* along with this program; if not, write to the Free Software\r
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA\r
*/\r
-\r
package jalview.math;\r
\r
import jalview.util.*;\r
\r
import java.io.*;\r
\r
-public class Matrix {\r
-\r
- /**\r
- * SMJSPUBLIC\r
- */\r
- public double[][] value;\r
- public int rows;\r
- public int cols;\r
- public double[] d; // Diagonal\r
- public double[] e; // off diagonal\r
-\r
- public Matrix(double[][] value, int rows, int cols) {\r
- this.rows = rows;\r
- this.cols = cols;\r
- this.value = value;\r
- }\r
-\r
- public Matrix transpose() {\r
- double[][] out = new double[cols][rows];\r
-\r
- for (int i = 0; i < cols; i++) {\r
- for (int j = 0; j < rows ; j++) {\r
- out[i][j] = value[j][i];\r
- }\r
- }\r
- return new Matrix(out,cols,rows);\r
- }\r
-\r
- public void print(PrintStream ps) {\r
\r
- for (int i = 0; i < rows; i++) {\r
- for (int j = 0; j < cols; j++) {\r
- Format.print(ps,"%8.2f",value[i][j]);\r
- }\r
- ps.println();\r
+public class Matrix {\r
+ /**\r
+ * SMJSPUBLIC\r
+ */\r
+ public double[][] value;\r
+ public int rows;\r
+ public int cols;\r
+ public double[] d; // Diagonal\r
+ public double[] e; // off diagonal\r
+\r
+ public Matrix(double[][] value, int rows, int cols) {\r
+ this.rows = rows;\r
+ this.cols = cols;\r
+ this.value = value;\r
}\r
- }\r
\r
+ public Matrix transpose() {\r
+ double[][] out = new double[cols][rows];\r
\r
- public Matrix preMultiply(Matrix in) {\r
- double[][] tmp = new double[in.rows][this.cols];\r
-\r
- for (int i = 0; i < in.rows; i++) {\r
- for (int j = 0; j < this.cols; j++ ) {\r
- tmp[i][j] = 0.0;\r
-\r
- for (int k = 0; k < in.cols; k++) {\r
- tmp[i][j] += in.value[i][k]*this.value[k][j];\r
+ for (int i = 0; i < cols; i++) {\r
+ for (int j = 0; j < rows; j++) {\r
+ out[i][j] = value[j][i];\r
+ }\r
}\r
\r
- }\r
+ return new Matrix(out, cols, rows);\r
}\r
\r
- return new Matrix(tmp,in.rows,this.cols);\r
- }\r
+ public void print(PrintStream ps) {\r
+ for (int i = 0; i < rows; i++) {\r
+ for (int j = 0; j < cols; j++) {\r
+ Format.print(ps, "%8.2f", value[i][j]);\r
+ }\r
\r
- public double[] vectorPostMultiply(double[] in) {\r
- double[] out = new double[in.length];\r
- for (int i = 0; i < in.length; i++) {\r
- out[i] = 0.0;\r
- for (int k=0; k < in.length; k++) {\r
- out[i] += value[i][k] * in[k];\r
- }\r
+ ps.println();\r
+ }\r
}\r
- return out;\r
- }\r
- public Matrix postMultiply(Matrix in) {\r
\r
- double[][] out = new double[this.rows][in.cols];\r
- for (int i = 0; i < this.rows; i++) {\r
- for (int j = 0; j < in.cols; j++ ) {\r
+ public Matrix preMultiply(Matrix in) {\r
+ double[][] tmp = new double[in.rows][this.cols];\r
\r
- out[i][j] = 0.0;\r
+ for (int i = 0; i < in.rows; i++) {\r
+ for (int j = 0; j < this.cols; j++) {\r
+ tmp[i][j] = 0.0;\r
\r
- for (int k = 0; k < rows; k++) {\r
- out[i][j] = out[i][j] + value[i][k]*in.value[k][j];\r
+ for (int k = 0; k < in.cols; k++) {\r
+ tmp[i][j] += (in.value[i][k] * this.value[k][j]);\r
+ }\r
+ }\r
}\r
\r
