hyperformula
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HyperFormula is a JavaScript engine for efficient processing of spreadsheet-like data and formulas
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JavaScript
function _typeof(obj) { "@babel/helpers - typeof"; if (typeof Symbol === "function" && typeof Symbol.iterator === "symbol") { _typeof = function _typeof(obj) { return typeof obj; }; } else { _typeof = function _typeof(obj) { return obj && typeof Symbol === "function" && obj.constructor === Symbol && obj !== Symbol.prototype ? "symbol" : typeof obj; }; } return _typeof(obj); }
function _createForOfIteratorHelper(o, allowArrayLike) { var it = typeof Symbol !== "undefined" && o[Symbol.iterator] || o["@@iterator"]; if (!it) { if (Array.isArray(o) || (it = _unsupportedIterableToArray(o)) || allowArrayLike && o && typeof o.length === "number") { if (it) o = it; var i = 0; var F = function F() {}; return { s: F, n: function n() { if (i >= o.length) return { done: true }; return { done: false, value: o[i++] }; }, e: function e(_e) { throw _e; }, f: F }; } throw new TypeError("Invalid attempt to iterate non-iterable instance.\nIn order to be iterable, non-array objects must have a [Symbol.iterator]() method."); } var normalCompletion = true, didErr = false, err; return { s: function s() { it = it.call(o); }, n: function n() { var step = it.next(); normalCompletion = step.done; return step; }, e: function e(_e2) { didErr = true; err = _e2; }, f: function f() { try { if (!normalCompletion && it.return != null) it.return(); } finally { if (didErr) throw err; } } }; }
function _unsupportedIterableToArray(o, minLen) { if (!o) return; if (typeof o === "string") return _arrayLikeToArray(o, minLen); var n = Object.prototype.toString.call(o).slice(8, -1); if (n === "Object" && o.constructor) n = o.constructor.name; if (n === "Map" || n === "Set") return Array.from(o); if (n === "Arguments" || /^(?:Ui|I)nt(?:8|16|32)(?:Clamped)?Array$/.test(n)) return _arrayLikeToArray(o, minLen); }
function _arrayLikeToArray(arr, len) { if (len == null || len > arr.length) len = arr.length; for (var i = 0, arr2 = new Array(len); i < len; i++) { arr2[i] = arr[i]; } return arr2; }
import "core-js/modules/es.array.reduce.js";
import "core-js/modules/es.object.get-prototype-of.js";
import "core-js/modules/es.reflect.construct.js";
import "core-js/modules/es.array.slice.js";
import "core-js/modules/es.object.to-string.js";
import "core-js/modules/es.function.name.js";
import "core-js/modules/es.array.from.js";
import "core-js/modules/es.string.iterator.js";
import "core-js/modules/es.symbol.js";
import "core-js/modules/es.symbol.description.js";
import "core-js/modules/es.symbol.iterator.js";
import "core-js/modules/es.array.iterator.js";
import "core-js/modules/web.dom-collections.iterator.js";
function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
function _defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if ("value" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } }
function _createClass(Constructor, protoProps, staticProps) { if (protoProps) _defineProperties(Constructor.prototype, protoProps); if (staticProps) _defineProperties(Constructor, staticProps); return Constructor; }
function _inherits(subClass, superClass) { if (typeof superClass !== "function" && superClass !== null) { throw new TypeError("Super expression must either be null or a function"); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, writable: true, configurable: true } }); if (superClass) _setPrototypeOf(subClass, superClass); }
function _setPrototypeOf(o, p) { _setPrototypeOf = Object.setPrototypeOf || function _setPrototypeOf(o, p) { o.__proto__ = p; return o; }; return _setPrototypeOf(o, p); }
function _createSuper(Derived) { var hasNativeReflectConstruct = _isNativeReflectConstruct(); return function _createSuperInternal() { var Super = _getPrototypeOf(Derived), result; if (hasNativeReflectConstruct) { var NewTarget = _getPrototypeOf(this).constructor; result = Reflect.construct(Super, arguments, NewTarget); } else { result = Super.apply(this, arguments); } return _possibleConstructorReturn(this, result); }; }
function _possibleConstructorReturn(self, call) { if (call && (_typeof(call) === "object" || typeof call === "function")) { return call; } else if (call !== void 0) { throw new TypeError("Derived constructors may only return object or undefined"); } return _assertThisInitialized(self); }
function _assertThisInitialized(self) { if (self === void 0) { throw new ReferenceError("this hasn't been initialised - super() hasn't been called"); } return self; }
function _isNativeReflectConstruct() { if (typeof Reflect === "undefined" || !Reflect.construct) return false; if (Reflect.construct.sham) return false; if (typeof Proxy === "function") return true; try { Boolean.prototype.valueOf.call(Reflect.construct(Boolean, [], function () {})); return true; } catch (e) { return false; } }
function _getPrototypeOf(o) { _getPrototypeOf = Object.setPrototypeOf ? Object.getPrototypeOf : function _getPrototypeOf(o) { return o.__proto__ || Object.getPrototypeOf(o); }; return _getPrototypeOf(o); }
/**
* @license
* Copyright (c) 2021 Handsoncode. All rights reserved.
