diff --git a/src/main/java/plugins/nherve/matrix/CholeskyDecomposition.java b/src/main/java/plugins/nherve/matrix/CholeskyDecomposition.java
new file mode 100644
index 0000000000000000000000000000000000000000..d8ccd0272519e70eea2916a888acd1ee33300a12
--- /dev/null
+++ b/src/main/java/plugins/nherve/matrix/CholeskyDecomposition.java
@@ -0,0 +1,202 @@
+package plugins.nherve.matrix;
+
+
+ /** Cholesky Decomposition.
+ <P>
+ For a symmetric, positive definite matrix A, the Cholesky decomposition
+ is an lower triangular matrix L so that A = L*L'.
+ <P>
+ If the matrix is not symmetric or positive definite, the constructor
+ returns a partial decomposition and sets an internal flag that may
+ be queried by the isSPD() method.
+ */
+
+public class CholeskyDecomposition implements java.io.Serializable {
+
+/* ------------------------
+ Class variables
+ * ------------------------ */
+
+ private static final long serialVersionUID = 4992469433140406640L;
+
+/** Array for internal storage of decomposition.
+ @serial internal array storage.
+ */
+ private double[][] L;
+
+ /** Row and column dimension (square matrix).
+ @serial matrix dimension.
+ */
+ private int n;
+
+ /** Symmetric and positive definite flag.
+ @serial is symmetric and positive definite flag.
+ */
+ private boolean isspd;
+
+/* ------------------------
+ Constructor
+ * ------------------------ */
+
+ /** Cholesky algorithm for symmetric and positive definite matrix.
+ @param A Square, symmetric matrix.
+ @return Structure to access L and isspd flag.
+ */
+
+ public CholeskyDecomposition (Matrix Arg) {
+
+
+ // Initialize.
+ double[][] A = Arg.getArray();
+ n = Arg.getRowDimension();
+ L = new double[n][n];
+ isspd = (Arg.getColumnDimension() == n);
+ // Main loop.
+ for (int j = 0; j < n; j++) {
+ double[] Lrowj = L[j];
+ double d = 0.0;
+ for (int k = 0; k < j; k++) {
+ double[] Lrowk = L[k];
+ double s = 0.0;
+ for (int i = 0; i < k; i++) {
+ s += Lrowk[i]*Lrowj[i];
+ }
+ Lrowj[k] = s = (A[j][k] - s)/L[k][k];
+ d = d + s*s;
+ isspd = isspd & (A[k][j] == A[j][k]);
+ }
+ d = A[j][j] - d;
+ isspd = isspd & (d > 0.0);
+ L[j][j] = Math.sqrt(Math.max(d,0.0));
+ for (int k = j+1; k < n; k++) {
+ L[j][k] = 0.0;
+ }
+ }
+ }
+
+/* ------------------------
+ Temporary, experimental code.
+ * ------------------------ *\
+
+ \** Right Triangular Cholesky Decomposition.
+ <P>
+ For a symmetric, positive definite matrix A, the Right Cholesky
+ decomposition is an upper triangular matrix R so that A = R'*R.
+ This constructor computes R with the Fortran inspired column oriented
+ algorithm used in LINPACK and MATLAB. In Java, we suspect a row oriented,
+ lower triangular decomposition is faster. We have temporarily included
+ this constructor here until timing experiments confirm this suspicion.
+ *\
+
+ \** Array for internal storage of right triangular decomposition. **\
+ private transient double[][] R;
+
+ \** Cholesky algorithm for symmetric and positive definite matrix.
+ @param A Square, symmetric matrix.
+ @param rightflag Actual value ignored.
+ @return Structure to access R and isspd flag.
+ *\
+
+ public CholeskyDecomposition (Matrix Arg, int rightflag) {
+ // Initialize.
+ double[][] A = Arg.getArray();
+ n = Arg.getColumnDimension();
+ R = new double[n][n];
+ isspd = (Arg.getColumnDimension() == n);
+ // Main loop.
+ for (int j = 0; j < n; j++) {
+ double d = 0.0;
+ for (int k = 0; k < j; k++) {
+ double s = A[k][j];
+ for (int i = 0; i < k; i++) {
+ s = s - R[i][k]*R[i][j];
+ }
+ R[k][j] = s = s/R[k][k];
+ d = d + s*s;
+ isspd = isspd & (A[k][j] == A[j][k]);
+ }
+ d = A[j][j] - d;
+ isspd = isspd & (d > 0.0);
+ R[j][j] = Math.sqrt(Math.max(d,0.0));
+ for (int k = j+1; k < n; k++) {
+ R[k][j] = 0.0;
+ }
+ }
+ }
+
+ \** Return upper triangular factor.
+ @return R
+ *\
+
+ public Matrix getR () {
+ return new Matrix(R,n,n);
+ }
+
+\* ------------------------
+ End of temporary code.
+ * ------------------------ */
+
+/* ------------------------
+ Public Methods
+ * ------------------------ */
+
+ /** Is the matrix symmetric and positive definite?
+ @return true if A is symmetric and positive definite.
+ */
+
+ public boolean isSPD () {
+ return isspd;
+ }
+
+ /** Return triangular factor.
+ @return L
+ */
+
+ public Matrix getL () {
+ return new Matrix(L,n,n);
+ }
+
+ /** Solve A*X = B
+ @param B A Matrix with as many rows as A and any number of columns.
+ @return X so that L*L'*X = B
+ @exception IllegalArgumentException Matrix row dimensions must agree.
+ @exception RuntimeException Matrix is not symmetric positive definite.
+ */
+
+ public Matrix solve (Matrix B) {
+ if (B.getRowDimension() != n) {
+ throw new IllegalArgumentException("Matrix row dimensions must agree.");
+ }
+ if (!isspd) {
+ throw new RuntimeException("Matrix is not symmetric positive definite.");
+ }
+
+ // Copy right hand side.
+ double[][] X = B.getArrayCopy();
+ int nx = B.getColumnDimension();
+
+ // Solve L*Y = B;
+ for (int k = 0; k < n; k++) {
+ for (int j = 0; j < nx; j++) {
+ for (int i = 0; i < k ; i++) {
+ X[k][j] -= X[i][j]*L[k][i];
+ }
+ X[k][j] /= L[k][k];
+ }
+ }
+
+ // Solve L'*X = Y;
+ for (int k = n-1; k >= 0; k--) {
+ for (int j = 0; j < nx; j++) {
+ for (int i = k+1; i < n ; i++) {
+ X[k][j] -= X[i][j]*L[i][k];
+ }
+ X[k][j] /= L[k][k];
+ }
+ }
+
+
+ return new Matrix(X,n,nx);
+ }
+}
+
diff --git a/src/main/java/plugins/nherve/matrix/EigenvalueDecomposition.java b/src/main/java/plugins/nherve/matrix/EigenvalueDecomposition.java
new file mode 100644
index 0000000000000000000000000000000000000000..35cf0dd583998362389b003210e1cd552e7b3aab
--- /dev/null
+++ b/src/main/java/plugins/nherve/matrix/EigenvalueDecomposition.java
@@ -0,0 +1,958 @@
+package plugins.nherve.matrix;
+
+import plugins.nherve.matrix.util.Maths;
+
+/** Eigenvalues and eigenvectors of a real matrix.
+<P>
+ If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is
+ diagonal and the eigenvector matrix V is orthogonal.
+ I.e. A = V.times(D.times(V.transpose())) and
+ V.times(V.transpose()) equals the identity matrix.
+<P>
+ If A is not symmetric, then the eigenvalue matrix D is block diagonal
+ with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
+ lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The
+ columns of V represent the eigenvectors in the sense that A*V = V*D,
+ i.e. A.times(V) equals V.times(D). The matrix V may be badly
+ conditioned, or even singular, so the validity of the equation
+ A = V*D*inverse(V) depends upon V.cond().
+**/
+
+public class EigenvalueDecomposition implements java.io.Serializable {
+
+/* ------------------------
+ Class variables
+ * ------------------------ */
+
+ private static final long serialVersionUID = 1377631688565277746L;
+
+/** Row and column dimension (square matrix).
+ @serial matrix dimension.