- }\r
+ return new Matrix(tmp, in.rows, this.cols);\r
}\r
- return new Matrix(out,this.cols,in.rows);\r
- }\r
\r
- public Matrix copy() {\r
- double[][] newmat = new double[rows][cols];\r
+ public double[] vectorPostMultiply(double[] in) {\r
+ double[] out = new double[in.length];\r
\r
- for (int i = 0; i < rows; i++) {\r
- for (int j = 0; j < cols; j++) {\r
- newmat[i][j] = value[i][j];\r
- }\r
- }\r
- return new Matrix(newmat,rows,cols);\r
- }\r
-\r
- public void tred() {\r
- int n = rows;\r
- int l;\r
- int k;\r
- int j;\r
- int i;\r
-\r
- double scale;\r
- double hh;\r
- double h;\r
- double g;\r
- double f;\r
-\r
- this.d = new double[rows];\r
- this.e = new double[rows];\r
-\r
- for (i=n; i >= 2;i--) {\r
- l=i-1;\r
- h = 0.0;\r
- scale = 0.0;\r
-\r
- if (l > 1) {\r
- for (k=1;k<=l;k++) {\r
- scale += Math.abs(value[i-1][k-1]);\r
- }\r
- if (scale == 0.0) {\r
- e[i-1] = value[i-1][l-1];\r
- } else {\r
- for (k=1; k <= l; k++) {\r
- value[i-1][k-1] /= scale;\r
- h += value[i-1][k-1]*value[i-1][k-1];\r
- }\r
- f = value[i-1][l-1];\r
- if (f>0) {\r
- g = -1.0*Math.sqrt(h);\r
- } else {\r
- g = Math.sqrt(h);\r
- }\r
- e[i-1] = scale*g;\r
- h -= f*g;\r
- value[i-1][l-1] = f-g;\r
- f=0.0;\r
- for (j=1; j <= l; j++) {\r
- value[j-1][i-1] = value[i-1][j-1]/h;\r
- g=0.0;\r
- for (k= 1; k <= j; k++) {\r
- g += value[j-1][k-1]*value[i-1][k-1];\r
- }\r
- for (k=j+1; k<=l;k++) {\r
- g+= value[k-1][j-1]*value[i-1][k-1];\r
- }\r
- e[j-1] = g/h;\r
- f+=e[j-1]*value[i-1][j-1];\r
- }\r
- hh=f/(h+h);\r
- for (j=1;j<=l;j++) {\r
- f=value[i-1][j-1];\r
- g = e[j-1] - hh*f;\r
- e[j-1] = g;\r
- for (k=1;k<=j;k++) {\r
- value[j-1][k-1] -= (f*e[k-1]+g*value[i-1][k-1]);\r
- }\r
- }\r
- }\r
- } else {\r
- e[i-1] = value[i-1][l-1];\r
- }\r
- d[i-1] = h;\r
- }\r
- d[0] = 0.0;\r
- e[0] = 0.0;\r
- for (i=1;i<=n;i++) {\r
- l=i-1;\r
- if (d[i-1] != 0.0) {\r
- for (j=1;j<=l;j++) {\r
- g=0.0;\r
- for (k=1;k<=l;k++) {\r
- g+= value[i-1][k-1]*value[k-1][j-1];\r
- }\r
- for (k=1;k<=l;k++) {\r
- value[k-1][j-1] -= g*value[k-1][i-1];\r
- }\r
- }\r
- }\r
- d[i-1] = value[i-1][i-1];\r
- value[i-1][i-1] = 1.0;\r
- for (j=1;j<=l;j++) {\r
- value[j-1][i-1] = 0.0;\r
- value[i-1][j-1] = 0.0;\r
- }\r
- }\r
- }\r
-\r
- public void tqli() {\r
- int n = rows;\r
-\r
- int m;\r
- int l;\r
- int iter;\r
- int i;\r
- int k;\r
- double s;\r
- double r;\r
- double p;\r
- ;\r
- double g;\r
- double f;\r
- double dd;\r
- double c;\r
- double b;\r
-\r
- for (i=2;i<=n;i++) {\r
- e[i-2] = e[i-1];\r
- }\r
- e[n-1] = 0.0;\r
- for (l=1;l<=n;l++) {\r
- iter=0;\r
- do {\r
- for (m=l;m<=(n-1);m++) {\r
- dd=Math.abs(d[m-1]) + Math.abs(d[m]);\r
- if (Math.abs(e[m-1]) + dd == dd)\r
- break;\r
- }\r
- if (m != l) {\r
- iter++;\r
- if (iter == 30) {\r
- System.err.print("Too many iterations in tqli");\r
- System.exit(0); // JBPNote - should this really be here ???\r
- } else {\r
- // System.out.println("Iteration " + iter);\r
- }\r
- g=(d[l]-d[l-1])/(2.0*e[l-1]);\r
- r = Math.sqrt((g*g) + 1.0);\r
