
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| 45 | },
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| 46 |
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| 47 | 'BigNumber': function (x) {
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| 48 | return x.exp().minus(1)
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| 49 | },
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| 50 |
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| 51 | 'Array | Matrix': function (x) {
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| 52 | return deepMap(x, expm1)
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| 53 | }
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| 54 | })
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| 55 |
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| 56 | /**
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| 57 | * Calculates exponentiation minus 1.
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| 58 | * @param {number} x
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| 59 | * @return {number} res
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| 60 | * @private
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| 61 | */
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| 62 | function _expm1 (x) {
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| 63 | return (x >= 2e-4 || x <= -2e-4)
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| 64 | ? Math.exp(x) - 1
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| 65 | : x + x * x / 2 + x * x * x / 6
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| 66 | }
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| 67 |
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| 68 | expm1.toTex = `\\left(e${latex.operators['pow']}{\${args[0]}}-1\\right)`
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| 69 |
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| 70 | return expm1
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| 71 | }
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| 72 |
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| 73 | exports.name = 'expm1'
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| 74 | exports.factory = factory
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