+ */
+ private int n;
+
+ /** Symmetry flag.
+ @serial internal symmetry flag.
+ */
+ private boolean issymmetric;
+
+ /** Arrays for internal storage of eigenvalues.
+ @serial internal storage of eigenvalues.
+ */
+ private double[] d, e;
+
+ /** Array for internal storage of eigenvectors.
+ @serial internal storage of eigenvectors.
+ */
+ private double[][] V;
+
+ /** Array for internal storage of nonsymmetric Hessenberg form.
+ @serial internal storage of nonsymmetric Hessenberg form.
+ */
+ private double[][] H;
+
+ /** Working storage for nonsymmetric algorithm.
+ @serial working storage for nonsymmetric algorithm.
+ */
+ private double[] ort;
+
+/* ------------------------
+ Private Methods
+ * ------------------------ */
+
+ // Symmetric Householder reduction to tridiagonal form.
+
+ private void tred2 () {
+
+ // This is derived from the Algol procedures tred2 by
+ // Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
+ // Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
+ // Fortran subroutine in EISPACK.
+
+ for (int j = 0; j < n; j++) {
+ d[j] = V[n-1][j];
+ }
+
+ // Householder reduction to tridiagonal form.
+
+ for (int i = n-1; i > 0; i--) {
+
+ // Scale to avoid under/overflow.
+
+ double scale = 0.0;
+ double h = 0.0;
+ for (int k = 0; k < i; k++) {
+ scale = scale + Math.abs(d[k]);
+ }
+ if (scale == 0.0) {
+ e[i] = d[i-1];
+ for (int j = 0; j < i; j++) {
+ d[j] = V[i-1][j];
+ V[i][j] = 0.0;
+ V[j][i] = 0.0;
+ }
+ } else {
+
+ // Generate Householder vector.
+
+ 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) {
+ p = p / x;
+ q = q / x;
+ r = r / x;
+ }
+ }
+ if (x == 0.0) {
+ break;
+ }
+ 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
+ @param A Square matrix
+ @return Structure to access D and V.
+ */
+
+ public EigenvalueDecomposition (Matrix Arg) {
+ double[][] A = Arg.getArray();
+ n = Arg.getColumnDimension();
+ 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,n,n);
+ }
+
+ /** 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 () {
+ Matrix X = new Matrix(n,n);
+ double[][] D = X.getArray();
+ for (int i = 0; i < n; i++) {
+ for (int j = 0; j < n; j++) {
+ D[i][j] = 0.0;
+ }
+ D[i][i] = d[i];
+ if (e[i] > 0) {
+ D[i][i+1] = e[i];
+ } else if (e[i] < 0) {
+ D[i][i-1] = e[i];
+ }
+ }
+ return X;
+ }
+}
diff --git a/src/main/java/plugins/nherve/matrix/LUDecomposition.java b/src/main/java/plugins/nherve/matrix/LUDecomposition.java
new file mode 100644
index 0000000000000000000000000000000000000000..b7b536f4fb4bdcb84388ea4a8090681c15cf85b3
--- /dev/null
+++ b/src/main/java/plugins/nherve/matrix/LUDecomposition.java
@@ -0,0 +1,314 @@
+package plugins.nherve.matrix;
+
+
+ /** 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 java.io.Serializable {
+
+/* ------------------------
+ Class variables
+ * ------------------------ */
+
+ private static final long serialVersionUID = -181695365290691888L;
+
+/** Array for internal storage of decomposition.
+ @serial internal array storage.
+ */
+ private double[][] LU;
+
+ /** Row and column dimensions, and pivot sign.
+ @serial column dimension.
+ @serial row dimension.
+ @serial pivot sign.
+ */
+ private int m, n, pivsign;
+
+ /** Internal storage of pivot vector.
+ @serial pivot vector.
+ */
+ private int[] piv;
+
+/* ------------------------
+ Constructor
+ * ------------------------ */
+
+ /** LU Decomposition
+ @param A Rectangular matrix
+ @return Structure to access L, U and piv.
+ */
+
+ public LUDecomposition (Matrix A) {
+
+ // Use a "left-looking", dot-product, Crout/Doolittle algorithm.
+
+ LU = A.getArrayCopy();
+ m = A.getRowDimension();
+ n = A.getColumnDimension();
+ piv = new int[m];
+ for (int i = 0; i < m; i++) {
+ piv[i] = i;
+ }
+ pivsign = 1;
+ double[] LUrowi;
+ double[] LUcolj = new double[m];
+
+ // Outer loop.
+
+ for (int j = 0; j < n; j++) {
+
+ // Make a copy of the j-th column to localize references.
+
+ for (int i = 0; i < m; i++) {
+ LUcolj[i] = LU[i][j];
+ }
+
+ // Apply previous transformations.
+
+ for (int 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 (int 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 (int i = j+1; i < m; i++) {
+ if (Math.abs(LUcolj[i]) > Math.abs(LUcolj[p])) {
+ p = i;
+ }
+ }
+ if (p != j) {
+ for (int k = 0; k < n; k++) {
+ double t = LU[p][k]; LU[p][k] = LU[j][k]; LU[j][k] = t;
+ }
+ int k = piv[p]; piv[p] = piv[j]; piv[j] = k;
+ pivsign = -pivsign;
+ }
+
+ // Compute multipliers.
+
+ if (j < m & LU[j][j] != 0.0) {
+ for (int 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>
+ @param A Rectangular matrix
+ @param linpackflag Use Gaussian elimination. Actual value ignored.
+ @return Structure to access L, U and piv.
+ *\
+
+ public LUDecomposition (Matrix A, int linpackflag) {
+ // Initialize.
+ LU = A.getArrayCopy();
+ m = A.getRowDimension();
+ n = A.getColumnDimension();
+ piv = new int[m];
+ for (int i = 0; i < m; i++) {
+ piv[i] = i;
+ }
+ pivsign = 1;
+ // Main loop.
+ for (int k = 0; k < n; k++) {
+ // Find pivot.
+ int p = k;
+ for (int 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 (int 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 (int i = k+1; i < m; i++) {
+ LU[i][k] /= LU[k][k];
+ for (int j = k+1; j < n; j++) {
+ LU[i][j] -= LU[i][k]*LU[k][j];
+ }
+ }
+ }
+ }
+ }
+
+\* ------------------------
+ End of temporary code.
+ * ------------------------ */
+
+/* ------------------------
+ Public Methods
+ * ------------------------ */
+
+ /** Is the matrix nonsingular?
+ @return true if U, and hence A, is nonsingular.
+ */
+
+ public boolean isNonsingular () {
+ for (int j = 0; j < n; j++) {
+ if (LU[j][j] == 0)
+ return false;
+ }
+ return true;
+ }
+
+ /** Return lower triangular factor
+ @return L
+ */
+
+ public Matrix getL () {
+ Matrix X = new Matrix(m,n);
+ double[][] L = X.getArray();
+ for (int i = 0; i < m; i++) {
+ for (int 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 () {
+ Matrix X = new Matrix(n,n);
+ double[][] U = X.getArray();
+ for (int i = 0; i < n; i++) {
+ for (int 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[] p = new int[m];
+ for (int i = 0; i < m; i++) {
+ p[i] = piv[i];
+ }
+ return p;
+ }
+
+ /** Return pivot permutation vector as a one-dimensional double array
+ @return (double) piv
+ */
+
+ public double[] getDoublePivot () {
+ double[] vals = new double[m];
+ for (int 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 () {
+ if (m != n) {
+ throw new IllegalArgumentException("Matrix must be square.");
+ }
+ double d = (double) pivsign;
+ for (int 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.getRowDimension() != m) {
+ throw new IllegalArgumentException("Matrix row dimensions must agree.");
+ }
+ if (!this.isNonsingular()) {
+ throw new RuntimeException("Matrix is singular.");
+ }
+
+ // Copy right hand side with pivoting
+ int nx = B.getColumnDimension();
+ Matrix Xmat = B.getMatrix(piv,0,nx-1);
+ double[][] X = Xmat.getArray();
+
+ // Solve L*Y = B(piv,:)
+ for (int k = 0; k < n; k++) {
+ for (int i = k+1; i < n; i++) {
+ for (int j = 0; j < nx; j++) {
+ X[i][j] -= X[k][j]*LU[i][k];
+ }
+ }
+ }
+ // Solve U*X = Y;
+ for (int k = n-1; k >= 0; k--) {
+ for (int j = 0; j < nx; j++) {
+ X[k][j] /= LU[k][k];
+ }
+ for (int i = 0; i < k; i++) {
+ for (int j = 0; j < nx; j++) {
+ X[i][j] -= X[k][j]*LU[i][k];
+ }
+ }
+ }
+ return Xmat;
+ }
+}
diff --git a/src/main/java/plugins/nherve/matrix/Matrix.java b/src/main/java/plugins/nherve/matrix/Matrix.java
new file mode 100644
index 0000000000000000000000000000000000000000..b38d648064c411376609d4fd85e75a2aeaf421ab
--- /dev/null
+++ b/src/main/java/plugins/nherve/matrix/Matrix.java
@@ -0,0 +1,1327 @@
+package plugins.nherve.matrix;
+
+
+import java.io.BufferedReader;
+import java.io.PrintWriter;
+import java.io.StreamTokenizer;
+import java.text.DecimalFormat;
+import java.text.DecimalFormatSymbols;
+import java.text.NumberFormat;
+import java.util.Locale;
+import java.util.Vector;
+
+import plugins.nherve.matrix.util.Maths;
+
+
+
+/**
+ * Jama = Java Matrix class.