*/
import { CellError, ErrorType } from '../../Cell';
import { ErrorMessage } from '../../error-message';
import { getRawValue, isExtendedNumber } from '../InterpreterValue';
import { centralF, chisquare, corrcoeff, covariance, geomean as _geomean, mean, normal, stdev, studentt, sumsqerr, variance } from './3rdparty/jstat/jstat';
import { ArgumentTypes, FunctionPlugin } from './FunctionPlugin';
export var StatisticalAggregationPlugin = /*#__PURE__*/function (_FunctionPlugin) {
_inherits(StatisticalAggregationPlugin, _FunctionPlugin);
var _super = _createSuper(StatisticalAggregationPlugin);
function StatisticalAggregationPlugin() {
_classCallCheck(this, StatisticalAggregationPlugin);
return _super.apply(this, arguments);
}
_createClass(StatisticalAggregationPlugin, [{
key: "avedev",
value: function avedev(ast, state) {
var _this = this;
return this.runFunction(ast.args, state, this.metadata('AVEDEV'), function () {
for (var _len = arguments.length, args = new Array(_len), _key = 0; _key < _len; _key++) {
args[_key] = arguments[_key];
}
var coerced = _this.arithmeticHelper.coerceNumbersExactRanges(args);
if (coerced instanceof CellError) {
return coerced;
}
if (coerced.length === 0) {
return new CellError(ErrorType.DIV_BY_ZERO);
}
var avg = mean(coerced);
return coerced.reduce(function (a, b) {
return a + Math.abs(b - avg);
}, 0) / coerced.length;
});
}
}, {
key: "devsq",
value: function devsq(ast, state) {
var _this2 = this;
return this.runFunction(ast.args, state, this.metadata('DEVSQ'), function () {
for (var _len2 = arguments.length, args = new Array(_len2), _key2 = 0; _key2 < _len2; _key2++) {
args[_key2] = arguments[_key2];
}
var coerced = _this2.arithmeticHelper.coerceNumbersExactRanges(args);
if (coerced instanceof CellError) {
return coerced;
}
if (coerced.length === 0) {
return 0;
}
return sumsqerr(coerced);
});
}
}, {
key: "geomean",
value: function geomean(ast, state) {
var _this3 = this;
return this.runFunction(ast.args, state, this.metadata('GEOMEAN'), function () {
for (var _len3 = arguments.length, args = new Array(_len3), _key3 = 0; _key3 < _len3; _key3++) {
args[_key3] = arguments[_key3];
}
var coerced = _this3.arithmeticHelper.coerceNumbersExactRanges(args);
if (coerced instanceof CellError) {
return coerced;
}
if (coerced.length === 0) {
return new CellError(ErrorType.NUM, ErrorMessage.OneValue);
}
var _iterator = _createForOfIteratorHelper(coerced),
_step;
try {
for (_iterator.s(); !(_step = _iterator.n()).done;) {
var val = _step.value;
if (val <= 0) {
return new CellError(ErrorType.NUM, ErrorMessage.ValueSmall);
}
}
} catch (err) {
_iterator.e(err);
} finally {
_iterator.f();
}
return _geomean(coerced);
});
}
}, {
key: "harmean",
value: function harmean(ast, state) {
var _this4 = this;
return this.runFunction(ast.args, state, this.metadata('HARMEAN'), function () {
for (var _len4 = arguments.length, args = new Array(_len4), _key4 = 0; _key4 < _len4; _key4++) {
args[_key4] = arguments[_key4];
}
var coerced = _this4.arithmeticHelper.coerceNumbersExactRanges(args);
if (coerced instanceof CellError) {
