Add some matrix classes in math\matrix package and standard libraries
This commit is contained in:
201
src/math/matrix/CholeskyDecomposition.java
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201
src/math/matrix/CholeskyDecomposition.java
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package math.matrix;
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import java.io.Serializable;
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/** Cholesky Decomposition.
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<P>
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For a symmetric, positive definite matrix A, the Cholesky decomposition
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is an lower triangular matrix L so that A = L*L'.
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<P>
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If the matrix is not symmetric or positive definite, the constructor
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returns a partial decomposition and sets an internal flag that may
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be queried by the isSPD() method.
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*/
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public class CholeskyDecomposition implements Serializable {
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/* ------------------------
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Class variables
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* ------------------------ */
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/** Array for internal storage of decomposition.
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@serial internal array storage.
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*/
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private double[][] L;
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/** Row and column dimension (square matrix).
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@serial matrix dimension.
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*/
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private int n;
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/** Symmetric and positive definite flag.
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@serial is symmetric and positive definite flag.
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*/
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private boolean isspd;
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/* ------------------------
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Constructor
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* ------------------------ */
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/** Cholesky algorithm for symmetric and positive definite matrix.
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Structure to access L and isspd flag.
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@param Arg Square, symmetric matrix.
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*/
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public CholeskyDecomposition (Matrix Arg) {
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// Initialize.
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double[][] A = Arg.getD();
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n = Arg.getM();
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L = new double[n][n];
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isspd = (Arg.getN() == n);
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// Main loop.
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for (int j = 0; j < n; j++) {
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double[] Lrowj = L[j];
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double d = 0.0;
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for (int k = 0; k < j; k++) {
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double[] Lrowk = L[k];
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double s = 0.0;
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for (int i = 0; i < k; i++) {
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s += Lrowk[i]*Lrowj[i];
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}
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Lrowj[k] = s = (A[j][k] - s)/L[k][k];
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d = d + s*s;
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isspd = isspd & (A[k][j] == A[j][k]);
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}
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d = A[j][j] - d;
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isspd = isspd & (d > 0.0);
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L[j][j] = Math.sqrt(Math.max(d,0.0));
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for (int k = j+1; k < n; k++) {
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L[j][k] = 0.0;
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}
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}
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}
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/* ------------------------
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Temporary, experimental code.
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* ------------------------ *\
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\** Right Triangular Cholesky Decomposition.
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<P>
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For a symmetric, positive definite matrix A, the Right Cholesky
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decomposition is an upper triangular matrix R so that A = R'*R.
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This constructor computes R with the Fortran inspired column oriented
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algorithm used in LINPACK and MATLAB. In Java, we suspect a row oriented,
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lower triangular decomposition is faster. We have temporarily included
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this constructor here until timing experiments confirm this suspicion.
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*\
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\** Array for internal storage of right triangular decomposition. **\
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private transient double[][] R;
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\** Cholesky algorithm for symmetric and positive definite matrix.
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@param A Square, symmetric matrix.
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@param rightflag Actual value ignored.
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@return Structure to access R and isspd flag.
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*\
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public CholeskyDecomposition (Matrix Arg, int rightflag) {
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// Initialize.
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double[][] A = Arg.getArray();
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n = Arg.getColumnDimension();
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R = new double[n][n];
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isspd = (Arg.getColumnDimension() == n);
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// Main loop.
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for (int j = 0; j < n; j++) {
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double d = 0.0;
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for (int k = 0; k < j; k++) {
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double s = A[k][j];
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for (int i = 0; i < k; i++) {
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s = s - R[i][k]*R[i][j];
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}
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R[k][j] = s = s/R[k][k];
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d = d + s*s;
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isspd = isspd & (A[k][j] == A[j][k]);
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}
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d = A[j][j] - d;
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isspd = isspd & (d > 0.0);
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R[j][j] = Math.sqrt(Math.max(d,0.0));
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for (int k = j+1; k < n; k++) {
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R[k][j] = 0.0;
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}
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}
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}
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\** Return upper triangular factor.
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@return R
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*\
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public Matrix getR () {
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return new Matrix(R,n,n);
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}
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\* ------------------------
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End of temporary code.
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* ------------------------ */
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/* ------------------------
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Public Methods
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* ------------------------ */
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/** Is the matrix symmetric and positive definite?
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@return true if A is symmetric and positive definite.
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*/
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public boolean isSPD () {
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return isspd;
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}
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/** Return triangular factor.
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@return L
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*/
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public Matrix getL () {
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return new Matrix(L);
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}
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/** Solve A*X = B
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@param B A Matrix with as many rows as A and any number of columns.
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@return X so that L*L'*X = B
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@exception IllegalArgumentException Matrix row dimensions must agree.
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@exception RuntimeException Matrix is not symmetric positive definite.
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*/
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public Matrix solve (Matrix B) {
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if (B.getM() != n) {
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throw new IllegalArgumentException("Matrix row dimensions must agree.");
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}
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if (!isspd) {
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throw new RuntimeException("Matrix is not symmetric positive definite.");
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}
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// Copy right hand side.
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double[][] X = B.getCopy();
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int nx = B.getN();
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// Solve L*Y = B;
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for (int k = 0; k < n; k++) {
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for (int j = 0; j < nx; j++) {
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for (int i = 0; i < k ; i++) {
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X[k][j] -= X[i][j]*L[k][i];
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}
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X[k][j] /= L[k][k];
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}
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}
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// Solve L'*X = Y;
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for (int k = n-1; k >= 0; k--) {
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for (int j = 0; j < nx; j++) {
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for (int i = k+1; i < n ; i++) {
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X[k][j] -= X[i][j]*L[i][k];
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}
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X[k][j] /= L[k][k];
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}
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}
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return new Matrix(X);
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}
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private static final long serialVersionUID = 1;
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}
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175
src/math/matrix/Diagonal.java
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175
src/math/matrix/Diagonal.java
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@@ -0,0 +1,175 @@
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package math.matrix;
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import exception.IllegalDimensionException;
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public class Diagonal extends Matrix{
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/**
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* UID
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*/
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private static final long serialVersionUID = 3206696282474150081L;
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public Diagonal(int n){
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this(n,n);
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}
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public Diagonal(int m, int n){
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this.m = m;
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this.n = n;
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data = new double[m>n?m:n];
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}
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public Diagonal(double... d){
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this(d.length);
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int i;
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for(i=0; i<n; i++)
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set(i, d[i]);
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}
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public Diagonal(Vector d){
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this(d.n());
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int i;
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for(i=0; i<n; i++)
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set(i, d.get(i));
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}
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/**
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* Create diagonal matrix with given main diagonal entries
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* @param d matrix
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*/
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public Diagonal(Matrix d){
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this(d.getM(), d.getN());
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int i;
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for(i=0; i<(m>n?m:n); i++)
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set(i, d.get(i, i));
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}
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/**
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* Generate an n-by-n identity matrix.
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* An n-by-n matrix with ones on the diagonal and zeros elsewhere.
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* @param n rows/columns
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* @return n-by-n identity matrix
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*/
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public static Diagonal identity(int n){
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int i;
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Diagonal c = new Diagonal(n);
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for(i=0; i<n; i++)
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c.set(i, 1);
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return c;
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}
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/**
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* Generate an m-by-n identity matrix.
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* An m-by-n matrix with ones on the diagonal and zeros elsewhere.
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* @param n rows/columns
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* @return n-by-n identity matrix
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*/
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public static Diagonal identity(int m, int n){
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int i;
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Diagonal c = new Diagonal(m, n);
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for(i=0; i<(m<n?m:n); i++)
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c.set(i, 1);
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return c;
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}
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public void set(int i, double d){
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data[i] = d;
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}
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public Matrix set(int i, int j, double d){
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if(i==j) set(i,d);
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return this;
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}
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public double get(int i){
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return data[i];
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}
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public double get(int i, int j){
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if(i==j) return get(i);
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else return 0;
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}
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/**
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* Unary minus
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* @return -D
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*/
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public Diagonal uminus(){
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Diagonal X = new Diagonal(m,n);
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int i;
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for(i=0; i<n; i++)
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X.set(i, -get(i));
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return X;
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}
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/**
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* Scalar multiplication. Multiply a matrix element-wise by a scalar.
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* @param s scalar
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* @return <b>C</b> = s <b>A</b>
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*/
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public Diagonal times(double s){
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int i;
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Diagonal c = new Diagonal(m,n);
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for(i=0; i<m; i++)
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c.set(i, s * get(i));
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return c;
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}
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/**
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* Scalar multiplication. Multiply a matrix element-wise by a scalar.
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* @param s scalar
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* @return <b>D</b> = s <b>D</b>
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*/
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public Diagonal timesEquals(double s){
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int i;
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for(i=0; i<m; i++)
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set(i, s * get(i));
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return this;
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}
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/**
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* Multiply by a vector right. matrix-vector multiplication
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* @param b vector
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* @return <b>C</b> = <b>A</b> • <b>b</b> = <b>A</b> <b>b</b>
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* @throws IllegalDimensionException Illegal vector dimensions.
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*/
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public Vector times(Vector b) throws IllegalDimensionException{
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int i;
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if(n != b.n()) throw new IllegalDimensionException("Illegal vector dimensions.");
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Vector c = new Vector(m);
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for(i=0; i<m; i++)
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c.set(i, get(i) * b.get(i));
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return c;
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}
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/**
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* @param e exponent
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* @return the matrix to the power of e
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*/
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public Diagonal pow(double e){
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int i;
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Diagonal C = new Diagonal(m,n);
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for(i=0; i<(m<n?m:n); i++)
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C.set(i, Math.pow(get(i), e));
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return C;
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}
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public double det(){
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int i;
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double det = 1;
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for(i=0; i<m; i++)
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det *= get(i);
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return det;
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}
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public String toString(){
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return Matrix.diag(data).toString();
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}
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public static void main(String[] args){
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Diagonal d1 = new Diagonal(1.);
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System.out.println(d1);
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Diagonal d2 = new Diagonal(1., 2.);
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System.out.println(d2);
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}
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}
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47
src/math/matrix/Diagonal2D.java
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47
src/math/matrix/Diagonal2D.java
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@@ -0,0 +1,47 @@
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package math.matrix;
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public class Diagonal2D extends Matrix2D {
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/**
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* UID
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*/
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private static final long serialVersionUID = 553077525134866149L;
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public Diagonal2D(int n){
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this(n,n);
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}
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public Diagonal2D(int m, int n){
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this.m = m;
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this.n = n;
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data = new double[m>n?m:n];
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}
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/**
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* Generate an n-by-n identity matrix.
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* An m-by-n matrix with ones on the diagonal and zeros elsewhere.
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* @param n rows/columns
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* @return n-by-n identity matrix
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*/
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public static Diagonal2D identity(int n){
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int i;
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Diagonal2D c = new Diagonal2D(n);
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for(i=0; i<n; i++)
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c.set(i, 1);
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return c;
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}
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public void set(int i, double d){
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data[i] = d;
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}
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public String toString(){
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return Matrix2D.diag(data).toString();
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}
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public static void main(String[] args) {
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}
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}
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961
src/math/matrix/EigenvalueDecomposition.java
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961
src/math/matrix/EigenvalueDecomposition.java
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@@ -0,0 +1,961 @@
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package math.matrix;
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import java.io.Serializable;
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import math.Maths;
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/** Eigenvalues and eigenvectors of a real matrix.
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<P>
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If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is
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diagonal and the eigenvector matrix V is orthogonal.
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I.e. A = V.times(D.times(V.transpose())) and
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V.times(V.transpose()) equals the identity matrix.
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<P>
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If A is not symmetric, then the eigenvalue matrix D is block diagonal
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with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
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lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The
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columns of V represent the eigenvectors in the sense that A*V = V*D,
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i.e. A.times(V) equals V.times(D). The matrix V may be badly
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conditioned, or even singular, so the validity of the equation
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A = V*D*inverse(V) depends upon V.cond().
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**/
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public class EigenvalueDecomposition implements Serializable {
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/**
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* UID
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*/
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private static final long serialVersionUID = -4489049767346210616L;
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/* ------------------------
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Class variables
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* ------------------------ */
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/** Row and column dimension (square matrix).
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@serial matrix dimension.
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*/
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private int n;
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/** Symmetry flag.
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@serial internal symmetry flag.
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*/
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private boolean issymmetric;
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/** Arrays for internal storage of eigenvalues.
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@serial internal storage of eigenvalues.
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*/
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private double[] d, e;
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/** Array for internal storage of eigenvectors.
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@serial internal storage of eigenvectors.
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*/
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private double[][] V;
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/** Array for internal storage of nonsymmetric Hessenberg form.
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@serial internal storage of nonsymmetric Hessenberg form.
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*/
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private double[][] H;
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/** Working storage for nonsymmetric algorithm.
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@serial working storage for nonsymmetric algorithm.
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*/
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private double[] ort;
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/* ------------------------
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Private Methods
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* ------------------------ */
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// Symmetric Householder reduction to tridiagonal form.
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private void tred2 () {
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// This is derived from the Algol procedures tred2 by
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// Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
|
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// Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
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// Fortran subroutine in EISPACK.
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for (int j = 0; j < n; j++) {
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d[j] = V[n-1][j];
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}
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// Householder reduction to tridiagonal form.
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for (int i = n-1; i > 0; i--) {
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// Scale to avoid under/overflow.
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double scale = 0.0;
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double h = 0.0;
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for (int k = 0; k < i; k++) {
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scale = scale + Math.abs(d[k]);
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}
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if (scale == 0.0) {
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e[i] = d[i-1];
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for (int j = 0; j < i; j++) {
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d[j] = V[i-1][j];
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V[i][j] = 0.0;
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V[j][i] = 0.0;
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}
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} else {
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// Generate Householder vector.
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for (int k = 0; k < i; k++) {
|
||||
d[k] /= scale;
|
||||
h += d[k] * d[k];
|
||||
}
|
||||
double f = d[i-1];
|
||||
double g = Math.sqrt(h);
|
||||
if (f > 0) {
|
||||
g = -g;
|
||||
}
|
||||
e[i] = scale * g;
|
||||
h = h - f * g;
|
||||
d[i-1] = f - g;
|
||||
for (int j = 0; j < i; j++) {
|
||||
e[j] = 0.0;
|
||||
}
|
||||
|
||||
// Apply similarity transformation to remaining columns.
|
||||
|
||||
for (int j = 0; j < i; j++) {
|
||||
f = d[j];
|
||||
V[j][i] = f;
|
||||
g = e[j] + V[j][j] * f;
|
||||
for (int k = j+1; k <= i-1; k++) {
|
||||
g += V[k][j] * d[k];
|
||||
e[k] += V[k][j] * f;
|
||||
}
|
||||
e[j] = g;
|
||||
}
|
||||
f = 0.0;
|
||||
for (int j = 0; j < i; j++) {
|
||||
e[j] /= h;
|
||||
f += e[j] * d[j];
|
||||
}
|
||||
double hh = f / (h + h);
|
||||
for (int j = 0; j < i; j++) {
|
||||
e[j] -= hh * d[j];
|
||||
}
|
||||
for (int j = 0; j < i; j++) {
|
||||
f = d[j];
|
||||
g = e[j];
|
||||
for (int k = j; k <= i-1; k++) {
|
||||
V[k][j] -= (f * e[k] + g * d[k]);
|
||||
}
|
||||
d[j] = V[i-1][j];
|
||||
V[i][j] = 0.0;
|
||||
}
|
||||
}
|
||||
d[i] = h;
|
||||
}
|
||||
|
||||
// Accumulate transformations.
|
||||
|
||||
for (int i = 0; i < n-1; i++) {
|
||||
V[n-1][i] = V[i][i];
|
||||
V[i][i] = 1.0;
|
||||
double h = d[i+1];
|
||||
if (h != 0.0) {
|
||||
for (int k = 0; k <= i; k++) {
|
||||
d[k] = V[k][i+1] / h;
|
||||
}
|
||||
for (int j = 0; j <= i; j++) {
|
||||
double g = 0.0;
|
||||
for (int k = 0; k <= i; k++) {
|
||||
g += V[k][i+1] * V[k][j];
|
||||
}
|
||||
for (int k = 0; k <= i; k++) {
|
||||
V[k][j] -= g * d[k];
|
||||
}
|
||||
}
|
||||
}
|
||||
for (int k = 0; k <= i; k++) {
|
||||
V[k][i+1] = 0.0;
|
||||
}
|
||||
}
|
||||
for (int j = 0; j < n; j++) {
|
||||
d[j] = V[n-1][j];
|
||||
V[n-1][j] = 0.0;
|
||||
}
|
||||
V[n-1][n-1] = 1.0;
|
||||
e[0] = 0.0;
|
||||
}
|
||||
|
||||
// Symmetric tridiagonal QL algorithm.
|
||||
|
||||
private void tql2 () {
|
||||
|
||||
// This is derived from the Algol procedures tql2, by
|
||||
// Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
|
||||
// Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
|
||||
// Fortran subroutine in EISPACK.
|
||||
|
||||
for (int i = 1; i < n; i++) {
|
||||
e[i-1] = e[i];
|
||||
}
|
||||
e[n-1] = 0.0;
|
||||
|
||||
double f = 0.0;
|
||||
double tst1 = 0.0;
|
||||
double eps = Math.pow(2.0,-52.0);
|
||||
for (int l = 0; l < n; l++) {
|
||||
|
||||
// Find small subdiagonal element
|
||||
|
||||
tst1 = Math.max(tst1,Math.abs(d[l]) + Math.abs(e[l]));
|
||||
int m = l;
|
||||
while (m < n) {
|
||||
if (Math.abs(e[m]) <= eps*tst1) {
|
||||
break;
|
||||
}
|
||||
m++;
|
||||
}
|
||||
|
||||
// If m == l, d[l] is an eigenvalue,
|
||||
// otherwise, iterate.
|
||||
|
||||
if (m > l) {
|
||||
int iter = 0;
|
||||
do {
|
||||
iter = iter + 1; // (Could check iteration count here.)
|
||||
|
||||
// Compute implicit shift
|
||||
|
||||
double g = d[l];
|
||||
double p = (d[l+1] - g) / (2.0 * e[l]);
|
||||
double r = Maths.hypot(p,1.0);
|
||||
if (p < 0) {
|
||||
r = -r;
|
||||
}
|
||||
d[l] = e[l] / (p + r);
|
||||
d[l+1] = e[l] * (p + r);
|
||||
double dl1 = d[l+1];
|
||||
double h = g - d[l];
|
||||
for (int i = l+2; i < n; i++) {
|
||||
d[i] -= h;
|
||||
}
|
||||
f = f + h;
|
||||
|
||||
// Implicit QL transformation.
|
||||
|
||||
p = d[m];
|
||||
double c = 1.0;
|
||||
double c2 = c;
|
||||
double c3 = c;
|
||||
double el1 = e[l+1];
|
||||
double s = 0.0;
|
||||
double s2 = 0.0;
|
||||
for (int i = m-1; i >= l; i--) {
|
||||
c3 = c2;
|
||||
c2 = c;
|
||||
s2 = s;
|
||||
g = c * e[i];
|
||||
h = c * p;
|
||||
r = Maths.hypot(p,e[i]);
|
||||
e[i+1] = s * r;
|
||||
s = e[i] / r;
|
||||
c = p / r;
|
||||
p = c * d[i] - s * g;
|
||||
d[i+1] = h + s * (c * g + s * d[i]);
|
||||
|
||||
// Accumulate transformation.
|
||||
|
||||
for (int k = 0; k < n; k++) {
|
||||
h = V[k][i+1];
|
||||
V[k][i+1] = s * V[k][i] + c * h;
|
||||
V[k][i] = c * V[k][i] - s * h;
|
||||
}
|
||||
}
|
||||
p = -s * s2 * c3 * el1 * e[l] / dl1;
|
||||
e[l] = s * p;
|
||||
d[l] = c * p;
|
||||
|
||||
// Check for convergence.
|
||||
|
||||
} while (Math.abs(e[l]) > eps*tst1);
|
||||
}
|
||||
d[l] = d[l] + f;
|
||||
e[l] = 0.0;
|
||||
}
|
||||
|
||||
// Sort eigenvalues and corresponding vectors.