+ * <P>
+ * The Java Matrix Class provides the fundamental operations of numerical linear
+ * algebra. Various constructors create Matrices from two dimensional arrays of
+ * double precision floating point numbers. Various "gets" and "sets" provide
+ * access to submatrices and matrix elements. Several methods implement basic
+ * matrix arithmetic, including matrix addition and multiplication, matrix
+ * norms, and element-by-element array operations. Methods for reading and
+ * printing matrices are also included. All the operations in this version of
+ * the Matrix Class involve real matrices. Complex matrices may be handled in a
+ * future version.
+ * <P>
+ * Five fundamental matrix decompositions, which consist of pairs or triples of
+ * matrices, permutation vectors, and the like, produce results in five
+ * decomposition classes. These decompositions are accessed by the Matrix class
+ * to compute solutions of simultaneous linear equations, determinants, inverses
+ * and other matrix functions. The five decompositions are:
+ * <P>
+ * <UL>
+ * <LI>Cholesky Decomposition of symmetric, positive definite matrices.
+ * <LI>LU Decomposition of rectangular matrices.
+ * <LI>QR Decomposition of rectangular matrices.
+ * <LI>Singular Value Decomposition of rectangular matrices.
+ * <LI>Eigenvalue Decomposition of both symmetric and nonsymmetric square
+ * matrices.
+ * </UL>
+ * <DL>
+ * <DT><B>Example of use:</B></DT>
+ * <P>
+ * <DD>Solve a linear system A x = b and compute the residual norm, ||b - A x||.
+ * <P>
+ *
+ * <PRE>
+ * double[][] vals = { { 1., 2., 3 }, { 4., 5., 6. }, { 7., 8., 10. } };
+ * Matrix A = new Matrix(vals);
+ * Matrix b = Matrix.random(3, 1);
+ * Matrix x = A.solve(b);
+ * Matrix r = A.times(x).minus(b);
+ * double rnorm = r.normInf();
+ * </PRE>
+ *
+ * </DD>
+ * </DL>
+ *
+ * @author The MathWorks, Inc. and the National Institute of Standards and
+ * Technology.
+ * @version 5 August 1998
+ */
+
+public class Matrix implements Cloneable, java.io.Serializable {
+
+ /*
+ * ------------------------ Class variables ------------------------
+ */
+
+ private static final long serialVersionUID = 3931280766651959467L;
+
+ public Matrix() {
+ super();
+ // TODO Auto-generated constructor stub
+ }
+
+ /**
+ * Array for internal storage of elements.
+ *
+ * @serial internal array storage.
+ */
+ protected double[][] A;
+
+ /**
+ * Row and column dimensions.
+ *
+ * @serial row dimension.
+ * @serial column dimension.
+ */
+ protected int m, n;
+
+ /*
+ * ------------------------ Constructors ------------------------
+ */
+
+ /**
+ * Construct an m-by-n matrix of zeros.
+ *
+ * @param m
+ * Number of rows.
+ * @param n
+ * Number of colums.
+ */
+
+ public Matrix(int m, int n) {
+ this.m = m;
+ this.n = n;
+ A = new double[m][n];
+ }
+
+ /**
+ * Construct an m-by-n constant matrix.
+ *
+ * @param m
+ * Number of rows.
+ * @param n
+ * Number of colums.
+ * @param s
+ * Fill the matrix with this scalar value.
+ */
+
+ public Matrix(int m, int n, double s) {
+ this.m = m;
+ this.n = n;
+ A = new double[m][n];
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ A[i][j] = s;
+ }
+ }
+ }
+
+ /**
+ * Construct a matrix from a 2-D array.
+ *
+ * @param A
+ * Two-dimensional array of doubles.
+ * @exception IllegalArgumentException
+ * All rows must have the same length
+ * @see #constructWithCopy
+ */
+
+ public Matrix(double[][] A) {
+ m = A.length;
+ n = A[0].length;
+ for (int i = 0; i < m; i++) {
+ if (A[i].length != n) {
+ throw new IllegalArgumentException("All rows must have the same length.");
+ }
+ }
+ this.A = A;
+ }
+
+ /**
+ * Construct a matrix quickly without checking arguments.
+ *
+ * @param A
+ * Two-dimensional array of doubles.
+ * @param m
+ * Number of rows.
+ * @param n
+ * Number of colums.
+ */
+
+ public Matrix(double[][] A, int m, int n) {
+ this.A = A;
+ this.m = m;
+ this.n = n;
+ }
+
+ /**
+ * Construct a matrix from a one-dimensional packed array
+ *
+ * @param vals
+ * One-dimensional array of doubles, packed by columns (ala
+ * Fortran).
+ * @param m
+ * Number of rows.
+ * @exception IllegalArgumentException
+ * Array length must be a multiple of m.
+ */
+
+ public Matrix(double vals[], int m) {
+ this.m = m;
+ n = (m != 0 ? vals.length / m : 0);
+ if (m * n != vals.length) {
+ throw new IllegalArgumentException("Array length must be a multiple of m.");
+ }
+ A = new double[m][n];
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ A[i][j] = vals[i + j * m];
+ }
+ }
+ }
+
+ /*
+ * ------------------------ Public Methods ------------------------
+ */
+
+ /**
+ * Construct a matrix from a copy of a 2-D array.
+ *
+ * @param A
+ * Two-dimensional array of doubles.
+ * @exception IllegalArgumentException
+ * All rows must have the same length
+ */
+
+ public static Matrix constructWithCopy(double[][] A) {
+ int m = A.length;
+ int n = A[0].length;
+ Matrix X = new Matrix(m, n);
+ double[][] C = X.getArray();
+ for (int i = 0; i < m; i++) {
+ if (A[i].length != n) {
+ throw new IllegalArgumentException("All rows must have the same length.");
+ }
+ for (int j = 0; j < n; j++) {
+ C[i][j] = A[i][j];
+ }
+ }
+ return X;
+ }
+
+ /**
+ * Make a deep copy of a matrix
+ */
+
+ public Matrix copy() {
+ Matrix X = new Matrix(m, n);
+ double[][] C = X.getArray();
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ C[i][j] = A[i][j];
+ }
+ }
+ return X;
+ }
+
+ /**
+ * Clone the Matrix object.
+ */
+
+ public Object clone() {
+ return this.copy();
+ }
+
+ /**
+ * Access the internal two-dimensional array.
+ *
+ * @return Pointer to the two-dimensional array of matrix elements.
+ */
+
+ public double[][] getArray() {
+ return A;
+ }
+
+ /**
+ * Copy the internal two-dimensional array.
+ *
+ * @return Two-dimensional array copy of matrix elements.