- g=d[m-1]-d[l-1]+e[l-1]/(g + sign(r,g));\r
- c = 1.0;\r
- s = c;\r
- p=0.0;\r
- for (i=m-1;i>=l;i--) {\r
- f = s*e[i-1];\r
- b = c*e[i-1];\r
- if (Math.abs(f) >= Math.abs(g)) {\r
- c=g/f;\r
- r = Math.sqrt((c*c)+1.0);\r
- e[i] = f*r;\r
- s = 1.0/r;\r
- c *= s;\r
- } else {\r
- s=f/g;\r
- r = Math.sqrt((s*s)+1.0);\r
- e[i] = g*r;\r
- c = 1.0/r;\r
- s *= c;\r
- }\r
- g=d[i] -p;\r
- r=(d[i-1]-g)*s + 2.0*c*b;\r
- p=s*r;\r
- d[i] = g + p;\r
- g = c * r - b;\r
- for (k=1; k <= n; k++) {\r
- f=value[k-1][i];\r
- value[k-1][i] = s*value[k-1][i-1] + c*f;\r
- value[k-1][i-1] = c*value[k-1][i-1] - s*f;\r
- }\r
- }\r
- d[l-1] = d[l-1] - p;\r
- e[l-1] = g;\r
- e[m-1] = 0.0;\r
- }\r
- } while ( m != l);\r
- }\r
- }\r
- public void tred2() {\r
- int n = rows;\r
- int l;\r
- int k;\r
- int j;\r
- int i;\r
-\r
- double scale;\r
- double hh;\r
- double h;\r
- double g;\r
- double f;\r
-\r
- this.d = new double[rows];\r
- this.e = new double[rows];\r
-\r
- for (i=n-1; i >= 1;i--) {\r
- l=i-1;\r
- h = 0.0;\r
- scale = 0.0;\r
-\r
- if (l > 0) {\r
- for (k=0;k<l;k++) {\r
- scale += Math.abs(value[i][k]);\r
- }\r
- if (scale == 0.0) {\r
- e[i] = value[i][l];\r
- } else {\r
- for (k=0; k < l; k++) {\r
- value[i][k] /= scale;\r
- h += value[i][k]*value[i][k];\r
- }\r
- f = value[i][l];\r
- if (f>0) {\r
- g = -1.0*Math.sqrt(h);\r
- } else {\r
- g = Math.sqrt(h);\r
- }\r
- e[i] = scale*g;\r
- h -= f*g;\r
- value[i][l] = f-g;\r
- f=0.0;\r
- for (j=0; j < l; j++) {\r
- value[j][i] = value[i][j]/h;\r
- g=0.0;\r
- for (k= 0; k < j; k++) {\r
- g += value[j][k]*value[i][k];\r
- }\r
- for (k=j; k<l;k++) {\r
- g+= value[k][j]*value[i][k];\r
- }\r
- e[j] = g/h;\r
- f+=e[j]*value[i][j];\r
- }\r
- hh=f/(h+h);\r
- for (j=0;j<l;j++) {\r
- f=value[i][j];\r
- g = e[j] - hh*f;\r
- e[j] = g;\r
- for (k=0;k<j;k++) {\r
- value[j][k] -= (f*e[k]+g*value[i][k]);\r
- }\r
- }\r
- }\r
- } else {\r
- e[i] = value[i][l];\r
- }\r
- d[i] = h;\r
- }\r
- d[0] = 0.0;\r
- e[0] = 0.0;\r
- for (i=0;i<n;i++) {\r
- l=i-1;\r
- if (d[i] != 0.0) {\r
- for (j=0;j<l;j++) {\r
- g=0.0;\r
- for (k=0;k<l;k++) {\r
- g+= value[i][k]*value[k][j];\r
- }\r
- for (k=0;k<l;k++) {\r
- value[k][j] -= g*value[k][i];\r
- }\r
- }\r
- }\r
- d[i] = value[i][i];\r
- value[i][i] = 1.0;\r
- for (j=0;j<l;j++) {\r
- value[j][i] = 0.0;\r
- value[i][j] = 0.0;\r
- }\r
- }\r
- }\r
-\r
- public void tqli2() {\r
- int n = rows;\r
-\r
- int m;\r
- int l;\r
- int iter;\r
- int i;\r
- int k;\r
- double s;\r
- double r;\r
- double p;\r
- ;\r
- double g;\r
- double f;\r
- double dd;\r
- double c;\r
- double b;\r
-\r
- for (i=2;i<=n;i++) {\r
- e[i-2] = e[i-1];\r
- }\r
- e[n-1] = 0.0;\r
- for (l=1;l<=n;l++) {\r
- iter=0;\r
- do {\r
- for (m=l;m<=(n-1);m++) {\r
- dd=Math.abs(d[m-1]) + Math.abs(d[m]);\r
- if (Math.abs(e[m-1]) + dd == dd)\r
- break;\r
- }\r
- if (m != l) {\r
- iter++;\r
- if (iter == 30) {\r
- System.err.print("Too many iterations in tqli");\r
- System.exit(0); // JBPNote - same as above - not a graceful exit!\r
- } else {\r