|
||||
|
||||
for (int i = 0; i < n-1; i++) {
|
||||
int k = i;
|
||||
double p = d[i];
|
||||
for (int j = i+1; j < n; j++) {
|
||||
if (d[j] < p) {
|
||||
k = j;
|
||||
p = d[j];
|
||||
}
|
||||
}
|
||||
if (k != i) {
|
||||
d[k] = d[i];
|
||||
d[i] = p;
|
||||
for (int j = 0; j < n; j++) {
|
||||
p = V[j][i];
|
||||
V[j][i] = V[j][k];
|
||||
V[j][k] = p;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Nonsymmetric reduction to Hessenberg form.
|
||||
|
||||
private void orthes () {
|
||||
|
||||
// This is derived from the Algol procedures orthes and ortran,
|
||||
// by Martin and Wilkinson, Handbook for Auto. Comp.,
|
||||
// Vol.ii-Linear Algebra, and the corresponding
|
||||
// Fortran subroutines in EISPACK.
|
||||
|
||||
int low = 0;
|
||||
int high = n-1;
|
||||
|
||||
for (int m = low+1; m <= high-1; m++) {
|
||||
|
||||
// Scale column.
|
||||
|
||||
double scale = 0.0;
|
||||
for (int i = m; i <= high; i++) {
|
||||
scale = scale + Math.abs(H[i][m-1]);
|
||||
}
|
||||
if (scale != 0.0) {
|
||||
|
||||
// Compute Householder transformation.
|
||||
|
||||
double h = 0.0;
|
||||
for (int i = high; i >= m; i--) {
|
||||
ort[i] = H[i][m-1]/scale;
|
||||
h += ort[i] * ort[i];
|
||||
}
|
||||
double g = Math.sqrt(h);
|
||||
if (ort[m] > 0) {
|
||||
g = -g;
|
||||
}
|
||||
h = h - ort[m] * g;
|
||||
ort[m] = ort[m] - g;
|
||||
|
||||
// Apply Householder similarity transformation
|
||||
// H = (I-u*u'/h)*H*(I-u*u')/h)
|
||||
|
||||
for (int j = m; j < n; j++) {
|
||||
double f = 0.0;
|
||||
for (int i = high; i >= m; i--) {
|
||||
f += ort[i]*H[i][j];
|
||||
}
|
||||
f = f/h;
|
||||
for (int i = m; i <= high; i++) {
|
||||
H[i][j] -= f*ort[i];
|
||||
}
|
||||
}
|
||||
|
||||
for (int i = 0; i <= high; i++) {
|
||||
double f = 0.0;
|
||||
for (int j = high; j >= m; j--) {
|
||||
f += ort[j]*H[i][j];
|
||||
}
|
||||
f = f/h;
|
||||
for (int j = m; j <= high; j++) {
|
||||
H[i][j] -= f*ort[j];
|
||||
}
|
||||
}
|
||||
ort[m] = scale*ort[m];
|
||||
H[m][m-1] = scale*g;
|
||||
}
|
||||
}
|
||||
|
||||
// Accumulate transformations (Algol's ortran).
|
||||
|
||||
for (int i = 0; i < n; i++) {
|
||||
for (int j = 0; j < n; j++) {
|
||||
V[i][j] = (i == j ? 1.0 : 0.0);
|
||||
}
|
||||
}
|
||||
|
||||
for (int m = high-1; m >= low+1; m--) {
|
||||
if (H[m][m-1] != 0.0) {
|
||||
for (int i = m+1; i <= high; i++) {
|
||||
ort[i] = H[i][m-1];
|
||||
}
|
||||
for (int j = m; j <= high; j++) {
|
||||
double g = 0.0;
|
||||
for (int i = m; i <= high; i++) {
|
||||
g += ort[i] * V[i][j];
|
||||
}
|
||||
// Double division avoids possible underflow
|
||||
g = (g / ort[m]) / H[m][m-1];
|
||||
for (int i = m; i <= high; i++) {
|
||||
V[i][j] += g * ort[i];
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// Complex scalar division.
|
||||
|
||||
private transient double cdivr, cdivi;
|
||||
private void cdiv(double xr, double xi, double yr, double yi) {
|
||||
double r,d;
|
||||
if (Math.abs(yr) > Math.abs(yi)) {
|
||||
r = yi/yr;
|
||||
d = yr + r*yi;
|
||||
cdivr = (xr + r*xi)/d;
|
||||
cdivi = (xi - r*xr)/d;
|
||||
} else {
|
||||
r = yr/yi;
|
||||
d = yi + r*yr;
|
||||
cdivr = (r*xr + xi)/d;
|
||||
cdivi = (r*xi - xr)/d;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// Nonsymmetric reduction from Hessenberg to real Schur form.
|
||||
|
||||
private void hqr2 () {
|
||||
|
||||
// This is derived from the Algol procedure hqr2,
|
||||
// by Martin and Wilkinson, Handbook for Auto. Comp.,
|
||||
// Vol.ii-Linear Algebra, and the corresponding
|
||||
// Fortran subroutine in EISPACK.
|
||||
|
||||
// Initialize
|
||||
|
||||
int nn = this.n;
|
||||
int n = nn-1;
|
||||
int low = 0;
|
||||
int high = nn-1;
|
||||
double eps = Math.pow(2.0,-52.0);
|
||||
double exshift = 0.0;
|
||||
double p=0,q=0,r=0,s=0,z=0,t,w,x,y;
|
||||
|
||||
// Store roots isolated by balanc and compute matrix norm
|
||||
|
||||
double norm = 0.0;
|
||||
for (int i = 0; i < nn; i++) {
|
||||
if (i < low | i > high) {
|
||||
d[i] = H[i][i];
|
||||
e[i] = 0.0;
|
||||
}
|
||||
for (int j = Math.max(i-1,0); j < nn; j++) {
|
||||
norm = norm + Math.abs(H[i][j]);
|
||||
}
|
||||
}
|
||||
|
||||
// Outer loop over eigenvalue index
|
||||
|
||||
int iter = 0;
|
||||
while (n >= low) {
|
||||
|
||||
// Look for single small sub-diagonal element
|
||||
|
||||
int l = n;
|
||||
while (l > low) {
|
||||
s = Math.abs(H[l-1][l-1]) + Math.abs(H[l][l]);
|
||||
if (s == 0.0) {
|
||||
s = norm;
|
||||
}
|
||||
if (Math.abs(H[l][l-1]) < eps * s) {
|
||||
break;
|
||||
}
|
||||
l--;
|
||||
}
|
||||
|
||||
// Check for convergence
|
||||
// One root found
|
||||
|
||||
if (l == n) {
|
||||
H[n][n] = H[n][n] + exshift;
|
||||
d[n] = H[n][n];
|
||||
e[n] = 0.0;
|
||||
n--;
|
||||
iter = 0;
|
||||
|
||||
// Two roots found
|
||||
|
||||
} else if (l == n-1) {
|
||||
w = H[n][n-1] * H[n-1][n];
|
||||
p = (H[n-1][n-1] - H[n][n]) / 2.0;
|
||||
q = p * p + w;
|
||||
z = Math.sqrt(Math.abs(q));
|
||||
H[n][n] = H[n][n] + exshift;
|
||||
H[n-1][n-1] = H[n-1][n-1] + exshift;
|
||||
x = H[n][n];
|
||||
|
||||
// Real pair
|
||||
|
||||
if (q >= 0) {
|
||||
if (p >= 0) {
|
||||
z = p + z;
|
||||
} else {
|
||||
z = p - z;
|
||||
}
|
||||
d[n-1] = x + z;
|
||||
d[n] = d[n-1];
|
||||
if (z != 0.0) {
|
||||
d[n] = x - w / z;
|
||||
}
|
||||
e[n-1] = 0.0;
|
||||
e[n] = 0.0;
|
||||
x = H[n][n-1];
|
||||
s = Math.abs(x) + Math.abs(z);
|
||||
p = x / s;
|
||||
q = z / s;
|
||||
r = Math.sqrt(p * p+q * q);
|
||||
p = p / r;
|
||||
q = q / r;
|
||||
|
||||
// Row modification
|
||||
|
||||
for (int j = n-1; j < nn; j++) {
|
||||
z = H[n-1][j];
|
||||
H[n-1][j] = q * z + p * H[n][j];
|
||||
H[n][j] = q * H[n][j] - p * z;
|
||||
}
|
||||
|
||||
// Column modification
|
||||
|
||||
for (int i = 0; i <= n; i++) {
|
||||
z = H[i][n-1];
|
||||
H[i][n-1] = q * z + p * H[i][n];
|
||||
H[i][n] = q * H[i][n] - p * z;
|
||||
}
|
||||
|
||||
// Accumulate transformations
|
||||
|
||||
for (int i = low; i <= high; i++) {
|
||||
z = V[i][n-1];
|
||||
V[i][n-1] = q * z + p * V[i][n];
|
||||
V[i][n] = q * V[i][n] - p * z;
|
||||
}
|
||||
|
||||
// Complex pair
|
||||
|
||||
} else {
|
||||
d[n-1] = x + p;
|
||||
d[n] = x + p;
|
||||
e[n-1] = z;
|
||||
e[n] = -z;
|
||||
}
|
||||
n = n - 2;
|
||||
iter = 0;
|
||||
|
||||
// No convergence yet
|
||||
|
||||
} else {
|
||||
|
||||
// Form shift
|
||||
|
||||
x = H[n][n];
|
||||
y = 0.0;
|
||||
w = 0.0;
|
||||
if (l < n) {
|
||||
y = H[n-1][n-1];
|
||||
w = H[n][n-1] * H[n-1][n];
|
||||
}
|
||||
|
||||
// Wilkinson's original ad hoc shift
|
||||
|
||||
if (iter == 10) {
|
||||
exshift += x;
|
||||
for (int i = low; i <= n; i++) {
|
||||
H[i][i] -= x;
|
||||
}
|
||||
s = Math.abs(H[n][n-1]) + Math.abs(H[n-1][n-2]);
|
||||
x = y = 0.75 * s;
|
||||
w = -0.4375 * s * s;
|
||||
}
|
||||
|
||||
// MATLAB's new ad hoc shift
|
||||
|
||||
if (iter == 30) {
|
||||
s = (y - x) / 2.0;
|
||||
s = s * s + w;
|
||||
if (s > 0) {
|
||||
s = Math.sqrt(s);
|
||||
if (y < x) {
|
||||
s = -s;
|
||||
}
|
||||
s = x - w / ((y - x) / 2.0 + s);
|
||||
for (int i = low; i <= n; i++) {
|
||||
H[i][i] -= s;
|
||||
}
|
||||
exshift += s;
|
||||
x = y = w = 0.964;
|
||||
}
|
||||
}
|
||||
|
||||
iter = iter + 1; // (Could check iteration count here.)
|
||||
|
||||
// Look for two consecutive small sub-diagonal elements
|
||||
|
||||
int m = n-2;
|
||||
while (m >= l) {
|
||||
z = H[m][m];
|
||||
r = x - z;
|
||||
s = y - z;
|
||||
p = (r * s - w) / H[m+1][m] + H[m][m+1];
|
||||
q = H[m+1][m+1] - z - r - s;
|
||||
r = H[m+2][m+1];
|
||||
s = Math.abs(p) + Math.abs(q) + Math.abs(r);
|
||||
p = p / s;
|
||||
q = q / s;
|
||||
r = r / s;
|
||||
if (m == l) {
|
||||
break;
|
||||
}
|
||||
if (Math.abs(H[m][m-1]) * (Math.abs(q) + Math.abs(r)) <
|
||||
eps * (Math.abs(p) * (Math.abs(H[m-1][m-1]) + Math.abs(z) +
|
||||
Math.abs(H[m+1][m+1])))) {
|
||||
break;
|
||||
}
|
||||
m--;
|
||||
}
|
||||
|
||||
for (int i = m+2; i <= n; i++) {
|
||||
H[i][i-2] = 0.0;
|
||||
if (i > m+2) {
|
||||
H[i][i-3] = 0.0;
|
||||
}
|
||||
}
|
||||
|
||||
// Double QR step involving rows l:n and columns m:n
|
||||
|
||||
|
||||
for (int k = m; k <= n-1; k++) {
|
||||
boolean notlast = (k != n-1);
|
||||
if (k != m) {
|
||||
p = H[k][k-1];
|
||||
q = H[k+1][k-1];
|
||||
r = (notlast ? H[k+2][k-1] : 0.0);
|
||||
x = Math.abs(p) + Math.abs(q) + Math.abs(r);
|
||||
if (x == 0.0) {
|
||||
continue;
|
||||
}
|
||||
p = p / x;
|
||||
q = q / x;
|
||||
r = r / x;
|
||||
}
|
||||
|
||||
s = Math.sqrt(p * p + q * q + r * r);
|
||||
if (p < 0) {
|
||||
s = -s;
|
||||
}
|
||||
if (s != 0) {
|
||||
if (k != m) {
|
||||
H[k][k-1] = -s * x;
|
||||
} else if (l != m) {
|
||||
H[k][k-1] = -H[k][k-1];
|
||||
}
|
||||
p = p + s;
|
||||
x = p / s;
|
||||
y = q / s;
|
||||
z = r / s;
|
||||
q = q / p;
|
||||
r = r / p;
|
||||
|
||||
// Row modification
|
||||
|
||||
for (int j = k; j < nn; j++) {
|
||||
p = H[k][j] + q * H[k+1][j];
|
||||
if (notlast) {
|
||||
p = p + r * H[k+2][j];
|
||||
H[k+2][j] = H[k+2][j] - p * z;
|
||||
}
|
||||
H[k][j] = H[k][j] - p * x;
|
||||
H[k+1][j] = H[k+1][j] - p * y;
|
||||
}
|
||||
|
||||
// Column modification
|
||||
|
||||
for (int i = 0; i <= Math.min(n,k+3); i++) {
|
||||
p = x * H[i][k] + y * H[i][k+1];
|
||||
if (notlast) {
|
||||
p = p + z * H[i][k+2];
|
||||
H[i][k+2] = H[i][k+2] - p * r;
|
||||
}
|
||||
H[i][k] = H[i][k] - p;
|
||||
H[i][k+1] = H[i][k+1] - p * q;
|
||||
}
|
||||
|
||||
// Accumulate transformations
|
||||
|
||||
for (int i = low; i <= high; i++) {
|
||||
p = x * V[i][k] + y * V[i][k+1];
|
||||
if (notlast) {
|
||||
p = p + z * V[i][k+2];
|
||||
V[i][k+2] = V[i][k+2] - p * r;
|
||||
}
|
||||
V[i][k] = V[i][k] - p;
|
||||
V[i][k+1] = V[i][k+1] - p * q;
|
||||
}
|
||||
} // (s != 0)
|
||||
} // k loop
|
||||
} // check convergence
|
||||
} // while (n >= low)
|
||||
|
||||
// Backsubstitute to find vectors of upper triangular form
|
||||
|
||||
if (norm == 0.0) {
|
||||
return;
|
||||
}
|
||||
|
||||
for (n = nn-1; n >= 0; n--) {
|
||||
p = d[n];
|
||||
q = e[n];
|
||||
|
||||
// Real vector
|
||||
|
||||
if (q == 0) {
|
||||
int l = n;
|
||||
H[n][n] = 1.0;
|
||||
for (int i = n-1; i >= 0; i--) {
|
||||
w = H[i][i] - p;
|
||||
r = 0.0;
|
||||
for (int j = l; j <= n; j++) {
|
||||
r = r + H[i][j] * H[j][n];
|
||||
}
|
||||
if (e[i] < 0.0) {
|
||||
z = w;
|
||||
s = r;
|
||||
} else {
|
||||
l = i;
|
||||
if (e[i] == 0.0) {
|
||||
if (w != 0.0) {
|
||||
H[i][n] = -r / w;
|
||||
} else {
|
||||
H[i][n] = -r / (eps * norm);
|
||||
}
|
||||
|
||||
// Solve real equations
|
||||
|
||||
} else {
|
||||
x = H[i][i+1];
|
||||
y = H[i+1][i];
|
||||
q = (d[i] - p) * (d[i] - p) + e[i] * e[i];
|
||||
t = (x * s - z * r) / q;
|
||||
H[i][n] = t;
|
||||
if (Math.abs(x) > Math.abs(z)) {
|
||||
H[i+1][n] = (-r - w * t) / x;
|
||||
} else {
|
||||
H[i+1][n] = (-s - y * t) / z;
|
||||
}
|
||||
}
|
||||
|
||||
// Overflow control
|
||||
|
||||
t = Math.abs(H[i][n]);
|
||||
if ((eps * t) * t > 1) {
|
||||
for (int j = i; j <= n; j++) {
|
||||
H[j][n] = H[j][n] / t;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Complex vector
|
||||
|
||||
} else if (q < 0) {
|
||||
int l = n-1;
|
||||
|
||||
// Last vector component imaginary so matrix is triangular
|
||||
|
||||
if (Math.abs(H[n][n-1]) > Math.abs(H[n-1][n])) {
|
||||
H[n-1][n-1] = q / H[n][n-1];
|
||||
H[n-1][n] = -(H[n][n] - p) / H[n][n-1];
|
||||
} else {
|
||||
cdiv(0.0,-H[n-1][n],H[n-1][n-1]-p,q);
|
||||
H[n-1][n-1] = cdivr;
|
||||
H[n-1][n] = cdivi;
|
||||
}
|
||||
H[n][n-1] = 0.0;
|
||||
H[n][n] = 1.0;
|
||||
for (int i = n-2; i >= 0; i--) {
|
||||
double ra,sa,vr,vi;
|
||||
ra = 0.0;
|
||||
sa = 0.0;
|
||||
for (int j = l; j <= n; j++) {
|
||||
ra = ra + H[i][j] * H[j][n-1];
|
||||
sa = sa + H[i][j] * H[j][n];
|
||||
}
|
||||
w = H[i][i] - p;
|
||||
|
||||
if (e[i] < 0.0) {
|
||||
z = w;
|
||||
r = ra;
|
||||
s = sa;
|
||||
} else {
|
||||
l = i;
|
||||
if (e[i] == 0) {
|
||||
cdiv(-ra,-sa,w,q);
|
||||
H[i][n-1] = cdivr;
|
||||
H[i][n] = cdivi;
|
||||
} else {
|
||||
|
||||
// Solve complex equations
|
||||
|
||||
x = H[i][i+1];
|
||||
y = H[i+1][i];
|
||||
vr = (d[i] - p) * (d[i] - p) + e[i] * e[i] - q * q;
|
||||
vi = (d[i] - p) * 2.0 * q;
|
||||
if (vr == 0.0 & vi == 0.0) {
|
||||
vr = eps * norm * (Math.abs(w) + Math.abs(q) +
|
||||
Math.abs(x) + Math.abs(y) + Math.abs(z));
|
||||
}
|
||||
cdiv(x*r-z*ra+q*sa,x*s-z*sa-q*ra,vr,vi);
|
||||
H[i][n-1] = cdivr;
|
||||
H[i][n] = cdivi;
|
||||
if (Math.abs(x) > (Math.abs(z) + Math.abs(q))) {
|
||||
H[i+1][n-1] = (-ra - w * H[i][n-1] + q * H[i][n]) / x;
|
||||
H[i+1][n] = (-sa - w * H[i][n] - q * H[i][n-1]) / x;
|
||||
} else {
|
||||
cdiv(-r-y*H[i][n-1],-s-y*H[i][n],z,q);
|
||||
H[i+1][n-1] = cdivr;
|
||||
H[i+1][n] = cdivi;
|
||||
}
|
||||
}
|
||||
|
||||
// Overflow control
|
||||
|
||||
t = Math.max(Math.abs(H[i][n-1]),Math.abs(H[i][n]));
|
||||
if ((eps * t) * t > 1) {
|
||||
for (int j = i; j <= n; j++) {
|
||||
H[j][n-1] = H[j][n-1] / t;
|
||||
H[j][n] = H[j][n] / t;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Vectors of isolated roots
|
||||
|
||||
for (int i = 0; i < nn; i++) {
|
||||
if (i < low | i > high) {
|
||||
for (int j = i; j < nn; j++) {
|
||||
V[i][j] = H[i][j];
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Back transformation to get eigenvectors of original matrix
|
||||
|
||||
for (int j = nn-1; j >= low; j--) {
|
||||
for (int i = low; i <= high; i++) {
|
||||
z = 0.0;
|
||||
for (int k = low; k <= Math.min(j,high); k++) {
|
||||
z = z + V[i][k] * H[k][j];
|
||||
}
|
||||
V[i][j] = z;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/* ------------------------
|
||||
Constructor
|
||||
* ------------------------ */
|
||||
|
||||
/** Check for symmetry, then construct the eigenvalue decomposition
|
||||
Structure to access D and V.
