X-Git-Url: http://source.jalview.org/gitweb/?a=blobdiff_plain;f=src%2Fjalview%2Fmath%2FMatrix.java;h=b6e77ed159212198d55e70751df1554f32208fb1;hb=797df64fa2a0a30773d0f48f5494d4155e5a8be3;hp=d08fe227478eaeb61008bac1baa774ee8f11e975;hpb=1ecf6419aba86993b3c223bf5ec0fa79427baf85;p=jalview.git diff --git a/src/jalview/math/Matrix.java b/src/jalview/math/Matrix.java index d08fe22..b6e77ed 100755 --- a/src/jalview/math/Matrix.java +++ b/src/jalview/math/Matrix.java @@ -1,572 +1,856 @@ -package jalview.math; - -import jalview.util.*; - -import java.io.*; - -public class Matrix { - - /** - * SMJSPUBLIC - */ - public double[][] value; - public int rows; - public int cols; - public double[] d; // Diagonal - public double[] e; // off diagonal - - public Matrix(double[][] value, int rows, int cols) { - this.rows = rows; - this.cols = cols; - this.value = value; - } - - public Matrix transpose() { - double[][] out = new double[cols][rows]; - - for (int i = 0; i < cols; i++) { - for (int j = 0; j < rows ; j++) { - out[i][j] = value[j][i]; - } - } - return new Matrix(out,cols,rows); - } - - public void print(PrintStream ps) { - - for (int i = 0; i < rows; i++) { - for (int j = 0; j < cols; j++) { - Format.print(ps,"%8.2f",value[i][j]); - } - ps.println(); - } - } - - - public Matrix preMultiply(Matrix in) { - double[][] tmp = new double[in.rows][this.cols]; - - for (int i = 0; i < in.rows; i++) { - for (int j = 0; j < this.cols; j++ ) { - tmp[i][j] = 0.0; - - for (int k = 0; k < in.cols; k++) { - tmp[i][j] += in.value[i][k]*this.value[k][j]; - } - - } - } - - return new Matrix(tmp,in.rows,this.cols); - } - - public double[] vectorPostMultiply(double[] in) { - double[] out = new double[in.length]; - for (int i = 0; i < in.length; i++) { - out[i] = 0.0; - for (int k=0; k < in.length; k++) { - out[i] += value[i][k] * in[k]; - } - } - return out; - } - public Matrix postMultiply(Matrix in) { - - double[][] out = new double[this.rows][in.cols]; - for (int i = 0; i < this.rows; i++) { - for (int j = 0; j < in.cols; j++ ) { - - out[i][j] = 0.0; - - for (int k = 0; k < rows; k++) { - out[i][j] = out[i][j] + value[i][k]*in.value[k][j]; - } - - } - } - return new Matrix(out,this.cols,in.rows); - } - - public Matrix copy() { - double[][] newmat = new double[rows][cols]; - - for (int i = 0; i < rows; i++) { - for (int j = 0; j < cols; j++) { - newmat[i][j] = value[i][j]; - } - } - return new Matrix(newmat,rows,cols); - } - - public void tred() { - int n = rows; - int l; - int k; - int j; - int i; - - double scale; - double hh; - double h; - double g; - double f; - - this.d = new double[rows]; - this.e = new double[rows]; - - for (i=n; i >= 2;i--) { - l=i-1; - h = 0.0; - scale = 0.0; - - if (l > 1) { - for (k=1;k<=l;k++) { - scale += Math.abs(value[i-1][k-1]); - } - if (scale == 0.0) { - e[i-1] = value[i-1][l-1]; - } else { - for (k=1; k <= l; k++) { - value[i-1][k-1] /= scale; - h += value[i-1][k-1]*value[i-1][k-1]; - } - f = value[i-1][l-1]; - if (f>0) { - g = -1.0*Math.sqrt(h); - } else { - g = Math.sqrt(h); - } - e[i-1] = scale*g; - h -= f*g; - value[i-1][l-1] = f-g; - f=0.0; - for (j=1; j <= l; j++) { - value[j-1][i-1] = value[i-1][j-1]/h; - g=0.0; - for (k= 1; k <= j; k++) { - g += value[j-1][k-1]*value[i-1][k-1]; - } - for (k=j+1; k<=l;k++) { - g+= value[k-1][j-1]*value[i-1][k-1]; - } - e[j-1] = g/h; - f+=e[j-1]*value[i-1][j-1]; - } - hh=f/(h+h); - for (j=1;j<=l;j++) { - f=value[i-1][j-1]; - g = e[j-1] - hh*f; - e[j-1] = g; - for (k=1;k<=j;k++) { - value[j-1][k-1] -= (f*e[k-1]+g*value[i-1][k-1]); - } - } - } - } else { - e[i-1] = value[i-1][l-1]; - } - d[i-1] = h; - } - d[0] = 0.0; - e[0] = 0.0; - for (i=1;i<=n;i++) { - l=i-1; - if (d[i-1] != 0.0) { - for (j=1;j<=l;j++) { - g=0.0; - for (k=1;k<=l;k++) { - g+= value[i-1][k-1]*value[k-1][j-1]; - } - for (k=1;k<=l;k++) { - value[k-1][j-1] -= g*value[k-1][i-1]; - } - } - } - d[i-1] = value[i-1][i-1]; - value[i-1][i-1] = 1.0; - for (j=1;j<=l;j++) { - value[j-1][i-1] = 0.0; - value[i-1][j-1] = 0.0; - } - } - } - - public void tqli() { - int n = rows; - - int m; - int l; - int iter; - int i; - int k; - double s; - double r; - double p; - ; - double g; - double f; - double dd; - double c; - double b; - - for (i=2;i<=n;i++) { - e[i-2] = e[i-1]; - } - e[n-1] = 0.0; - for (l=1;l<=n;l++) { - iter=0; - do { - for (m=l;m<=(n-1);m++) { - dd=Math.abs(d[m-1]) + Math.abs(d[m]); - if (Math.abs(e[m-1]) + dd == dd) - break; - } - if (m != l) { - iter++; - if (iter == 30) { - System.out.print("Too many iterations in tqli"); - System.exit(0); - } else { - // System.out.println("Iteration " + iter); - } - g=(d[l]-d[l-1])/(2.0*e[l-1]); - r = Math.sqrt((g*g) + 1.0); - g=d[m-1]-d[l-1]+e[l-1]/(g + sign(r,g)); - c = 1.0; - s = c; - p=0.0; - for (i=m-1;i>=l;i--) { - f = s*e[i-1]; - b = c*e[i-1]; - if (Math.abs(f) >= Math.abs(g)) { - c=g/f; - r = Math.sqrt((c*c)+1.0); - e[i] = f*r; - s = 1.0/r; - c *= s; - } else { - s=f/g; - r = Math.sqrt((s*s)+1.0); - e[i] = g*r; - c = 1.0/r; - s *= c; - } - g=d[i] -p; - r=(d[i-1]-g)*s + 2.0*c*b; - p=s*r; - d[i] = g + p; - g = c * r - b; - for (k=1; k <= n; k++) { - f=value[k-1][i]; - value[k-1][i] = s*value[k-1][i-1] + c*f; - value[k-1][i-1] = c*value[k-1][i-1] - s*f; - } - } - d[l-1] = d[l-1] - p; - e[l-1] = g; - e[m-1] = 0.0; - } - } while ( m != l); - } - } - public void tred2() { - int n = rows; - int l; - int k; - int j; - int i; - - double scale; - double hh; - double h; - double g; - double f; - - this.d = new double[rows]; - this.e = new double[rows]; - - for (i=n-1; i >= 1;i--) { - l=i-1; - h = 0.0; - scale = 0.0; - - if (l > 0) { - for (k=0;k0) { - g = -1.0*Math.sqrt(h); - } else { - g = Math.sqrt(h); - } - e[i] = scale*g; - h -= f*g; - value[i][l] = f-g; - f=0.0; - for (j=0; j < l; j++) { - value[j][i] = value[i][j]/h; - g=0.0; - for (k= 0; k < j; k++) { - g += value[j][k]*value[i][k]; - } - for (k=j; k=l;i--) { - f = s*e[i-1]; - b = c*e[i-1]; - if (Math.abs(f) >= Math.abs(g)) { - c=g/f; - r = Math.sqrt((c*c)+1.0); - e[i] = f*r; - s = 1.0/r; - c *= s; - } else { - s=f/g; - r = Math.sqrt((s*s)+1.0); - e[i] = g*r; - c = 1.0/r; - s *= c; - } - g=d[i] -p; - r=(d[i-1]-g)*s + 2.0*c*b; - p=s*r; - d[i] = g + p; - g = c * r - b; - for (k=1; k <= n; k++) { - f=value[k-1][i]; - value[k-1][i] = s*value[k-1][i-1] + c*f; - value[k-1][i-1] = c*value[k-1][i-1] - s*f; - } - } - d[l-1] = d[l-1] - p; - e[l-1] = g; - e[m-1] = 0.0; - } - } while ( m != l); - } - } - - public double sign(double a, double b) { - if (b < 0) { - return -Math.abs(a); - } else { - return Math.abs(a); - } - } - - public double[] getColumn(int n) { - double[] out = new double[rows]; - for (int i=0;i. + */ +package jalview.math; + +import java.io.