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 | /**
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7 | * Calculate the hyperbolic secant of a value,
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8 | * defined as `sech(x) = 1 / cosh(x)`.
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9 | *
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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.sech(x)
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15 | *
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16 | * Examples:
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17 | *
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18 | * // sech(x) = 1/ cosh(x)
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19 | * math.sech(0.5) // returns 0.886818883970074
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20 | * 1 / math.cosh(0.5) // returns 0.886818883970074
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21 | *
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22 | * See also:
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23 | *
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24 | * cosh, csch, coth
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25 | *
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26 | * @param {number | Complex | Unit | Array | Matrix} x Function input
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27 | * @return {number | Complex | Array | Matrix} Hyperbolic secant of x
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28 | */
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29 | const sech = typed('sech', {
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30 | 'number': _sech,
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31 |
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32 | 'Complex': function (x) {
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33 | return x.sech()
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34 | },
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35 |
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36 | 'BigNumber': function (x) {
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37 | return new type.BigNumber(1).div(x.cosh())
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38 | },
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39 |
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40 | 'Unit': function (x) {
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41 | if (!x.hasBase(type.Unit.BASE_UNITS.ANGLE)) {
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42 | throw new TypeError('Unit in function sech is no angle')
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43 | }
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44 | return sech(x.value)
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45 | },
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46 |
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47 | 'Array | Matrix': function (x) {
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48 | return deepMap(x, sech)
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49 | }
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50 | })
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51 |
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52 | sech.toTex = { 1: `\\mathrm{sech}\\left(\${args[0]}\\right)` }
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53 |
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54 | return sech
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55 | }
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56 |
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57 | /**
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58 | * Calculate the hyperbolic secant of a number
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59 | * @param {number} x
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60 | * @returns {number}
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61 | * @private
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62 | */
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63 | function _sech (x) {
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64 | return 2 / (Math.exp(x) + Math.exp(-x))
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65 | }
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66 |
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67 | exports.name = 'sech'
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68 | exports.factory = factory
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