|
||||
@param Arg Square matrix
|
||||
*/
|
||||
|
||||
public EigenvalueDecomposition (Matrix Arg) {
|
||||
double[][] A = Arg.getD();
|
||||
n = Arg.getN();
|
||||
V = new double[n][n];
|
||||
d = new double[n];
|
||||
e = new double[n];
|
||||
|
||||
issymmetric = true;
|
||||
for (int j = 0; (j < n) & issymmetric; j++) {
|
||||
for (int i = 0; (i < n) & issymmetric; i++) {
|
||||
issymmetric = (A[i][j] == A[j][i]);
|
||||
}
|
||||
}
|
||||
|
||||
if (issymmetric) {
|
||||
for (int i = 0; i < n; i++) {
|
||||
for (int j = 0; j < n; j++) {
|
||||
V[i][j] = A[i][j];
|
||||
}
|
||||
}
|
||||
|
||||
// Tridiagonalize.
|
||||
tred2();
|
||||
|
||||
// Diagonalize.
|
||||
tql2();
|
||||
|
||||
} else {
|
||||
H = new double[n][n];
|
||||
ort = new double[n];
|
||||
|
||||
for (int j = 0; j < n; j++) {
|
||||
for (int i = 0; i < n; i++) {
|
||||
H[i][j] = A[i][j];
|
||||
}
|
||||
}
|
||||
|
||||
// Reduce to Hessenberg form.
|
||||
orthes();
|
||||
|
||||
// Reduce Hessenberg to real Schur form.
|
||||
hqr2();
|
||||
}
|
||||
}
|
||||
|
||||
/* ------------------------
|
||||
Public Methods
|
||||
* ------------------------ */
|
||||
|
||||
/**
|
||||
* Return the eigenvector matrix
|
||||
* @return V
|
||||
*/
|
||||
public Matrix getV () {
|
||||
return new Matrix(V);
|
||||
}
|
||||
|
||||
/**
|
||||
* Return the real parts of the eigenvalues
|
||||
* @return real(diag(D))
|
||||
*/
|
||||
public double[] getRealEigenvalues(){
|
||||
return d;
|
||||
}
|
||||
|
||||
/**
|
||||
* Return the imaginary parts of the eigenvalues
|
||||
* @return imag(diag(D))
|
||||
*/
|
||||
public double[] getImagEigenvalues(){
|
||||
return e;
|
||||
}
|
||||
|
||||
/**
|
||||
* Return the block diagonal eigenvalue matrix
|
||||
* @return D
|
||||
*/
|
||||
public Matrix getD(){
|
||||
int i, j;
|
||||
Matrix D = new Matrix(n,n);
|
||||
for(i=0; i<n; i++) {
|
||||
for(j=0; j<n; j++)
|
||||
D.set(i, j, 0.0);
|
||||
D.set(i, i, d[i]);
|
||||
if(e[i] > 0)
|
||||
D.set(i, i+1, e[i]);
|
||||
else if (e[i] < 0)
|
||||
D.set(i, i-1, e[i]);
|
||||
}
|
||||
return D;
|
||||
}
|
||||
}
|
||||
282
src/math/matrix/LUDecomposition.java
Normal file
282
src/math/matrix/LUDecomposition.java
Normal file
@@ -0,0 +1,282 @@
|
||||
package math.matrix;
|
||||
|
||||
import java.io.Serializable;
|
||||
|
||||
/**
|
||||
* LU Decomposition.
|
||||
* <P>
|
||||
* For an m-by-n matrix A with m ≥ n, the LU decomposition is an m-by-n
|
||||
* unit lower triangular matrix L, an n-by-n upper triangular matrix U,
|
||||
* and a permutation vector piv of length m so that A(piv,:) = L*U.
|
||||
* If m < n, then L is m-by-m and U is m-by-n.
|
||||
* <P>
|
||||
* The LU decompostion with pivoting always exists, even if the matrix is
|
||||
* singular, so the constructor will never fail. The primary use of the
|
||||
* LU decomposition is in the solution of square systems of simultaneous
|
||||
* linear equations. This will fail if isNonsingular() returns false.
|
||||
*/
|
||||
public class LUDecomposition implements Serializable {
|
||||
|
||||
/**
|
||||
* UID
|
||||
*/
|
||||
private static final long serialVersionUID = -3852210156107961377L;
|
||||
|
||||
/**
|
||||
* Array for internal storage of decomposition.
|
||||
* @serial internal array storage
|
||||
*/
|
||||
private double[][] LU;
|
||||
|
||||
/**
|
||||
* @serial row dimension
|
||||
*/
|
||||
private int m;
|
||||
|
||||
/**
|
||||
* @serial column dimension
|
||||
*/
|
||||
private int n;
|
||||
|
||||
/**
|
||||
* @serial pivot sign
|
||||
*/
|
||||
private int pivsign;
|
||||
|
||||
/**
|
||||
* Internal storage of pivot vector.
|
||||
* @serial pivot vector.
|
||||
*/
|
||||
private int[] piv;
|
||||
|
||||
/**
|
||||
* LU Decomposition
|
||||
* Structure to access L, U and piv.
|
||||
* @param A Rectangular matrix
|
||||
*/
|
||||
public LUDecomposition(Matrix A){
|
||||
int i, j, k;
|
||||
|
||||
// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
|
||||
LU = A.getCopy();
|
||||
m = A.getM();
|
||||
n = A.getN();
|
||||
piv = new int[m];
|
||||
for(i=0; i<m; i++)
|
||||
piv[i] = i;
|
||||
pivsign = 1;
|
||||
double[] LUrowi;
|
||||
double[] LUcolj = new double[m];
|
||||
|
||||
// Outer loop.
|
||||
for(j=0; j<n; j++){
|
||||
// Make a copy of the j-th column to localize references.
|
||||
for(i=0; i<m; i++)
|
||||
LUcolj[i] = LU[i][j];
|
||||
// Apply previous transformations.
|
||||
for(i=0; i<m; i++){
|
||||
LUrowi = LU[i];
|
||||
// Most of the time is spent in the following dot product.
|
||||
int kmax = Math.min(i,j);
|
||||
double s = 0.0;
|
||||
for(k=0; k<kmax; k++)
|
||||
s += LUrowi[k]*LUcolj[k];
|
||||
LUrowi[j] = LUcolj[i] -= s;
|
||||
}
|
||||
// Find pivot and exchange if necessary.
|
||||
int p = j;
|
||||
for(i=j+1; i<m; i++)
|
||||
if(Math.abs(LUcolj[i]) > Math.abs(LUcolj[p]))
|
||||
p = i;
|
||||
if(p!=j){
|
||||
for(k=0; k<n; k++) {
|
||||
double t = LU[p][k];
|
||||
LU[p][k] = LU[j][k];
|
||||
LU[j][k] = t;
|
||||
}
|
||||
k = piv[p];
|
||||
piv[p] = piv[j];
|
||||
piv[j] = k;
|
||||
pivsign = -pivsign;
|
||||
}
|
||||
// Compute multipliers.
|
||||
if(j<m & LU[j][j] != 0.0)
|
||||
for(i=j+1; i<m; i++)
|
||||
LU[i][j] /= LU[j][j];
|
||||
}
|
||||
}
|
||||
|
||||
/* ------------------------
|
||||
Temporary, experimental code.
|
||||
------------------------ */
|
||||
|
||||
/** LU Decomposition, computed by Gaussian elimination.
|
||||
<P>
|
||||
This constructor computes L and U with the "daxpy"-based elimination
|
||||
algorithm used in LINPACK and MATLAB. In Java, we suspect the dot-product,
|
||||
Crout algorithm will be faster. We have temporarily included this
|
||||
constructor until timing experiments confirm this suspicion.
|
||||
<P>
|
||||
Structure to access L, U and piv.
|
||||
@param A Rectangular matrix
|
||||
@param linpackflag Use Gaussian elimination. Actual value ignored.
|
||||
*/
|
||||
public LUDecomposition(Matrix A, int linpackflag){
|
||||
int i, j, k;
|
||||
// Initialize.
|
||||
LU = A.getCopy();
|
||||
m = A.getM();
|
||||
n = A.getN();
|
||||
piv = new int[m];
|
||||
for(i=0; i<m; i++)
|
||||
piv[i] = i;
|
||||
pivsign = 1;
|
||||
// Main loop.
|
||||
for(k=0; k<n; k++){
|
||||
// Find pivot.
|
||||
int p = k;
|
||||
for(i=k+1; i<m; i++)
|
||||
if(Math.abs(LU[i][k]) > Math.abs(LU[p][k]))
|
||||
p = i;
|
||||
// Exchange if necessary.
|
||||
if(p != k) {
|
||||
for(j=0; j<n; j++){
|
||||
double t = LU[p][j]; LU[p][j] = LU[k][j]; LU[k][j] = t;
|
||||
}
|
||||
int t = piv[p]; piv[p] = piv[k]; piv[k] = t;
|
||||
pivsign = -pivsign;
|
||||
}
|
||||
// Compute multipliers and eliminate k-th column.
|
||||
if(LU[k][k] != 0.0)
|
||||
for(i=k+1; i<m; i++){
|
||||
LU[i][k] /= LU[k][k];
|
||||
for(j=k+1; j<n; j++)
|
||||
LU[i][j] -= LU[i][k]*LU[k][j];
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* ------------------------
|
||||
End of temporary code.
|
||||
* ------------------------ */
|
||||
|
||||
|
||||
/**
|
||||
* Is the matrix nonsingular?
|
||||
* @return true if U, and hence A, is nonsingular.
|
||||
*/
|
||||
public boolean isNonsingular (){
|
||||
int j;
|
||||
for(j=0; j<n; j++)
|
||||
if(LU[j][j] == 0)
|
||||
return false;
|
||||
return true;
|
||||
}
|
||||
|
||||
/**
|
||||
* Return lower triangular factor
|
||||
* @return L
|
||||
*/
|
||||
public Matrix getL(){
|
||||
int i, j;
|
||||
Matrix X = new Matrix(m,n);
|
||||
double[][] L = X.getD();
|
||||
for(i=0; i<m; i++){
|
||||
for(j=0; j<n; j++){
|
||||
if(i>j)
|
||||
L[i][j] = LU[i][j];
|
||||
else if(i==j)
|
||||
L[i][j] = 1.0;
|
||||
else
|
||||
L[i][j] = 0.0;
|
||||
}
|
||||
}
|
||||
return X;
|
||||
}
|
||||
|
||||
/**
|
||||
* Return upper triangular factor
|
||||
* @return U
|
||||
*/
|
||||
public Matrix getU(){
|
||||
int i, j;
|
||||
Matrix X = new Matrix(n,n);
|
||||
double[][] U = X.getD();
|
||||
for(i=0; i<n; i++){
|
||||
for(j=0; j<n; j++){
|
||||
if(i<=j)
|
||||
U[i][j] = LU[i][j];
|
||||
else
|
||||
U[i][j] = 0.0;
|
||||
}
|
||||
}
|
||||
return X;
|
||||
}
|
||||
|
||||
/**
|
||||
* Return pivot permutation vector
|
||||
* @return piv
|
||||
*/
|
||||
public int[] getPivot(){
|
||||
int i;
|
||||
int[] p = new int[m];
|
||||
for(i=0; i<m; i++)
|
||||
p[i] = piv[i];
|
||||
return p;
|
||||
}
|
||||
|
||||
/**
|
||||
* Return pivot permutation vector as a one-dimensional double array
|
||||
* @return piv
|
||||
*/
|
||||
public double[] getDoublePivot(){
|
||||
int i;
|
||||
double[] vals = new double[m];
|
||||
for(i=0; i<m; i++)
|
||||
vals[i] = (double) piv[i];
|
||||
return vals;
|
||||
}
|
||||
|
||||
/**
|
||||
* Determinant
|
||||
* @return det(A)
|
||||
* @exception IllegalArgumentException Matrix must be square
|
||||
*/
|
||||
public double det(){
|
||||
int j;
|
||||
if(m != n) throw new IllegalArgumentException("Matrix must be square.");
|
||||
double d = (double) pivsign;
|
||||
for(j=0; j<n; j++)
|
||||
d *= LU[j][j];
|
||||
return d;
|
||||
}
|
||||
|
||||
/**
|
||||
* Solve A*X = B
|
||||
* @param B A Matrix with as many rows as A and any number of columns.
|
||||
* @return X so that L*U*X = B(piv,:)
|
||||
* @exception IllegalArgumentException Matrix row dimensions must agree.
|
||||
* @exception RuntimeException Matrix is singular.
|
||||
*/
|
||||
public Matrix solve (Matrix B) {
|
||||
if(B.getM() != m) throw new IllegalArgumentException("Matrix row dimensions must agree.");
|
||||
if(!this.isNonsingular()) throw new RuntimeException("Matrix is singular.");
|
||||
int i, j, k;
|
||||
// Copy right hand side with pivoting
|
||||
int nx = B.getN();
|
||||
double[][] X = B.get(piv,0,nx-1).getD();
|
||||
// Solve L*Y = B(piv,:)
|
||||
for(k=0; k<n; k++)
|
||||
for(i=k+1; i<n; i++)
|
||||
for(j=0; j<nx; j++)
|
||||
X[i][j] -= X[k][j]*LU[i][k];
|
||||
// Solve U*X = Y;
|
||||
for(k=n-1; k>=0; k--)
|
||||
for(j=0; j<nx; j++)
|
||||
X[k][j] /= LU[k][k];
|
||||
for(i=0; i<k; i++)
|
||||
for(j=0; j<nx; j++)
|
||||
X[i][j] -= X[k][j]*LU[i][k];
|
||||
return new Matrix(X);
|
||||
}
|
||||
}
|
||||
334
src/math/matrix/Matrix2D.java
Normal file
334
src/math/matrix/Matrix2D.java
Normal file
@@ -0,0 +1,334 @@
|
||||
package math.matrix;
|
||||
|
||||
import math.Maths;
|
||||
import math.equation.Polynomial;
|
||||
import stdlib.StdDraw;
|
||||
import exception.ComplexException;
|
||||
import exception.IllegalDimensionException;
|
||||
import exception.NoSquareException;
|
||||
import exception.SingularException;
|
||||
|
||||
/**
|
||||
* Matrix 2xn, m is always 2
|
||||
* @author Daniel
|
||||
*
|
||||
*/
|
||||
public class Matrix2D extends Matrix{
|
||||
|
||||
/**
|
||||
* UID
|
||||
*/
|
||||
private static final long serialVersionUID = 2228035464656481002L;
|
||||
|
||||
/**
|
||||
* Create an null matrix.
|
||||
*/
|
||||
public Matrix2D(){
|
||||
super();
|
||||
}
|
||||
|
||||
/**
|
||||
* Create an 2-by-n matrix with zeros.
|
||||
* @param n number of columns
|
||||
*/
|
||||
public Matrix2D(int n){
|
||||
super(2,n);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create an 2-by-n matrix based on a 2d array.
|
||||
* @param a 2d double array
|
||||
*/
|
||||
public Matrix2D(double[][] a){
|
||||
super(a);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create an 2-by-2 matrix based on a 2d array.
|
||||
* @param a11
|
||||
* @param a12
|
||||
* @param a21
|
||||
* @param a22
|
||||
*/
|
||||
public Matrix2D(double a11, double a12, double a21, double a22){
|
||||
super(2,2);
|
||||
set(0,0,a11);
|
||||
set(0,1,a12);
|
||||
set(1,0,a21);
|
||||
set(1,1,a22);
|
||||
}
|
||||
|
||||
public Matrix2D(Matrix B){
|
||||
super(B);
|
||||
}
|
||||
|
||||
/**
|
||||
* Set the matrix with given vector at given row
|
||||
* @param i row
|
||||
* @param x value
|
||||
* @param y value
|
||||
* @return filled matrix
|
||||
*/
|
||||
public Matrix set(int i, double x, double y){
|
||||
set(0, i, x);
|
||||
set(1, i, y);
|
||||
return this;
|
||||
}
|
||||
|
||||
/**
|
||||
* Rotation by ϑ degrees counterclockwise or -ϑ degrees clockwise.
|
||||
* @param ϑ in degrees
|
||||
* @return 2d rotated matrix
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix2D rotate(double ϑ) throws IllegalDimensionException{
|
||||
if(!isM2()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return (Matrix2D) TensorII2D.rotation(ϑ).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* Rotation by 45 degrees counterclockwise
|
||||
* @return 2d rotated matrix
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix2D rotate45() throws IllegalDimensionException{
|
||||
if(!isM2()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return (Matrix2D) new Matrix2D(new double[][]{{1,-1},{1,1}}).times(Math.sqrt(2)/2,this);
|
||||
}
|
||||
|
||||
/**
|
||||
* Rotation by 90 degrees counterclockwise
|
||||
* @return 2d rotated matrix
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix2D rotate90() throws IllegalDimensionException{
|
||||
if(!isM2()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return (Matrix2D) new Matrix2D(new double[][]{{0,-1},{1,0}}).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* Rotation by 180 degrees counterclockwise
|
||||
* @return 2d rotated matrix
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix2D rotate180() throws IllegalDimensionException{
|
||||
if(!isM2()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return (Matrix2D) new Matrix2D(new double[][]{{-1,0},{0,-1}}).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* Rotation by 270 degrees counterclockwise or 90 degrees clockwise.
|
||||
* @return 2d rotated matrix
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix2D rotate270() throws IllegalDimensionException{
|
||||
if(!isM2()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return (Matrix2D) new Matrix2D(new double[][]{{-1,0},{0,-1}}).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* Reflection against the x axis
|
||||
* @return matrix reflected against the x axis
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix2D flipVertical() throws IllegalDimensionException{
|
||||
if(!isR2()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return (Matrix2D) new Matrix2D(new double[][]{{1,0},{0,-1}}).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* Reflection against the y axis.
|
||||
* @return matrix reflected against the y axis
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix2D flipHoriontal() throws IllegalDimensionException{
|
||||
if(!isR2()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return (Matrix2D) new Matrix2D(new double[][]{{-1,0},{0,1}}).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* Reflection against the x and y axis.
|
||||
* @return matrix reflected against the x and y axis
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix2D flipBoth() throws IllegalDimensionException{
|
||||
if(!isR2()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return rotate180();
|
||||
}
|
||||
|
||||
/**
|
||||
* Horizontal shear.
|
||||
* @param s shear factor
|
||||
* @return horizontal sheared matrix
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix2D shearHorizontal(double s) throws IllegalDimensionException{
|
||||
if(!isR2()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return (Matrix2D) new Matrix2D(new double[][]{{1,s},{0,1}}).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* Vertical shear
|
||||
* @param s shear factor
|
||||
* @return vertical sheared matrix
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix2D shearVertical(double s) throws IllegalDimensionException{
|
||||
if(!isR2()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return (Matrix2D) new Matrix2D(new double[][]{{1,0},{s,1}}).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* @param s scalar
|
||||
* @return squeezed matrix
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix2D squeezeMapping(double s) throws IllegalDimensionException{
|
||||
if(!isR2()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return (Matrix2D) new Matrix2D(new double[][]{{s,0},{0,1/s}}).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* Projection onto the x axis
|
||||
* @return matrix projected onto the x axis
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix2D projectionToX() throws IllegalDimensionException{
|
||||
if(!isR2()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return (Matrix2D) new Matrix2D(new double[][]{{1,0},{0,0}}).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* Projection onto the y axis
|
||||
* @return matrix projected onto the y
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix2D projectionToY() throws IllegalDimensionException{
|
||||
if(!isR2()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return (Matrix2D) new Matrix2D(new double[][]{{0,0},{0,1}}).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* @return Mirror matrix (orthogonal). Mirrored vector due to a plane defined through a vector v.
