问题
I am currently developing a class to represent matrices, it represents any general mxn matrix. I have worked out addition and scalar multiplication but I am struggling to develop the multiplication of two matrices. The data of the matrix is held in a 2D array of doubles.
The method looks a little bit like this:
public Matrix multiply(Matrix A) {
////code
}
It will return the product matrix. This is multiplication on the right. So, if I called A.multiply(B) then it would return the matrix AB, with B on the right.
I don't yet need to worry about checking whether the multiplication is defined on the given matrices, I can assume that I will be given matrices of the correct dimensions.
Does anyone know of an easy algorithm, possibly even in pseudocode to carry out the multiplication process?
Thanks in advance.
回答1:
Mathematically the Product of Matrices A (l x m) and B (m x n) is defined as a Matrix C (l x n) consisting of the elements:
m
c_i_j = ∑ a_i_k * b_k_j
k=1
So if you're not too much up for speed you might be happy with the straight forward O(n^3) implementation:
for (int i=0; i<l; ++i)
for (int j=0; j<n; ++j)
for (int k=0; k<m; ++k)
c[i][j] += a[i][k] * b[k][j]
If instead you're up for speed you might want to check for other alternatives like Strassen algorithm (see: Strassen algorithm).
Nevertheless be warned - especially if you're multiplying small matrices on modern processor architectures speed heavily depends on matrix data and multiplication order arranged in a way to make best use of in cache lines.
I strongly doubt there will be any chance to influence this factor from withing a vm, so I'm not sure if this is to be taken into consideration.
回答2:
Java. Matrix multiplication.
Here is the "code to carry out the multiplication process". Tested with matrices of different size.
public class Matrix {
/**
* Matrix multiplication method.
* @param m1 Multiplicand
* @param m2 Multiplier
* @return Product
*/
public static double[][] multiplyByMatrix(double[][] m1, double[][] m2) {
int m1ColLength = m1[0].length; // m1 columns length
int m2RowLength = m2.length; // m2 rows length
if(m1ColLength != m2RowLength) return null; // matrix multiplication is not possible
int mRRowLength = m1.length; // m result rows length
int mRColLength = m2[0].length; // m result columns length
double[][] mResult = new double[mRRowLength][mRColLength];
for(int i = 0; i < mRRowLength; i++) { // rows from m1
for(int j = 0; j < mRColLength; j++) { // columns from m2
for(int k = 0; k < m1ColLength; k++) { // columns from m1
mResult[i][j] += m1[i][k] * m2[k][j];
}
}
}
return mResult;
}
public static String toString(double[][] m) {
String result = "";
for(int i = 0; i < m.length; i++) {
for(int j = 0; j < m[i].length; j++) {
result += String.format("%11.2f", m[i][j]);
}
result += "\n";
}
return result;
}
public static void main(String[] args) {
// #1
double[][] multiplicand = new double[][] {
{3, -1, 2},
{2, 0, 1},
{1, 2, 1}
};
double[][] multiplier = new double[][] {
{2, -1, 1},
{0, -2, 3},
{3, 0, 1}
};
System.out.println("#1\n" + toString(multiplyByMatrix(multiplicand, multiplier)));
// #2
multiplicand = new double[][] {
{1, 2, 0},
{-1, 3, 1},
{2, -2, 1}
};
multiplier = new double[][] {
{2},
{-1},
{1}
};
System.out.println("#2\n" + toString(multiplyByMatrix(multiplicand, multiplier)));
// #3
multiplicand = new double[][] {
{1, 2, -1},
{0, 1, 0}
};
multiplier = new double[][] {
{1, 1, 0, 0},
{0, 2, 1, 1},
{1, 1, 2, 2}
};
System.out.println("#3\n" + toString(multiplyByMatrix(multiplicand, multiplier)));
}
}
Output:
#1
12.00 -1.00 2.00
7.00 -2.00 3.00
5.00 -5.00 8.00
#2
0.00
-4.00
7.00
#3
0.00 4.00 0.00 0.00
0.00 2.00 1.00 1.00
回答3:
In this answer, I created a class named Matrix, and another class is known as MatrixOperations which defines the various operations that can be performed on matrices (except for row operations of course). But I will extract the code for multiplication from MatrixOperations. The full project can be found on my GitHub page here.