+ */
+
+ public double[][] getArrayCopy() {
+ double[][] C = new double[m][n];
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ C[i][j] = A[i][j];
+ }
+ }
+ return C;
+ }
+
+ /**
+ * Make a one-dimensional column packed copy of the internal array.
+ *
+ * @return Matrix elements packed in a one-dimensional array by columns.
+ */
+
+ public double[] getColumnPackedCopy() {
+ double[] vals = new double[m * n];
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ vals[i + j * m] = A[i][j];
+ }
+ }
+ return vals;
+ }
+
+ /**
+ * Make a one-dimensional row packed copy of the internal array.
+ *
+ * @return Matrix elements packed in a one-dimensional array by rows.
+ */
+
+ public double[] getRowPackedCopy() {
+ double[] vals = new double[m * n];
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ vals[i * n + j] = A[i][j];
+ }
+ }
+ return vals;
+ }
+
+ /**
+ * Get row dimension.
+ *
+ * @return m, the number of rows.
+ */
+
+ public int getRowDimension() {
+ return m;
+ }
+
+ /**
+ * Get column dimension.
+ *
+ * @return n, the number of columns.
+ */
+
+ public int getColumnDimension() {
+ return n;
+ }
+
+ /**
+ * Get a single element.
+ *
+ * @param i
+ * Row index.
+ * @param j
+ * Column index.
+ * @return A(i,j)
+ * @exception ArrayIndexOutOfBoundsException
+ */
+
+ public double get(int i, int j) {
+ return A[i][j];
+ }
+
+ /**
+ * Get a submatrix.
+ *
+ * @param i0
+ * Initial row index
+ * @param i1
+ * Final row index
+ * @param j0
+ * Initial column index
+ * @param j1
+ * Final column index
+ * @return A(i0:i1,j0:j1)
+ * @exception ArrayIndexOutOfBoundsException
+ * Submatrix indices
+ */
+
+ public Matrix getMatrix(int i0, int i1, int j0, int j1) {
+ Matrix X = new Matrix(i1 - i0 + 1, j1 - j0 + 1);
+ double[][] B = X.getArray();
+ try {
+ for (int i = i0; i <= i1; i++) {
+ for (int j = j0; j <= j1; j++) {
+ B[i - i0][j - j0] = A[i][j];
+ }
+ }
+ } catch (ArrayIndexOutOfBoundsException e) {
+ throw new ArrayIndexOutOfBoundsException("Submatrix indices");
+ }
+ return X;
+ }
+
+ /**
+ * Get a submatrix.
+ *
+ * @param r
+ * Array of row indices.
+ * @param c
+ * Array of column indices.
+ * @return A(r(:),c(:))
+ * @exception ArrayIndexOutOfBoundsException
+ * Submatrix indices
+ */
+
+ public Matrix getMatrix(int[] r, int[] c) {
+ Matrix X = new Matrix(r.length, c.length);
+ double[][] B = X.getArray();
+ try {
+ for (int i = 0; i < r.length; i++) {
+ for (int j = 0; j < c.length; j++) {
+ B[i][j] = A[r[i]][c[j]];
+ }
+ }
+ } catch (ArrayIndexOutOfBoundsException e) {
+ throw new ArrayIndexOutOfBoundsException("Submatrix indices");
+ }
+ return X;
+ }
+
+ /**
+ * Get a submatrix.
+ *
+ * @param i0
+ * Initial row index
+ * @param i1
+ * Final row index
+ * @param c
+ * Array of column indices.
+ * @return A(i0:i1,c(:))
+ * @exception ArrayIndexOutOfBoundsException
+ * Submatrix indices
+ */
+
+ public Matrix getMatrix(int i0, int i1, int[] c) {
+ Matrix X = new Matrix(i1 - i0 + 1, c.length);
+ double[][] B = X.getArray();
+ try {
+ for (int i = i0; i <= i1; i++) {
+ for (int j = 0; j < c.length; j++) {
+ B[i - i0][j] = A[i][c[j]];
+ }
+ }
+ } catch (ArrayIndexOutOfBoundsException e) {
+ throw new ArrayIndexOutOfBoundsException("Submatrix indices");
+ }
+ return X;
+ }
+
+ /**
+ * Get a submatrix.
+ *
+ * @param r
+ * Array of row indices.
+ * @param i0
+ * Initial column index
+ * @param i1
+ * Final column index
+ * @return A(r(:),j0:j1)
+ * @exception ArrayIndexOutOfBoundsException
+ * Submatrix indices
+ */
+
+ public Matrix getMatrix(int[] r, int j0, int j1) {
+ Matrix X = new Matrix(r.length, j1 - j0 + 1);
+ double[][] B = X.getArray();
+ try {
+ for (int i = 0; i < r.length; i++) {
+ for (int j = j0; j <= j1; j++) {
+ B[i][j - j0] = A[r[i]][j];
+ }
+ }
+ } catch (ArrayIndexOutOfBoundsException e) {
+ throw new ArrayIndexOutOfBoundsException("Submatrix indices");
+ }
+ return X;
+ }
+
+ /**
+ * Set a single element.
+ *
+ * @param i
+ * Row index.
+ * @param j
+ * Column index.
+ * @param s
+ * A(i,j).
+ * @exception ArrayIndexOutOfBoundsException
+ */
+
+ public void set(int i, int j, double s) {
+ A[i][j] = s;
+ }
+
+ public void add(int i, int j, double s) {
+ A[i][j] += s;
+ }
+
+ /**
+ * Set a submatrix.
+ *
+ * @param i0
+ * Initial row index
+ * @param i1
+ * Final row index
+ * @param j0
+ * Initial column index
+ * @param j1
+ * Final column index
+ * @param X
+ * A(i0:i1,j0:j1)
+ * @exception ArrayIndexOutOfBoundsException
+ * Submatrix indices
+ */
+
+ public void setMatrix(int i0, int i1, int j0, int j1, Matrix X) {
+ try {
+ for (int i = i0; i <= i1; i++) {
+ for (int j = j0; j <= j1; j++) {
+ A[i][j] = X.get(i - i0, j - j0);
+ }
+ }
+ } catch (ArrayIndexOutOfBoundsException e) {
+ throw new ArrayIndexOutOfBoundsException("Submatrix indices");
+ }
+ }
+
+ /**
+ * Set a submatrix.
+ *
+ * @param r
+ * Array of row indices.
+ * @param c
+ * Array of column indices.
+ * @param X
+ * A(r(:),c(:))
+ * @exception ArrayIndexOutOfBoundsException
+ * Submatrix indices
+ */
+
+ public void setMatrix(int[] r, int[] c, Matrix X) {
+ try {
+ for (int i = 0; i < r.length; i++) {
+ for (int j = 0; j < c.length; j++) {
+ A[r[i]][c[j]] = X.get(i, j);
+ }
+ }
+ } catch (ArrayIndexOutOfBoundsException e) {
+ throw new ArrayIndexOutOfBoundsException("Submatrix indices");
+ }
+ }
+
+ /**
+ * Set a submatrix.
+ *
+ * @param r
+ * Array of row indices.
+ * @param j0
+ * Initial column index
+ * @param j1
+ * Final column index
+ * @param X
+ * A(r(:),j0:j1)
+ * @exception ArrayIndexOutOfBoundsException
+ * Submatrix indices
+ */
+
+ public void setMatrix(int[] r, int j0, int j1, Matrix X) {
+ try {
+ for (int i = 0; i < r.length; i++) {
+ for (int j = j0; j <= j1; j++) {
+ A[r[i]][j] = X.get(i, j - j0);
+ }
+ }
+ } catch (ArrayIndexOutOfBoundsException e) {
+ throw new ArrayIndexOutOfBoundsException("Submatrix indices");
+ }
+ }
+
+ /**
+ * Set a submatrix.
+ *
+ * @param i0
+ * Initial row index
+ * @param i1
+ * Final row index
+ * @param c
+ * Array of column indices.