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public static Matrix2D mirror(Vector v) throws IllegalDimensionException{
|
||||
// P = I - alpha v v'; alpha = 2 / (v'v)
|
||||
return (Matrix2D) Diagonal2D.identity(v.n()).minus(v.tensorProduct(v).times(2/v.dot(v)));
|
||||
}
|
||||
|
||||
/**
|
||||
* Real eigenvalue calculated with the root formula of second and third degree.
|
||||
* @return eigenvalues λ<sub>i</sub>
|
||||
* @throws NoSquareException
|
||||
* @throws IllegalDimensionException
|
||||
* @throws ComplexException
|
||||
*/
|
||||
public Vector2D eigenvaluesRe(int analytic) throws NoSquareException, IllegalDimensionException, ComplexException{
|
||||
// TODO: also Imaginary
|
||||
if(m!=n && m!=2) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
// A = [ a, b; c, d]
|
||||
// det| a-l, b; c, d-l| = l^2 - tr(A)*l + det (A)
|
||||
Polynomial p = new Polynomial(1,-trace(),det(analytic));
|
||||
return new Vector2D(p.rootsRe());
|
||||
}
|
||||
|
||||
/**
|
||||
* @return eigenvectors x<sub>i</sub> in matrix Λ
|
||||
* @throws IllegalDimensionException
|
||||
* @throws NoSquareException
|
||||
* @throws ComplexException
|
||||
*/
|
||||
public Matrix2D eigenvectors(int analytic) throws NoSquareException, IllegalDimensionException, ComplexException{
|
||||
Vector lambda = eigenvaluesRe(analytic);
|
||||
Matrix2D S = new Matrix2D();
|
||||
if(isR2()){
|
||||
Matrix2D Al;
|
||||
Vector2D x = new Vector2D();
|
||||
int i;
|
||||
double a1, a2;
|
||||
for(i=0;i<2;i++){
|
||||
Al = (Matrix2D) this.minus(Matrix.identity(2).times(lambda.get(i)));
|
||||
a2 = Al.get(1, 0);
|
||||
a1 = -Al.get(1, 1); // to the other side: a1*x1 = -a2*x2
|
||||
if(a1 == 0 && a2 == 0){
|
||||
a2 = Al.get(0, 0);
|
||||
a1 = -Al.get(0, 1); // to the other side: a1*x1 = -a2*x2
|
||||
if(a2 > 0){
|
||||
x.set(0, a1);
|
||||
x.set(1, a2);
|
||||
} else {
|
||||
x.set(0, -a1);
|
||||
x.set(1, -a2);
|
||||
}
|
||||
} else
|
||||
if(a2 > 0){
|
||||
x.set(0, a1);
|
||||
x.set(1, a2);
|
||||
} else {
|
||||
x.set(0, -a1);
|
||||
x.set(1, -a2);
|
||||
}
|
||||
S.setN(i, x.normalize());
|
||||
}
|
||||
}
|
||||
return S;
|
||||
}
|
||||
|
||||
public void plot() throws IllegalDimensionException{
|
||||
if(!isR2()) throw new IllegalDimensionException();
|
||||
StdDraw sd = new StdDraw();
|
||||
double maxM0 = Maths.sumAbs(getM(0).getArray());
|
||||
double maxM1 = Maths.sumAbs(getM(1).getArray());
|
||||
double maxN0 = Maths.sumAbs(getN(0).getArray());
|
||||
double maxN1 = Maths.sumAbs(getN(1).getArray());
|
||||
double max = Maths.max(maxM0,maxM1,maxN0,maxN1);
|
||||
sd.setScale(-max, max);
|
||||
StdDraw.polygon(
|
||||
new double[]{0,get(0,0),get(0,0)+get(0,1),get(0,1)},
|
||||
new double[]{0,get(1,0),get(1,0)+get(1,1),get(1,1)});
|
||||
StdDraw.filledPolygon(
|
||||
new double[]{0,get(0,0),get(0,0)+get(0,1),get(0,1)},
|
||||
new double[]{0,get(1,0),get(1,0)+get(1,1),get(1,1)});
|
||||
}
|
||||
|
||||
public static void main(String[] args) {
|
||||
Matrix2D a = new Matrix2D(0,1,1,0);
|
||||
try {
|
||||
Matrix b = new Matrix2D(new double[][]{{0,-1},{1,0}}).times(a);
|
||||
System.out.println(b);
|
||||
// System.out.println((Matrix2D) b);
|
||||
|
||||
Matrix2D P = new Matrix2D(new double[][]{ { 1 }, { 1 } });
|
||||
System.out.println(P.setName("P"));
|
||||
System.out.println("rot(P,45°) = \n" + P.rotate(45));
|
||||
|
||||
Vector2D v = new Vector2D(1,1);
|
||||
Vector2D w = new Vector2D(0,1);
|
||||
System.out.println(Diagonal2D.identity(v.n()));
|
||||
P = (Matrix2D) Matrix2D.mirror(v);
|
||||
System.out.println("Pw = ");
|
||||
P.times(w).println();
|
||||
|
||||
Matrix A = new Matrix2D(new double[][]{ { 2, 1 }, { 0, 1 } });
|
||||
System.out.println(A.setName("A"));
|
||||
Matrix B = A.transpose().times(A);
|
||||
System.out.println("A'A = \n" + B);
|
||||
Matrix X = B.eigenvectors();
|
||||
System.out.println("X = \n" + X);
|
||||
System.out.println("X'A'A = \n" + X.transpose().times(B));
|
||||
Matrix L2 = X.transpose().times(B).times(X);
|
||||
System.out.println("L^2 = X'A'AX = \n" + L2);
|
||||
Matrix L = L2.times(new Matrix(new double[][]{ { 1/Math.sqrt(L2.get(0, 0)), 0 }, { 0, 1/Math.sqrt(L2.get(1, 1)) } }));
|
||||
System.out.println("L = \n" + L);
|
||||
Matrix S = X.times(L).times(X);
|
||||
System.out.println("S = XLX' = \n" + S);
|
||||
Matrix2D Q = (Matrix2D) A.times(S.inverse());
|
||||
System.out.println("Q = AS^-1 = \n" + Q);
|
||||
Q.plot();
|
||||
} catch (IllegalDimensionException | SingularException e) {
|
||||
e.printStackTrace();
|
||||
}
|
||||
}
|
||||
|
||||
}
|
||||
193
src/math/matrix/Matrix3D.java
Normal file
193
src/math/matrix/Matrix3D.java
Normal file
@@ -0,0 +1,193 @@
|
||||
package math.matrix;
|
||||
|
||||
import math.Maths;
|
||||
import math.equation.Polynomial;
|
||||
import exception.ComplexException;
|
||||
import exception.IllegalDimensionException;
|
||||
import exception.NoSquareException;
|
||||
|
||||
|
||||
public class Matrix3D extends Matrix{
|
||||
/**
|
||||
* UID
|
||||
*/
|
||||
private static final long serialVersionUID = 2505785127150028971L;
|
||||
|
||||
/**
|
||||
* Create an null matrix.
|
||||
*/
|
||||
public Matrix3D(){
|
||||
super();
|
||||
}
|
||||
|
||||
/**
|
||||
* Create an 3-by-n matrix with zeros.
|
||||
* @param n number of columns
|
||||
*/
|
||||
public Matrix3D(int n){
|
||||
super(3,n);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create an 3-by-3 matrix based on components.
|
||||
* @param a11
|
||||
* @param a12
|
||||
* @param a13
|
||||
* @param a21
|
||||
* @param a22
|
||||
* @param a23
|
||||
* @param a31
|
||||
* @param a32
|
||||
* @param a33
|
||||
*/
|
||||
public Matrix3D(double a11, double a12, double a13,
|
||||
double a21, double a22, double a23,
|
||||
double a31, double a32, double a33){
|
||||
super(3,3);
|
||||
set(0,0,a11);
|
||||
set(0,1,a12);
|
||||
set(0,2,a13);
|
||||
set(1,0,a21);
|
||||
set(1,1,a22);
|
||||
set(1,2,a23);
|
||||
set(2,0,a31);
|
||||
set(2,1,a32);
|
||||
set(2,2,a33);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create an 3-by-3 matrix based on a 2d array.
|
||||
* @param a 3d double array
|
||||
*/
|
||||
public Matrix3D(double[][] a){
|
||||
super(a);
|
||||
}
|
||||
|
||||
public Matrix3D(Matrix B){
|
||||
super(B);
|
||||
}
|
||||
|
||||
/**
|
||||
* 3d rotation around unit vector u by ϑ degrees counterclockwise or
|
||||
* clockwise with negative degrees for a right-hand system.
|
||||
* @param ϑ in degrees
|
||||
* @param u unit vector
|
||||
* @return 3d rotated matrix
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix3D rotate(double ϑ, double[] u) throws IllegalDimensionException{
|
||||
if(!isR3() && u.length == 3) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
// TODO: verify
|
||||
double u1 = u[0], u2 = u[1], u3 = u[2];
|
||||
return (Matrix3D) new Matrix3D(new double[][]{
|
||||
{u1*u1*(1-Maths.cosd(ϑ))+Maths.cosd(ϑ),
|
||||
u1*u2*(1-Maths.cosd(ϑ))-u3*Maths.sind(ϑ),
|
||||
u1*u3*(1-Maths.cosd(ϑ))+u2*Maths.sind(ϑ)},
|
||||
{u2*u1*(1-Maths.cosd(ϑ))+u3*Maths.sind(ϑ),
|
||||
u2*u2*(1-Maths.cosd(ϑ))+Maths.cosd(ϑ),
|
||||
u2*u3*(1-Maths.cosd(ϑ))-u1*Maths.sind(ϑ)},
|
||||
{u3*u1*(1-Maths.cosd(ϑ))-u2*Maths.sind(ϑ),
|
||||
u3*u2*(1-Maths.cosd(ϑ))+u1*Maths.sind(ϑ),
|
||||
u3*u3*(1-Maths.cosd(ϑ))+Maths.cosd(ϑ)}}).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* Rotation about the x axis by φ degrees counterclockwise for a right-hand system.
|
||||
* @param φ in degrees
|
||||
* @return 3d rotated matrix
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix3D rotateX(double φ) throws IllegalDimensionException{
|
||||
if(!isR3()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return (Matrix3D) new Matrix3D(new double[][]{
|
||||
{1,0,0},
|
||||
{0,Maths.cosd(φ),Maths.sind(φ)},
|
||||
{0,-Maths.sind(φ),Maths.cosd(φ)}}).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* Rotation about the y axis by ϑ degrees counterclockwise for a right-hand system.
|
||||
* @param ϑ in degrees
|
||||
* @return 3d rotated matrix
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix3D rotateY(double ϑ) throws IllegalDimensionException{
|
||||
if(!isR3()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return (Matrix3D) new Matrix3D(new double[][]{
|
||||
{Maths.cosd(ϑ),0,-Maths.sind(ϑ)},
|
||||
{0,1,0},
|
||||
{Maths.sind(ϑ),0,Maths.cosd(ϑ)}}).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* Rotation about the z axis by ψ degrees counterclockwise for a right-hand system.
|
||||
* @param ψ in degrees
|
||||
* @return 3d rotated matrix
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix3D rotateZ(double ψ) throws IllegalDimensionException{
|
||||
if(!isR3()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return (Matrix3D) new Matrix3D(new double[][]{
|
||||
{Maths.cosd(ψ),Maths.sind(ψ),0},
|
||||
{-Maths.sind(ψ),Maths.cosd(ψ),0},
|
||||
{0,0,1}}).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* 3d rotation by φ around x axis, ϑ around y axis and ψ degrees around z axis counterclockwise or
|
||||
* clockwise with negative degrees for a right-hand system.
|
||||
* @param φ in degrees
|
||||
* @param ϑ in degrees
|
||||
* @param ψ in degrees
|
||||
* @return 3d rotated matrix
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix3D rotateXYZ(double φ, double ϑ, double ψ) throws IllegalDimensionException{
|
||||
if(!isR3()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return (Matrix3D) rotateX(φ).times(rotateY(ϑ)).times(rotateZ(ψ)).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* Projection onto the x-y plane
|
||||
* @return matrix projected onto the x-y plane
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Matrix3D projectionToXY() throws IllegalDimensionException{
|
||||
if(!isR3()) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
return (Matrix3D) new Matrix(new double[][]{{1,0,0},{0,1,0},{0,0,0}}).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* Real eigenvalue calculated with the root formula of second and third degree.
|
||||
* @return eigenvalues λ<sub>i</sub>
|
||||
* @throws NoSquareException
|
||||
* @throws IllegalDimensionException
|
||||
* @throws ComplexException
|
||||
*/
|
||||
public Vector3D eigenvaluesRe(int analytic) throws NoSquareException, IllegalDimensionException, ComplexException{
|
||||
if(m!=n && m!=3) throw new IllegalDimensionException("Illegal matrix dimensions.");
|
||||
Vector3D lambda = new Vector3D(m);
|
||||
// matrix diagonal?
|
||||
double a12 = get(0, 1);
|
||||
double a13 = get(0, 2);
|
||||
double a23 = get(1, 2);
|
||||
double d = a12*a12 + a13*a13 + a23*a23;
|
||||
if (d == 0){ // A is diagonal.
|
||||
lambda = new Vector3D(get(0,0),get(1,1),get(2,2));
|
||||
lambda.sort(); // don't have to but ...
|
||||
} else {
|
||||
Polynomial p = new Polynomial(1,
|
||||
-trace(),
|
||||
-((this.times(this)).trace()-trace()*trace())/2,
|
||||
-det(analytic));
|
||||
lambda = new Vector3D(p.rootsRe());
|
||||
}
|
||||
return lambda;
|
||||
}
|
||||
|
||||
public static void main(String[] args) {
|
||||
Matrix3D a = new Matrix3D(0,0,1,0,1,0,1,0,0);
|
||||
System.out.println(a);
|
||||
}
|
||||
|
||||
}
|
||||
197
src/math/matrix/QRDecomposition.java
Normal file
197
src/math/matrix/QRDecomposition.java
Normal file
@@ -0,0 +1,197 @@
|
||||
package math.matrix;
|
||||
|
||||
import java.io.Serializable;
|
||||
|
||||
import math.Maths;
|
||||
|
||||
/** QR Decomposition.
|
||||
* <p>
|
||||
* For an m-by-n matrix A with m ≥ n, the QR decomposition is an m-by-n
|
||||
* orthogonal matrix Q and an n-by-n upper triangular matrix R so that
|
||||
* A = Q*R.
|
||||
* <p>
|
||||
* The QR decompostion always exists, even if the matrix does not have
|
||||
* full rank, so the constructor will never fail. The primary use of the
|
||||
* QR decomposition is in the least squares solution of nonsquare systems
|
||||
* of simultaneous linear equations. This will fail if isFullRank()
|
||||
* returns false.
|
||||
*/
|
||||
public class QRDecomposition implements Serializable {
|
||||
|
||||
/**
|
||||
* UID
|
||||
*/
|
||||
private static final long serialVersionUID = 6913030878857169502L;
|
||||
|
||||
/**
|
||||
* Array for internal storage of decomposition.
|
||||
* @serial internal array storage.
|
||||
*/
|
||||
private double[][] QR;
|
||||
|
||||
/**
|
||||
* Row dimensions.
|
||||
* @serial row dimension.
|
||||
*/
|
||||
private int m;
|
||||
|
||||
/**
|
||||
* Column dimensions.
|
||||
* @serial column dimension.
|
||||
*/
|
||||
private int n;
|
||||
|
||||
/**
|
||||
* Array for internal storage of diagonal of R.
|
||||
* @serial diagonal of R.
|
||||
*/
|
||||
private double[] Rdiag;
|
||||
|
||||
/**
|
||||
* QR Decomposition, computed by Householder reflections.
|
||||
* Structure to access R and the Householder vectors and compute Q.
|
||||
* @param A rectangular matrix
|
||||
*/
|
||||
public QRDecomposition(Matrix A){
|
||||
int i, j, k;
|
||||
// Initialize.
|
||||
QR = A.getCopy();
|
||||
m = A.getM();
|
||||
n = A.getN();
|
||||
Rdiag = new double[n];
|
||||
// Main loop.
|
||||
for(k=0; k<n; k++){
|
||||
// Compute 2-norm of k-th column without under/overflow.
|
||||
double nrm = 0;
|
||||
for(i=k; i<m; i++)
|
||||
nrm = Maths.hypot(nrm,QR[i][k]);
|
||||
if(nrm != 0.0){
|
||||
// Form k-th Householder vector.
|
||||
if(QR[k][k] < 0)
|
||||
nrm = -nrm;
|
||||
for(i=k; i<m; i++)
|
||||
QR[i][k] /= nrm;
|
||||
QR[k][k] += 1.0;
|
||||
// Apply transformation to remaining columns.
|
||||
for(j=k+1; j<n; j++){
|
||||
double s = 0.0;
|
||||
for(i=k; i<m; i++)
|
||||
s += QR[i][k]*QR[i][j];
|
||||
s = -s/QR[k][k];
|
||||
for(i=k; i<m; i++)
|
||||
QR[i][j] += s*QR[i][k];
|
||||
}
|
||||
}
|
||||
Rdiag[k] = -nrm;
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* Is the matrix full rank?
|
||||
* @return true if R, and hence A, has full rank.
|
||||
*/
|
||||
public boolean isFullRank(){
|
||||
int j;
|
||||
for(j=0; j<n; j++)
|
||||
if(Rdiag[j] == 0)
|
||||
return false;
|
||||
return true;
|
||||
}
|
||||
|
||||
/**
|
||||
* Return the Householder vectors
|
||||
* @return lower trapezoidal matrix whose columns define the reflections
|
||||
*/
|
||||
public Matrix getH(){
|
||||
int i, j;
|
||||
Matrix H = new Matrix(m,n);
|
||||
for(i=0; i<m; i++)
|
||||
for(j=0; j<n; j++){
|
||||
if(i >= j)
|
||||
H.set(i,j, QR[i][j]);
|
||||
else
|
||||
H.set(i,j, 0.0);
|
||||
}
|
||||
return H;
|
||||
}
|
||||
|
||||
/**
|
||||
* Return the upper triangular factor
|
||||
* @return R
|
||||
*/
|
||||
public Matrix getR(){
|
||||
int i, j;
|
||||
Matrix R = new Matrix(n,n);
|
||||
for(i=0; i<n; i++)
|
||||
for(j=0; j<n; j++){
|
||||
if(i < j)
|
||||
R.set(i,j, QR[i][j]);
|
||||
else if(i == j)
|
||||
R.set(i,j, Rdiag[i]);
|
||||
else
|
||||
R.set(i,j, 0.0);
|
||||
}
|
||||
return R;
|
||||
}
|
||||
|
||||
/**
|
||||
* Generate and return the (economy-sized) orthogonal factor
|
||||
* @return Q
|
||||
*/
|
||||
public Matrix getQ(){
|
||||
int i, j, k;
|
||||
Matrix Q = new Matrix(m,n);
|
||||
for(k=n-1; k>=0; k--) {
|
||||
for(i=0; i<m; i++)
|
||||
Q.set(i,k, 0.0);
|
||||
Q.set(k,k, 1.0);
|
||||
for(j=k; j<n; j++)
|
||||
if(QR[k][k] != 0){
|
||||
double s = 0.0;
|
||||
for(i=k; i<m; i++)
|
||||
s += QR[i][k]*Q.get(i, j);
|
||||
s = -s/QR[k][k];
|
||||
for(i=k; i<m; i++)
|
||||
Q.plus(i,j, s*QR[i][k]);
|
||||
}
|
||||
}
|
||||
return Q;
|
||||
}
|
||||
|
||||
/**
|
||||
* Least squares solution of A*X = B
|
||||
* @param B a Matrix with as many rows as A and any number of columns.
