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HermitePolynomialApproximation.js
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HermitePolynomialApproximation.js
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import defaultValue from "./defaultValue.js";
import defined from "./defined.js";
import DeveloperError from "./DeveloperError.js";
import CesiumMath from "./Math.js";
var factorial = CesiumMath.factorial;
function calculateCoefficientTerm(
x,
zIndices,
xTable,
derivOrder,
termOrder,
reservedIndices
) {
var result = 0;
var reserved;
var i;
var j;
if (derivOrder > 0) {
for (i = 0; i < termOrder; i++) {
reserved = false;
for (j = 0; j < reservedIndices.length && !reserved; j++) {
if (i === reservedIndices[j]) {
reserved = true;
}
}
if (!reserved) {
reservedIndices.push(i);
result += calculateCoefficientTerm(
x,
zIndices,
xTable,
derivOrder - 1,
termOrder,
reservedIndices
);
reservedIndices.splice(reservedIndices.length - 1, 1);
}
}
return result;
}
result = 1;
for (i = 0; i < termOrder; i++) {
reserved = false;
for (j = 0; j < reservedIndices.length && !reserved; j++) {
if (i === reservedIndices[j]) {
reserved = true;
}
}
if (!reserved) {
result *= x - xTable[zIndices[i]];
}
}
return result;
}
/**
* An {@link InterpolationAlgorithm} for performing Hermite interpolation.
*
* @namespace HermitePolynomialApproximation
*/
var HermitePolynomialApproximation = {
type: "Hermite",
};
/**
* Given the desired degree, returns the number of data points required for interpolation.
*
* @param {Number} degree The desired degree of interpolation.
* @param {Number} [inputOrder=0] The order of the inputs (0 means just the data, 1 means the data and its derivative, etc).
* @returns {Number} The number of required data points needed for the desired degree of interpolation.
* @exception {DeveloperError} degree must be 0 or greater.
* @exception {DeveloperError} inputOrder must be 0 or greater.
*/
HermitePolynomialApproximation.getRequiredDataPoints = function (
degree,
inputOrder
) {
inputOrder = defaultValue(inputOrder, 0);
//>>includeStart('debug', pragmas.debug);
if (!defined(degree)) {
throw new DeveloperError("degree is required.");
}
if (degree < 0) {
throw new DeveloperError("degree must be 0 or greater.");
}
if (inputOrder < 0) {
throw new DeveloperError("inputOrder must be 0 or greater.");
}
//>>includeEnd('debug');
return Math.max(Math.floor((degree + 1) / (inputOrder + 1)), 2);
};
/**
* Interpolates values using Hermite Polynomial Approximation.
*
* @param {Number} x The independent variable for which the dependent variables will be interpolated.
* @param {Number[]} xTable The array of independent variables to use to interpolate. The values
* in this array must be in increasing order and the same value must not occur twice in the array.
* @param {Number[]} yTable The array of dependent variables to use to interpolate. For a set of three
* dependent values (p,q,w) at time 1 and time 2 this should be as follows: {p1, q1, w1, p2, q2, w2}.
* @param {Number} yStride The number of dependent variable values in yTable corresponding to
* each independent variable value in xTable.
* @param {Number[]} [result] An existing array into which to store the result.
* @returns {Number[]} The array of interpolated values, or the result parameter if one was provided.
*/
HermitePolynomialApproximation.interpolateOrderZero = function (
x,
xTable,
yTable,
yStride,
result
) {
if (!defined(result)) {
result = new Array(yStride);
}
var i;
var j;
var d;
var s;
var len;
var index;
var length = xTable.length;
var coefficients = new Array(yStride);
for (i = 0; i < yStride; i++) {
result[i] = 0;
var l = new Array(length);
coefficients[i] = l;
for (j = 0; j < length; j++) {
l[j] = [];
}
}
var zIndicesLength = length,
zIndices = new Array(zIndicesLength);
for (i = 0; i < zIndicesLength; i++) {
zIndices[i] = i;
}
var highestNonZeroCoef = length - 1;
for (s = 0; s < yStride; s++) {
for (j = 0; j < zIndicesLength; j++) {
index = zIndices[j] * yStride + s;
coefficients[s][0].push(yTable[index]);
}
for (i = 1; i < zIndicesLength; i++) {
var nonZeroCoefficients = false;
for (j = 0; j < zIndicesLength - i; j++) {
var zj = xTable[zIndices[j]];
var zn = xTable[zIndices[j + i]];
var numerator;
if (zn - zj <= 0) {
index = zIndices[j] * yStride + yStride * i + s;
numerator = yTable[index];
coefficients[s][i].push(numerator / factorial(i));
} else {
numerator = coefficients[s][i - 1][j + 1] - coefficients[s][i - 1][j];
coefficients[s][i].push(numerator / (zn - zj));
}
nonZeroCoefficients = nonZeroCoefficients || numerator !== 0;
}
if (!nonZeroCoefficients) {
highestNonZeroCoef = i - 1;
}
}
}
for (d = 0, len = 0; d <= len; d++) {
for (i = d; i <= highestNonZeroCoef; i++) {
var tempTerm = calculateCoefficientTerm(x, zIndices, xTable, d, i, []);
for (s = 0; s < yStride; s++) {
var coeff = coefficients[s][i][0];
result[s + d * yStride] += coeff * tempTerm;
}
}
}
return result;
};
var arrayScratch = [];
/**
* Interpolates values using Hermite Polynomial Approximation.
