// Array Example:

// Linear Modeling of an ImageCollection

// longitude and latitude

var lon = 114.05;

var lat = 30.49;

var roi= ee.FeatureCollection("users/comingboy1118/China/CH_shi");

var roi= roi.filter(ee.Filter.eq("市","武汉市"));

Map.addLayer(roi,{},"roi")

// This function masks the input with a threshold on the simple cloud score.

var cloudMask = function(img) {

var cloudscore = ee.Algorithms.Landsat.simpleCloudScore(img).select('cloud');

return img.updateMask(cloudscore.lt(50));

};

// Load a Landsat 5 image collection.

var collection = ee.ImageCollection('LANDSAT/LT5_L1T_TOA')

// Filter to get only two years of data.

.filterDate('2005-04-01', '2018-04-01')

// Filter to get only imagery at a point of interest.

.filterBounds(ee.Geometry.Point(lon, lat))

// Mask clouds by mapping the cloudMask function over the collection.

.map(cloudMask)

// Select NIR and red bands only.

.select(['B4', 'B3'])

// Sort the collection in chronological order.

.sort('system:time_start', true);

// This function computes the predictors and the response from the input.

var makeVariables = function(image) {

// Compute time in fractional years relative to the start of the Epoch.

var year = image.date().difference(ee.Date('1970-01-01'), 'year');

// Compute the season in radians, one cycle per year.

var season = ee.Image(year.multiply(2 * Math.PI));

// Return an image of the predictors followed by the response.

return image.select()

.addBands(ee.Image(1))                                  // 0. constant term

.addBands(ee.Image(year).rename('t'))                   // 1. linear change

.addBands(season.sin().rename('sin'))                   // 2. seasonal change

.addBands(season.cos().rename('cos'))                   // 3. seasonal change

.addBands(image.normalizedDifference().rename('NDVI'))  // 4. response variable

.toFloat();

};

// Define the axes of variation in the collection array.

var imageAxis = 0;

var bandAxis = 1;

// Convert the collection to an array.

var array = collection.map(makeVariables).toArray();

// Check the length of the image axis (number of images).

var arrayLength = array.arrayLength(imageAxis);

// Update the mask to ensure that the number of images is greater than or

// equal to the number of predictors (the linear model is solveable).

array = array.updateMask(arrayLength.gt(4));

// Get slices of the array according to positions along the band axis.

var predictors = array.arraySlice(bandAxis, 0, 4);

var response = array.arraySlice(bandAxis, 4);

// Solve for linear regression coefficients in three different ways.

// All three methods produce equivalent results, but some are easier.

// coefficients the hard way

var coefficients1 = predictors.arrayTranspose().matrixMultiply(predictors)

.matrixInverse().matrixMultiply(predictors.arrayTranspose())

.matrixMultiply(response);

// coefficients the easy way

var coefficients2 = predictors.matrixPseudoInverse()

.matrixMultiply(response);

// coefficients the easiest way

var coefficients3 = predictors.matrixSolve(response);

// turn the results into a multi-band image

var coefficientsImage = coefficients3

.arrayProject([0]) // get rid of the extra dimensions

.arrayFlatten([

['constant', 'trend', 'sin', 'cos']

]);

// use this mask for cartographic purposes, to get rid of water areas

var hansenImage = ee.Image('UMD/hansen/global_forest_change_2013');

var mask = hansenImage.select('datamask').eq(1);

// display the result

Map.setCenter(lon, lat, 8);

Map.addLayer(coefficientsImage.mask(mask).clip(roi), {

bands: ['sin', 'trend', 'cos'],

min: [-0.05, -0.1, -0.05],

max: [0.05, 0.1, 0.05],

});

// plot the results

var fitted = collection.map(makeVariables).map(function(image) {

var coeffs = coefficientsImage.select(['constant', 'trend', 'sin', 'cos']);

var predicted = image

.select(['constant', 't', 'sin', 'cos'])

.multiply(coeffs)

.reduce('sum')

.rename('fitted');

return image.select('NDVI').addBands(predicted);

});

print(fitted,'fitted')

var roi = ee.Geometry.Point(lon, lat);

print(Chart.image.series(fitted.select(['NDVI','fitted']), roi, ee.Reducer.mean(), 30)

.setChartType('LineChart')

.setSeriesNames([ 'NDVI',"fitted"])

.setOptions({

title: 'Original and fitted values',

lineWidth: 1,

pointSize: 3,

fontSize: 16

}));