Various number-related routines and classes that are frequently used
/*
* Copyright (C) 2007 The Android Open Source Project
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
import java.util.ArrayList;
import java.util.concurrent.TimeUnit;
import java.util.concurrent.locks.Lock;
import java.util.concurrent.locks.ReentrantLock;
/**
* Various number-related routines and classes that are frequently used.
*
* @author barclay
*/
public class Number {
/**
* Default number of decimal places to round to:
*/
public static final int DECIMAL_PLACES = 2;
/**
* Round a float to the default number of decimal places.
*
* @param value
* The value to round.
* @return The rounded value as a float.
* @see #DECIMAL_PLACES
*/
public static float Round(float value) {
return Round(value, DECIMAL_PLACES);
}
/**
* Round a float to the specified number of decimal places.
*
* @param value
* The value to round.
* @param places
* The number of decimal points.
* @return The rounded value as a float.
*/
public static float Round(float value, int places) {
float p = (float) Math.pow(10, places);
value = value * p;
float tmp = Math.round(value);
return (float) tmp / p;
}
/**
* Clamp a <code>value</code> to <code>min</code> or <code>max</code>,
* inclusive.
*
* @param value
* The value to clamp.
* @param min
* The minimum value.
* @param max
* The maximum value.
* @return If <code>value</code> is greater than <code>max</code> then
* <code>max</code>, else if <code>value</code> is less than
* <code>min</code> then <code>min</code>, else <code>value</code>.
*/
public static float Clamp(float value, float min, float max) {
if (value > max)
return max;
if (value < min)
return min;
return value;
}
public enum TrendState {
DOWN_15_GOOD,
DOWN_15_BAD,
DOWN_30_GOOD,
DOWN_30_BAD,
DOWN_45_GOOD,
DOWN_45_BAD,
UP_15_GOOD,
UP_15_BAD,
UP_30_GOOD,
UP_30_BAD,
UP_45_GOOD,
UP_45_BAD,
DOWN_15,
UP_15,
FLAT,
FLAT_GOAL,
UNKNOWN
};
public static TrendState getTrendState(float oldTrend, float newTrend,
float goal, float sensitivity, float stdDev) {
sensitivity = sensitivity * stdDev;
float half = sensitivity / 2.0f;
float quarter = sensitivity / 4.0f;
if (oldTrend == newTrend) {
// truly flat trend
if (newTrend == goal)
// perfect!
return TrendState.FLAT_GOAL;
else if (newTrend < goal && newTrend + quarter > goal)
// flat near the goal!
return TrendState.FLAT_GOAL;
else if (newTrend > goal && newTrend - quarter < goal)
// flat near the goal!
return TrendState.FLAT_GOAL;
else
return TrendState.FLAT;
} else if (oldTrend > newTrend) {
// going down
if (oldTrend > goal && newTrend > goal) {
// toward goal
if (oldTrend - newTrend > sensitivity)
// huge drop
return TrendState.DOWN_45_GOOD;
else if (oldTrend - newTrend > half)
// big drop
return TrendState.DOWN_30_GOOD;
else if (oldTrend - newTrend > quarter)
// little drop
return TrendState.DOWN_15_GOOD;
else {
// under bounds for flat
if (newTrend - quarter < goal)
// flat near the goal!
return TrendState.FLAT_GOAL;
else
// flat elsewhere
return TrendState.FLAT;
}
} else if (oldTrend < goal && newTrend < goal) {
// away from goal
if (oldTrend - newTrend > sensitivity)
// huge drop
return TrendState.DOWN_45_BAD;
else if (oldTrend - newTrend > half)
// big drop
return TrendState.DOWN_30_BAD;
else if (oldTrend - newTrend > quarter)
// little drop
return TrendState.DOWN_15_BAD;
else {
// under bounds for flat
if (newTrend + quarter > goal)
// flat near the goal!
return TrendState.FLAT_GOAL;
else
// flat elsewhere
return TrendState.FLAT;
}
} else
// crossing goal line
return TrendState.DOWN_15;
} else if (oldTrend < newTrend) {
// going up
if (oldTrend < goal && newTrend < goal) {
// toward goal
if (newTrend - oldTrend > sensitivity)
// big rise
return TrendState.UP_45_GOOD;
else if (newTrend - oldTrend > half)
// little rise
return TrendState.UP_30_GOOD;
else if (newTrend - oldTrend > quarter)
// little rise
return TrendState.UP_15_GOOD;
else {
// under bounds for flat
if (newTrend + quarter > goal)
// flat near the goal!