return coerced;
}
if (coerced.length === 0) {
return new CellError(ErrorType.NUM, ErrorMessage.OneValue);
}
var _iterator2 = _createForOfIteratorHelper(coerced),
_step2;
try {
for (_iterator2.s(); !(_step2 = _iterator2.n()).done;) {
var val = _step2.value;
if (val <= 0) {
return new CellError(ErrorType.NUM, ErrorMessage.ValueSmall);
}
}
} catch (err) {
_iterator2.e(err);
} finally {
_iterator2.f();
}
return coerced.length / coerced.reduce(function (a, b) {
return a + 1 / b;
}, 0);
});
}
}, {
key: "correl",
value: function correl(ast, state) {
return this.runFunction(ast.args, state, this.metadata('CORREL'), function (dataX, dataY) {
if (dataX.numberOfElements() !== dataY.numberOfElements()) {
return new CellError(ErrorType.NA, ErrorMessage.EqualLength);
}
var ret = parseTwoArrays(dataX, dataY);
if (ret instanceof CellError) {
return ret;
}
var n = ret[0].length;
if (n <= 1) {
return new CellError(ErrorType.DIV_BY_ZERO, ErrorMessage.TwoValues);
}
return corrcoeff(ret[0], ret[1]);
});
}
}, {
key: "rsq",
value: function rsq(ast, state) {
return this.runFunction(ast.args, state, this.metadata('RSQ'), function (dataX, dataY) {
if (dataX.numberOfElements() !== dataY.numberOfElements()) {
return new CellError(ErrorType.NA, ErrorMessage.EqualLength);
}
var ret = parseTwoArrays(dataX, dataY);
if (ret instanceof CellError) {
return ret;
}
var n = ret[0].length;
if (n <= 1) {
return new CellError(ErrorType.DIV_BY_ZERO, ErrorMessage.TwoValues);
}
return Math.pow(corrcoeff(ret[0], ret[1]), 2);
});
}
}, {
key: "covariancep",
value: function covariancep(ast, state) {
return this.runFunction(ast.args, state, this.metadata('COVARIANCE.P'), function (dataX, dataY) {
if (dataX.numberOfElements() !== dataY.numberOfElements()) {
return new CellError(ErrorType.NA, ErrorMessage.EqualLength);
}
var ret = parseTwoArrays(dataX, dataY);
if (ret instanceof CellError) {
return ret;
}
var n = ret[0].length;
if (n < 1) {
return new CellError(ErrorType.DIV_BY_ZERO, ErrorMessage.OneValue);
}
if (n === 1) {
return 0;
}
return covariance(ret[0], ret[1]) * (n - 1) / n;
});
}
}, {
key: "covariances",
value: function covariances(ast, state) {
return this.runFunction(ast.args, state, this.metadata('COVARIANCE.S'), function (dataX, dataY) {
if (dataX.numberOfElements() !== dataY.numberOfElements()) {
return new CellError(ErrorType.NA, ErrorMessage.EqualLength);
}
var ret = parseTwoArrays(dataX, dataY);
if (ret instanceof CellError) {
return ret;
}
var n = ret[0].length;
if (n <= 1) {
return new CellError(ErrorType.DIV_BY_ZERO, ErrorMessage.TwoValues);
}
return covariance(ret[0], ret[1]);
});
}
}, {
key: "ztest",
value: function ztest(ast, state) {
var _this5 = this;
return this.runFunction(ast.args, state, this.metadata('Z.TEST'), function (range, x, sigma) {
var vals = _this5.arithmeticHelper.manyToExactNumbers(range.valuesFromTopLeftCorner());
if (vals instanceof CellError) {
return vals;
}
var n = vals.length;
if (sigma === undefined) {
if (n < 2) {
return new CellError(ErrorType.DIV_BY_ZERO, ErrorMessage.TwoValues);
}
sigma = stdev(vals, true);