|
||||
* @return X that minimizes the two norm of Q*R*X-B.
|
||||
* @exception IllegalArgumentException Matrix row dimensions must agree.
|
||||
* @exception RuntimeException Matrix is rank deficient.
|
||||
*/
|
||||
public Matrix solve(Matrix B){
|
||||
if(B.getM() != m)
|
||||
throw new IllegalArgumentException("Matrix row dimensions must agree.");
|
||||
if(!this.isFullRank())
|
||||
throw new RuntimeException("Matrix is rank deficient.");
|
||||
int i, j, k;
|
||||
// Copy right hand side
|
||||
int nx = B.getN();
|
||||
double[][] X = B.getCopy();
|
||||
// Compute Y = transpose(Q)*B
|
||||
for(k=0; k<n; k++)
|
||||
for(j=0; j<nx; j++){
|
||||
double s = 0.0;
|
||||
for(i=k; i<m; i++)
|
||||
s += QR[i][k]*X[i][j];
|
||||
s = -s/QR[k][k];
|
||||
for(i=k; i<m; i++)
|
||||
X[i][j] += s*QR[i][k];
|
||||
}
|
||||
// Solve R*X = Y;
|
||||
for(k=n-1; k>=0; k--){
|
||||
for(j=0; j<nx; j++)
|
||||
X[k][j] /= Rdiag[k];
|
||||
for(i=0; i<k; i++)
|
||||
for(j=0; j<nx; j++)
|
||||
X[i][j] -= X[k][j]*QR[i][k];
|
||||
}
|
||||
return (new Matrix(X).get(0,n-1,0,nx-1));
|
||||
}
|
||||
}
|
||||
467
src/math/matrix/SingularValueDecomposition.java
Normal file
467
src/math/matrix/SingularValueDecomposition.java
Normal file
@@ -0,0 +1,467 @@
|
||||
package math.matrix;
|
||||
|
||||
import java.io.Serializable;
|
||||
|
||||
import math.Maths;
|
||||
|
||||
/** Singular Value Decomposition.
|
||||
* <p>
|
||||
* For an m-by-n matrix A with m ≥ n, the singular value decomposition is
|
||||
* an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and
|
||||
* an n-by-n orthogonal matrix V so that A = U*S*V'.
|
||||
* <p>
|
||||
* The singular values, σ<sub>k</sub> = S<sub>kk</sub>, are ordered so that
|
||||
* σ<sub>1</sub> ≥ σ<sub>2</sub> ≥ ... ≥ σ<sub>n</sub>.
|
||||
* <p>
|
||||
* The singular value decompostion always exists, so the constructor will
|
||||
* never fail. The matrix condition number and the effective numerical
|
||||
* rank can be computed from this decomposition.
|
||||
*/
|
||||
public class SingularValueDecomposition implements Serializable {
|
||||
|
||||
/**
|
||||
* UID
|
||||
*/
|
||||
private static final long serialVersionUID = -4816488865370991490L;
|
||||
|
||||
/**
|
||||
* Array for internal storage of U.
|
||||
* @serial internal storage of U.
|
||||
*/
|
||||
private double[][] U;
|
||||
|
||||
/**
|
||||
* Array for internal storage of V.
|
||||
* @serial internal storage of V.
|
||||
*/
|
||||
private double[][] V;
|
||||
|
||||
/**
|
||||
* Array for internal storage of singular values.
|
||||
* @serial internal storage of singular values.
|
||||
*/
|
||||
private double[] s;
|
||||
|
||||
/**
|
||||
* Row dimensions.
|
||||
* @serial row dimension.
|
||||
*/
|
||||
private int m;
|
||||
|
||||
/**
|
||||
* Column dimensions.
|
||||
* @serial column dimension.
|
||||
*/
|
||||
private int n;
|
||||
|
||||
/* ------------------------
|
||||
Constructor
|
||||
* ------------------------ */
|
||||
|
||||
/**
|
||||
* Construct the singular value decomposition Structure to access U, S and V.
|
||||
* @param Arg rectangular matrix
|
||||
*/
|
||||
public SingularValueDecomposition(Matrix Arg){
|
||||
int i, j, k;
|
||||
// Derived from LINPACK code.
|
||||
// Initialize.
|
||||
double[][] A = Arg.getCopy();
|
||||
m = Arg.getM();
|
||||
n = Arg.getN();
|
||||
/* TODO: Apparently the failing cases are only a proper subset of (m<n),
|
||||
* so let's not throw error. Correct fix to come later?
|
||||
* if (m<n) {
|
||||
* throw new IllegalArgumentException("SVD only works for m >= n"); }
|
||||
*/
|
||||
int nu = Math.min(m,n);
|
||||
s = new double [Math.min(m+1,n)];
|
||||
U = new double [m][nu];
|
||||
V = new double [n][n];
|
||||
double[] e = new double [n];
|
||||
double[] work = new double [m];
|
||||
boolean wantu = true;
|
||||
boolean wantv = true;
|
||||
// Reduce A to bidiagonal form, storing the diagonal elements
|
||||
// in s and the super-diagonal elements in e.
|
||||
int nct = Math.min(m-1,n);
|
||||
int nrt = Math.max(0,Math.min(n-2,m));
|
||||
for(k=0; k<Math.max(nct,nrt); k++){
|
||||
if(k<nct){
|
||||
// Compute the transformation for the k-th column and
|
||||
// place the k-th diagonal in s[k].
|
||||
// Compute 2-norm of k-th column without under/overflow.
|
||||
s[k] = 0;
|
||||
for(i=k; i<m; i++)
|
||||
s[k] = Maths.hypot(s[k],A[i][k]);
|
||||
if(s[k] != 0.0){
|
||||
if(A[k][k] < 0.0)
|
||||
s[k] = -s[k];
|
||||
for(i=k; i<m; i++)
|
||||
A[i][k] /= s[k];
|
||||
A[k][k] += 1.0;
|
||||
}
|
||||
s[k] = -s[k];
|
||||
}
|
||||
for(j=k+1; j<n; j++){
|
||||
if((k < nct) & (s[k] != 0.0)){
|
||||
// Apply the transformation.
|
||||
double t = 0;
|
||||
for(i=k; i<m; i++)
|
||||
t += A[i][k]*A[i][j];
|
||||
t = -t/A[k][k];
|
||||
for(i=k; i<m; i++)
|
||||
A[i][j] += t*A[i][k];
|
||||
}
|
||||
// Place the k-th row of A into e for the
|
||||
// subsequent calculation of the row transformation.
|
||||
e[j] = A[k][j];
|
||||
}
|
||||
if(wantu & (k < nct)){
|
||||
// Place the transformation in U for subsequent back
|
||||
// multiplication.
|
||||
for(i=k; i<m; i++)
|
||||
U[i][k] = A[i][k];
|
||||
}
|
||||
if(k < nrt){
|
||||
// Compute the k-th row transformation and place the
|
||||
// k-th super-diagonal in e[k].
|
||||
// Compute 2-norm without under/overflow.
|
||||
e[k] = 0;
|
||||
for(i=k+1; i<n; i++)
|
||||
e[k] = Maths.hypot(e[k],e[i]);
|
||||
if(e[k] != 0.0){
|
||||
if(e[k+1] < 0.0)
|
||||
e[k] = -e[k];
|
||||
for(i=k+1; i<n; i++)
|
||||
e[i] /= e[k];
|
||||
e[k+1] += 1.0;
|
||||
}
|
||||
e[k] = -e[k];
|
||||
if((k+1 < m) & (e[k] != 0.0)){
|
||||
// Apply the transformation.
|
||||
for(i=k+1; i<m; i++)
|
||||
work[i] = 0.0;
|
||||
for(j=k+1; j<n; j++)
|
||||
for(i=k+1; i<m; i++)
|
||||
work[i] += e[j]*A[i][j];
|
||||
for(j=k+1; j<n; j++){
|
||||
double t = -e[j]/e[k+1];
|
||||
for(i=k+1; i<m; i++)
|
||||
A[i][j] += t*work[i];
|
||||
}
|
||||
}
|
||||
if(wantv){
|
||||
// Place the transformation in V for subsequent
|
||||
// back multiplication.
|
||||
for(i=k+1; i<n; i++)
|
||||
V[i][k] = e[i];
|
||||
}
|
||||
}
|
||||
}
|
||||
// Set up the final bidiagonal matrix or order p.
|
||||
int p = Math.min(n,m+1);
|
||||
if(nct < n) s[nct] = A[nct][nct];
|
||||
if(m < p) s[p-1] = 0.0;
|
||||
if(nrt+1 < p) e[nrt] = A[nrt][p-1];
|
||||
e[p-1] = 0.0;
|
||||
// If required, generate U.
|
||||
if(wantu){
|
||||
for(j=nct; j<nu; j++){
|
||||
for(i=0; i<m; i++)
|
||||
U[i][j] = 0.0;
|
||||
U[j][j] = 1.0;
|
||||
}
|
||||
for(k=nct-1; k>=0; k--){
|
||||
if(s[k] != 0.0) {
|
||||
for(j=k+1; j<nu; j++){
|
||||
double t = 0;
|
||||
for(i=k; i < m; i++)
|
||||
t += U[i][k]*U[i][j];
|
||||
t = -t/U[k][k];
|
||||
for(i=k; i<m; i++)
|
||||
U[i][j] += t*U[i][k];
|
||||
}
|
||||
for(i=k; i < m; i++)
|
||||
U[i][k] = -U[i][k];
|
||||
U[k][k] = 1.0 + U[k][k];
|
||||
for(i=0; i<k-1; i++)
|
||||
U[i][k] = 0.0;
|
||||
} else {
|
||||
for(i=0; i < m; i++)
|
||||
U[i][k] = 0.0;
|
||||
U[k][k] = 1.0;
|
||||
}
|
||||
}
|
||||
}
|
||||
// If required, generate V.
|
||||
if(wantv)
|
||||
for(k=n-1; k>=0; k--){
|
||||
if((k < nrt) & (e[k] != 0.0))
|
||||
for(j=k+1; j<nu; j++){
|
||||
double t = 0;
|
||||
for(i=k+1; i < n; i++)
|
||||
t += V[i][k]*V[i][j];
|
||||
t = -t/V[k+1][k];
|
||||
for(i=k+1; i<n; i++)
|
||||
V[i][j] += t*V[i][k];
|
||||
}
|
||||
for(i=0; i<n; i++)
|
||||
V[i][k] = 0.0;
|
||||
V[k][k] = 1.0;
|
||||
}
|
||||
// Main iteration loop for the singular values.
|
||||
int pp = p-1;
|
||||
int iter = 0;
|
||||
double eps = Math.pow(2.0,-52.0);
|
||||
double tiny = Math.pow(2.0,-966.0);
|
||||
while(p > 0){
|
||||
int kase;
|
||||
// Here is where a test for too many iterations would go.
|
||||
//
|
||||
// This section of the program inspects for
|
||||
// negligible elements in the s and e arrays. On
|
||||
// completion the variables kase and k are set as follows.
|
||||
// kase = 1 if s(p) and e[k-1] are negligible and k<p
|
||||
// kase = 2 if s(k) is negligible and k<p
|
||||
// kase = 3 if e[k-1] is negligible, k<p, and
|
||||
// s(k), ..., s(p) are not negligible (qr step).
|
||||
// kase = 4 if e(p-1) is negligible (convergence).
|
||||
for(k=p-2; k>=-1; k--){
|
||||
if(k == -1) break;
|
||||
if(Math.abs(e[k]) <=
|
||||
tiny + eps*(Math.abs(s[k]) + Math.abs(s[k+1]))){
|
||||
e[k] = 0.0;
|
||||
break;
|
||||
}
|
||||
}
|
||||
if(k == p-2)
|
||||
kase = 4;
|
||||
else {
|
||||
int ks;
|
||||
for(ks=p-1; ks>=k; ks--){
|
||||
if (ks == k) break;
|
||||
double t = (ks != p ? Math.abs(e[ks]) : 0.) +
|
||||
(ks != k+1 ? Math.abs(e[ks-1]) : 0.);
|
||||
if(Math.abs(s[ks]) <= tiny + eps*t){
|
||||
s[ks] = 0.0;
|
||||
break;
|
||||
}
|
||||
}
|
||||
if(ks == k)
|
||||
kase = 3;
|
||||
else if(ks == p-1)
|
||||
kase = 1;
|
||||
else {
|
||||
kase = 2;
|
||||
k = ks;
|
||||
}
|
||||
}
|
||||
k++;
|
||||
// Perform the task indicated by kase.
|
||||
switch (kase) {
|
||||
// Deflate negligible s(p).
|
||||
case 1: {
|
||||
double f = e[p-2];
|
||||
e[p-2] = 0.0;
|
||||
for(j=p-2; j>=k; j--){
|
||||
double t = Maths.hypot(s[j],f);
|
||||
double cs = s[j]/t;
|
||||
double sn = f/t;
|
||||
s[j] = t;
|
||||
if(j != k){
|
||||
f = -sn*e[j-1];
|
||||
e[j-1] = cs*e[j-1];
|
||||
}
|
||||
if(wantv)
|
||||
for(i=0; i<n; i++){
|
||||
t = cs*V[i][j] + sn*V[i][p-1];
|
||||
V[i][p-1] = -sn*V[i][j] + cs*V[i][p-1];
|
||||
V[i][j] = t;
|
||||
}
|
||||
}
|
||||
}
|
||||
break;
|
||||
// Split at negligible s(k).
|
||||
case 2: {
|
||||
double f = e[k-1];
|
||||
e[k-1] = 0.0;
|
||||
for(j=k; j<p; j++){
|
||||
double t = Maths.hypot(s[j],f);
|
||||
double cs = s[j]/t;
|
||||
double sn = f/t;
|
||||
s[j] = t;
|
||||
f = -sn*e[j];
|
||||
e[j] = cs*e[j];
|
||||
if(wantu)
|
||||
for(i=0; i<m; i++){
|
||||
t = cs*U[i][j] + sn*U[i][k-1];
|
||||
U[i][k-1] = -sn*U[i][j] + cs*U[i][k-1];
|
||||
U[i][j] = t;
|
||||
}
|
||||
}
|
||||
}
|
||||
break;
|
||||
// Perform one qr step.
|
||||
case 3: {
|
||||
// Calculate the shift.
|
||||
double scale = Math.max(Math.max(Math.max(Math.max(
|
||||
Math.abs(s[p-1]),Math.abs(s[p-2])),Math.abs(e[p-2])),
|
||||
Math.abs(s[k])),Math.abs(e[k]));
|
||||
double sp = s[p-1]/scale;
|
||||
double spm1 = s[p-2]/scale;
|
||||
double epm1 = e[p-2]/scale;
|
||||
double sk = s[k]/scale;
|
||||
double ek = e[k]/scale;
|
||||
double b = ((spm1 + sp)*(spm1 - sp) + epm1*epm1)/2.0;
|
||||
double c = (sp*epm1)*(sp*epm1);
|
||||
double shift = 0.0;
|
||||
if((b != 0.0) | (c != 0.0)){
|
||||
shift = Math.sqrt(b*b + c);
|
||||
if(b < 0.0)
|
||||
shift = -shift;
|
||||
shift = c/(b + shift);
|
||||
}
|
||||
double f = (sk + sp)*(sk - sp) + shift;
|
||||
double g = sk*ek;
|
||||
// Chase zeros.
|
||||
for(j=k; j<p-1; j++){
|
||||
double t = Maths.hypot(f,g);
|
||||
double cs = f/t;
|
||||
double sn = g/t;
|
||||
if(j != k)
|
||||
e[j-1] = t;
|
||||
f = cs*s[j] + sn*e[j];
|
||||
e[j] = cs*e[j] - sn*s[j];
|
||||
g = sn*s[j+1];
|
||||
s[j+1] = cs*s[j+1];
|
||||
if(wantv)
|
||||
for(i=0; i<n; i++){
|
||||
t = cs*V[i][j] + sn*V[i][j+1];
|
||||
V[i][j+1] = -sn*V[i][j] + cs*V[i][j+1];
|
||||
V[i][j] = t;
|
||||
}
|
||||
t = Maths.hypot(f,g);
|
||||
cs = f/t;
|
||||
sn = g/t;
|
||||
s[j] = t;
|
||||
f = cs*e[j] + sn*s[j+1];
|
||||
s[j+1] = -sn*e[j] + cs*s[j+1];
|
||||
g = sn*e[j+1];
|
||||
e[j+1] = cs*e[j+1];
|
||||
if(wantu && (j < m-1))
|
||||
for(i=0; i<m; i++){
|
||||
t = cs*U[i][j] + sn*U[i][j+1];
|
||||
U[i][j+1] = -sn*U[i][j] + cs*U[i][j+1];
|
||||
U[i][j] = t;
|
||||
}
|
||||
}
|
||||
e[p-2] = f;
|
||||
iter = iter + 1;
|
||||
}
|
||||
break;
|
||||
// Convergence.
|
||||
case 4: {
|
||||
// Make the singular values positive.
|
||||
if(s[k] <= 0.0){
|
||||
s[k] = (s[k] < 0.0 ? -s[k] : 0.0);
|
||||
if(wantv)
|
||||
for(i=0; i<=pp; i++)
|
||||
V[i][k] = -V[i][k];
|
||||
}
|
||||
// Order the singular values.
|
||||
while(k < pp){
|
||||
if (s[k] >= s[k+1])
|
||||
break;
|
||||
double t = s[k];
|
||||
s[k] = s[k+1];
|
||||
s[k+1] = t;
|
||||
if(wantv && (k < n-1)){
|
||||
for(i=0; i<n; i++){
|
||||
t = V[i][k+1];
|
||||
V[i][k+1] = V[i][k];
|
||||
V[i][k] = t;
|
||||
}
|
||||
}
|
||||
if(wantu && (k < m-1)){
|
||||
for(i=0; i<m; i++){
|
||||
t = U[i][k+1];
|
||||
U[i][k+1] = U[i][k];
|
||||
U[i][k] = t;
|
||||
}
|
||||
}
|
||||
k++;
|
||||
}
|
||||
iter = 0;
|
||||
p--;
|
||||
}
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* @return the left singular vectors U
|
||||
*/
|
||||
public Matrix getU(){
|
||||
return new Matrix(U);
|
||||
}
|
||||
|
||||
/**
|
||||
* @return the right singular vectors V
|
||||
*/
|
||||
public Matrix getV(){
|
||||
return new Matrix(V);
|
||||
}
|
||||
|
||||
/**
|
||||
* @return the one-dimensional array of singular values, diagonal of S.
|
||||
*/
|
||||
public double[] getSingularValues(){
|
||||
return s;
|
||||
}
|
||||
|
||||
/**
|
||||
* @return the diagonal matrix of singular values S
|
||||
*/
|
||||
public Matrix getS(){
|
||||
int i, j;
|
||||
Matrix S = new Matrix(n,n);
|
||||
for(i=0; i<n; i++){
|
||||
for(j=0; j<n; j++)
|
||||
S.set(i,j, 0.0);
|
||||
S.set(i,i, this.s[i]);
|
||||
}
|
||||
return S;
|
||||
}
|
||||
|
||||
/**
|
||||
* Two norm
|
||||
* @return max(S)
|
||||
*/
|
||||
public double norm2(){
|
||||
return s[0];
|
||||
}
|
||||
|
||||
/**
|
||||
* Two norm condition number
|
||||
* @return max(S)/min(S)
|
||||
*/
|
||||
public double cond(){
|
||||
return s[0]/s[Math.min(m,n)-1];
|
||||
}
|
||||
|
||||
/**
|
||||
* Effective numerical matrix rank
|
||||
* @return number of nonnegligible singular values.