+ * @param X
+ * A(i0:i1,c(:))
+ * @exception ArrayIndexOutOfBoundsException
+ * Submatrix indices
+ */
+
+ public void setMatrix(int i0, int i1, int[] c, Matrix X) {
+ try {
+ for (int i = i0; i <= i1; i++) {
+ for (int j = 0; j < c.length; j++) {
+ A[i][c[j]] = X.get(i - i0, j);
+ }
+ }
+ } catch (ArrayIndexOutOfBoundsException e) {
+ throw new ArrayIndexOutOfBoundsException("Submatrix indices");
+ }
+ }
+
+ /**
+ * Matrix transpose.
+ *
+ * @return A'
+ */
+
+ public Matrix transpose() {
+ Matrix X = new Matrix(n, m);
+ double[][] C = X.getArray();
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ C[j][i] = A[i][j];
+ }
+ }
+ return X;
+ }
+
+ /**
+ * One norm
+ *
+ * @return maximum column sum.
+ */
+
+ public double norm1() {
+ double f = 0;
+ for (int j = 0; j < n; j++) {
+ double s = 0;
+ for (int i = 0; i < m; i++) {
+ s += Math.abs(A[i][j]);
+ }
+ f = Math.max(f, s);
+ }
+ return f;
+ }
+
+ /**
+ * Two norm
+ *
+ * @return maximum singular value.
+ */
+
+ public double norm2() {
+ return (new SingularValueDecomposition(this).norm2());
+ }
+
+ /**
+ * Infinity norm
+ *
+ * @return maximum row sum.
+ */
+
+ public double normInf() {
+ double f = 0;
+ for (int i = 0; i < m; i++) {
+ double s = 0;
+ for (int j = 0; j < n; j++) {
+ s += Math.abs(A[i][j]);
+ }
+ f = Math.max(f, s);
+ }
+ return f;
+ }
+
+ /**
+ * Frobenius norm
+ *
+ * @return sqrt of sum of squares of all elements.
+ */
+
+ public double normF() {
+ double f = 0;
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ f = Maths.hypot(f, A[i][j]);
+ }
+ }
+ return f;
+ }
+
+ /**
+ * Unary minus
+ *
+ * @return -A
+ */
+
+ public Matrix uminus() {
+ Matrix X = new Matrix(m, n);
+ double[][] C = X.getArray();
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ C[i][j] = -A[i][j];
+ }
+ }
+ return X;
+ }
+
+ /**
+ * C = A + B
+ *
+ * @param B
+ * another matrix
+ * @return A + B
+ */
+
+ public Matrix plus(Matrix B) {
+ checkMatrixDimensions(B);
+ Matrix X = new Matrix(m, n);
+ double[][] C = X.getArray();
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ C[i][j] = A[i][j] + B.A[i][j];
+ }
+ }
+ return X;
+ }
+
+ /**
+ * A = A + B
+ *
+ * @param B
+ * another matrix
+ * @return A + B
+ */
+
+ public Matrix plusEquals(Matrix B) {
+ checkMatrixDimensions(B);
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ A[i][j] = A[i][j] + B.A[i][j];
+ }
+ }
+ return this;
+ }
+
+ /**
+ * C = A - B
+ *
+ * @param B
+ * another matrix
+ * @return A - B
+ */
+
+ public Matrix minus(Matrix B) {
+ checkMatrixDimensions(B);
+ Matrix X = new Matrix(m, n);
+ double[][] C = X.getArray();
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ C[i][j] = A[i][j] - B.A[i][j];
+ }
+ }
+ return X;
+ }
+
+ /**
+ * A = A - B
+ *
+ * @param B
+ * another matrix
+ * @return A - B
+ */
+
+ public Matrix minusEquals(Matrix B) {
+ checkMatrixDimensions(B);
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ A[i][j] = A[i][j] - B.A[i][j];
+ }
+ }
+ return this;
+ }
+
+ /**
+ * Element-by-element multiplication, C = A.*B
+ *
+ * @param B
+ * another matrix
+ * @return A.*B
+ */
+
+ public Matrix arrayTimes(Matrix B) {
+ checkMatrixDimensions(B);
+ Matrix X = new Matrix(m, n);
+ double[][] C = X.getArray();
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ C[i][j] = A[i][j] * B.A[i][j];
+ }
+ }
+ return X;
+ }
+
+ /**
+ * Element-by-element multiplication in place, A = A.*B
+ *
+ * @param B
+ * another matrix
+ * @return A.*B
+ */
+
+ public Matrix arrayTimesEquals(Matrix B) {
+ checkMatrixDimensions(B);
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ A[i][j] = A[i][j] * B.A[i][j];
+ }
+ }
+ return this;
+ }
+
+ /**
+ * Element-by-element right division, C = A./B
+ *
+ * @param B
+ * another matrix
+ * @return A./B
+ */
+
+ public Matrix arrayRightDivide(Matrix B) {
+ checkMatrixDimensions(B);
+ Matrix X = new Matrix(m, n);
+ double[][] C = X.getArray();
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ C[i][j] = A[i][j] / B.A[i][j];
+ }
+ }
+ return X;
+ }
+
+ /**
+ * Element-by-element right division in place, A = A./B
+ *
+ * @param B
+ * another matrix
+ * @return A./B
+ */
+
+ public Matrix arrayRightDivideEquals(Matrix B) {
+ checkMatrixDimensions(B);
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ A[i][j] = A[i][j] / B.A[i][j];
+ }
+ }
+ return this;
+ }
+
+ /**
+ * Element-by-element left division, C = A.\B
+ *
+ * @param B
+ * another matrix
+ * @return A.\B
+ */
+
+ public Matrix arrayLeftDivide(Matrix B) {
+ checkMatrixDimensions(B);
+ Matrix X = new Matrix(m, n);
+ double[][] C = X.getArray();
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ C[i][j] = B.A[i][j] / A[i][j];
+ }
+ }
+ return X;
+ }
+
+ /**
+ * Element-by-element left division in place, A = A.\B
+ *
+ * @param B
+ * another matrix
+ * @return A.\B
+ */
+
+ public Matrix arrayLeftDivideEquals(Matrix B) {
+ checkMatrixDimensions(B);
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ A[i][j] = B.A[i][j] / A[i][j];
+ }
+ }
+ return this;
+ }
+
+ /**
+ * Multiply a matrix by a scalar, C = s*A
+ *
+ * @param s
+ * scalar
+ * @return s*A
+ */
+
+ public Matrix times(double s) {
+ Matrix X = new Matrix(m, n);
+ double[][] C = X.getArray();
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ C[i][j] = s * A[i][j];
+ }
+ }
+ return X;
+ }
+
+ /**
+ * Multiply a matrix by a scalar in place, A = s*A
+ *
+ * @param s
+ * scalar
+ * @return replace A by s*A
+ */
+
+ public Matrix timesEquals(double s) {
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ A[i][j] = s * A[i][j];
+ }
+ }
+ return this;
+ }
+
+ /**
+ * Linear algebraic matrix multiplication, A * B
+ *
+ * @param B
+ * another matrix
+ * @return Matrix product, A * B
+ * @exception IllegalArgumentException
+ * Matrix inner dimensions must agree.