- // System.out.println("Iteration " + iter);\r
- }\r
- g=(d[l]-d[l-1])/(2.0*e[l-1]);\r
- r = Math.sqrt((g*g) + 1.0);\r
- g=d[m-1]-d[l-1]+e[l-1]/(g + sign(r,g));\r
- c = 1.0;\r
- s = c;\r
- p=0.0;\r
- for (i=m-1;i>=l;i--) {\r
- f = s*e[i-1];\r
- b = c*e[i-1];\r
- if (Math.abs(f) >= Math.abs(g)) {\r
- c=g/f;\r
- r = Math.sqrt((c*c)+1.0);\r
- e[i] = f*r;\r
- s = 1.0/r;\r
- c *= s;\r
- } else {\r
- s=f/g;\r
- r = Math.sqrt((s*s)+1.0);\r
- e[i] = g*r;\r
- c = 1.0/r;\r
- s *= c;\r
- }\r
- g=d[i] -p;\r
- r=(d[i-1]-g)*s + 2.0*c*b;\r
- p=s*r;\r
- d[i] = g + p;\r
- g = c * r - b;\r
- for (k=1; k <= n; k++) {\r
- f=value[k-1][i];\r
- value[k-1][i] = s*value[k-1][i-1] + c*f;\r
- value[k-1][i-1] = c*value[k-1][i-1] - s*f;\r
+ for (int i = 0; i < in.length; i++) {\r
+ out[i] = 0.0;\r
+\r
+ for (int k = 0; k < in.length; k++) {\r
+ out[i] += (value[i][k] * in[k]);\r
}\r
- }\r
- d[l-1] = d[l-1] - p;\r
- e[l-1] = g;\r
- e[m-1] = 0.0;\r
}\r
- } while ( m != l);\r
- }\r
- }\r
\r
- public double sign(double a, double b) {\r
- if (b < 0) {\r
- return -Math.abs(a);\r
- } else {\r
- return Math.abs(a);\r
+ return out;\r
}\r
- }\r
\r
- public double[] getColumn(int n) {\r
- double[] out = new double[rows];\r
- for (int i=0;i<rows;i++) {\r
- out[i] = value[i][n];\r
- }\r
- return out;\r
- }\r
+ public Matrix postMultiply(Matrix in) {\r
+ double[][] out = new double[this.rows][in.cols];\r
\r
+ for (int i = 0; i < this.rows; i++) {\r
+ for (int j = 0; j < in.cols; j++) {\r
+ out[i][j] = 0.0;\r
\r
- public void printD(PrintStream ps) {\r
+ for (int k = 0; k < rows; k++) {\r
+ out[i][j] = out[i][j] + (value[i][k] * in.value[k][j]);\r
+ }\r
+ }\r
+ }\r
\r
- for (int j = 0; j < rows;j++) {\r
- Format.print(ps,"%15.4e",d[j]);\r
+ return new Matrix(out, this.cols, in.rows);\r
}\r
- }\r
- public void printE(PrintStream ps) {\r
\r
- for (int j = 0; j < rows;j++) {\r
- Format.print(ps,"%15.4e",e[j]);\r
- }\r
- }\r
+ public Matrix copy() {\r
+ double[][] newmat = new double[rows][cols];\r
\r
- public static void main(String[] args) {\r
- int n = Integer.parseInt(args[0]);\r
- double[][] in = new double[n][n];\r
+ for (int i = 0; i < rows; i++) {\r
+ for (int j = 0; j < cols; j++) {\r
+ newmat[i][j] = value[i][j];\r
+ }\r
+ }\r
\r
- for (int i = 0;i < n;i++) {\r
- for (int j = 0; j < n; j++) {\r
- in[i][j] = (double)Math.random();\r
- }\r
+ return new Matrix(newmat, rows, cols);\r
}\r
\r
- Matrix origmat = new Matrix(in,n,n);\r
- // System.out.println(" --- Original matrix ---- ");\r
- /// origmat.print(System.out);\r
- //System.out.println();\r
-\r
- //System.out.println(" --- transpose matrix ---- ");\r
- Matrix trans = origmat.transpose();\r
- //trans.print(System.out);\r
- //System.out.println();\r
-\r
- //System.out.println(" --- OrigT * Orig ---- ");\r
-\r
- Matrix symm = trans.postMultiply(origmat);\r
- //symm.print(System.out);\r
- //System.out.println();\r
-\r
- // Copy the symmetric matrix for later\r
- Matrix origsymm = symm.copy();\r
+ public void tred() {\r
+ int n = rows;\r
+ int l;\r