return TrendState.FLAT_GOAL;
else
// flat elsewhere
return TrendState.FLAT;
}
} else if (oldTrend > goal && newTrend > goal) {
// away from goal
if (newTrend - oldTrend > sensitivity)
// big rise
return TrendState.UP_45_BAD;
else if (newTrend - oldTrend > half)
// little rise
return TrendState.UP_30_BAD;
else if (newTrend - oldTrend > quarter)
// little rise
return TrendState.UP_15_BAD;
else {
// under bounds for flat
if (newTrend - quarter < goal)
// flat near the goal!
return TrendState.FLAT_GOAL;
else
// flat elsewhere
return TrendState.FLAT;
}
} else {
// crossing goal line
return TrendState.UP_15;
}
} else
// ??
return TrendState.UNKNOWN;
}
/**
* An exponentially smoothed weighted moving average. Not thread safe. Trend
* is calculated thusly: <br>
* <code>
* trend[n] := trend[n-1] + smoothing_percentage * (value[n] - value[n-1])
* </code>
*
* @author barclay
*/
public static class Trend {
/**
* Default smoothing percentage. This value will be used to scale the
* previous entry by multiplying the previous entry's value and adding that
* to the current value, so a smoothing percentage of 0.1 is 10%.
*/
private static final float DEFAULT_SMOOTHING = 0.1f;
private int mNEntries = 0;
private float mSmoothing = DEFAULT_SMOOTHING;
private float mSum = 0.0f;
private boolean mFirst = true;
private float mTrendLast = 0.0f;
public float mTrendPrev = 0.0f;
public float mTrend = 0.0f;
public float mMin = 0.0f;
public float mMax = 0.0f;
public float mMean = 0.0f;
/**
* Default constructor. Set the smoothing percentage to the default.
*
* @see #DEFAULT_SMOOTHING
*/
public Trend() {
}
/**
* Constructor
*
* @param smoothing
* Sets the smoothing percentage to the specified value.
* @see #DEFAULT_SMOOTHING
*/
public Trend(float smoothing) {
mSmoothing = smoothing;
}
/**
* Copy Constructor
*
* @param source
* Returns a new instance of Trend with all data set to source.
* @see #DEFAULT_SMOOTHING
*/
public Trend(Trend source) {
mNEntries = source.mNEntries;
mSmoothing = source.mSmoothing;
mSum = source.mSum;
mFirst = source.mFirst;
mTrendLast = source.mTrendLast;
mTrendPrev = source.mTrendPrev;
mTrend = source.mTrend;
mMin = source.mMin;
mMax = source.mMax;
mMean = source.mMean;
}
/**
* Return the smoothing constant used by the Trend.
*
* @return The smoothing constant as a float.
*/
public float getSmoothing() {
return mSmoothing;
}
/**
* Update the trend with a new value. The value is implicitly "later" in the
* sequence than all previous values.
*
* @param val
* The value to add to the series.
*/
public void update(float val) {
mNEntries++;
mSum += val;
float oldMean = mMean;
mMean += (val - oldMean) / mNEntries;
// T(n) = T(n-1) + 0.1(V(n) - T(n-1))
// : T(n) is the trend number for day n
// : V(n) is the value number for day n
// : S is the smoothing factor (default 0.1)
if (mFirst == true) {
mFirst = false;
mTrend = val;
mMin = val;
mMax = val;
} else {
mTrend = mTrendLast + (mSmoothing * (val - mTrendLast));
if (mTrend < mMin)
mMin = mTrend;
if (mTrend > mMax)
mMax = mTrend;
}
mTrendPrev = mTrendLast;
mTrendLast = mTrend;
}
}
/**
* Class for keeping track of various statistics intended to be updated
* incrementally, including total number of updates, sum, mean, variance, and
* standard deviation of the series. Not thread safe.
*
* @author barclay
*/
public static class RunningStats {
public int mNDatapoints = 0;
public int mNEntries = 0;
public float mSum = 0.0f;
public float mMean = 0.0f;
public float mEntryMean = 0.0f;
public float mVarSum = 0.0f;
public float mVar = 0.0f;
public float mStdDev = 0.0f;
/**
* Sole constructor. Initializes all stats to 0.