|
||||
*/
|
||||
public int rank(){
|
||||
double eps = Math.pow(2.0,-52.0);
|
||||
double tol = Math.max(m,n)*s[0]*eps;
|
||||
int i, r = 0;
|
||||
for(i=0; i<s.length; i++)
|
||||
if(s[i] > tol)
|
||||
r++;
|
||||
return r;
|
||||
}
|
||||
}
|
||||
13
src/math/matrix/TensorII.java
Normal file
13
src/math/matrix/TensorII.java
Normal file
@@ -0,0 +1,13 @@
|
||||
package math.matrix;
|
||||
|
||||
public class TensorII extends Matrix3D {
|
||||
|
||||
/**
|
||||
* UID
|
||||
*/
|
||||
private static final long serialVersionUID = -5664678448598889794L;
|
||||
|
||||
public static void main(String[] args) {
|
||||
}
|
||||
|
||||
}
|
||||
58
src/math/matrix/TensorII2D.java
Normal file
58
src/math/matrix/TensorII2D.java
Normal file
@@ -0,0 +1,58 @@
|
||||
package math.matrix;
|
||||
|
||||
import math.Maths;
|
||||
import exception.IllegalDimensionException;
|
||||
|
||||
/**
|
||||
* Tensor 2x2
|
||||
* @author Daniel
|
||||
*
|
||||
*/
|
||||
public class TensorII2D extends Matrix2D {
|
||||
|
||||
/**
|
||||
* UID
|
||||
*/
|
||||
private static final long serialVersionUID = -3195354821730519791L;
|
||||
|
||||
public TensorII2D() {
|
||||
super(2);
|
||||
}
|
||||
|
||||
public TensorII2D(double a11, double a12, double a21, double a22) {
|
||||
super(a11, a12, a21, a22);
|
||||
}
|
||||
|
||||
public TensorII2D(double[][] a) {
|
||||
super(a);
|
||||
}
|
||||
|
||||
public TensorII2D(Matrix B) {
|
||||
super(B);
|
||||
}
|
||||
|
||||
/**
|
||||
* @param ϑ in degrees
|
||||
* @return 2d rotation matrix
|
||||
*/
|
||||
public static TensorII2D rotation(double ϑ){
|
||||
return new TensorII2D(new double[][]{
|
||||
{Maths.cosd(ϑ),-Maths.sind(ϑ)},
|
||||
{Maths.sind(ϑ), Maths.cosd(ϑ)}});
|
||||
}
|
||||
|
||||
public TensorII2D rotate(double ϑ){
|
||||
try {
|
||||
return (TensorII2D) rotation(ϑ).times(this).times(rotation(ϑ).transpose());
|
||||
} catch (IllegalDimensionException e) {
|
||||
e.printStackTrace();
|
||||
return null;
|
||||
}
|
||||
}
|
||||
|
||||
public static void main(String[] args) {
|
||||
TensorII2D tau = new TensorII2D(1, -1, -1, 1);
|
||||
double ϑ = 45;
|
||||
tau.rotate(ϑ).println();
|
||||
}
|
||||
}
|
||||
899
src/math/matrix/Vector.java
Normal file
899
src/math/matrix/Vector.java
Normal file
@@ -0,0 +1,899 @@
|
||||
package math.matrix;
|
||||
|
||||
import java.io.Serializable;
|
||||
import java.util.ArrayList;
|
||||
import java.util.Collections;
|
||||
import java.util.List;
|
||||
|
||||
import math.Maths;
|
||||
import math.geometry.Point;
|
||||
import thisandthat.WObject;
|
||||
import exception.IllegalDimensionException;
|
||||
|
||||
/**
|
||||
* Vector of real numbers, v∈ℝ.
|
||||
* @author Daniel Weschke
|
||||
*/
|
||||
public class Vector extends WObject implements Cloneable, Serializable{
|
||||
|
||||
/**
|
||||
* UID
|
||||
*/
|
||||
private static final long serialVersionUID = 7909642082289701909L;
|
||||
|
||||
protected List<Double> vector;
|
||||
// protected double[] vector;
|
||||
|
||||
public Vector(){
|
||||
}
|
||||
|
||||
/**
|
||||
* Create zero vector
|
||||
* @param n
|
||||
*/
|
||||
public Vector(int n){
|
||||
int i;
|
||||
// vector = new double[n];
|
||||
vector = new ArrayList<Double>();
|
||||
for(i=0; i<n; i++)
|
||||
add(0);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector with given x value
|
||||
* @param x
|
||||
*/
|
||||
public Vector(double x){
|
||||
// vector = new double[]{x};
|
||||
this(1);
|
||||
set(0, x);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector with given x and y value
|
||||
* @param x
|
||||
* @param y
|
||||
*/
|
||||
public Vector(double x, double y){
|
||||
// vector = new double[]{x, y};
|
||||
this(2);
|
||||
set(0, x);
|
||||
set(1, y);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector with given x, y and z value
|
||||
* @param x
|
||||
* @param y
|
||||
* @param z
|
||||
*/
|
||||
public Vector(double x, double y, double z){
|
||||
// vector = new double[]{x, y, z};
|
||||
this(3);
|
||||
set(0, x);
|
||||
set(1, y);
|
||||
set(2, z);
|
||||
}
|
||||
|
||||
private void add(double s){
|
||||
vector.add(s);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector with given array
|
||||
* @param data array
|
||||
*/
|
||||
public Vector(double... data){
|
||||
this(data.length);
|
||||
int i;
|
||||
int n = data.length;
|
||||
// vector = new double[n];
|
||||
for(i=0; i<n; i++)
|
||||
set(i, data[i]);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector with given array (integers)
|
||||
* @param v array
|
||||
*/
|
||||
public Vector(int[] v){
|
||||
this(v.length);
|
||||
int i;
|
||||
int n = v.length;
|
||||
// vector = new double[n];
|
||||
for(i=0; i<n; i++)
|
||||
set(i, (v[i]));
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector with given array
|
||||
* @param data array
|
||||
*/
|
||||
public Vector(List<Double> data){
|
||||
this(data.size());
|
||||
int i;
|
||||
int n = data.size();
|
||||
for(i=0; i<n; i++)
|
||||
set(i, data.get(i));
|
||||
}
|
||||
|
||||
public Vector(Point p){
|
||||
this(p.get());
|
||||
}
|
||||
|
||||
/**
|
||||
* Copy vector
|
||||
* @param v vector
|
||||
*/
|
||||
public Vector(Vector v){
|
||||
this(v.vector);
|
||||
}
|
||||
|
||||
private Vector create(int n){
|
||||
if(this instanceof Vector2D) return new Vector2D();
|
||||
if(this instanceof Vector3D) return new Vector3D();
|
||||
else return new Vector(n);
|
||||
}
|
||||
|
||||
private Vector create(double[] v){
|
||||
if(this instanceof Vector2D) return new Vector2D(v);
|
||||
if(this instanceof Vector3D) return new Vector3D(v);
|
||||
else return new Vector(v);
|
||||
}
|
||||
|
||||
private Matrix create(int m, int n){
|
||||
if(this instanceof Vector2D) return new Matrix2D(n);
|
||||
if(this instanceof Vector3D) return new Matrix3D(n);
|
||||
else return new Matrix(m,n);
|
||||
}
|
||||
|
||||
/**
|
||||
* @return vector array
|
||||
*/
|
||||
public double[] getArray(){
|
||||
int i, n = n();
|
||||
double[] v = new double[n];
|
||||
for(i=0; i<n; i++)
|
||||
v[i] = get(i);
|
||||
return v;
|
||||
}
|
||||
|
||||
/**
|
||||
* @return vector array
|
||||
*/
|
||||
public List<Double> get(){
|
||||
return vector;
|
||||
}
|
||||
|
||||
/**
|
||||
* @param i index
|
||||
* @return corresponding coordinate
|
||||
*/
|
||||
public double get(int i){
|
||||
return vector.get(i);
|
||||
}
|
||||
|
||||
/**
|
||||
* @return vector array (integers)
|
||||
*/
|
||||
public int[] getInts(){
|
||||
int i;
|
||||
int[] result = new int[n()];
|
||||
for(i=0; i<n(); i++)
|
||||
result[i] = (int) get(i);
|
||||
return result;
|
||||
}
|
||||
|
||||
/**
|
||||
* set value at index
|
||||
* @param i index
|
||||
* @param a value
|
||||
*/
|
||||
public Vector set(int i, double a){
|
||||
vector.set(i, a);
|
||||
return this;
|
||||
}
|
||||
|
||||
/**
|
||||
* get x (first element)
|
||||
* @return x value
|
||||
*/
|
||||
public double x(){
|
||||
return n()>0?get(0):Double.NaN;
|
||||
}
|
||||
|
||||
/**
|
||||
* get y (second element)
|
||||
* @return y value
|
||||
*/
|
||||
public double y(){
|
||||
return n()>1?get(1):Double.NaN;
|
||||
}
|
||||
|
||||
/**
|
||||
* get z (third element)
|
||||
* @return z value
|
||||
*/
|
||||
public double z(){
|
||||
return n()>2?get(2):Double.NaN;
|
||||
}
|
||||
|
||||
/**
|
||||
* length of vector
|
||||
* @return dimension
|
||||
*/
|
||||
public int n(){
|
||||
return length();
|
||||
}
|
||||
|
||||
/**
|
||||
* length of vector
|
||||
* @return dimension
|
||||
*/
|
||||
public int length(){
|
||||
// return vector.length;
|
||||
return vector.size();
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector with zeros
|
||||
* @param n size
|
||||
* @return zero vector
|
||||
*/
|
||||
public static Vector zeros(int n){
|
||||
return new Vector(n);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector with ones
|
||||
* @param n size
|
||||
* @return one vector
|
||||
*/
|
||||
public static Vector ones(int n){
|
||||
return fill(n, 1);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector with given scalar
|
||||
* @param n size
|
||||
* @param s scalar
|
||||
* @return filled vector
|
||||
*/
|
||||
public static Vector fill(int n, double s){
|
||||
Vector a = new Vector(n);
|
||||
int i;
|
||||
for(i=0; i<n; i++)
|
||||
a.set(i, s);
|
||||
return a;
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector and fill it from a start value to an end value
|
||||
* @param start
|
||||
* @param end
|
||||
* @return filled vector [start,start+1,...,end]
|
||||
*/
|
||||
public static Vector fill(double start, double end){
|
||||
double delta = end-start;
|
||||
int increment = delta>0 ? 1 : -1;
|
||||
return fill(start, increment, end);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector and fill it from a start value to an end value with n equidistant steps
|
||||
* @param start
|
||||
* @param end
|
||||
* @param n steps
|
||||
* @return filled vector [start,(end-start)*1/n,(end-start)*2/n,...,end]
|
||||
*/
|
||||
public static Vector fillN(double start, double end, int n){
|
||||
double increment = (end-start)/n;
|
||||
return fill(start, increment, end);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector and fill it from a start value and increments it to an end value
|
||||
* @param start
|
||||
* @param increment
|
||||
* @param end
|
||||
* @return filled vector [start,start+increment,start+2*increment,...,end]
|
||||
*/
|
||||
public static Vector fill(double start, double increment, double end){
|
||||
double delta = end-start;
|
||||
int n = (int)(delta/increment)+1;
|
||||
if((delta>=0&&increment<0)||(delta<0&&increment>=0)||increment==0) return new Vector();
|
||||
Vector a = new Vector(n);
|
||||
int i;
|
||||
for(i=0; i<n; i++)
|
||||
a.set(i, start + i*increment);
|
||||
return a;
|
||||
}
|
||||
|
||||
/**
|
||||
* Create zero vector and fill it with given values at given positions (first position is 1)
|
||||
* @param n
|
||||
* @param position
|
||||
* @param a value array
|
||||
* @return filled vector
|
||||
*/
|
||||
public static Vector fill(int n, int[] position, double[] a){
|
||||
Vector c = new Vector(n);
|
||||
for(int i=0; i<position.length; i++)
|
||||
c.set(position[i]-1, a[i]);
|
||||
return c;
|
||||
}
|
||||
|
||||
/**
|
||||
* Create zero vector and fill it with given values at given positions (first position is 1)
|
||||
* @param n
|
||||
* @param position
|
||||
* @param a value vector
|
||||
* @return filled vector
|
||||
*/
|
||||
public static Vector fill(int n, int[] position, Vector a){
|
||||
Vector c = new Vector(n);
|
||||
for(int i=0; i<position.length; i++)
|
||||
c.set(position[i]-1, a.get(i));
|
||||
return c;
|
||||
}
|
||||
|
||||
/**
|
||||
* Create zero vector and fill it with given values at given positions (first position is 1)
|
||||
* @param n
|
||||
* @param position
|
||||
* @param a value vector
|
||||
* @return filled vector
|
||||
*/
|
||||
public static Vector fill(int n, Vector position, Vector a){
|
||||
Vector c = new Vector(n);
|
||||
for(int i=0; i<position.n(); i++)
|
||||
c.set((int) position.get(i)-1, a.get(i));
|
||||
return c;
|
||||
}
|
||||
|
||||
/**
|
||||
* Fill vector with given values at given indices (first index is 0)
|
||||
* @param indices
|
||||
* @param a value vector
|
||||
*/
|
||||
public void fill(int[] indices, Vector a){
|
||||
for(int i=0; i<indices.length; i++)
|
||||
set(indices[i], a.get(i));
|
||||
}
|
||||
|
||||
/**
|
||||
* Fill vector with given values at given positions (indices +1)
|
||||
* @param positions
|
||||
* @param a vector
|
||||
*/
|
||||
public void fillPos(int[] positions, Vector a){
|
||||
fill(new Vector(positions).minus(1).getInts(),a);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector and fill it with random values [0,1)
|
||||
* @param n rows
|
||||
* @return random number filled vector
|
||||
*/
|
||||
public static Vector rand(int n){
|
||||
Vector a = new Vector(n);
|
||||
int i;
|
||||
for(i=0; i<n; i++)
|
||||
a.set(i, Math.random());
|
||||
return a;
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector and fill it with random values [0,s]
|
||||
* @param n rows
|
||||
* @param s scalar
|
||||
* @return random number filled vector
|
||||
*/
|
||||
public static Vector rand(int n, double s){
|
||||
Vector a = new Vector(n);
|
||||
int i;
|
||||
for(i=0; i<n; i++)
|
||||
a.set(i, Math.random()*s);
|
||||
return a;
|
||||
}
|
||||
|
||||
/**
|
||||
* add a Vector.
|
||||
* @param a vector to add
|
||||
* @return added Vector
|
||||
*/
|
||||
public Vector plus(Vector a){
|
||||
int i;
|
||||
Vector c = create(n());
|
||||
for(i=0; i<n(); i++)
|
||||
c.set(i, get(i) + a.get(i));
|
||||
return c;
|
||||
}
|
||||
|
||||
/**
|
||||
* add a Vector.
|
||||
* @param s as vector to add
|
||||
* @return added Vector
|
||||
*/
|
||||
public Vector plus(double s){
|
||||
return plus(Vector.fill(n(), s));
|
||||
}
|
||||
|
||||
public void plus(int i, double s){
|
||||
set(i, get(i)+s);
|
||||
}
|
||||
|
||||
/**
|
||||
* subtract a Vector.
|
||||
* @param a vector to subtract
|
||||
* @return subtracted Vector
|
||||
*/
|
||||
public Vector minus(Vector a){
|
||||
return plus(a.times(-1));
|
||||
}
|
||||
|
||||
/**
|
||||
* subtract a Vector.
|
||||
* @param s as vector to subtract
|
||||
* @return subtracted Vector
|
||||
*/
|
||||
public Vector minus(double s){
|
||||
return plus(Vector.fill(n(), -s));
|
||||
}
|
||||
|
||||
/**
|
||||
* lengthen the vector due scalar multiplication
|
||||
* @param s scalar
|
||||
* @return C = s A
|
||||
*/
|
||||
public Vector times(double s){
|
||||
int i;
|
||||
Vector c = create(n());
|
||||
for(i=0; i<n(); i++)
|
||||
c.set(i, get(i) * s);
|
||||
return c;
|
||||
}
|
||||
|
||||
/**
|
||||
* Multiply a matrix right. Linear algebraic matrix multiplication.
|
||||
* @param B matrix
|
||||
* @return <b>C</b> = <b>A</b> • <b>B</b> = <b>A</b><sup>T</sup><b>B</b>
|
||||
* @throws IllegalDimensionException Inner matrix dimensions must agree.
|
||||
*/
|
||||
public Vector times(Matrix B) throws IllegalDimensionException{
|
||||
int i,j;
|
||||
if(n() != B.getM()) throw new IllegalDimensionException("Inner matrix dimensions must agree.");
|
||||
double[] c = new double[n()];
|
||||
for(i=0; i<n(); i++)
|
||||
for(j=0; j<B.getM(); j++)
|
||||
c[i] += (get(j) * B.get(j,i));
|
||||
return create(c);
|
||||
}
|
||||
|
||||
/**
|
||||
* Dot / inner / scalar product x<sup>T</sup>x.
|
||||
* A • B = a<sub>1</sub>b<sub>1</sub> + a<sub>2</sub>b<sub>2</sub> +
|
||||
* … + a<sub>n</sub>b<sub>n</sub>;
|
||||
* a scalar quantity
|
||||
* @return scalar
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public double dot() throws IllegalDimensionException{
|
||||
return dot(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* Dot / inner / scalar product x<sup>T</sup>y.
|
||||
* A • B = a<sub>1</sub>b<sub>1</sub> + a<sub>2</sub>b<sub>2</sub> +
|
||||
* … + a<sub>n</sub>b<sub>n</sub>;
|
||||
* a scalar quantity
|
||||
* @param a vector
|
||||
* @return scalar
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public double dot(Vector a) throws IllegalDimensionException{
|
||||
if(n() != a.n()) throw new IllegalDimensionException("Illegal vector dimension.");
|
||||
int i;
|
||||
double c = 0;
|
||||
for(i=0; i<n(); i++)
|
||||
c += get(i) * a.get(i);
|
||||
return c;
|
||||
}
|
||||
|
||||
/**
|
||||
* Outer / tensor product vv'
|
||||
* @param b vector
|
||||
* @return matrix
|
||||
*/
|
||||
public Matrix tensorProduct(Vector b){
|
||||
int i, j;
|
||||
Matrix c = create(n(),b.n());
|
||||
for(i=0; i<n(); i++)
|
||||
for(j=0; j<b.n(); j++)
|
||||
c.set(i, j, get(i) * b.get(j));
|
||||
return c;
|
||||
}
|
||||
|
||||
/**
|
||||
* Multiplicate the vector a element wise with vector b.
|
||||
* c<sub>i</sub> = a<sub>i</sub>b<sub>i</sub>
|
||||
* @param b vector
|
||||
* @return vector
|
||||
*/
|
||||
public Vector timesE(Vector b){
|
||||
int i;
|
||||
Vector c = create(n());
|
||||
for(i=0; i<n(); i++)
|
||||
c.set(i, get(i) * b.get(i));
|
||||
return c;
|
||||
}
|
||||
|
||||
/**
|
||||
* shorten the vector due scalar division
|
||||
* @param s scalar
|
||||
* @return C = A/s
|
||||
*/
|
||||
public Vector over(double s){
|
||||
int i;
|
||||
Vector c = create(n());
|
||||
for(i=0; i<n(); i++)
|
||||
c.set(i, get(i) / s);
|
||||
return c;
|
||||
}
|
||||
|
||||
/**
|
||||
* Divide the vector a element wise with vector b.
|
||||
* c<sub>i</sub> = a<sub>i</sub>/b<sub>i</sub>
|
||||
* @param b vector
|
||||
* @return vector
|
||||
*/
|
||||
public Vector overE(Vector b){
|
||||
int i;
|
||||
Vector c = create(n());
|
||||
for(i=0; i<n(); i++)
|
||||
c.set(i, get(i) / b.get(i));
|
||||
return c;
|
||||
}
|
||||
|
||||
/**
|
||||
* @return length or magnitude or Euclidean norm
|
||||
*/
|
||||
public double norm(){
|
||||
try {
|
||||
return Math.sqrt(dot(this));
|
||||
} catch (IllegalDimensionException e) {
|
||||
e.printStackTrace();
|
||||
return Double.NaN;
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* @param b
|
||||
* @return Euclidean distance between both vectors
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public double distanceTo(Vector b) throws IllegalDimensionException {
|
||||
if(n() != b.n()) throw new IllegalDimensionException("Illegal vector dimension.");
|
||||
return b.minus(this).norm();
|
||||
}
|
||||
|
||||
/**
|
||||
* normalizing a vector.