+ int k;\r
+ int j;\r
+ int i;\r
+\r
+ double scale;\r
+ double hh;\r
+ double h;\r
+ double g;\r
+ double f;\r
+\r
+ this.d = new double[rows];\r
+ this.e = new double[rows];\r
+\r
+ for (i = n; i >= 2; i--) {\r
+ l = i - 1;\r
+ h = 0.0;\r
+ scale = 0.0;\r
+\r
+ if (l > 1) {\r
+ for (k = 1; k <= l; k++) {\r
+ scale += Math.abs(value[i - 1][k - 1]);\r
+ }\r
+\r
+ if (scale == 0.0) {\r
+ e[i - 1] = value[i - 1][l - 1];\r
+ } else {\r
+ for (k = 1; k <= l; k++) {\r
+ value[i - 1][k - 1] /= scale;\r
+ h += (value[i - 1][k - 1] * value[i - 1][k - 1]);\r
+ }\r
+\r
+ f = value[i - 1][l - 1];\r
+\r
+ if (f > 0) {\r
+ g = -1.0 * Math.sqrt(h);\r
+ } else {\r
+ g = Math.sqrt(h);\r
+ }\r
+\r
+ e[i - 1] = scale * g;\r
+ h -= (f * g);\r
+ value[i - 1][l - 1] = f - g;\r
+ f = 0.0;\r
+\r
+ for (j = 1; j <= l; j++) {\r
+ value[j - 1][i - 1] = value[i - 1][j - 1] / h;\r
+ g = 0.0;\r
+\r
+ for (k = 1; k <= j; k++) {\r
+ g += (value[j - 1][k - 1] * value[i - 1][k - 1]);\r
+ }\r
+\r
+ for (k = j + 1; k <= l; k++) {\r
+ g += (value[k - 1][j - 1] * value[i - 1][k - 1]);\r
+ }\r
+\r
+ e[j - 1] = g / h;\r
+ f += (e[j - 1] * value[i - 1][j - 1]);\r
+ }\r
+\r
+ hh = f / (h + h);\r
+\r
+ for (j = 1; j <= l; j++) {\r
+ f = value[i - 1][j - 1];\r
+ g = e[j - 1] - (hh * f);\r
+ e[j - 1] = g;\r
+\r
+ for (k = 1; k <= j; k++) {\r
+ value[j - 1][k - 1] -= ((f * e[k - 1]) +\r
+ (g * value[i - 1][k - 1]));\r
+ }\r
+ }\r
+ }\r
+ } else {\r
+ e[i - 1] = value[i - 1][l - 1];\r
+ }\r
\r
+ d[i - 1] = h;\r
+ }\r
\r
- // This produces the tridiagonal transformation matrix\r
- long tstart = System.currentTimeMillis();\r
- symm.tred();\r
- long tend = System.currentTimeMillis();\r
- //System.out.println("Time take for tred = " + (tend-tstart) + "ms");\r
- //System.out.println(" ---Tridiag transform matrix ---");\r
- //symm.print(System.out);\r
- //System.out.println();\r
+ d[0] = 0.0;\r
+ e[0] = 0.0;\r
\r
- //System.out.println(" --- D vector ---");\r
- //symm.printD(System.out);\r
- //System.out.println();\r
- //System.out.println(" --- E vector ---");\r
- //symm.printE(System.out);\r
- //System.out.println();\r
+ for (i = 1; i <= n; i++) {\r
+ l = i - 1;\r
\r
+ if (d[i - 1] != 0.0) {\r
+ for (j = 1; j <= l; j++) {\r
+ g = 0.0;\r
\r
- // Now produce the diagonalization matrix\r
- tstart = System.currentTimeMillis();\r
- symm.tqli();\r
- tend = System.currentTimeMillis();\r
- //System.out.println("Time take for tqli = " + (tend-tstart) + " ms");\r
+ for (k = 1; k <= l; k++) {\r
+ g += (value[i - 1][k - 1] * value[k - 1][j - 1]);\r
+ }\r
\r
- //System.out.println(" --- New diagonalization matrix ---");\r
- //symm.print(System.out);\r
- //System.out.println();\r
+ for (k = 1; k <= l; k++) {\r
+ value[k - 1][j - 1] -= (g * value[k - 1][i - 1]);\r
+ }\r
+ }\r
+ }\r
\r
- //System.out.println(" --- D vector ---");\r
- //symm.printD(System.out);\r
- //System.out.println();\r
- //System.out.println(" --- E vector ---");\r
- //symm.printE(System.out);\r
- //System.out.println();\r