*/
public RunningStats() {
}
/**
* Copy Constructor
*
* @param source
* Returns a new instance of RunningStats with all data set to
* source.
*/
public RunningStats(RunningStats source) {
mNDatapoints = source.mNDatapoints;
mNEntries = source.mNEntries;
mSum = source.mSum;
mMean = source.mMean;
mEntryMean = source.mEntryMean;
mVarSum = source.mVarSum;
mVar = source.mVar;
mStdDev = source.mStdDev;
}
/**
* update the statistics with the specified value. The value may be an
* aggregate of several other values, as indicated by the second parameter.
* A separate value will be recored for per-entry and and per-update means.
*
* @param val
* The value to update the statistics with.
* @param nEntries
* The number of entries this value is an aggregate of.
*/
public void update(float val, int nEntries) {
mNDatapoints++;
mNEntries += nEntries;
mSum += val;
// Mean is calculated thusly to avoid float expansion and contraction,
// which
// would minimize accuracy.
float oldMean = mMean;
mMean += (val - oldMean) / mNDatapoints;
mVarSum += (val - oldMean) * (val - mMean);
mVar = mVarSum / mNDatapoints;
mStdDev = (float) Math.sqrt(mVar);
if (mNEntries > 0) {
float oldEntryMean = mEntryMean;
mEntryMean += (val - oldEntryMean) / mNEntries;
}
return;
}
}
/**
* Class for keeping track of the Standard Deviation over the last X values.
*
* @author barclay
*/
public static class WindowedStdDev {
private Lock mLock;
private ArrayList<Float> mValues;
private int mHistory;
/**
* Sole constructor. Initializes all stats to 0.
*/
public WindowedStdDev(int history) {
mHistory = history;
mValues = new ArrayList<Float>(mHistory);
mLock = new ReentrantLock();
}
/**
* Copy Constructor
*
* @param source
* Returns a new instance of WindowedStdDev with all data set to
* source.
*/
public WindowedStdDev(WindowedStdDev source) {
mLock = new ReentrantLock();
source.waitForLock();
mHistory = source.mHistory;
mValues = new ArrayList<Float>(mHistory);
for (int i = 0; i < source.mValues.size(); i++) {
try {
mValues.add(new Float(source.mValues.get(i)));
} catch(IndexOutOfBoundsException e) {
break;
}
}
source.unlock();
}
public void waitForLock() {
while (lock() == false) {
}
}
public boolean lock() {
try {
return mLock.tryLock(250L, TimeUnit.MILLISECONDS);
} catch (InterruptedException e) {
return false;
}
}
public void unlock() {
mLock.unlock();
}
/**
* update the std dev with the specified value.
*
* @param val
* The value to update the statistics with.
*/
public void update(float val) {
waitForLock();
mValues.add(new Float(val));
if (mValues.size() > mHistory) {
try {
mValues.remove(0);
} catch(IndexOutOfBoundsException e) {
// nothing
}
}
unlock();
return;
}
/**
* Fetch current Standard Deviation.
*
* @param val
* The value to update the statistics with.
*/
public float getStandardDev() {
float mean = 0.0f;
float meanSqr = 0.0f;
float variance = 0.0f;
float delta = 0.0f;
float val = 0.0f;
waitForLock();
int nValues = mValues.size();
for (int i = 0; i < nValues; i++) {
try {
val = mValues.get(i);
delta = val - mean;
mean = mean + delta / (i + 1);
meanSqr = meanSqr + delta * (val - mean);
} catch(IndexOutOfBoundsException e) {
break;
}
}
unlock();
variance = meanSqr / nValues;
return (float) Math.sqrt(variance);
}
}
/**
* Performs a standard Pearson linear correlation on multiple series of data
* at one, returning the results in a matrix.
*
* @author barclay
*/
public static class LinearMatrixCorrelation {
private int mNumSeries = 0;
private int mNEntries = 0;
private Float[] mSum;
private Float[] mMean;
private Float[] mSumSquare;
private Float[] mStdDev;
private Float[][] mSumCoproduct;
private Float[][] mCovariance;
private Float[][] mCorrelation;
/**
* Constructor. Allocates internal data structures and zero's out the output
* matrix data.
*
* @param numSeries
* The number of series that will be included in each call to
* <code>update()</code>.