+ */
+
+ public Matrix times(Matrix B) {
+ if (B.m != n) {
+ throw new IllegalArgumentException("Matrix inner dimensions must agree.");
+ }
+ Matrix X = new Matrix(m, B.n);
+ double[][] C = X.getArray();
+ double[] Bcolj = new double[n];
+ for (int j = 0; j < B.n; j++) {
+ for (int k = 0; k < n; k++) {
+ Bcolj[k] = B.A[k][j];
+ }
+ for (int i = 0; i < m; i++) {
+ double[] Arowi = A[i];
+ double s = 0;
+ for (int k = 0; k < n; k++) {
+ s += Arowi[k] * Bcolj[k];
+ }
+ C[i][j] = s;
+ }
+ }
+ return X;
+ }
+
+ /**
+ * LU Decomposition
+ *
+ * @return LUDecomposition
+ * @see LUDecomposition
+ */
+
+ public LUDecomposition lu() {
+ return new LUDecomposition(this);
+ }
+
+ /**
+ * QR Decomposition
+ *
+ * @return QRDecomposition
+ * @see QRDecomposition
+ */
+
+ public QRDecomposition qr() {
+ return new QRDecomposition(this);
+ }
+
+ /**
+ * Cholesky Decomposition
+ *
+ * @return CholeskyDecomposition
+ * @see CholeskyDecomposition
+ */
+
+ public CholeskyDecomposition chol() {
+ return new CholeskyDecomposition(this);
+ }
+
+ /**
+ * Singular Value Decomposition
+ *
+ * @return SingularValueDecomposition
+ * @see SingularValueDecomposition
+ */
+
+ public SingularValueDecomposition svd() {
+ return new SingularValueDecomposition(this);
+ }
+
+ /**
+ * Eigenvalue Decomposition
+ *
+ * @return EigenvalueDecomposition
+ * @see EigenvalueDecomposition
+ */
+
+ public EigenvalueDecomposition eig() {
+ return new EigenvalueDecomposition(this);
+ }
+
+ /**
+ * Solve A*X = B
+ *
+ * @param B
+ * right hand side
+ * @return solution if A is square, least squares solution otherwise
+ */
+
+ public Matrix solve(Matrix B) {
+ return (m == n ? (new LUDecomposition(this)).solve(B) : (new QRDecomposition(this)).solve(B));
+ }
+
+ /**
+ * Solve X*A = B, which is also A'*X' = B'
+ *
+ * @param B
+ * right hand side
+ * @return solution if A is square, least squares solution otherwise.
+ */
+
+ public Matrix solveTranspose(Matrix B) {
+ return transpose().solve(B.transpose());
+ }
+
+ /**
+ * Matrix inverse or pseudoinverse
+ *
+ * @return inverse(A) if A is square, pseudoinverse otherwise.
+ */
+
+ public Matrix inverse() {
+ return solve(identity(m, m));
+ }
+
+ /**
+ * Matrix determinant
+ *
+ * @return determinant
+ */
+
+ public double det() {
+ return new LUDecomposition(this).det();
+ }
+
+ /**
+ * Matrix rank
+ *
+ * @return effective numerical rank, obtained from SVD.
+ */
+
+ public int rank() {
+ return new SingularValueDecomposition(this).rank();
+ }
+
+ /**
+ * Matrix condition (2 norm)
+ *
+ * @return ratio of largest to smallest singular value.
+ */
+
+ public double cond() {
+ return new SingularValueDecomposition(this).cond();
+ }
+
+ /**
+ * Matrix trace.
+ *
+ * @return sum of the diagonal elements.
+ */
+
+ public double trace() {
+ double t = 0;
+ for (int i = 0; i < Math.min(m, n); i++) {
+ t += A[i][i];
+ }
+ return t;
+ }
+
+ /**
+ * Generate matrix with random elements
+ *
+ * @param m
+ * Number of rows.
+ * @param n
+ * Number of colums.
+ * @return An m-by-n matrix with uniformly distributed random elements.
+ */
+
+ public static Matrix random(int m, int n) {
+ Matrix A = new Matrix(m, n);
+ double[][] X = A.getArray();
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ X[i][j] = Math.random();
+ }
+ }
+ return A;
+ }
+
+ /**
+ * Generate identity matrix
+ *
+ * @param m
+ * Number of rows.
+ * @param n
+ * Number of colums.
+ * @return An m-by-n matrix with ones on the diagonal and zeros elsewhere.
+ */
+
+ public static Matrix identity(int m, int n) {
+ Matrix A = new Matrix(m, n);
+ double[][] X = A.getArray();
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ X[i][j] = (i == j ? 1.0 : 0.0);
+ }
+ }
+ return A;
+ }
+
+ /**
+ * Print the matrix to stdout. Line the elements up in columns with a
+ * Fortran-like 'Fw.d' style format.
+ *
+ * @param w
+ * Column width.
+ * @param d
+ * Number of digits after the decimal.
+ */
+
+ public void print(int w, int d) {
+ print(new PrintWriter(System.out, true), w, d);
+ }
+
+ /**
+ * Print the matrix to the output stream. Line the elements up in columns
+ * with a Fortran-like 'Fw.d' style format.
+ *
+ * @param output
+ * Output stream.
+ * @param w
+ * Column width.
+ * @param d
+ * Number of digits after the decimal.
+ */
+
+ public void print(PrintWriter output, int w, int d) {
+ DecimalFormat format = new DecimalFormat();
+ format.setDecimalFormatSymbols(new DecimalFormatSymbols(Locale.US));
+ format.setMinimumIntegerDigits(1);
+ format.setMaximumFractionDigits(d);
+ format.setMinimumFractionDigits(d);
+ format.setGroupingUsed(false);
+ print(output, format, w + 2);
+ }
+
+ /**
+ * Print the matrix to stdout. Line the elements up in columns. Use the
+ * format object, and right justify within columns of width characters. Note
+ * that is the matrix is to be read back in, you probably will want to use a
+ * NumberFormat that is set to US Locale.
+ *
+ * @param format
+ * A Formatting object for individual elements.
+ * @param width
+ * Field width for each column.
+ * @see java.text.DecimalFormat#setDecimalFormatSymbols
+ */
+
+ public void print(NumberFormat format, int width) {
+ print(new PrintWriter(System.out, true), format, width);
+ }
+
+ // DecimalFormat is a little disappointing coming from Fortran or C's
+ // printf.
+ // Since it doesn't pad on the left, the elements will come out different
+ // widths. Consequently, we'll pass the desired column width in as an
+ // argument and do the extra padding ourselves.
+
+ /**
+ * Print the matrix to the output stream. Line the elements up in columns.
+ * Use the format object, and right justify within columns of width
+ * characters. Note that is the matrix is to be read back in, you probably
+ * will want to use a NumberFormat that is set to US Locale.
+ *
+ * @param output
+ * the output stream.
+ * @param format
+ * A formatting object to format the matrix elements
+ * @param width
+ * Column width.
+ * @see java.text.DecimalFormat#setDecimalFormatSymbols
+ */
+
+ public void print(PrintWriter output, NumberFormat format, int width) {
+ output.println(); // start on new line.
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ String s = format.format(A[i][j]); // format the number
+ int padding = Math.max(1, width - s.length()); // At _least_ 1
+ // space
+ for (int k = 0; k < padding; k++)
+ output.print(' ');
+ output.print(s);
+ }
+ output.println();
+ }
+ output.println(); // end with blank line.
+ }
+
+ /**
+ * Read a matrix from a stream. The format is the same the print method, so
+ * printed matrices can be read back in (provided they were printed using US
+ * Locale). Elements are separated by whitespace, all the elements for each
+ * row appear on a single line, the last row is followed by a blank line.
+ *
+ * @param input
+ * the input stream.
+ */
+
+ public static Matrix read(BufferedReader input) throws java.io.IOException {
+ StreamTokenizer tokenizer = new StreamTokenizer(input);
+
+ // Although StreamTokenizer will parse numbers, it doesn't recognize
+ // scientific notation (E or D); however, Double.valueOf does.
+ // The strategy here is to disable StreamTokenizer's number parsing.
+ // We'll only get whitespace delimited words, EOL's and EOF's.
+ // These words should all be numbers, for Double.valueOf to parse.
+
+ tokenizer.resetSyntax();
+ tokenizer.wordChars(0, 255);
+ tokenizer.whitespaceChars(0, ' ');
+ tokenizer.eolIsSignificant(true);
+ Vector<Double> v1 = new Vector<Double>();
+
+ // Ignore initial empty lines
+ while (tokenizer.nextToken() == StreamTokenizer.TT_EOL)
+ ;
+ if (tokenizer.ttype == StreamTokenizer.TT_EOF)
+ throw new java.io.IOException("Unexpected EOF on matrix read.");
+ do {
+ v1.addElement(Double.valueOf(tokenizer.sval)); // Read & store 1st
+ // row.
+ } while (tokenizer.nextToken() == StreamTokenizer.TT_WORD);
+
+ int n = v1.size(); // Now we've got the number of columns!
+ double row[] = new double[n];
+ for (int j = 0; j < n; j++)
+ // extract the elements of the 1st row.
+ row[j] = ((Double) v1.elementAt(j)).doubleValue();
+
+ Vector<double[]> v = new Vector<double[]>();
+ v.addElement(row); // Start storing rows instead of columns.