+ d[i - 1] = value[i - 1][i - 1];\r
+ value[i - 1][i - 1] = 1.0;\r
\r
- //System.out.println(" --- First eigenvector --- ");\r
- //double[] eigenv = symm.getColumn(0);\r
- //for (int i=0; i < eigenv.length;i++) {\r
- // Format.print(System.out,"%15.4f",eigenv[i]);\r
- // }\r
- //System.out.println();\r
+ for (j = 1; j <= l; j++) {\r
+ value[j - 1][i - 1] = 0.0;\r
+ value[i - 1][j - 1] = 0.0;\r
+ }\r
+ }\r
+ }\r
\r
- //double[] neigenv = origsymm.vectorPostMultiply(eigenv);\r
+ public void tqli() {\r
+ int n = rows;\r
+\r
+ int m;\r
+ int l;\r
+ int iter;\r
+ int i;\r
+ int k;\r
+ double s;\r
+ double r;\r
+ double p;\r
+ ;\r
+\r
+ double g;\r
+ double f;\r
+ double dd;\r
+ double c;\r
+ double b;\r
+\r
+ for (i = 2; i <= n; i++) {\r
+ e[i - 2] = e[i - 1];\r
+ }\r
\r
- //for (int i=0; i < neigenv.length;i++) {\r
- // Format.print(System.out,"%15.4f",neigenv[i]/symm.d[0]);\r
- //}\r
+ e[n - 1] = 0.0;\r
+\r
+ for (l = 1; l <= n; l++) {\r
+ iter = 0;\r
+\r
+ do {\r
+ for (m = l; m <= (n - 1); m++) {\r
+ dd = Math.abs(d[m - 1]) + Math.abs(d[m]);\r
+\r
+ if ((Math.abs(e[m - 1]) + dd) == dd) {\r
+ break;\r
+ }\r
+ }\r
+\r
+ if (m != l) {\r
+ iter++;\r
+\r
+ if (iter == 30) {\r
+ System.err.print("Too many iterations in tqli");\r
+ System.exit(0); // JBPNote - should this really be here ???\r
+ } else {\r
+ // System.out.println("Iteration " + iter);\r
+ }\r
+\r
+ g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);\r
+ r = Math.sqrt((g * g) + 1.0);\r
+ g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));\r
+ c = 1.0;\r
+ s = c;\r
+ p = 0.0;\r
+\r
+ for (i = m - 1; i >= l; i--) {\r
+ f = s * e[i - 1];\r
+ b = c * e[i - 1];\r
+\r
+ if (Math.abs(f) >= Math.abs(g)) {\r
+ c = g / f;\r
+ r = Math.sqrt((c * c) + 1.0);\r
+ e[i] = f * r;\r
+ s = 1.0 / r;\r
+ c *= s;\r
+ } else {\r
+ s = f / g;\r
+ r = Math.sqrt((s * s) + 1.0);\r
+ e[i] = g * r;\r
+ c = 1.0 / r;\r
+ s *= c;\r
+ }\r
+\r
+ g = d[i] - p;\r
+ r = ((d[i - 1] - g) * s) + (2.0 * c * b);\r
+ p = s * r;\r
+ d[i] = g + p;\r
+ g = (c * r) - b;\r
+\r
+ for (k = 1; k <= n; k++) {\r
+ f = value[k - 1][i];\r
+ value[k - 1][i] = (s * value[k - 1][i - 1]) +\r
+ (c * f);\r
+ value[k - 1][i - 1] = (c * value[k - 1][i - 1]) -\r
+ (s * f);\r
+ }\r
+ }\r
+\r
+ d[l - 1] = d[l - 1] - p;\r
+ e[l - 1] = g;\r
+ e[m - 1] = 0.0;\r
+ }\r
+ } while (m != l);\r
+ }\r
+ }\r
\r
- //System.out.println();\r
- }\r
+ public void tred2() {\r
+ int n = rows;\r
+ int l;\r
+ int k;\r
+ int j;\r
+ int i;\r
+\r
+ double scale;\r
+ double hh;\r
+ double h;\r
+ double g;\r
+ double f;\r
+\r
+ this.d = new double[rows];\r
+ this.e = new double[rows];\r
+\r
+ for (i = n - 1; i >= 1; i--) {\r
+ l = i - 1;\r
+ h = 0.0;\r
+ scale = 0.0;\r
+\r
+ if (l > 0) {\r
+ for (k = 0; k < l; k++) {\r
+ scale += Math.abs(value[i][k]);\r
+ }\r
+\r
+ if (scale == 0.0) {\r
+ e[i] = value[i][l];\r
+ } else {\r
+ for (k = 0; k < l; k++) {\r
+ value[i][k] /= scale;\r
+ h += (value[i][k] * value[i][k]);\r
+ }\r
+\r
+ f = value[i][l];\r
+\r
+ if (f > 0) {\r