}
if (n < 1) {
return new CellError(ErrorType.NA, ErrorMessage.OneValue);
}
if (sigma === 0) {
return new CellError(ErrorType.DIV_BY_ZERO);
}
return 1 - normal.cdf((mean(vals) - x) / (sigma / Math.sqrt(n)), 0, 1);
});
}
}, {
key: "ftest",
value: function ftest(ast, state) {
var _this6 = this;
return this.runFunction(ast.args, state, this.metadata('F.TEST'), function (dataX, dataY) {
var arrX = _this6.arithmeticHelper.manyToExactNumbers(dataX.valuesFromTopLeftCorner());
var arrY = _this6.arithmeticHelper.manyToExactNumbers(dataY.valuesFromTopLeftCorner());
if (arrX instanceof CellError) {
return arrX;
}
if (arrY instanceof CellError) {
return arrY;
}
if (arrX.length <= 1 || arrY.length <= 1) {
return new CellError(ErrorType.DIV_BY_ZERO);
}
var vx = variance(arrX, true);
var vy = variance(arrY, true);
if (vx === 0 || vy === 0) {
return new CellError(ErrorType.DIV_BY_ZERO);
}
var r = vx / vy;
var v = centralF.cdf(r, arrX.length - 1, arrY.length - 1);
return 2 * Math.min(v, 1 - v);
});
}
}, {
key: "steyx",
value: function steyx(ast, state) {
return this.runFunction(ast.args, state, this.metadata('STEYX'), function (dataX, dataY) {
if (dataX.numberOfElements() !== dataY.numberOfElements()) {
return new CellError(ErrorType.NA, ErrorMessage.EqualLength);
}
var ret = parseTwoArrays(dataX, dataY);
if (ret instanceof CellError) {
return ret;
}
var n = ret[0].length;
if (n <= 2) {
return new CellError(ErrorType.DIV_BY_ZERO, ErrorMessage.ThreeValues);
}
return Math.sqrt((sumsqerr(ret[0]) - Math.pow(covariance(ret[0], ret[1]) * (n - 1), 2) / sumsqerr(ret[1])) / (n - 2));
});
}
}, {
key: "slope",
value: function slope(ast, state) {
return this.runFunction(ast.args, state, this.metadata('SLOPE'), function (dataX, dataY) {
if (dataX.numberOfElements() !== dataY.numberOfElements()) {
return new CellError(ErrorType.NA, ErrorMessage.EqualLength);
}
var ret = parseTwoArrays(dataX, dataY);
if (ret instanceof CellError) {
return ret;
}
var n = ret[0].length;
if (n <= 1) {
return new CellError(ErrorType.DIV_BY_ZERO, ErrorMessage.TwoValues);
}
return covariance(ret[0], ret[1]) * (n - 1) / sumsqerr(ret[1]);
});
}
}, {
key: "chisqtest",
value: function chisqtest(ast, state) {
return this.runFunction(ast.args, state, this.metadata('CHISQ.TEST'), function (dataX, dataY) {
var r = dataX.height();
var c = dataX.width();
if (dataY.height() !== r || dataY.width() !== c) {
return new CellError(ErrorType.NA, ErrorMessage.EqualLength);
}
var ret = parseTwoArrays(dataX, dataY);
if (ret instanceof CellError) {
return ret;
}
if (ret[0].length <= 1) {
return new CellError(ErrorType.DIV_BY_ZERO, ErrorMessage.TwoValues);
}
var sum = 0;
for (var i = 0; i < ret[0].length; i++) {
if (ret[1][i] === 0) {
return new CellError(ErrorType.DIV_BY_ZERO);
}
sum += Math.pow(ret[0][i] - ret[1][i], 2) / ret[1][i];
}
if (sum < 0) {
return new CellError(ErrorType.NUM, ErrorMessage.NaN);
}
return 1 - chisquare.cdf(sum, r > 1 && c > 1 ? (r - 1) * (c - 1) : r * c - 1);
});
}
}, {
key: "ttest",
value: function ttest(ast, state) {
var _this7 = this;
