[SCM] GeoGebra: Dynamic mathematics software for education branch, upstream, updated. upstream/3.2.40.0+dfsg1-3-g7be5b78
Giovanni Mascellani
gio at alioth.debian.org
Sat Jul 10 14:36:44 UTC 2010
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Summary of changes:
geogebra/kernel/jama/CholeskyDecomposition.java | 199 ----
geogebra/kernel/jama/EigenvalueDecomposition.java | 955 ------------------
geogebra/kernel/jama/LUDecomposition.java | 311 ------
geogebra/kernel/jama/Matrix.java | 1049 --------------------
geogebra/kernel/jama/QRDecomposition.java | 218 ----
.../kernel/jama/SingularValueDecomposition.java | 547 ----------
geogebra/kernel/jama/util/Maths.java | 20 -
7 files changed, 0 insertions(+), 3299 deletions(-)
diff --git a/geogebra/kernel/jama/CholeskyDecomposition.java b/geogebra/kernel/jama/CholeskyDecomposition.java
deleted file mode 100644
index c24b073..0000000
--- a/geogebra/kernel/jama/CholeskyDecomposition.java
+++ /dev/null
@@ -1,199 +0,0 @@
-package geogebra.kernel.jama;
-
- /** 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
- * ------------------------ */
-
- /** 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/geogebra/kernel/jama/EigenvalueDecomposition.java b/geogebra/kernel/jama/EigenvalueDecomposition.java
deleted file mode 100644
index d4dd03c..0000000
--- a/geogebra/kernel/jama/EigenvalueDecomposition.java
+++ /dev/null
@@ -1,955 +0,0 @@
-package geogebra.kernel.jama;
-import geogebra.kernel.jama.util.*;
-
-/** 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
- * ------------------------ */
-
- /** 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/geogebra/kernel/jama/LUDecomposition.java b/geogebra/kernel/jama/LUDecomposition.java
deleted file mode 100644
index 1badc15..0000000
--- a/geogebra/kernel/jama/LUDecomposition.java
+++ /dev/null
@@ -1,311 +0,0 @@
-package geogebra.kernel.jama;
-
- /** 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
- * ------------------------ */
-
- /** 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/geogebra/kernel/jama/Matrix.java b/geogebra/kernel/jama/Matrix.java
deleted file mode 100644
index a795173..0000000
--- a/geogebra/kernel/jama/Matrix.java
+++ /dev/null
@@ -1,1049 +0,0 @@
-package geogebra.kernel.jama;
-
-import geogebra.kernel.jama.util.*;
-
-import java.text.NumberFormat;
-import java.text.DecimalFormat;
-import java.text.DecimalFormatSymbols;
-import java.util.Locale;
-import java.text.FieldPosition;
-import java.io.PrintWriter;
-import java.io.BufferedReader;
-import java.io.StreamTokenizer;
-
-/**
- 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>
-
- at author The MathWorks, Inc. and the National Institute of Standards and Technology.
- at version 5 August 1998
-*/
-
-public class Matrix implements Cloneable, java.io.Serializable {
-
-/* ------------------------
- Class variables
- * ------------------------ */
-
- /** 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
- * ------------------------ */
-
- public Matrix () {
- }
-
- /** 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;
- }
-
- /** 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);
- java.util.Vector v = new java.util.Vector();
-
- // 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 {
- v.addElement(Double.valueOf(tokenizer.sval)); // Read & store 1st row.
- } while (tokenizer.nextToken() == StreamTokenizer.TT_WORD);
-
- int n = v.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)v.elementAt(j)).doubleValue();
- v.removeAllElements();
- 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.");
- }
- }
-
-}
diff --git a/geogebra/kernel/jama/QRDecomposition.java b/geogebra/kernel/jama/QRDecomposition.java
deleted file mode 100644
index 0f71bbc..0000000
--- a/geogebra/kernel/jama/QRDecomposition.java
+++ /dev/null
@@ -1,218 +0,0 @@
-package geogebra.kernel.jama;
-import geogebra.kernel.jama.util.*;
-
-/** 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
- * ------------------------ */
-
- /** 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/geogebra/kernel/jama/SingularValueDecomposition.java b/geogebra/kernel/jama/SingularValueDecomposition.java
deleted file mode 100644
index ea7054b..0000000
--- a/geogebra/kernel/jama/SingularValueDecomposition.java
+++ /dev/null
@@ -1,547 +0,0 @@
-package geogebra.kernel.jama;
-import geogebra.kernel.jama.util.*;
-
- /** 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
- * ------------------------ */
-
- /** 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/geogebra/kernel/jama/util/Maths.java b/geogebra/kernel/jama/util/Maths.java
deleted file mode 100644
index 1776a51..0000000
--- a/geogebra/kernel/jama/util/Maths.java
+++ /dev/null
@@ -1,20 +0,0 @@
-package geogebra.kernel.jama.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;
- }
-}
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