+ g = -1.0 * Math.sqrt(h);\r
+ } else {\r
+ g = Math.sqrt(h);\r
+ }\r
+\r
+ e[i] = scale * g;\r
+ h -= (f * g);\r
+ value[i][l] = f - g;\r
+ f = 0.0;\r
+\r
+ for (j = 0; j < l; j++) {\r
+ value[j][i] = value[i][j] / h;\r
+ g = 0.0;\r
+\r
+ for (k = 0; k < j; k++) {\r
+ g += (value[j][k] * value[i][k]);\r
+ }\r
+\r
+ for (k = j; k < l; k++) {\r
+ g += (value[k][j] * value[i][k]);\r
+ }\r
+\r
+ e[j] = g / h;\r
+ f += (e[j] * value[i][j]);\r
+ }\r
+\r
+ hh = f / (h + h);\r
+\r
+ for (j = 0; j < l; j++) {\r
+ f = value[i][j];\r
+ g = e[j] - (hh * f);\r
+ e[j] = g;\r
+\r
+ for (k = 0; k < j; k++) {\r
+ value[j][k] -= ((f * e[k]) + (g * value[i][k]));\r
+ }\r
+ }\r
+ }\r
+ } else {\r
+ e[i] = value[i][l];\r
+ }\r
\r
-}\r
+ d[i] = h;\r
+ }\r
\r
+ d[0] = 0.0;\r
+ e[0] = 0.0;\r
\r
+ for (i = 0; i < n; i++) {\r
+ l = i - 1;\r
\r
+ if (d[i] != 0.0) {\r
+ for (j = 0; j < l; j++) {\r
+ g = 0.0;\r
\r
+ for (k = 0; k < l; k++) {\r
+ g += (value[i][k] * value[k][j]);\r
+ }\r
\r
+ for (k = 0; k < l; k++) {\r
+ value[k][j] -= (g * value[k][i]);\r
+ }\r
+ }\r
+ }\r
\r
+ d[i] = value[i][i];\r
+ value[i][i] = 1.0;\r
\r
+ for (j = 0; j < l; j++) {\r
+ value[j][i] = 0.0;\r
+ value[i][j] = 0.0;\r
+ }\r
+ }\r
+ }\r
\r
+ public void tqli2() {\r
+ int n = rows;\r
+\r
+ int m;\r
+ int l;\r
+ int iter;\r
+ int i;\r
+ int k;\r
+ double s;\r
+ double r;\r
+ double p;\r
+ ;\r
+\r
+ double g;\r
+ double f;\r
+ double dd;\r
+ double c;\r
+ double b;\r
+\r
+ for (i = 2; i <= n; i++) {\r
+ e[i - 2] = e[i - 1];\r
+ }\r
\r
+ e[n - 1] = 0.0;\r
+\r
+ for (l = 1; l <= n; l++) {\r
+ iter = 0;\r
+\r
+ do {\r
+ for (m = l; m <= (n - 1); m++) {\r
+ dd = Math.abs(d[m - 1]) + Math.abs(d[m]);\r
+\r
+ if ((Math.abs(e[m - 1]) + dd) == dd) {\r
+ break;\r
+ }\r
+ }\r
+\r
+ if (m != l) {\r
+ iter++;\r
+\r
+ if (iter == 30) {\r
+ System.err.print("Too many iterations in tqli");\r
+ System.exit(0); // JBPNote - same as above - not a graceful exit!\r
+ } else {\r
+ // System.out.println("Iteration " + iter);\r
+ }\r
+\r
+ g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);\r
+ r = Math.sqrt((g * g) + 1.0);\r
+ g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));\r
+ c = 1.0;\r
+ s = c;\r
+ p = 0.0;\r
+\r
+ for (i = m - 1; i >= l; i--) {\r
+ f = s * e[i - 1];\r
+ b = c * e[i - 1];\r
+\r
+ if (Math.abs(f) >= Math.abs(g)) {\r
+ c = g / f;\r
+ r = Math.sqrt((c * c) + 1.0);\r
+ e[i] = f * r;\r
+ s = 1.0 / r;\r
+ c *= s;\r
+ } else {\r
+ s = f / g;\r
+ r = Math.sqrt((s * s) + 1.0);\r
+ e[i] = g * r;\r
+ c = 1.0 / r;\r
+ s *= c;\r
+ }\r
+\r
+ g = d[i] - p;\r
+ r = ((d[i - 1] - g) * s) + (2.0 * c * b);\r
+ p = s * r;\r
+ d[i] = g + p;\r
+ g = (c * r) - b;\r
+\r
+ for (k = 1; k <= n; k++) {\r
+ f = value[k - 1][i];\r
+ value[k - 1][i] = (s * value[k - 1][i - 1]) +\r
+ (c * f);\r
+ value[k - 1][i - 1] = (c * value[k - 1][i - 1]) -\r
+ (s * f);\r
+ }\r
+ }\r
+\r
+ d[l - 1] = d[l - 1] - p;\r
+ e[l - 1] = g;\r
+ e[m - 1] = 0.0;\r
+ }\r
+ } while (m != l);\r
+ }\r
+ }\r
\r
+ public double sign(double a, double b) {\r