*/
public LinearMatrixCorrelation(int numSeries) {
mNumSeries = numSeries;
mSum = new Float[numSeries];
mMean = new Float[numSeries];
mSumSquare = new Float[numSeries];
mStdDev = new Float[numSeries];
mSumCoproduct = new Float[numSeries][];
mCovariance = new Float[numSeries][];
mCorrelation = new Float[numSeries][];
for (int i = 0; i < numSeries; i++) {
mSum[i] = 0.0f;
mMean[i] = 0.0f;
mSumSquare[i] = 0.0f;
mStdDev[i] = 0.0f;
mSumCoproduct[i] = new Float[numSeries];
mCovariance[i] = new Float[numSeries];
mCorrelation[i] = new Float[numSeries];
for (int j = 0; j < numSeries; j++) {
mSumCoproduct[i][j] = 0.0f;
mCovariance[i][j] = 0.0f;
mCorrelation[i][j] = 0.0f;
}
}
}
/**
* Adds a vector (array) of values, 1 per series, to the calculations.
* Graphically, all values are considered to be the at the same X (or Y)
* position, and the values in the array argument denote the corresponding Y
* (or X) value specific to the each series. Thus, the parameter x is an
* array of values x[0 .. numSeries-1], one value per series, all of which
* occured at the same "time." If a series has no such value, the entry in
* the array should be null, as the length of the array must match the
* <code>numSeries</code> past into the constructor at each invocation.
*
* @param x
* The values for each series as Floats.
* @return true if the input acceptable, else false if the length of
* <code>x[]</code> does not match <code>numSeries</code> or a value
* less than 1 was passed to the constructor.
* @see LinearMatrixCorrelation#LinearMatrixCorrelation
*/
public boolean update(Float[] x) {
float oldMean;
if (x.length != mNumSeries)
return false;
if (mNEntries + 1 > mNumSeries)
return false;
mNEntries++;
float sweep = (mNEntries - 1.0f) / mNEntries;
for (int i = 0; i < x.length; i++) {
if (x[i] != null) {
mSum[i] += x[i];
oldMean = mMean[i];
mMean[i] += (x[i] - oldMean) / mNEntries;
mSumSquare[i] += (x[i] - oldMean) * (x[i] - mMean[i]);
mStdDev[i] = (float) Math.sqrt(mSumSquare[i] * sweep);
}
}
for (int i = 0; i < x.length; i++) {
if (x[i] != null) {
for (int j = i + 1; j < x.length; j++) {
if (x[j] != null) {
mSumCoproduct[i][j] += (x[i] - mMean[i]) * (x[j] - mMean[j]);
mCovariance[i][j] = mSumCoproduct[i][j] * sweep;
mCorrelation[i][j] = mCovariance[i][j]
/ (mStdDev[i] * mStdDev[j]);
mCorrelation[j][i] = mCovariance[i][j]
/ (mStdDev[i] * mStdDev[j]);
mCorrelation[i][j] = mCovariance[i][j]
/ (mStdDev[i] * mStdDev[j]);
}
}
}
mCorrelation[i][i] = 1.0f;
}
return true;
}
/**
* Returns a reference to the correlation output matrix. The upper right
* triangle is a mirror of the lower left, and the dividing diagonal the
* identity correlation, i.e., 1.0f. In order to run through the matrix
* without duplicates (e.g., processing both output[i][j] and output[j][i],
* use a construct like: <br>
*
* <pre>
* for (int i = 0; i < output.length; i++) {
* for (int j = i+1; j < output.length; j++) {
* if (output[i][j] != null) { ... }
* }
* }
* </pre>
*
* Note that any correlations that could not be calculated, either due to
* lack of datapoints or structure of the data, will be null.
*
* @return Float[][], the output correlation matrix.
*/
public Float[][] getCorrelations() {
return mCorrelation;
}
/**
* Return a string interpretation of the linear correlation value. Note that
* this is highly dependent on the data being correlated, and should be no
* means be taken as gospel.
*
* @param c
* The correlation value, should be -1.0f <= c <= 1.0f.
* @return A string interpretation.
*/
public static String correlationToString(float c) {
if (c > 0.5)
return "Strong";
if (c < -0.5)
return "Inverse Strong";
if (c > 0.3)
return "Medium";
if (c < -0.3)
return "Inverse Medium";
return "Weak";
}
}
}
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