|
||||
* A vector of arbitrary length divided by its length.
|
||||
* <b>a</b>/||<b>a</b>||
|
||||
* @return unit vector
|
||||
*/
|
||||
public Vector normalize(){
|
||||
Vector c = times(1.0/norm());
|
||||
this.vector = c.vector;
|
||||
return this;
|
||||
}
|
||||
|
||||
/**
|
||||
* @return the corresponding unit vector
|
||||
*/
|
||||
public Vector direction() {
|
||||
if(norm() == 0.0) throw new RuntimeException("Zero-vector has no direction");
|
||||
return times(1.0 / norm());
|
||||
}
|
||||
|
||||
/**
|
||||
* Element-wise cosine of argument in radians.
|
||||
* @return the cosine for each element of the matrix
|
||||
*/
|
||||
public Vector cos() {
|
||||
int i;
|
||||
int n = n();
|
||||
Vector c = new Vector(n);
|
||||
for(i=0; i<n; i++)
|
||||
c.set(i, Math.cos(get(i)));
|
||||
return c;
|
||||
}
|
||||
|
||||
/**
|
||||
* Element-wise cosine of argument in radians.
|
||||
* @return the cosine for each element of the matrix
|
||||
*/
|
||||
public Vector sin() {
|
||||
int i;
|
||||
int n = n();
|
||||
Vector c = new Vector(n);
|
||||
for(i=0; i<n; i++)
|
||||
c.set(i, Math.sin(get(i)));
|
||||
return c;
|
||||
}
|
||||
|
||||
/**
|
||||
* cosine between this and given vector
|
||||
* @param v vector
|
||||
* @return cosθ
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public double cos(Vector v) throws IllegalDimensionException{
|
||||
return dot(v)/(norm()*v.norm());
|
||||
}
|
||||
|
||||
// sine see in Vector3D
|
||||
|
||||
public double angleD(Vector v) throws IllegalDimensionException{
|
||||
return Maths.acosd(cos(v));
|
||||
}
|
||||
|
||||
/**
|
||||
* swap index i and j
|
||||
* @param i index
|
||||
* @param j index
|
||||
*/
|
||||
public Vector swap(int i, int j) {
|
||||
double temp = get(i);
|
||||
set(i, get(j));
|
||||
set(j, temp);
|
||||
return this;
|
||||
}
|
||||
|
||||
/**
|
||||
* swap min value and max value
|
||||
*/
|
||||
public Vector swapMinMax() {
|
||||
int imin = indexOfMin();
|
||||
int imax = indexOfMax();
|
||||
double temp = get(imin);
|
||||
set(imin, get(imax));
|
||||
set(imax, temp);
|
||||
return this;
|
||||
}
|
||||
|
||||
/**
|
||||
* Creates a sub vector only with chosen rows
|
||||
* @param indices rows
|
||||
* @return the sub vector
|
||||
*/
|
||||
public Vector sub(int[] indices){
|
||||
return sub(indices,false);
|
||||
}
|
||||
|
||||
/**
|
||||
* Creates a sub vector only with chosen rows
|
||||
* @param indices rows
|
||||
* @return the sub vector
|
||||
*/
|
||||
public Vector sub(int[] indices, boolean positions){
|
||||
int n = indices.length;
|
||||
int d = positions?1:0;
|
||||
double[] red = new double[n];
|
||||
for(int i=0; i<n; i++)
|
||||
red[i] = get(indices[i]-d);
|
||||
return new Vector(red);
|
||||
}
|
||||
|
||||
/**
|
||||
* element wise absolute value.
|
||||
* v = { |v<sub>1</sub>|, |v<sub>2</sub>|, …, |v<sub>n</sub>| }
|
||||
* @return vector with absolute values
|
||||
*/
|
||||
public Vector abs(){
|
||||
int i;
|
||||
Vector c = create(n());
|
||||
for(i=0; i<n(); i++)
|
||||
c.set(i, get(i)>=0 ? get(i) : -get(i));
|
||||
return c;
|
||||
}
|
||||
|
||||
/**
|
||||
* Reflection against a plane due to a vector
|
||||
* @return reflected vector
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Vector flip(Vector v) throws IllegalDimensionException{
|
||||
// P = I - alpha v v'; alpha = 2 / (v'v)
|
||||
return Matrix.mirror(v).times(this);
|
||||
}
|
||||
|
||||
/**
|
||||
* Maximum value of the vector
|
||||
* @return maximum value in vector, -∞ if no such value.
|
||||
*/
|
||||
public double max(){
|
||||
return Maths.max(getArray());
|
||||
}
|
||||
|
||||
/**
|
||||
* Minimum value of the vector
|
||||
* @return minimum value in vector, +∞ if no such value.
|
||||
*/
|
||||
public double min(){
|
||||
return Maths.min(getArray());
|
||||
}
|
||||
|
||||
/**
|
||||
* Find value in vector.
|
||||
* @param a value
|
||||
* @return index
|
||||
*/
|
||||
public int indexOf(double a){
|
||||
int i;
|
||||
for(i=0; i<n(); i++)
|
||||
if(a == get(i)) return i;
|
||||
return -1;
|
||||
}
|
||||
|
||||
/**
|
||||
* Find max value in vector.
|
||||
* @return index
|
||||
*/
|
||||
public int indexOfMax(){
|
||||
return indexOf(max());
|
||||
}
|
||||
|
||||
/**
|
||||
* Find min value in vector.
|
||||
* @return index
|
||||
*/
|
||||
public int indexOfMin(){
|
||||
return indexOf(min());
|
||||
}
|
||||
|
||||
/**
|
||||
* Sort vector in ascending order.
|
||||
* @return sorted vector
|
||||
*/
|
||||
public Vector sort(){
|
||||
// Arrays.sort(vector);
|
||||
Collections.sort(vector);
|
||||
return this;
|
||||
}
|
||||
|
||||
/**
|
||||
* Sort vector in descending order.
|
||||
* @return sorted vector
|
||||
*/
|
||||
public Vector sortR(){
|
||||
sort();
|
||||
int i,j;
|
||||
Vector tmp = create(n());
|
||||
for(i = length()-1, j=0; i >= 0; i--, j++)
|
||||
tmp.set(j, get(i));
|
||||
vector = tmp.vector;
|
||||
return this;
|
||||
}
|
||||
|
||||
/**
|
||||
* Zero vector?
|
||||
* @return boolean
|
||||
*/
|
||||
public boolean isZero(){
|
||||
int i;
|
||||
boolean result = true;
|
||||
for(i=0; i<n(); i++){
|
||||
if(get(i) > 0){
|
||||
result = false;
|
||||
break;
|
||||
}
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
public boolean isNormalized(){
|
||||
return Math.abs(norm()-1)<Maths.ε;
|
||||
}
|
||||
|
||||
/**
|
||||
* Vector in euclidean plane ℝ<sup>2</sup>.
|
||||
* n=2
|
||||
* @return true or false
|
||||
*/
|
||||
public boolean isR2(){
|
||||
return (n()==2);
|
||||
}
|
||||
|
||||
/**
|
||||
* Vector in euclidean plane ℝ<sup>3</sup>.
|
||||
* n=3
|
||||
* @return true or false
|
||||
*/
|
||||
public boolean isR3(){
|
||||
return (n()==3);
|
||||
}
|
||||
|
||||
/**
|
||||
*
|
||||
* @param a int array
|
||||
* @param b int array
|
||||
* @return true if two integer arrays have same length and
|
||||
* all corresponding pairs of integers are equal
|
||||
*/
|
||||
public static boolean equals(int[] a, int[] b){
|
||||
if(a.length != b.length) return false; // same length?
|
||||
int i;
|
||||
for(i=0; i<a.length; i++) // check each corresponding pair
|
||||
if(a[i] != b[i]) return false;
|
||||
return true; // all elements must be equal
|
||||
}
|
||||
|
||||
/**
|
||||
* A string representation of the vector.
|
||||
*/
|
||||
@Override
|
||||
public String toString(){
|
||||
return new Matrix(this).setName(getName()).toString();
|
||||
}
|
||||
|
||||
/**
|
||||
* Transpose (horizontal)
|
||||
* @return string of vector in transposed form
|
||||
*/
|
||||
public String toStringT(){
|
||||
return new Matrix(this).transpose().toString();
|
||||
}
|
||||
|
||||
public void println(){
|
||||
System.out.println(toString());
|
||||
}
|
||||
|
||||
/**
|
||||
* Transpose (horizontal)
|
||||
*/
|
||||
public void toConsoleT(){
|
||||
System.out.println(toStringT());
|
||||
}
|
||||
|
||||
/**
|
||||
* test client
|
||||
* @param args
|
||||
*/
|
||||
public static void main(String[] args) {
|
||||
Vector a = new Vector(5, 1, 1);
|
||||
a.println();
|
||||
Vector b = a.normalize();
|
||||
a.println();
|
||||
b.println();
|
||||
Vector.fill(2., 2.5).println();
|
||||
Vector.fill(2., 8).println();
|
||||
Vector.fill(8., 2).toConsoleT();
|
||||
Vector.fill(2., 2, 8).println();
|
||||
Vector.fill(8., -2, 2).toConsoleT();
|
||||
System.out.println("a isNull? : " + a.isZero());
|
||||
System.out.println("a-a isNull? : " + a.minus(a).isZero());
|
||||
a = new Vector(1, 1);
|
||||
a.println();
|
||||
try {
|
||||
System.out.println(a.dot(a));
|
||||
} catch (IllegalDimensionException e1) {
|
||||
e1.printStackTrace();
|
||||
}
|
||||
a.tensorProduct(a).println();
|
||||
b = new Vector(1, 2, 3);
|
||||
a.tensorProduct(b).println();
|
||||
Vector v = new Vector(1, 1);
|
||||
Vector w = new Vector(0, 1);
|
||||
try {
|
||||
w.flip(v).println();
|
||||
} catch (IllegalDimensionException e) {
|
||||
e.printStackTrace();
|
||||
}
|
||||
Vector c = new Vector(4, -21.0, 3);
|
||||
c.setName("c").println();
|
||||
c.sort().println();
|
||||
c.sortR().println();
|
||||
}
|
||||
}
|
||||
80
src/math/matrix/Vector2D.java
Normal file
80
src/math/matrix/Vector2D.java
Normal file
@@ -0,0 +1,80 @@
|
||||
package math.matrix;
|
||||
|
||||
import exception.IllegalDimensionException;
|
||||
|
||||
public class Vector2D extends Vector{
|
||||
|
||||
/**
|
||||
* UID
|
||||
*/
|
||||
private static final long serialVersionUID = -4752129361019389194L;
|
||||
|
||||
public Vector2D(){
|
||||
super(2);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector with given x and y value
|
||||
* @param x
|
||||
* @param y
|
||||
*/
|
||||
public Vector2D(double x, double y){
|
||||
super(x,y);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector with given array
|
||||
* @param data array
|
||||
*/
|
||||
public Vector2D(double... data){
|
||||
super(data);
|
||||
}
|
||||
|
||||
/**
|
||||
* Copy vector
|
||||
* @param v vector
|
||||
*/
|
||||
public Vector2D(Vector v){
|
||||
super(v);
|
||||
}
|
||||
|
||||
/**
|
||||
* revolve vector 90°. max 2 dimension vector.
|
||||
* @return 90° revolved vector
|
||||
*/
|
||||
public Vector2D orthogonal(){
|
||||
return new Vector2D(get(1),get(0));
|
||||
}
|
||||
|
||||
/**
|
||||
* revolve normalized vector 90°.
|
||||
* @return 90° revolved normalized vector
|
||||
*/
|
||||
public Vector2D orthonormalized(){
|
||||
return (Vector2D) orthogonal().normalize();
|
||||
}
|
||||
|
||||
/**
|
||||
* lengthen the vector and revolve 90°.
|
||||
* @param a lengthen factor
|
||||
* @return 90° revolved lengthened vector
|
||||
*/
|
||||
public Vector2D orthogonalScalarMultiplication(Double a){
|
||||
return (Vector2D) orthonormalized().times(a);
|
||||
}
|
||||
|
||||
/**
|
||||
* Rotation by ϑ degrees counterclockwise or -ϑ degrees clockwise.
|
||||
* @param ϑ in degrees
|
||||
* @return rotated vector
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Vector2D rotate(double ϑ) throws IllegalDimensionException{
|
||||
if(!isR2()) throw new IllegalDimensionException("Illegal vector dimensions.");
|
||||
return (Vector2D) TensorII2D.rotation(ϑ).times(this);
|
||||
}
|
||||
|
||||
public static void main(String[] args) {
|
||||
}
|
||||
|
||||
}
|
||||
120
src/math/matrix/Vector3D.java
Normal file
120
src/math/matrix/Vector3D.java
Normal file
@@ -0,0 +1,120 @@
|
||||
package math.matrix;
|
||||
|
||||
import exception.IllegalDimensionException;
|
||||
|
||||
public class Vector3D extends Vector{
|
||||
|
||||
/**
|
||||
* UID
|
||||
*/
|
||||
private static final long serialVersionUID = 1904780583446397290L;
|
||||
|
||||
public Vector3D(){
|
||||
super(3);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector with given x, y and z value
|
||||
* @param x
|
||||
* @param y
|
||||
* @param z
|
||||
*/
|
||||
public Vector3D(double x, double y, double z){
|
||||
super(x, y, z);
|
||||
}
|
||||
|
||||
/**
|
||||
* Create vector with given array
|
||||
* @param data array
|
||||
*/
|
||||
public Vector3D(double... data){
|
||||
super(data);
|
||||
}
|
||||
|
||||
/**
|
||||
* Copy vector
|
||||
* @param v vector
|
||||
*/
|
||||
public Vector3D(Vector v){
|
||||
super(v);
|
||||
}
|
||||
|
||||
/**
|
||||
* Cross product v x v.
|
||||
* A x B = (a<sub>2</sub>b<sub>3</sub> - a<sub>3</sub>b<sub>2</sub>,
|
||||
* a<sub>3</sub>b<sub>1</sub> - a<sub>1</sub>b<sub>3</sub>,
|
||||
* a<sub>1</sub>b<sub>2</sub> - a<sub>2</sub>b<sub>1</sub>)<sup>T</sup>;
|
||||
* a vector quantity
|
||||
* @param a vector
|
||||
* @return vector
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Vector3D cross(Vector3D a){
|
||||
Vector3D c = new Vector3D();
|
||||
c.set(0, get(1)*a.get(2) - get(2)*a.get(1));
|
||||
c.set(1, get(2)*a.get(0) - get(0)*a.get(2));
|
||||
c.set(2, get(0)*a.get(1) - get(1)*a.get(0));
|
||||
return c;
|
||||
}
|
||||
|
||||
/**
|
||||
* Scalar triple product.
|
||||
* A • (B x C); a scalar quantity
|
||||
* @param b vector
|
||||
* @param c vector
|
||||
* @return scalar
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public double scalTrip(Vector3D b, Vector3D c){
|
||||
try {
|
||||
return dot(b.cross(c));
|
||||
} catch (IllegalDimensionException e) {
|
||||
e.printStackTrace();
|
||||
return Double.NaN;
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* Vector triple product.
|
||||
* A x (B x C); a vector quantity
|
||||
* @param b vector
|
||||
* @param c vector
|
||||
* @return vector
|
||||
* @throws IllegalDimensionException
|
||||
*/
|
||||
public Vector3D vecTrip(Vector3D b, Vector3D c) {
|
||||
return this.cross(b.cross(c));
|
||||
}
|
||||
|
||||
/**
|
||||
* cosine between this and given vector
|
||||
* @param a vector
|
||||
* @return cosθ
|
||||
*/
|
||||
public double cos(Vector3D a){
|
||||
try {
|
||||
return dot(a)/(norm()*a.norm());
|
||||
} catch (IllegalDimensionException e) {
|
||||
e.printStackTrace();
|
||||
return Double.NaN;
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* sine between this and given vector
|
||||
* @param a vector
|
||||
* @return sinθ
|
||||
*/
|
||||
public double sin(Vector3D a){
|
||||
return cross(a).norm()/(norm()*a.norm());
|
||||
}
|
||||
|
||||
public static void main(String[] args) {
|
||||
Vector3D u = new Vector3D(3,3,0);
|
||||
Vector3D v = new Vector3D(0,2,2);
|
||||
System.out.println("cos = " + u.cos(v) + " : " + (u.cos(v)==0.5));
|
||||
System.out.println("|w| = " + u.cross(v).norm() + " : " +
|
||||
((u.cross(v).norm())==(6*Math.sqrt(3))));
|
||||
}
|
||||
|
||||
}
|
||||
256
src/stdlib/StdArrayIO.java
Normal file
256
src/stdlib/StdArrayIO.java
Normal file
@@ -0,0 +1,256 @@
|
||||
package stdlib;
|
||||
|
||||
/*************************************************************************
|
||||
* Compilation: javac StdArrayIO.java
|
||||
* Execution: java StdArrayIO < input.txt
|
||||
*
|
||||
* A library for reading in 1D and 2D arrays of integers, doubles,
|
||||
* and booleans from standard input and printing them out to
|
||||
* standard output.
|
||||
*
|
||||
* % more tinyDouble1D.txt
|
||||
* 4
|
||||
* .000 .246 .222 -.032
|
||||
*
|
||||
* % more tinyDouble2D.txt
|
||||
* 4 3
|
||||
* .000 .270 .000
|
||||
* .246 .224 -.036
|
||||
* .222 .176 .0893
|
||||
* -.032 .739 .270
|
||||
*
|
||||
* % more tinyBoolean2D.txt
|
||||
* 4 3
|
||||
* 1 1 0
|
||||
* 0 0 0
|
||||
* 0 1 1
|
||||
* 1 1 1
|
||||
*
|
||||
* % cat tinyDouble1D.txt tinyDouble2D.txt tinyBoolean2D.txt | java StdArrayIO
|
||||
* 4
|
||||
* 0.00000 0.24600 0.22200 -0.03200
|
||||
*
|
||||
* 4 3
|
||||
* 0.00000 0.27000 0.00000
|
||||
* 0.24600 0.22400 -0.03600
|
||||
* 0.22200 0.17600 0.08930
|
||||
* 0.03200 0.73900 0.27000
|
||||
*
|
||||
* 4 3
|
||||
* 1 1 0
|
||||
* 0 0 0
|
||||
* 0 1 1
|
||||
* 1 1 1
|
||||
*
|
||||
*************************************************************************/
|
||||
|
||||
|
||||
/**
|
||||
* <i>Standard array IO</i>. This class provides methods for reading
|
||||
* in 1D and 2D arrays from standard input and printing out to
|
||||
* standard output.
|
||||
* <p>
|
||||
* For additional documentation, see
|
||||
* <a href="http://introcs.cs.princeton.edu/22libary">Section 2.2</a> of
|
||||
* <i>Introduction to Programming in Java: An Interdisciplinary Approach</i>
|
||||
* by Robert Sedgewick and Kevin Wayne.
|
||||
*
|
||||
* @author Robert Sedgewick
|
||||
* @author Kevin Wayne
|
||||
*/
|
||||
public class StdArrayIO {
|
||||
|
||||
// it doesn't make sense to instantiate this class
|
||||
private StdArrayIO() { }
|
||||
|
||||
/**
|
||||
* Read in and return an array of doubles from standard input.
|
||||
*/
|
||||
public static double[] readDouble1D() {
|
||||
int N = StdIn.readInt();
|
||||
double[] a = new double[N];
|
||||
for (int i = 0; i < N; i++) {
|
||||
a[i] = StdIn.readDouble();
|
||||
}
|
||||
return a;
|
||||
}
|
||||
|
||||
/**
|
||||
* Print an array of doubles to standard output.