+ if (b < 0) {\r
+ return -Math.abs(a);\r
+ } else {\r
+ return Math.abs(a);\r
+ }\r
+ }\r
\r
+ public double[] getColumn(int n) {\r
+ double[] out = new double[rows];\r
\r
+ for (int i = 0; i < rows; i++) {\r
+ out[i] = value[i][n];\r
+ }\r
\r
+ return out;\r
+ }\r
\r
+ public void printD(PrintStream ps) {\r
+ for (int j = 0; j < rows; j++) {\r
+ Format.print(ps, "%15.4e", d[j]);\r
+ }\r
+ }\r
\r
+ public void printE(PrintStream ps) {\r
+ for (int j = 0; j < rows; j++) {\r
+ Format.print(ps, "%15.4e", e[j]);\r
+ }\r
+ }\r
\r
+ public static void main(String[] args) {\r
+ int n = Integer.parseInt(args[0]);\r
+ double[][] in = new double[n][n];\r
\r
+ for (int i = 0; i < n; i++) {\r
+ for (int j = 0; j < n; j++) {\r
+ in[i][j] = (double) Math.random();\r
+ }\r
+ }\r
\r
+ Matrix origmat = new Matrix(in, n, n);\r
+\r
+ // System.out.println(" --- Original matrix ---- ");\r
+ /// origmat.print(System.out);\r
+ //System.out.println();\r
+ //System.out.println(" --- transpose matrix ---- ");\r
+ Matrix trans = origmat.transpose();\r
+\r
+ //trans.print(System.out);\r
+ //System.out.println();\r
+ //System.out.println(" --- OrigT * Orig ---- ");\r
+ Matrix symm = trans.postMultiply(origmat);\r
+\r
+ //symm.print(System.out);\r
+ //System.out.println();\r
+ // Copy the symmetric matrix for later\r
+ Matrix origsymm = symm.copy();\r
+\r
+ // This produces the tridiagonal transformation matrix\r
+ long tstart = System.currentTimeMillis();\r
+ symm.tred();\r
+\r
+ long tend = System.currentTimeMillis();\r
+\r
+ //System.out.println("Time take for tred = " + (tend-tstart) + "ms");\r
+ //System.out.println(" ---Tridiag transform matrix ---");\r
+ //symm.print(System.out);\r
+ //System.out.println();\r
+ //System.out.println(" --- D vector ---");\r
+ //symm.printD(System.out);\r
+ //System.out.println();\r
+ //System.out.println(" --- E vector ---");\r
+ //symm.printE(System.out);\r
+ //System.out.println();\r
+ // Now produce the diagonalization matrix\r
+ tstart = System.currentTimeMillis();\r
+ symm.tqli();\r
+ tend = System.currentTimeMillis();\r
+\r
+ //System.out.println("Time take for tqli = " + (tend-tstart) + " ms");\r
+ //System.out.println(" --- New diagonalization matrix ---");\r
+ //symm.print(System.out);\r
+ //System.out.println();\r
+ //System.out.println(" --- D vector ---");\r
+ //symm.printD(System.out);\r
+ //System.out.println();\r
+ //System.out.println(" --- E vector ---");\r
+ //symm.printE(System.out);\r
+ //System.out.println();\r
+ //System.out.println(" --- First eigenvector --- ");\r
+ //double[] eigenv = symm.getColumn(0);\r
+ //for (int i=0; i < eigenv.length;i++) {\r
+ // Format.print(System.out,"%15.4f",eigenv[i]);\r
+ // }\r
+ //System.out.println();\r
+ //double[] neigenv = origsymm.vectorPostMultiply(eigenv);\r
+ //for (int i=0; i < neigenv.length;i++) {\r
+ // Format.print(System.out,"%15.4f",neigenv[i]/symm.d[0]);\r
+ //}\r
+ //System.out.println();\r
+ }\r
+}\r
git://source.jalview.org / jalview.git / blobdiff