我最近需要计算大量(大约 800,000,000) double 的均值和标准差。考虑到一个double需要8个字节,如果将所有double都读入ram,大约需要6GB。我认为我可以对 C++ 或其他高级语言使用分而治之的方法,但这似乎很乏味。有没有一种方法可以使用 R、Scilab 或 Octave 等高级语言一次完成所有这些工作?谢谢。
最佳答案
听起来您可以充分利用 R-Grid 或 Hadoop。
您当然意识到,无需将所有值读入内存即可轻松计算均值和标准差。就像这个 Java 类一样,只保留一个总计。您只需要总和、总平方和和点数即可。我免费保留最小值和最大值。
这也清楚地说明了 map-reduce 的工作原理。您将实例化多个 Statistics 实例,让每个实例都保留 800M 点中各自部分的总和、平方和和点数。然后让 reduce 步骤将它们组合起来,并使用相同的公式得到最终结果。
import org.apache.commons.lang3.StringUtils;
import java.util.Collection;
/**
* Statistics accumulates simple statistics for a given quantity "on the fly" - no array needed.
* Resets back to zero when adding a value will overflow the sum of squares.
* @author mduffy
* @since 9/19/12 8:16 AM
*/
public class Statistics {
private String quantityName;
private int numValues;
private double x;
private double xsq;
private double xmin;
private double xmax;
/**
* Constructor
*/
public Statistics() {
this(null);
}
/**
* Constructor
* @param quantityName to describe the quantity (e.g. "heap size")
*/
public Statistics(String quantityName) {
this.quantityName = (StringUtils.isBlank(quantityName) ? "x" : quantityName);
this.reset();
}
/**
* Reset the object in the event of overflow by the sum of squares
*/
public synchronized void reset() {
this.numValues = 0;
this.x = 0.0;
this.xsq = 0.0;
this.xmin = Double.MAX_VALUE;
this.xmax = -Double.MAX_VALUE;
}
/**
* Add a List of values
* @param values to add to the statistics
*/
public synchronized void addAll(Collection<Double> values) {
for (Double value : values) {
add(value);
}
}
/**
* Add an array of values
* @param values to add to the statistics
*/
public synchronized void allAll(double [] values) {
for (double value : values) {
add(value);
}
}
/**
* Add a value to current statistics
* @param value to add for this quantity
*/
public synchronized void add(double value) {
double vsq = value*value;
++this.numValues;
this.x += value;
this.xsq += vsq; // TODO: how to detect overflow in Java?
if (value < this.xmin) {
this.xmin = value;
}
if (value > this.xmax) {
this.xmax = value;
}
}
/**
* Get the current value of the mean or average
* @return mean or average if one or more values have been added or zero for no values added
*/
public synchronized double getMean() {
double mean = 0.0;
if (this.numValues > 0) {
mean = this.x/this.numValues;
}
return mean;
}
/**
* Get the current min value
* @return current min value or Double.MAX_VALUE if no values added
*/
public synchronized double getMin() {
return this.xmin;
}
/**
* Get the current max value
* @return current max value or Double.MIN_VALUE if no values added
*/
public synchronized double getMax() {
return this.xmax;
}
/**
* Get the current standard deviation
* @return standard deviation for (N-1) dof or zero if one or fewer values added
*/
public synchronized double getStdDev() {
double stdDev = 0.0;
if (this.numValues > 1) {
stdDev = Math.sqrt((this.xsq-this.x*this.x/this.numValues)/(this.numValues-1));
}
return stdDev;
}
/**
* Get the current number of values added
* @return current number of values added or zero if overflow condition is encountered
*/
public synchronized int getNumValues() {
return this.numValues;
}
@Override
public String toString() {
final StringBuilder sb = new StringBuilder();
sb.append("Statistics");
sb.append("{quantityName='").append(quantityName).append('\'');
sb.append(", numValues=").append(numValues);
sb.append(", xmin=").append(xmin);
sb.append(", mean=").append(this.getMean());
sb.append(", std dev=").append(this.getStdDev());
sb.append(", xmax=").append(xmax);
sb.append('}');
return sb.toString();
}
}
这里是 JUnit 测试以证明它的工作:
import org.junit.Assert;
import org.junit.Test;
import java.util.Arrays;
import java.util.List;
/**
* StatisticsTest
* @author mduffy
* @since 9/19/12 11:21 AM
*/
public class StatisticsTest {
public static final double TOLERANCE = 1.0e-4;
@Test
public void testAddAll() {
// The test uses a full array, but it's obvious that you could read them from a file one at a time and process until you're done.
List<Double> values = Arrays.asList( 2.0, 4.0, 4.0, 4.0, 5.0, 5.0, 7.0, 9.0 );
Statistics stats = new Statistics();
stats.addAll(values);
Assert.assertEquals(8, stats.getNumValues());
Assert.assertEquals(2.0, stats.getMin(), TOLERANCE);
Assert.assertEquals(9.0, stats.getMax(), TOLERANCE);
Assert.assertEquals(5.0, stats.getMean(), TOLERANCE);
Assert.assertEquals(2.138089935299395, stats.getStdDev(), TOLERANCE);
}
}
关于c++ - C++ 或 Scilab 或 Octave 或 R 中大量数据的统计,我们在Stack Overflow上找到一个类似的问题: https://stackoverflow.com/questions/12712756/