|
||||
*/
|
||||
public static void print(double[] a) {
|
||||
int N = a.length;
|
||||
StdOut.println(N);
|
||||
for (int i = 0; i < N; i++) {
|
||||
StdOut.printf("%9.5f ", a[i]);
|
||||
}
|
||||
StdOut.println();
|
||||
}
|
||||
|
||||
|
||||
/**
|
||||
* Read in and return an M-by-N array of doubles from standard input.
|
||||
*/
|
||||
public static double[][] readDouble2D() {
|
||||
int M = StdIn.readInt();
|
||||
int N = StdIn.readInt();
|
||||
double[][] a = new double[M][N];
|
||||
for (int i = 0; i < M; i++) {
|
||||
for (int j = 0; j < N; j++) {
|
||||
a[i][j] = StdIn.readDouble();
|
||||
}
|
||||
}
|
||||
return a;
|
||||
}
|
||||
|
||||
/**
|
||||
* Print the M-by-N array of doubles to standard output.
|
||||
*/
|
||||
public static void print(double[][] a) {
|
||||
int M = a.length;
|
||||
int N = a[0].length;
|
||||
StdOut.println(M + " " + N);
|
||||
for (int i = 0; i < M; i++) {
|
||||
for (int j = 0; j < N; j++) {
|
||||
StdOut.printf("%9.5f ", a[i][j]);
|
||||
}
|
||||
StdOut.println();
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/**
|
||||
* Read in and return an array of ints from standard input.
|
||||
*/
|
||||
public static int[] readInt1D() {
|
||||
int N = StdIn.readInt();
|
||||
int[] a = new int[N];
|
||||
for (int i = 0; i < N; i++) {
|
||||
a[i] = StdIn.readInt();
|
||||
}
|
||||
return a;
|
||||
}
|
||||
|
||||
/**
|
||||
* Print an array of ints to standard output.
|
||||
*/
|
||||
public static void print(int[] a) {
|
||||
int N = a.length;
|
||||
StdOut.println(N);
|
||||
for (int i = 0; i < N; i++) {
|
||||
StdOut.printf("%9d ", a[i]);
|
||||
}
|
||||
StdOut.println();
|
||||
}
|
||||
|
||||
|
||||
/**
|
||||
* Read in and return an M-by-N array of ints from standard input.
|
||||
*/
|
||||
public static int[][] readInt2D() {
|
||||
int M = StdIn.readInt();
|
||||
int N = StdIn.readInt();
|
||||
int[][] a = new int[M][N];
|
||||
for (int i = 0; i < M; i++) {
|
||||
for (int j = 0; j < N; j++) {
|
||||
a[i][j] = StdIn.readInt();
|
||||
}
|
||||
}
|
||||
return a;
|
||||
}
|
||||
|
||||
/**
|
||||
* Print the M-by-N array of ints to standard output.
|
||||
*/
|
||||
public static void print(int[][] a) {
|
||||
int M = a.length;
|
||||
int N = a[0].length;
|
||||
StdOut.println(M + " " + N);
|
||||
for (int i = 0; i < M; i++) {
|
||||
for (int j = 0; j < N; j++) {
|
||||
StdOut.printf("%9d ", a[i][j]);
|
||||
}
|
||||
StdOut.println();
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/**
|
||||
* Read in and return an array of booleans from standard input.
|
||||
*/
|
||||
public static boolean[] readBoolean1D() {
|
||||
int N = StdIn.readInt();
|
||||
boolean[] a = new boolean[N];
|
||||
for (int i = 0; i < N; i++) {
|
||||
a[i] = StdIn.readBoolean();
|
||||
}
|
||||
return a;
|
||||
}
|
||||
|
||||
/**
|
||||
* Print an array of booleans to standard output.
|
||||
*/
|
||||
public static void print(boolean[] a) {
|
||||
int N = a.length;
|
||||
StdOut.println(N);
|
||||
for (int i = 0; i < N; i++) {
|
||||
if (a[i]) StdOut.print("1 ");
|
||||
else StdOut.print("0 ");
|
||||
}
|
||||
StdOut.println();
|
||||
}
|
||||
|
||||
/**
|
||||
* Read in and return an M-by-N array of booleans from standard input.
|
||||
*/
|
||||
public static boolean[][] readBoolean2D() {
|
||||
int M = StdIn.readInt();
|
||||
int N = StdIn.readInt();
|
||||
boolean[][] a = new boolean[M][N];
|
||||
for (int i = 0; i < M; i++) {
|
||||
for (int j = 0; j < N; j++) {
|
||||
a[i][j] = StdIn.readBoolean();
|
||||
}
|
||||
}
|
||||
return a;
|
||||
}
|
||||
|
||||
/**
|
||||
* Print the M-by-N array of booleans to standard output.
|
||||
*/
|
||||
public static void print(boolean[][] a) {
|
||||
int M = a.length;
|
||||
int N = a[0].length;
|
||||
StdOut.println(M + " " + N);
|
||||
for (int i = 0; i < M; i++) {
|
||||
for (int j = 0; j < N; j++) {
|
||||
if (a[i][j]) StdOut.print("1 ");
|
||||
else StdOut.print("0 ");
|
||||
}
|
||||
StdOut.println();
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/**
|
||||
* Test client.
|
||||
*/
|
||||
public static void main(String[] args) {
|
||||
|
||||
// read and print an array of doubles
|
||||
double[] a = StdArrayIO.readDouble1D();
|
||||
StdArrayIO.print(a);
|
||||
StdOut.println();
|
||||
|
||||
// read and print a matrix of doubles
|
||||
double[][] b = StdArrayIO.readDouble2D();
|
||||
StdArrayIO.print(b);
|
||||
StdOut.println();
|
||||
|
||||
// read and print a matrix of doubles
|
||||
boolean[][] d = StdArrayIO.readBoolean2D();
|
||||
StdArrayIO.print(d);
|
||||
StdOut.println();
|
||||
}
|
||||
|
||||
}
|
||||
210
src/stdlib/StdIn.java
Normal file
210
src/stdlib/StdIn.java
Normal file
@@ -0,0 +1,210 @@
|
||||
package stdlib;
|
||||
|
||||
/*************************************************************************
|
||||
* Compilation: javac StdIn.java
|
||||
* Execution: java StdIn
|
||||
*
|
||||
* Reads in data of various types from standard input.
|
||||
*
|
||||
*************************************************************************/
|
||||
|
||||
import java.io.BufferedInputStream;
|
||||
import java.util.Locale;
|
||||
import java.util.Scanner;
|
||||
|
||||
/**
|
||||
* <i>Standard input</i>. This class provides methods for reading strings
|
||||
* and numbers from standard input.
|
||||
* <p>
|
||||
* The Locale used is: language = English, country = US. This is consistent
|
||||
* with the formatting conventions with Java floating-point literals,
|
||||
* command-line arguments (via <tt>Double.parseDouble()</tt>)
|
||||
* and standard output (via <tt>System.out.print()</tt>). It ensures that
|
||||
* standard input works with the input files used in the textbook.
|
||||
* <p>
|
||||
* For additional documentation, see <a href="http://introcs.cs.princeton.edu/15inout">Section 1.5</a> of
|
||||
* <i>Introduction to Programming in Java: An Interdisciplinary Approach</i> by Robert Sedgewick and Kevin Wayne.
|
||||
*/
|
||||
public final class StdIn {
|
||||
|
||||
// assume Unicode UTF-8 encoding
|
||||
private static String charsetName = "UTF-8";
|
||||
|
||||
// assume language = English, country = US for consistency with System.out.
|
||||
private static Locale usLocale = new Locale("en", "US");
|
||||
|
||||
// the scanner object
|
||||
private static Scanner scanner = new Scanner(new BufferedInputStream(System.in), charsetName);
|
||||
|
||||
// static initializer
|
||||
static { scanner.useLocale(usLocale); }
|
||||
|
||||
// singleton pattern - can't instantiate
|
||||
private StdIn() { }
|
||||
|
||||
|
||||
/**
|
||||
* Is there only whitespace left on standard input?
|
||||
*/
|
||||
public static boolean isEmpty() {
|
||||
return !scanner.hasNext();
|
||||
}
|
||||
|
||||
/**
|
||||
* Return next string from standard input
|
||||
*/
|
||||
public static String readString() {
|
||||
return scanner.next();
|
||||
}
|
||||
|
||||
/**
|
||||
* Return next int from standard input
|
||||
*/
|
||||
public static int readInt() {
|
||||
return scanner.nextInt();
|
||||
}
|
||||
|
||||
/**
|
||||
* Return next double from standard input
|
||||
*/
|
||||
public static double readDouble() {
|
||||
return scanner.nextDouble();
|
||||
}
|
||||
|
||||
/**
|
||||
* Return next float from standard input
|
||||
*/
|
||||
public static float readFloat() {
|
||||
return scanner.nextFloat();
|
||||
}
|
||||
|
||||
/**
|
||||
* Return next short from standard input
|
||||
*/
|
||||
public static short readShort() {
|
||||
return scanner.nextShort();
|
||||
}
|
||||
|
||||
/**
|
||||
* Return next long from standard input
|
||||
*/
|
||||
public static long readLong() {
|
||||
return scanner.nextLong();
|
||||
}
|
||||
|
||||
/**
|
||||
* Return next byte from standard input
|
||||
*/
|
||||
public static byte readByte() {
|
||||
return scanner.nextByte();
|
||||
}
|
||||
|
||||
/**
|
||||
* Return next boolean from standard input, allowing "true" or "1" for true,
|
||||
* and "false" or "0" for false
|
||||
*/
|
||||
public static boolean readBoolean() {
|
||||
String s = readString();
|
||||
if (s.equalsIgnoreCase("true")) return true;
|
||||
if (s.equalsIgnoreCase("false")) return false;
|
||||
if (s.equals("1")) return true;
|
||||
if (s.equals("0")) return false;
|
||||
throw new java.util.InputMismatchException();
|
||||
}
|
||||
|
||||
/**
|
||||
* Does standard input have a next line?
|
||||
*/
|
||||
public static boolean hasNextLine() {
|
||||
return scanner.hasNextLine();
|
||||
}
|
||||
|
||||
/**
|
||||
* Return rest of line from standard input
|
||||
*/
|
||||
public static String readLine() {
|
||||
return scanner.nextLine();
|
||||
}
|
||||
|
||||
/**
|
||||
* Return next char from standard input
|
||||
*/
|
||||
// a complete hack and inefficient - email me if you have a better
|
||||
public static char readChar() {
|
||||
// (?s) for DOTALL mode so . matches a line termination character
|
||||
// 1 says look only one character ahead
|
||||
// consider precompiling the pattern
|
||||
String s = scanner.findWithinHorizon("(?s).", 1);
|
||||
return s.charAt(0);
|
||||
}
|
||||
|
||||
/**
|
||||
* Return rest of input from standard input
|
||||
*/
|
||||
public static String readAll() {
|
||||
if (!scanner.hasNextLine()) return null;
|
||||
|
||||
// reference: http://weblogs.java.net/blog/pat/archive/2004/10/stupid_scanner_1.html
|
||||
return scanner.useDelimiter("\\A").next();
|
||||
}
|
||||
|
||||
/**
|
||||
* Read rest of input as array of ints
|
||||
*/
|
||||
public static int[] readInts() {
|
||||
String[] fields = readAll().trim().split("\\s+");
|
||||
int[] vals = new int[fields.length];
|
||||
for (int i = 0; i < fields.length; i++)
|
||||
vals[i] = Integer.parseInt(fields[i]);
|
||||
return vals;
|
||||
}
|
||||
|
||||
/**
|
||||
* Read rest of input as array of doubles
|
||||
*/
|
||||
public static double[] readDoubles() {
|
||||
String[] fields = readAll().trim().split("\\s+");
|
||||
double[] vals = new double[fields.length];
|
||||
for (int i = 0; i < fields.length; i++)
|
||||
vals[i] = Double.parseDouble(fields[i]);
|
||||
return vals;
|
||||
}
|
||||
|
||||
/**
|
||||
* Read rest of input as array of strings
|
||||
*/
|
||||
public static String[] readStrings() {
|
||||
String[] fields = readAll().trim().split("\\s+");
|
||||
return fields;
|
||||
}
|
||||
|
||||
|
||||
|
||||
/**
|
||||
* Unit test
|
||||
*/
|
||||
public static void main(String[] args) {
|
||||
|
||||
System.out.println("Type a string: ");
|
||||
String s = StdIn.readString();
|
||||
System.out.println("Your string was: " + s);
|
||||
System.out.println();
|
||||
|
||||
System.out.println("Type an int: ");
|
||||
int a = StdIn.readInt();
|
||||
System.out.println("Your int was: " + a);
|
||||
System.out.println();
|
||||
|
||||
System.out.println("Type a boolean: ");
|
||||
boolean b = StdIn.readBoolean();
|
||||
System.out.println("Your boolean was: " + b);
|
||||
System.out.println();
|
||||
|
||||
System.out.println("Type a double: ");
|
||||
double c = StdIn.readDouble();
|
||||
System.out.println("Your double was: " + c);
|
||||
System.out.println();
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
230
src/stdlib/StdOut.java
Normal file
230
src/stdlib/StdOut.java
Normal file
@@ -0,0 +1,230 @@
|
||||
package stdlib;
|
||||
|
||||
/*************************************************************************
|
||||
* Compilation: javac StdOut.java
|
||||
* Execution: java StdOut
|
||||
*
|
||||
* Writes data of various types to standard output.
|
||||
*
|
||||
*************************************************************************/
|
||||
|
||||
import java.io.OutputStreamWriter;
|
||||
import java.io.PrintWriter;
|
||||
import java.io.UnsupportedEncodingException;
|
||||
import java.util.Locale;
|
||||
|
||||
/**
|
||||
* <i>Standard output</i>. This class provides methods for writing strings
|
||||
* and numbers to standard output.
|
||||
* <p>
|
||||
* For additional documentation, see <a href="http://introcs.cs.princeton.edu/15inout">Section 1.5</a> of
|
||||
* <i>Introduction to Programming in Java: An Interdisciplinary Approach</i> by Robert Sedgewick and Kevin Wayne.
|
||||
*/
|
||||
public final class StdOut {
|
||||
|
||||
// force Unicode UTF-8 encoding; otherwise it's system dependent
|
||||
private static final String UTF8 = "UTF-8";
|
||||
|
||||
// assume language = English, country = US for consistency with StdIn
|
||||
private static final Locale US_LOCALE = new Locale("en", "US");
|
||||
|
||||
// send output here
|
||||
private static PrintWriter out;
|
||||
|
||||
// this is called before invoking any methods
|
||||
static {
|
||||
try {
|
||||
out = new PrintWriter(new OutputStreamWriter(System.out, UTF8), true);
|
||||
}
|
||||
catch (UnsupportedEncodingException e) { System.out.println(e); }
|
||||
}
|
||||
|
||||
// singleton pattern - can't instantiate
|
||||
private StdOut() { }
|
||||
|
||||
// close the output stream (not required)
|
||||
/**
|
||||
* Close standard output.
|
||||
*/
|
||||
public static void close() {
|
||||
out.close();
|
||||
}
|
||||
|
||||
/**
|
||||
* Terminate the current line by printing the line separator string.
|
||||
*/
|
||||
public static void println() {
|
||||
out.println();
|
||||
}
|
||||
|
||||
/**
|
||||
* Print an object to standard output and then terminate the line.
|
||||
*/
|
||||
public static void println(Object x) {
|
||||
out.println(x);
|
||||
}
|
||||
|
||||
/**
|
||||
* Print a boolean to standard output and then terminate the line.
|
||||
*/
|
||||
public static void println(boolean x) {
|
||||
out.println(x);
|
||||
}
|
||||
|
||||
/**
|
||||
* Print a char to standard output and then terminate the line.
|
||||
*/
|
||||
public static void println(char x) {
|
||||
out.println(x);
|
||||
}
|
||||
|
||||
/**
|
||||
* Print a double to standard output and then terminate the line.
|
||||
*/
|
||||
public static void println(double x) {
|
||||
out.println(x);
|
||||
}
|
||||
|
||||
/**
|
||||
* Print a float to standard output and then terminate the line.
|
||||
*/
|
||||
public static void println(float x) {
|
||||
out.println(x);
|
||||
}
|
||||
|
||||
/**
|
||||
* Print an int to standard output and then terminate the line.
|
||||
*/
|
||||
public static void println(int x) {
|
||||
out.println(x);
|
||||
}
|
||||
|
||||
/**
|
||||
* Print a long to standard output and then terminate the line.
|
||||
*/
|
||||
public static void println(long x) {
|
||||
out.println(x);
|
||||
}
|
||||
|
||||
/**
|
||||
* Print a short to standard output and then terminate the line.
|
||||
*/
|
||||
public static void println(short x) {
|
||||
out.println(x);
|
||||
}
|
||||
|
||||
/**
|
||||
* Print a byte to standard output and then terminate the line.
|
||||
*/
|
||||
public static void println(byte x) {
|
||||
out.println(x);
|
||||
}
|
||||
|
||||
/**
|
||||
* Flush standard output.
|
||||
*/
|
||||
public static void print() {
|
||||
out.flush();
|
||||
}
|
||||
|
||||
/**
|
||||
* Print an Object to standard output and flush standard output.
|
||||
*/
|
||||
public static void print(Object x) {
|
||||
out.print(x);
|
||||
out.flush();
|
||||
}
|
||||
|
||||
/**
|
||||
* Print a boolean to standard output and flush standard output.
|
||||
*/
|
||||
public static void print(boolean x) {
|
||||
out.print(x);
|
||||
out.flush();
|
||||
}
|
||||
|
||||
/**
|
||||
* Print a char to standard output and flush standard output.
|
||||
*/
|
||||
public static void print(char x) {
|
||||
out.print(x);
|
||||
out.flush();
|
||||
}
|
||||
|
||||
/**
|
||||
* Print a double to standard output and flush standard output.
|
||||
*/
|
||||
public static void print(double x) {
|
||||
out.print(x);
|
||||
out.flush();
|
||||
}
|
||||
|
||||
/**
|
||||
* Print a float to standard output and flush standard output.
|
||||
*/
|
||||
public static void print(float x) {
|
||||
out.print(x);
|
||||
out.flush();
|
||||
}
|
||||
|
||||
/**
|
||||
* Print an int to standard output and flush standard output.
|
||||
*/
|
||||
public static void print(int x) {
|
||||
out.print(x);
|
||||
out.flush();
|
||||
}
|
||||
|
||||
/**
|
||||
* Print a long to standard output and flush standard output.
|
||||
*/
|
||||
public static void print(long x) {
|
||||
out.print(x);
|
||||
out.flush();
|
||||
}
|
||||
|
||||
/**
|
||||
* Print a short to standard output and flush standard output.
|
||||
*/
|
||||
public static void print(short x) {
|
||||
out.print(x);
|
||||
out.flush();
|
||||
}
|
||||
|
||||
/**
|
||||
* Print a byte to standard output and flush standard output.
|
||||
*/
|
||||
public static void print(byte x) {
|
||||
out.print(x);
|
||||
out.flush();
|
||||
}
|
||||
|
||||
/**
|
||||
* Print a formatted string to standard output using the specified
|
||||
* format string and arguments, and flush standard output.
|
||||
*/
|
||||
public static void printf(String format, Object... args) {
|
||||
out.printf(US_LOCALE, format, args);
|
||||
out.flush();
|
||||
}
|
||||
|
||||
/**
|
||||
* Print a formatted string to standard output using the specified
|
||||
* locale, format string, and arguments, and flush standard output.
|
||||
*/
|
||||
public static void printf(Locale locale, String format, Object... args) {
|
||||
out.printf(locale, format, args);
|
||||
out.flush();
|
||||
}
|
||||
|
||||
// This method is just here to test the class
|
||||
public static void main(String[] args) {
|
||||
|
||||
// write to stdout
|
||||
StdOut.println("Test");
|
||||
StdOut.println(17);
|
||||
StdOut.println(true);
|
||||
StdOut.printf("%.6f\n", 1.0/7.0);
|
||||
}
|
||||
|
||||
}
|
||||
Reference in New Issue
Block a user