*; + +import jalview.util.*; + +/** + * DOCUMENT ME! + * + * @author $author$ + * @version $Revision$ + */ +public class Matrix +{ + /** + * SMJSPUBLIC + */ + public double[][] value; + + /** DOCUMENT ME!! */ + public int rows; + + /** DOCUMENT ME!! */ + public int cols; + + /** DOCUMENT ME!! */ + public double[] d; // Diagonal + + /** DOCUMENT ME!! */ + public double[] e; // off diagonal + + /** + * Creates a new Matrix object. + * + * @param value + * DOCUMENT ME! + * @param rows + * DOCUMENT ME! + * @param cols + * DOCUMENT ME! + */ + public Matrix(double[][] value, int rows, int cols) + { + this.rows = rows; + this.cols = cols; + this.value = value; + } + + /** + * DOCUMENT ME! + * + * @return DOCUMENT ME! + */ + public Matrix transpose() + { + double[][] out = new double[cols][rows]; + + for (int i = 0; i < cols; i++) + { + for (int j = 0; j < rows; j++) + { + out[i][j] = value[j][i]; + } + } + + return new Matrix(out, cols, rows); + } + + /** + * DOCUMENT ME! + * + * @param ps + * DOCUMENT ME! + */ + public void print(PrintStream ps) + { + for (int i = 0; i < rows; i++) + { + for (int j = 0; j < cols; j++) + { + Format.print(ps, "%8.2f", value[i][j]); + } + + ps.println(); + } + } + + /** + * DOCUMENT ME! + * + * @param in + * DOCUMENT ME! + * + * @return DOCUMENT ME! + */ + public Matrix preMultiply(Matrix in) + { + double[][] tmp = new double[in.rows][this.cols]; + + for (int i = 0; i < in.rows; i++) + { + for (int j = 0; j < this.cols; j++) + { + tmp[i][j] = 0.0; + + for (int k = 0; k < in.cols; k++) + { + tmp[i][j] += (in.value[i][k] * this.value[k][j]); + } + } + } + + return new Matrix(tmp, in.rows, this.cols); + } + + /** + * DOCUMENT ME! + * + * @param in + * DOCUMENT ME! + * + * @return DOCUMENT ME! + */ + public double[] vectorPostMultiply(double[] in) + { + double[] out = new double[in.length]; + + for (int i = 0; i < in.length; i++) + { + out[i] = 0.0; + + for (int k = 0; k < in.length; k++) + { + out[i] += (value[i][k] * in[k]); + } + } + + return out; + } + + /** + * DOCUMENT ME! + * + * @param in + * DOCUMENT ME! + * + * @return DOCUMENT ME! + */ + public Matrix postMultiply(Matrix in) + { + double[][] out = new double[this.rows][in.cols]; + + for (int i = 0; i < this.rows; i++) + { + for (int j = 0; j < in.cols; j++) + { + out[i][j] = 0.0; + + for (int k = 0; k < rows; k++) + { + out[i][j] = out[i][j] + (value[i][k] * in.value[k][j]); + } + } + } + + return new Matrix(out, this.cols, in.rows); + } + + /** + * DOCUMENT ME! + * + * @return DOCUMENT ME! + */ + public Matrix copy() + { + double[][] newmat = new double[rows][cols]; + + for (int i = 0; i < rows; i++) + { + for (int j = 0; j < cols; j++) + { + newmat[i][j] = value[i][j]; + } + } + + return new Matrix(newmat, rows, cols); + } + + /** + * DOCUMENT ME! + */ + public void tred() + { + int n = rows; + int l; + int k; + int j; + int i; + + double scale; + double hh; + double h; + double g; + double f; + + this.d = new double[rows]; + this.e = new double[rows]; + + for (i = n; i >= 2; i--) + { + l = i - 1; + h = 0.0; + scale = 0.0; + + if (l > 1) + { + for (k = 1; k <= l; k++) + { + scale += Math.abs(value[i - 1][k - 1]); + } + + if (scale == 0.0) + { + e[i - 1] = value[i - 1][l - 1]; + } + else + { + for (k = 1; k <= l; k++) + { + value[i - 1][k - 1] /= scale; + h += (value[i - 1][k - 1] * value[i - 1][k - 1]); + } + + f = value[i - 1][l - 1]; + + if (f > 0) + { + g = -1.0 * Math.sqrt(h); + } + else + { + g = Math.sqrt(h); + } + + e[i - 1] = scale * g; + h -= (f * g); + value[i - 1][l - 1] = f - g; + f = 0.0; + + for (j = 1; j <= l; j++) + { + value[j - 1][i - 1] = value[i - 1][j - 1] / h; + g = 0.0; + + for (k = 1; k <= j; k++) + { + g += (value[j - 1][k - 1] * value[i - 1][k - 1]); + } + + for (k = j + 1; k <= l; k++) + { + g += (value[k - 1][j - 1] * value[i - 1][k - 1]); + } + + e[j - 1] = g / h; + f += (e[j - 1] * value[i - 1][j - 1]); + } + + hh = f / (h + h); + + for (j = 1; j <= l; j++) + { + f = value[i - 1][j - 1]; + g = e[j - 1] - (hh * f); + e[j - 1] = g; + + for (k = 1; k <= j; k++) + { + value[j - 1][k - 1] -= ((f * e[k - 1]) + (g * value[i - 1][k - 1])); + } + } + } + } + else + { + e[i - 1] = value[i - 1][l - 1]; + } + + d[i - 1] = h; + } + + d[0] = 0.0; + e[0] = 0.0; + + for (i = 1; i <= n; i++) + { + l = i - 1; + + if (d[i - 1] != 0.0) + { + for (j = 1; j <= l; j++) + { + g = 0.0; + + for (k = 1; k <= l; k++) + { + g += (value[i - 1][k - 1] * value[k - 1][j - 1]); + } + + for (k = 1; k <= l; k++) + { + value[k - 1][j - 1] -= (g * value[k - 1][i - 1]); + } + } + } + + d[i - 1] = value[i - 1][i - 1]; + value[i - 1][i - 1] = 1.0; + + for (j = 1; j <= l; j++) + { + value[j - 1][i - 1] = 0.0; + value[i - 1][j - 1] = 0.0; + } + } + } + + /** + * DOCUMENT ME! + */ + public void tqli() + { + int n = rows; + + int m; + int l; + int iter; + int i; + int k; + double s; + double r; + double p; + ; + + double g; + double f; + double dd; + double c; + double b; + + for (i = 2; i <= n; i++) + { + e[i - 2] = e[i - 1]; + } + + e[n - 1] = 0.0; + + for (l = 1; l <= n; l++) + { + iter = 0; + + do + { + for (m = l; m <= (n - 1); m++) + { + dd = Math.abs(d[m - 1]) + Math.abs(d[m]); + + if ((Math.abs(e[m - 1]) + dd) == dd) + { + break; + } + } + + if (m != l) + { + iter++; + + if (iter == 30) + { + System.err.print("Too many iterations in tqli"); + System.exit(0); // JBPNote - should this really be here ??? + } + else + { + // System.out.println("Iteration " + iter); + } + + g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]); + r = Math.sqrt((g * g) + 1.0); + g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g))); + c = 1.0; + s = c; + p = 0.0; + + for (i = m - 1; i >= l; i--) + { + f = s * e[i - 1]; + b = c * e[i - 1]; + + if (Math.abs(f) >= Math.abs(g)) + { + c = g / f; + r = Math.sqrt((c * c) + 1.0); + e[i] = f * r; + s = 1.0 / r; + c *= s; + } + else + { + s = f / g; + r = Math.sqrt((s * s) + 1.0); + e[i] = g * r; + c = 1.0 / r; + s *= c; + } + + g = d[i] - p; + r = ((d[i - 1] - g) * s) + (2.0 * c * b); + p = s * r; + d[i] = g + p; + g = (c * r) - b; + + for (k = 1; k <= n; k++) + { + f = value[k - 1][i]; + value[k - 1][i] = (s * value[k - 1][i - 1]) + (c * f); + value[k - 1][i - 1] = (c * value[k - 1][i - 1]) - (s * f); + } + } + + d[l - 1] = d[l - 1] - p; + e[l - 1] = g; + e[m - 1] = 0.0; + } + } while (m != l); + } + } + + /** + * DOCUMENT ME! + */ + public void tred2() + { + int