return this.runFunction(ast.args, state, this.metadata('T.TEST'), function (dataX, dataY, tails, type) {
var arrX = _this7.arithmeticHelper.manyToExactNumbers(dataX.valuesFromTopLeftCorner());
var arrY = _this7.arithmeticHelper.manyToExactNumbers(dataY.valuesFromTopLeftCorner());
if (arrX instanceof CellError) {
return arrX;
}
if (arrY instanceof CellError) {
return arrY;
}
var n = arrX.length;
var m = arrY.length;
if (type === 1) {
if (m !== n) {
return new CellError(ErrorType.NA, ErrorMessage.EqualLength);
}
if (n <= 1) {
return new CellError(ErrorType.DIV_BY_ZERO, ErrorMessage.TwoValues);
}
var sub = Array(n);
for (var i = 0; i < n; i++) {
sub[i] = arrX[i] - arrY[i];
}
var s = stdev(sub, true);
if (s === 0) {
return new CellError(ErrorType.DIV_BY_ZERO);
}
var t = Math.abs(Math.sqrt(n) * mean(sub) / s);
return tails * (1 - studentt.cdf(t, n - 1));
} else if (type === 2) {
if (n <= 1 || m <= 1) {
return new CellError(ErrorType.DIV_BY_ZERO, ErrorMessage.TwoValues);
}
var _s = (sumsqerr(arrX) + sumsqerr(arrY)) / (n + m - 2);
if (_s === 0) {
return new CellError(ErrorType.DIV_BY_ZERO);
}
var _t = Math.abs((mean(arrX) - mean(arrY)) / Math.sqrt(_s * (1 / n + 1 / m)));
return tails * (1 - studentt.cdf(_t, n + m - 2));
} else {
//type === 3
if (n <= 1 || m <= 1) {
return new CellError(ErrorType.DIV_BY_ZERO, ErrorMessage.TwoValues);
}
var sx = variance(arrX, true);
var sy = variance(arrY, true);
if (sx === 0 && sy === 0) {
return new CellError(ErrorType.DIV_BY_ZERO);
}
var _t2 = Math.abs((mean(arrX) - mean(arrY)) / Math.sqrt(sx / n + sy / m));
var v = Math.pow(sx / n + sy / m, 2) / (Math.pow(sx / n, 2) / (n - 1) + Math.pow(sy / m, 2) / (m - 1));
return tails * (1 - studentt.cdf(_t2, v));
}
});
}
}, {
key: "skew",
value: function skew(ast, state) {
var _this8 = this;
return this.runFunction(ast.args, state, this.metadata('SKEW'), function () {
for (var _len5 = arguments.length, args = new Array(_len5), _key5 = 0; _key5 < _len5; _key5++) {
args[_key5] = arguments[_key5];
}
var coerced = _this8.arithmeticHelper.coerceNumbersExactRanges(args);
if (coerced instanceof CellError) {
return coerced;
}
var n = coerced.length;
if (n < 3) {
return new CellError(ErrorType.DIV_BY_ZERO, ErrorMessage.ThreeValues);
}
var avg = mean(coerced);
var s = stdev(coerced, true);
if (s === 0) {
return new CellError(ErrorType.DIV_BY_ZERO);
}
return coerced.reduce(function (a, b) {
return a + Math.pow((b - avg) / s, 3);
}, 0) * n / (n - 1) / (n - 2);
});
}
}, {
key: "skewp",
value: function skewp(ast, state) {
var _this9 = this;
return this.runFunction(ast.args, state, this.metadata('SKEW.P'), function () {
for (var _len6 = arguments.length, args = new Array(_len6), _key6 = 0; _key6 < _len6; _key6++) {
args[_key6] = arguments[_key6];
}
var coerced = _this9.arithmeticHelper.coerceNumbersExactRanges(args);
if (coerced instanceof CellError) {
return coerced;
}
var n = coerced.length;
if (n < 3) {
return new CellError(ErrorType.DIV_BY_ZERO, ErrorMessage.ThreeValues);
}
var avg = mean(coerced);
var s = stdev(coerced, false);
if (s === 0) {