Below is the definition of the Matrix class.
package app.matrix;
import app.matrix.util.MatrixException;
public class Matrix {
private double[][] entries;
public void setEntries(double[][] entries) {
this.entries = entries;
}
private String name;
public double[][] getEntries() {
return entries;
}
public String getName() {
return name;
}
public void setName(String name) {
this.name = name;
}
public class Dimension {
private int rows;
private int columns;
public int getRows() {
return rows;
}
public void setRows(int rows) {
this.rows = rows;
}
public int getColumns() {
return columns;
}
public void setColumns(int columns) {
this.columns = columns;
}
public Dimension(int rows, int columns) {
this.setRows(rows);
this.setColumns(columns);
}
@Override
public boolean equals(Object obj) {
if(obj instanceof Dimension){
return (this.getColumns() == ((Dimension) obj).getColumns()) && (this.getRows() == ((Dimension) obj).getRows());
}
return false;
}
}
private Dimension dimension;
public Dimension getDimension() {
return dimension;
}
public void setDimension(Dimension dimension) {
this.dimension = dimension;
}
public Matrix(int dimension, String name) throws MatrixException {
if (dimension == 0) throw new MatrixException(ZERO_UNIT_DIMENSION);
else this.setEntries(new double[Math.abs(dimension)][Math.abs(dimension)]);
this.setDimension(new Dimension(dimension, dimension));
this.setName(name);
}
public Matrix(int dimensionH, int dimensionV, String name) throws MatrixException {
if (dimensionH == 0 || dimensionV == 0) throw new MatrixException(ZERO_UNIT_DIMENSION);
else this.setEntries(new double[Math.abs(dimensionH)][Math.abs(dimensionV)]);
this.setDimension(new Dimension(dimensionH, dimensionV));
this.setName(name);
}
private static final String OVERFLOW_ITEMS_MSG = "The values are too many for the matrix's specified dimensions";
private static final String ZERO_UNIT_DIMENSION = "Zero cannot be a value for a dimension";
public Matrix(int dimensionH, int dimensionV, String name, double... values) throws MatrixException {
if (dimensionH == 0 || dimensionV == 0) throw new MatrixException(ZERO_UNIT_DIMENSION);
else if (values.length > dimensionH * dimensionV) throw new MatrixException(Matrix.OVERFLOW_ITEMS_MSG);
else this.setEntries(new double[Math.abs(dimensionH)][Math.abs(dimensionV)]);
this.setDimension(new Dimension(dimensionH, dimensionV));
this.setName(name);
int iterator = 0;
int j;
for (int i = 0; i < dimensionH; i++) {
j = 0;
while (j < dimensionV) {
this.entries[i][j] = values[iterator];
j++;
iterator++;
}
}
}
public Matrix(Dimension dimension) throws MatrixException {
this(dimension.getRows(), dimension.getColumns(), null);
}
public static Matrix identityMatrix(int dim) throws MatrixException {
if (dim == 0) throw new MatrixException(ZERO_UNIT_DIMENSION);
double[] i = new double[dim * dim];
int constant = dim + 1;
for (int j = 0; j < i.length; j = j + constant) {
i[j] = 1.0;
}
return new Matrix(dim, dim, null, i);
}
public String toString() {
StringBuilder builder = new StringBuilder("Matrix \"" + (this.getName() == null ? "Null Matrix" : this.getName()) + "\": {\n");
for (int i = 0; i < this.getDimension().getRows(); i++) {
for (int j = 0; j < this.getDimension().getColumns(); j++) {
if (j == 0) builder.append("\t");
builder.append(this.entries[i][j]);
if (j != this.getDimension().getColumns() - 1)
builder.append(", ");
}
if (i != this.getDimension().getRows()) builder.append("\n");
}
builder.append("}");
return builder.toString();
}
public boolean isSquare() {
return this.getDimension().getColumns() == this.getDimension().getRows();
}
}
and here is the code method for matrix multiplication from MatrixOperations
public static Matrix multiply(Matrix matrix1, Matrix matrix2) throws MatrixException {
if (matrix1.getDimension().getColumns() != matrix2.getDimension().getRows())
throw new MatrixException(MATRIX_MULTIPLICATION_ERROR_MSG);
Matrix retVal = new Matrix(matrix1.getDimension().getRows(), matrix2.getDimension().getColumns(), matrix1.getName() + " x " + matrix2.getName());
for (int i = 0; i < matrix1.getDimension().getRows(); i++) {
for (int j = 0; j < matrix2.getDimension().getColumns(); j++) {
retVal.getEntries()[i][j] = sum(arrayProduct(matrix1.getEntries()[i], getColumnMatrix(matrix2, j)));
}
}
return retVal;
}
and below again are the codes for methods sum, arrayProduct, and getColumnMatrix
private static double sum(double... values) {
double sum = 0;
for (double value : values) {
sum += value;
}
return sum;
}
private static double[] arrayProduct(double[] arr1, double[] arr2) throws MatrixException {
if (arr1.length != arr2.length) throw new MatrixException("Array lengths must be the same");
double[] retVal = new double[arr1.length];
for (int i = 0; i < arr1.length; i++) {
retVal[i] = arr1[i] * arr2[i];
}
return retVal;
}
private static double[] getColumnMatrix(Matrix matrix, int col) {
double[] ret = new double[matrix.getDimension().getRows()];
for (int i = 0; i < matrix.getDimension().getRows(); i++) {
ret[i] = matrix.getEntries()[i][col];
}
return ret;
}
来源：https://stackoverflow.com/questions/15733829/multiplying-two-matrices-in-java