n = rows; + int l; + int k; + int j; + int i; + + double scale; + double hh; + double h; + double g; + double f; + + this.d = new double[rows]; + this.e = new double[rows]; + + for (i = n - 1; i >= 1; i--) + { + l = i - 1; + h = 0.0; + scale = 0.0; + + if (l > 0) + { + for (k = 0; k < l; k++) + { + scale += Math.abs(value[i][k]); + } + + if (scale == 0.0) + { + e[i] = value[i][l]; + } + else + { + for (k = 0; k < l; k++) + { + value[i][k] /= scale; + h += (value[i][k] * value[i][k]); + } + + f = value[i][l]; + + if (f > 0) + { + g = -1.0 * Math.sqrt(h); + } + else + { + g = Math.sqrt(h); + } + + e[i] = scale * g; + h -= (f * g); + value[i][l] = f - g; + f = 0.0; + + for (j = 0; j < l; j++) + { + value[j][i] = value[i][j] / h; + g = 0.0; + + for (k = 0; k < j; k++) + { + g += (value[j][k] * value[i][k]); + } + + for (k = j; k < l; k++) + { + g += (value[k][j] * value[i][k]); + } + + e[j] = g / h; + f += (e[j] * value[i][j]); + } + + hh = f / (h + h); + + for (j = 0; j < l; j++) + { + f = value[i][j]; + g = e[j] - (hh * f); + e[j] = g; + + for (k = 0; k < j; k++) + { + value[j][k] -= ((f * e[k]) + (g * value[i][k])); + } + } + } + } + else + { + e[i] = value[i][l]; + } + + d[i] = h; + } + + d[0] = 0.0; + e[0] = 0.0; + + for (i = 0; i < n; i++) + { + l = i - 1; + + if (d[i] != 0.0) + { + for (j = 0; j < l; j++) + { + g = 0.0; + + for (k = 0; k < l; k++) + { + g += (value[i][k] * value[k][j]); + } + + for (k = 0; k < l; k++) + { + value[k][j] -= (g * value[k][i]); + } + } + } + + d[i] = value[i][i]; + value[i][i] = 1.0; + + for (j = 0; j < l; j++) + { + value[j][i] = 0.0; + value[i][j] = 0.0; + } + } + } + + /** + * DOCUMENT ME! + */ + public void tqli2() + { + int n = rows; + + int m; + int l; + int iter; + int i; + int k; + double s; + double r; + double p; + ; + + double g; + double f; + double dd; + double c; + double b; + + for (i = 2; i <= n; i++) + { + e[i - 2] = e[i - 1]; + } + + e[n - 1] = 0.0; + + for (l = 1; l <= n; l++) + { + iter = 0; + + do + { + for (m = l; m <= (n - 1); m++) + { + dd = Math.abs(d[m - 1]) + Math.abs(d[m]); + + if ((Math.abs(e[m - 1]) + dd) == dd) + { + break; + } + } + + if (m != l) + { + iter++; + + if (iter == 30) + { + System.err.print("Too many iterations in tqli"); + System.exit(0); // JBPNote - same as above - not a graceful exit! + } + else + { + // System.out.println("Iteration " + iter); + } + + g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]); + r = Math.sqrt((g * g) + 1.0); + g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g))); + c = 1.0; + s = c; + p = 0.0; + + for (i = m - 1; i >= l; i--) + { + f = s * e[i - 1]; + b = c * e[i - 1]; + + if (Math.abs(f) >= Math.abs(g)) + { + c = g / f; + r = Math.sqrt((c * c) + 1.0); + e[i] = f * r; + s = 1.0 / r; + c *= s; + } + else + { + s = f / g; + r = Math.sqrt((s * s) + 1.0); + e[i] = g * r; + c = 1.0 / r; + s *= c; + } + + g = d[i] - p; + r = ((d[i - 1] - g) * s) + (2.0 * c * b); + p = s * r; + d[i] = g + p; + g = (c * r) - b; + + for (k = 1; k <= n; k++) + { + f = value[k - 1][i]; + value[k - 1][i] = (s * value[k - 1][i - 1]) + (c * f); + value[k - 1][i - 1] = (c * value[k - 1][i - 1]) - (s * f); + } + } + + d[l - 1] = d[l - 1] - p; + e[l - 1] = g; + e[m - 1] = 0.0; + } + } while (m != l); + } + } + + /** + * DOCUMENT