+ while (tokenizer.nextToken() == StreamTokenizer.TT_WORD) {
+ // While non-empty lines
+ v.addElement(row = new double[n]);
+ int j = 0;
+ do {
+ if (j >= n)
+ throw new java.io.IOException("Row " + v.size() + " is too long.");
+ row[j++] = Double.valueOf(tokenizer.sval).doubleValue();
+ } while (tokenizer.nextToken() == StreamTokenizer.TT_WORD);
+ if (j < n)
+ throw new java.io.IOException("Row " + v.size() + " is too short.");
+ }
+ int m = v.size(); // Now we've got the number of rows.
+ double[][] A = new double[m][];
+ v.copyInto(A); // copy the rows out of the vector
+ return new Matrix(A);
+ }
+
+ /*
+ * ------------------------ Private Methods ------------------------
+ */
+
+ /** Check if size(A) == size(B) **/
+
+ private void checkMatrixDimensions(Matrix B) {
+ if (B.m != m || B.n != n) {
+ throw new IllegalArgumentException("Matrix dimensions must agree.");
+ }
+ }
+
+ public double[][] getA() {
+ return A;
+ }
+
+ public void setA(double[][] a) {
+ A = a;
+ }
+
+ public int getM() {
+ return m;
+ }
+
+ public void setM(int m) {
+ this.m = m;
+ }
+
+ public int getN() {
+ return n;
+ }
+
+ public void setN(int n) {
+ this.n = n;
+ }
+
+ public double sum() {
+ double s = 0;
+ for (int j = 0; j < n; j++) {
+ for (int i = 0; i < m; i++) {
+ s += A[i][j];
+ }
+ }
+ return s;
+ }
+
+ public void normalizeSumTo(double nrm) {
+ double s = sum() / nrm;
+ if (s != 0) {
+ for (int j = 0; j < n; j++) {
+ for (int i = 0; i < m; i++) {
+ A[i][j] /= s;
+ }
+ }
+ }
+ }
+
+}
diff --git a/src/main/java/plugins/nherve/matrix/NHerveMatrix.java b/src/main/java/plugins/nherve/matrix/NHerveMatrix.java
new file mode 100644
index 0000000000000000000000000000000000000000..6d5e44e7f06300a3be45c96c72086b542b275c96
--- /dev/null
+++ b/src/main/java/plugins/nherve/matrix/NHerveMatrix.java
@@ -0,0 +1,31 @@
+/*
+ * Copyright 2010, 2011 Institut Pasteur.
+ *
+ * This file is part of NHerveMatrix, which is an ICY plugin.
+ *
+ * NHerveMatrix is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * NHerveMatrix is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with NHerveMatrix. If not, see <http://www.gnu.org/licenses/>.
+ */
+package plugins.nherve.matrix;
+
+import icy.plugin.abstract_.Plugin;
+import icy.plugin.interface_.PluginLibrary;
+
+/**
+ * The Class NHerveMatrix.
+ *
+ * @author Nicolas HERVE - nicolas.herve@pasteur.fr
+ */
+public class NHerveMatrix extends Plugin implements PluginLibrary {
+
+}
diff --git a/src/main/java/plugins/nherve/matrix/NHerveMatrix.png b/src/main/java/plugins/nherve/matrix/NHerveMatrix.png
new file mode 100644
index 0000000000000000000000000000000000000000..f75ef54feb679fe3d9f12c30d25765c38041db5c
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diff --git a/src/main/java/plugins/nherve/matrix/NHerveMatrix_icon.png b/src/main/java/plugins/nherve/matrix/NHerveMatrix_icon.png
new file mode 100644
index 0000000000000000000000000000000000000000..fff2b728c91caaffd518badbee2dedc791ef92ac
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diff --git a/src/main/java/plugins/nherve/matrix/NHerveMatrix_miniscreen.png b/src/main/java/plugins/nherve/matrix/NHerveMatrix_miniscreen.png
new file mode 100644
index 0000000000000000000000000000000000000000..52d1e7d80530bf5bb3503f433402bc0b2e8536a5
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diff --git a/src/main/java/plugins/nherve/matrix/QRDecomposition.java b/src/main/java/plugins/nherve/matrix/QRDecomposition.java
new file mode 100644
index 0000000000000000000000000000000000000000..fc79248bd2abebe0dc941a9f4ddddbe8367b6203
--- /dev/null
+++ b/src/main/java/plugins/nherve/matrix/QRDecomposition.java
@@ -0,0 +1,221 @@
+package plugins.nherve.matrix;
+
+import plugins.nherve.matrix.util.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 java.io.Serializable {
+
+/* ------------------------
+ Class variables
+ * ------------------------ */
+
+ private static final long serialVersionUID = -8996621858744874937L;
+
+/** Array for internal storage of decomposition.
+ @serial internal array storage.
+ */
+ private double[][] QR;
+
+ /** Row and column dimensions.
+ @serial column dimension.
+ @serial row dimension.
+ */
+ private int m, n;
+
+ /** Array for internal storage of diagonal of R.
+ @serial diagonal of R.
+ */
+ private double[] Rdiag;
+
+/* ------------------------
+ Constructor
+ * ------------------------ */
+
+ /** QR Decomposition, computed by Householder reflections.
+ @param A Rectangular matrix
+ @return Structure to access R and the Householder vectors and compute Q.
+ */
+
+ public QRDecomposition (Matrix A) {
+ // Initialize.
+ QR = A.getArrayCopy();
+ m = A.getRowDimension();
+ n = A.getColumnDimension();
+ Rdiag = new double[n];
+
+ // Main loop.
+ for (int k = 0; k < n; k++) {
+ // Compute 2-norm of k-th column without under/overflow.
+ double nrm = 0;
+ for (int 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 (int i = k; i < m; i++) {
+ QR[i][k] /= nrm;
+ }
+ QR[k][k] += 1.0;
+
+ // Apply transformation to remaining columns.
+ for (int j = k+1; j < n; j++) {
+ double s = 0.0;
+ for (int i = k; i < m; i++) {
+ s += QR[i][k]*QR[i][j];
+ }
+ s = -s/QR[k][k];
+ for (int i = k; i < m; i++) {
+ QR[i][j] += s*QR[i][k];
+ }
+ }
+ }
+ Rdiag[k] = -nrm;
+ }
+ }
+
+/* ------------------------
+ Public Methods
+ * ------------------------ */
+
+ /** Is the matrix full rank?
+ @return true if R, and hence A, has full rank.