return new CellError(ErrorType.DIV_BY_ZERO);
}
return coerced.reduce(function (a, b) {
return a + Math.pow((b - avg) / s, 3);
}, 0) / n;
});
}
}]);
return StatisticalAggregationPlugin;
}(FunctionPlugin);
StatisticalAggregationPlugin.implementedFunctions = {
'AVEDEV': {
method: 'avedev',
parameters: [{
argumentType: ArgumentTypes.ANY
}],
repeatLastArgs: 1
},
'DEVSQ': {
method: 'devsq',
parameters: [{
argumentType: ArgumentTypes.ANY
}],
repeatLastArgs: 1
},
'GEOMEAN': {
method: 'geomean',
parameters: [{
argumentType: ArgumentTypes.ANY
}],
repeatLastArgs: 1
},
'HARMEAN': {
method: 'harmean',
parameters: [{
argumentType: ArgumentTypes.ANY
}],
repeatLastArgs: 1
},
'CORREL': {
method: 'correl',
parameters: [{
argumentType: ArgumentTypes.RANGE
}, {
argumentType: ArgumentTypes.RANGE
}]
},
'RSQ': {
method: 'rsq',
parameters: [{
argumentType: ArgumentTypes.RANGE
}, {
argumentType: ArgumentTypes.RANGE
}]
},
'COVARIANCE.P': {
method: 'covariancep',
parameters: [{
argumentType: ArgumentTypes.RANGE
}, {
argumentType: ArgumentTypes.RANGE
}]
},
'COVARIANCE.S': {
method: 'covariances',
parameters: [{
argumentType: ArgumentTypes.RANGE
}, {
argumentType: ArgumentTypes.RANGE
}]
},
'Z.TEST': {
method: 'ztest',
parameters: [{
argumentType: ArgumentTypes.RANGE
}, {
argumentType: ArgumentTypes.NUMBER
}, {
argumentType: ArgumentTypes.NUMBER,
optionalArg: true
}]
},
'F.TEST': {
method: 'ftest',
parameters: [{
argumentType: ArgumentTypes.RANGE
}, {
argumentType: ArgumentTypes.RANGE
}]
},
'STEYX': {
method: 'steyx',
parameters: [{
argumentType: ArgumentTypes.RANGE
}, {
argumentType: ArgumentTypes.RANGE
}]
},
'SLOPE': {
method: 'slope',
parameters: [{
argumentType: ArgumentTypes.RANGE
}, {
argumentType: ArgumentTypes.RANGE
}]
},
'CHISQ.TEST': {
method: 'chisqtest',
parameters: [{
argumentType: ArgumentTypes.RANGE
}, {
argumentType: ArgumentTypes.RANGE
}]
},
'T.TEST': {
method: 'ttest',
parameters: [{
argumentType: ArgumentTypes.RANGE
}, {
argumentType: ArgumentTypes.RANGE
}, {
argumentType: ArgumentTypes.INTEGER,
minValue: 1,
maxValue: 2
}, {
argumentType: ArgumentTypes.INTEGER,
minValue: 1,
maxValue: 3
}]
},
'SKEW': {
method: 'skew',
parameters: [{
argumentType: ArgumentTypes.ANY
}],
repeatLastArgs: 1
},
'SKEW.P': {
method: 'skewp',
parameters: [{
argumentType: ArgumentTypes.ANY
}],
repeatLastArgs: 1
}
};
StatisticalAggregationPlugin.aliases = {
COVAR: 'COVARIANCE.P',
FTEST: 'F.TEST',
PEARSON: 'CORREL',
ZTEST: 'Z.TEST',
CHITEST: 'CHISQ.TEST',
TTEST: 'T.TEST',
COVARIANCEP: 'COVARIANCE.P',
COVARIANCES: 'COVARIANCE.S',
SKEWP: 'SKEW.P'
};
function parseTwoArrays(dataX, dataY) {
var xit = dataX.iterateValuesFromTopLeftCorner();
var yit = dataY.iterateValuesFromTopLeftCorner();
var x, y;
var arrX = [];
var arrY = [];
while (x = xit.next(), y = yit.next(), !x.done && !y.done) {
var xval = x.value;
var yval = y.value;
if (xval instanceof CellError) {
return xval;
} else if (yval instanceof CellError) {
return yval;
} else if (isExtendedNumber(xval) && isExtendedNumber(yval)) {
arrX.push(getRawValue(xval));
arrY.push(getRawValue(yval));
}
}
return [arrX, arrY];
}