ME! + * + * @param a + * DOCUMENT ME! + * @param b + * DOCUMENT ME! + * + * @return DOCUMENT ME! + */ + public double sign(double a, double b) + { + if (b < 0) + { + return -Math.abs(a); + } + else + { + return Math.abs(a); + } + } + + /** + * DOCUMENT ME! + * + * @param n + * DOCUMENT ME! + * + * @return DOCUMENT ME! + */ + public double[] getColumn(int n) + { + double[] out = new double[rows]; + + for (int i = 0; i < rows; i++) + { + out[i] = value[i][n]; + } + + return out; + } + + /** + * DOCUMENT ME! + * + * @param ps + * DOCUMENT ME! + */ + public void printD(PrintStream ps) + { + for (int j = 0; j < rows; j++) + { + Format.print(ps, "%15.4e", d[j]); + } + } + + /** + * DOCUMENT ME! + * + * @param ps + * DOCUMENT ME! + */ + public void printE(PrintStream ps) + { + for (int j = 0; j < rows; j++) + { + Format.print(ps, "%15.4e", e[j]); + } + } + + /** + * DOCUMENT ME! + * + * @param args + * DOCUMENT ME! + */ + public static void main(String[] args) + { + int n = Integer.parseInt(args[0]); + double[][] in = new double[n][n]; + + for (int i = 0; i < n; i++) + { + for (int j = 0; j < n; j++) + { + in[i][j] = (double) Math.random(); + } + } + + Matrix origmat = new Matrix(in, n, n); + + // System.out.println(" --- Original matrix ---- "); + // / origmat.print(System.out); + // System.out.println(); + // System.out.println(" --- transpose matrix ---- "); + Matrix trans = origmat.transpose(); + + // trans.print(System.out); + // System.out.println(); + // System.out.println(" --- OrigT * Orig ---- "); + Matrix symm = trans.postMultiply(origmat); + + // symm.print(System.out); + // System.out.println(); + // Copy the symmetric matrix for later + // Matrix origsymm = symm.copy(); + + // This produces the tridiagonal transformation matrix + // long tstart = System.currentTimeMillis(); + symm.tred(); + + // long tend = System.currentTimeMillis(); + + // System.out.println("Time take for tred = " + (tend-tstart) + "ms"); + // System.out.println(" ---Tridiag transform matrix ---"); + // symm.print(System.out); + // System.out.println(); + // System.out.println(" --- D vector ---"); + // symm.printD(System.out); + // System.out.println(); + // System.out.println(" --- E vector ---"); + // symm.printE(System.out); + // System.out.println(); + // Now produce the diagonalization matrix + // tstart = System.currentTimeMillis(); + symm.tqli(); + // tend = System.currentTimeMillis(); + + // System.out.println("Time take for tqli = " + (tend-tstart) + " ms"); + // System.out.println(" --- New diagonalization matrix ---"); + // symm.print(System.out); + // System.out.println(); + // System.out.println(" --- D vector ---"); + // symm.printD(System.out); + // System.out.println(); + // System.out.println(" --- E vector ---"); + // symm.printE(System.out); + // System.out.println(); + // System.out.println(" --- First eigenvector --- "); + // double[] eigenv = symm.getColumn(0); + // for (int i=0; i < eigenv.length;i++) { + // Format.print(System.out,"%15.4f",eigenv[i]); + // } + // System.out.println(); + // double[] neigenv = origsymm.vectorPostMultiply(eigenv); + // for (int i=0; i < neigenv.length;i++) { + // Format.print(System.out,"%15.4f",neigenv[i]/symm.d[0]); + // } + // System.out.println(); + } +}