*
* @param {Number} x The independent variable for which the dependent variables will be interpolated.
* @param {Number[]} xTable The array of independent variables to use to interpolate. The values
* in this array must be in increasing order and the same value must not occur twice in the array.
* @param {Number[]} yTable The array of dependent variables to use to interpolate. For a set of three
* dependent values (p,q,w) at time 1 and time 2 this should be as follows: {p1, q1, w1, p2, q2, w2}.
* @param {Number} yStride The number of dependent variable values in yTable corresponding to
* each independent variable value in xTable.
* @param {Number} inputOrder The number of derivatives supplied for input.
* @param {Number} outputOrder The number of derivatives desired for output.
* @param {Number[]} [result] An existing array into which to store the result.
*
* @returns {Number[]} The array of interpolated values, or the result parameter if one was provided.
*/
HermitePolynomialApproximation.interpolate = function (
x,
xTable,
yTable,
yStride,
inputOrder,
outputOrder,
result
) {
var resultLength = yStride * (outputOrder + 1);
if (!defined(result)) {
result = new Array(resultLength);
}
for (var r = 0; r < resultLength; r++) {
result[r] = 0;
}
var length = xTable.length;
// The zIndices array holds copies of the addresses of the xTable values
// in the range we're looking at. Even though this just holds information already
// available in xTable this is a much more convenient format.
var zIndices = new Array(length * (inputOrder + 1));
var i;
for (i = 0; i < length; i++) {
for (var j = 0; j < inputOrder + 1; j++) {
zIndices[i * (inputOrder + 1) + j] = i;
}
}
var zIndiceslength = zIndices.length;
var coefficients = arrayScratch;
var highestNonZeroCoef = fillCoefficientList(
coefficients,
zIndices,
xTable,
yTable,
yStride,
inputOrder
);
var reservedIndices = [];
var tmp = (zIndiceslength * (zIndiceslength + 1)) / 2;
var loopStop = Math.min(highestNonZeroCoef, outputOrder);
for (var d = 0; d <= loopStop; d++) {
for (i = d; i <= highestNonZeroCoef; i++) {
reservedIndices.length = 0;
var tempTerm = calculateCoefficientTerm(
x,
zIndices,
xTable,
d,
i,
reservedIndices
);
var dimTwo = Math.floor((i * (1 - i)) / 2) + zIndiceslength * i;
for (var s = 0; s < yStride; s++) {
var dimOne = Math.floor(s * tmp);
var coef = coefficients[dimOne + dimTwo];
result[s + d * yStride] += coef * tempTerm;
}
}
}
return result;
};
function fillCoefficientList(
coefficients,
zIndices,
xTable,
yTable,
yStride,
inputOrder
) {
var j;
var index;
var highestNonZero = -1;
var zIndiceslength = zIndices.length;
var tmp = (zIndiceslength * (zIndiceslength + 1)) / 2;
for (var s = 0; s < yStride; s++) {
var dimOne = Math.floor(s * tmp);
for (j = 0; j < zIndiceslength; j++) {
index = zIndices[j] * yStride * (inputOrder + 1) + s;
coefficients[dimOne + j] = yTable[index];
}
for (var i = 1; i < zIndiceslength; i++) {
var coefIndex = 0;
var dimTwo = Math.floor((i * (1 - i)) / 2) + zIndiceslength * i;
var nonZeroCoefficients = false;
for (j = 0; j < zIndiceslength - i; j++) {
var zj = xTable[zIndices[j]];
var zn = xTable[zIndices[j + i]];
var numerator;
var coefficient;
if (zn - zj <= 0) {
index = zIndices[j] * yStride * (inputOrder + 1) + yStride * i + s;
numerator = yTable[index];
coefficient = numerator / CesiumMath.factorial(i);
coefficients[dimOne + dimTwo + coefIndex] = coefficient;
coefIndex++;
} else {
var dimTwoMinusOne =
Math.floor(((i - 1) * (2 - i)) / 2) + zIndiceslength * (i - 1);
numerator =
coefficients[dimOne + dimTwoMinusOne + j + 1] -
coefficients[dimOne + dimTwoMinusOne + j];
coefficient = numerator / (zn - zj);
coefficients[dimOne + dimTwo + coefIndex] = coefficient;
coefIndex++;
}
nonZeroCoefficients = nonZeroCoefficients || numerator !== 0.0;
}
if (nonZeroCoefficients) {
highestNonZero = Math.max(highestNonZero, i);
}
}
}
return highestNonZero;
}
export default HermitePolynomialApproximation;