+ */
+
+ public boolean isFullRank () {
+ for (int 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 () {
+ Matrix X = new Matrix(m,n);
+ double[][] H = X.getArray();
+ for (int i = 0; i < m; i++) {
+ for (int j = 0; j < n; j++) {
+ if (i >= j) {
+ H[i][j] = QR[i][j];
+ } else {
+ H[i][j] = 0.0;
+ }
+ }
+ }
+ return X;
+ }
+
+ /** Return the upper triangular factor
+ @return R
+ */
+
+ public Matrix getR () {
+ Matrix X = new Matrix(n,n);
+ double[][] R = X.getArray();
+ for (int i = 0; i < n; i++) {
+ for (int j = 0; j < n; j++) {
+ if (i < j) {
+ R[i][j] = QR[i][j];
+ } else if (i == j) {
+ R[i][j] = Rdiag[i];
+ } else {
+ R[i][j] = 0.0;
+ }
+ }
+ }
+ return X;
+ }
+
+ /** Generate and return the (economy-sized) orthogonal factor
+ @return Q
+ */
+
+ public Matrix getQ () {
+ Matrix X = new Matrix(m,n);
+ double[][] Q = X.getArray();
+ for (int k = n-1; k >= 0; k--) {
+ for (int i = 0; i < m; i++) {
+ Q[i][k] = 0.0;
+ }
+ Q[k][k] = 1.0;
+ for (int j = k; j < n; j++) {
+ if (QR[k][k] != 0) {
+ double s = 0.0;
+ for (int i = k; i < m; i++) {
+ s += QR[i][k]*Q[i][j];
+ }
+ s = -s/QR[k][k];
+ for (int i = k; i < m; i++) {
+ Q[i][j] += s*QR[i][k];
+ }
+ }
+ }
+ }
+ return X;
+ }
+
+ /** 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.getRowDimension() != m) {
+ throw new IllegalArgumentException("Matrix row dimensions must agree.");
+ }
+ if (!this.isFullRank()) {
+ throw new RuntimeException("Matrix is rank deficient.");
+ }
+
+ // Copy right hand side
+ int nx = B.getColumnDimension();
+ double[][] X = B.getArrayCopy();
+
+ // Compute Y = transpose(Q)*B
+ for (int k = 0; k < n; k++) {
+ for (int j = 0; j < nx; j++) {
+ double s = 0.0;
+ for (int i = k; i < m; i++) {
+ s += QR[i][k]*X[i][j];
+ }
+ s = -s/QR[k][k];
+ for (int i = k; i < m; i++) {
+ X[i][j] += s*QR[i][k];
+ }
+ }
+ }
+ // Solve R*X = Y;
+ for (int k = n-1; k >= 0; k--) {
+ for (int j = 0; j < nx; j++) {
+ X[k][j] /= Rdiag[k];
+ }
+ for (int i = 0; i < k; i++) {
+ for (int j = 0; j < nx; j++) {
+ X[i][j] -= X[k][j]*QR[i][k];
+ }
+ }
+ }
+ return (new Matrix(X,n,nx).getMatrix(0,n-1,0,nx-1));
+ }
+}
diff --git a/src/main/java/plugins/nherve/matrix/SingularValueDecomposition.java b/src/main/java/plugins/nherve/matrix/SingularValueDecomposition.java
new file mode 100644
index 0000000000000000000000000000000000000000..70d26c85db944e745fb7f49ad765e572dccb5c5c
--- /dev/null
+++ b/src/main/java/plugins/nherve/matrix/SingularValueDecomposition.java
@@ -0,0 +1,550 @@
+package plugins.nherve.matrix;
+
+import plugins.nherve.matrix.util.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, sigma[k] = S[k][k], are ordered so that
+ sigma[0] >= sigma[1] >= ... >= sigma[n-1].
+ <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 java.io.Serializable {
+
+/* ------------------------
+ Class variables
+ * ------------------------ */
+
+ private static final long serialVersionUID = -3999731802305419225L;
+
+/** Arrays for internal storage of U and V.
+ @serial internal storage of U.
+ @serial internal storage of V.
+ */
+ private double[][] U, V;
+
+ /** Array for internal storage of singular values.
+ @serial internal storage of singular values.
+ */
+ private double[] s;
+
+ /** Row and column dimensions.
+ @serial row dimension.
+ @serial column dimension.
+ */
+ private int m, n;
+
+/* ------------------------
+ Constructor
+ * ------------------------ */
+
+ /** Construct the singular value decomposition
+ @param A Rectangular matrix
+ @return Structure to access U, S and V.
+ */
+
+ public SingularValueDecomposition (Matrix Arg) {
+
+ // Derived from LINPACK code.
+ // Initialize.
+ double[][] A = Arg.getArrayCopy();
+ m = Arg.getRowDimension();
+ n = Arg.getColumnDimension();
+
+ /* 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("Jama 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 (int 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 (int 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 (int i = k; i < m; i++) {
+ A[i][k] /= s[k];
+ }
+ A[k][k] += 1.0;
+ }
+ s[k] = -s[k];
+ }
+ for (int j = k+1; j < n; j++) {
+ if ((k < nct) & (s[k] != 0.0)) {
+
+ // Apply the transformation.
+
+ double t = 0;
+ for (int i = k; i < m; i++) {
+ t += A[i][k]*A[i][j];
+ }
+ t = -t/A[k][k];
+ for (int 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 (int 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 (int 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 (int 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 (int i = k+1; i < m; i++) {
+ work[i] = 0.0;
+ }
+ for (int j = k+1; j < n; j++) {
+ for (int i = k+1; i < m; i++) {
+ work[i] += e[j]*A[i][j];
+ }
+ }
+ for (int j = k+1; j < n; j++) {
+ double t = -e[j]/e[k+1];
+ for (int i = k+1; i < m; i++) {
+ A[i][j] += t*work[i];
+ }
+ }
+ }
+ if (wantv) {
+
+ // Place the transformation in V for subsequent
+ // back multiplication.
+
+ for (int 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 (int j = nct; j < nu; j++) {
+ for (int i = 0; i < m; i++) {
+ U[i][j] = 0.0;
+ }
+ U[j][j] = 1.0;
+ }
+ for (int k = nct-1; k >= 0; k--) {
+ if (s[k] != 0.0) {
+ for (int j = k+1; j < nu; j++) {
+ double t = 0;
+ for (int i = k; i < m; i++) {
+ t += U[i][k]*U[i][j];
+ }
+ t = -t/U[k][k];
+ for (int i = k; i < m; i++) {
+ U[i][j] += t*U[i][k];
+ }
+ }
+ for (int i = k; i < m; i++ ) {
+ U[i][k] = -U[i][k];
+ }
+ U[k][k] = 1.0 + U[k][k];
+ for (int i = 0; i < k-1; i++) {
+ U[i][k] = 0.0;
+ }
+ } else {
+ for (int i = 0; i < m; i++) {
+ U[i][k] = 0.0;
+ }
+ U[k][k] = 1.0;
+ }
+ }
+ }
+
+ // If required, generate V.
+
+ if (wantv) {
+ for (int k = n-1; k >= 0; k--) {
+ if ((k < nrt) & (e[k] != 0.0)) {
+ for (int j = k+1; j < nu; j++) {
+ double t = 0;
+ for (int i = k+1; i < n; i++) {
+ t += V[i][k]*V[i][j];
+ }
+ t = -t/V[k+1][k];
+ for (int i = k+1; i < n; i++) {
+ V[i][j] += t*V[i][k];
+ }
+ }
+ }
+ for (int 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 k,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 (int 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 (int 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 (int 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 (int 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 (int 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 (int 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 (int 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 (int 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 (int 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 (int 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;
+ }
+ }
+ }
+
+/* ------------------------
+ Public Methods
+ * ------------------------ */
+
+ /** Return the left singular vectors
+ @return U
+ */
+
+ public Matrix getU () {
+ return new Matrix(U,m,Math.min(m+1,n));
+ }
+
+ /** Return the right singular vectors
+ @return V
+ */
+
+ public Matrix getV () {
+ return new Matrix(V,n,n);
+ }
+
+ /** Return the one-dimensional array of singular values
+ @return diagonal of S.
+ */
+
+ public double[] getSingularValues () {
+ return s;
+ }
+
+ /** Return the diagonal matrix of singular values
+ @return S
+ */
+
+ public Matrix getS () {
+ Matrix X = new Matrix(n,n);
+ double[][] S = X.getArray();
+ for (int i = 0; i < n; i++) {
+ for (int j = 0; j < n; j++) {
+ S[i][j] = 0.0;
+ }
+ S[i][i] = this.s[i];
+ }
+ return X;
+ }
+
+ /** 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 r = 0;
+ for (int i = 0; i < s.length; i++) {
+ if (s[i] > tol) {
+ r++;
+ }
+ }
+ return r;
+ }
+}
diff --git a/src/main/java/plugins/nherve/matrix/util/Maths.java b/src/main/java/plugins/nherve/matrix/util/Maths.java
new file mode 100644
index 0000000000000000000000000000000000000000..46ff5b81b6033f646290f383d2ba7c07c60bd107
--- /dev/null
+++ b/src/main/java/plugins/nherve/matrix/util/Maths.java
@@ -0,0 +1,20 @@
+package plugins.nherve.matrix.util;
+
+public class Maths {
+
+ /** sqrt(a^2 + b^2) without under/overflow. **/
+
+ public static double hypot(double a, double b) {
+ double r;
+ if (Math.abs(a) > Math.abs(b)) {
+ r = b/a;
+ r = Math.abs(a)*Math.sqrt(1+r*r);
+ } else if (b != 0) {
+ r = a/b;
+ r = Math.abs(b)*Math.sqrt(1+r*r);
+ } else {
+ r = 0.0;
+ }
+ return r;
+ }
+}