house.java

JAVA 数学程序库 提供常规的数值计算程序包

package jmathlib.toolbox.jmathlib.matrix._private.Jampack;

/**
   House provides static methods to generate and apply Householder
   transformations.

   @version Pre-alpha
   @author G. W. Stewart
*/

public class House{

/**
   Generates a Householder transformation from within the part of
   column c of a Zmat (altered) extending from rows
   r1 to r2.  The method overwrites the
   column with the result of applying the transformation.

   @param A   The matrix from which the transformation
              is to be generated (altered)
   @param r1  The index of the row in which the generating column
              begins
   @param r2  The index of the row in which the generating column
              ends
   @param c   The index of the generating column
   @return    A Z1 of length r2-r1+1
              containing the Householder vector
   @exception JampackException
              Passed from below.
*/
   public static Z1 genc(Zmat A,  int r1, int r2, int c)
   throws JampackException{

      int i, ru;
      double norm;
      double s;
      Z scale;
      Z t = new Z();
      Z t1 = new Z();

      c = c - A.basex;
      r1 = r1 - A.basex;
      r2 = r2 - A.basex;

      ru = r2-r1+1;

      Z1 u = new Z1(r2-r1+1);

      for (i=r1; i<=r2; i++){
         u.put(i-r1, A.re[i][c], A.im[i][c]) ;
         A.re[i][c] = 0.0;
         A.im[i][c] = 0.0;
      }               

      norm = Norm.fro(u);

      if (r1 == r2 || norm == 0){
         A.re[r1][c] = -u.re[0];
         A.im[r1][c] = -u.im[0];
         u.put(0, Math.sqrt(2), 0);
         return u;
      }

      scale = new Z(1/norm, 0);

      if (u.re[0] != 0 || u.im[0] != 0){
         t = u.get(0);
         scale.Times(scale, Z.Div(t1.Conj(t), t.abs(), 0.0));
      }


      A.put(r1+A.basex, c+A.basex, t.Minus(t.Div(Z.ONE, scale)));

      for (i=0; i<ru; i++){
         u.Times(i, scale);
      }

      u.re[0] = u.re[0] + 1;
      u.im[0] = 0;
      s = Math.sqrt(1/u.re[0]);

      for (i=0; i<ru; i++){
        u.re[i] = s*u.re[i];
        u.im[i] = s*u.im[i];
      }

      return u;
   }

/**
   Generates a Householder transformation from within the part of row
   r of a Zmat (altered) extending from columns c1 to
   c2.  The method overwrites the row with the result
   of applying the transformation.

   @param A   The matrix from which the transformation
              is to be generated (altered)
   @param r   The index of the generating row
   @param c1  The index of the column in which the generating row
              begins
   @param c2  The index of the column in which the generating row
              ends
   @return             A Z1 of length r2-r1+1
                       containing the Householder vector
   @exception JampackException
              Passed from below.
*/
   public static Z1 genr(Zmat A,  int r, int c1, int c2)
   throws JampackException{

      int j, cu;
      double norm, s;
      Z scale;
      Z t = new Z();
      Z t1 = new Z();

      r = r - A.basex;
      c1 = c1 - A.basex;
      c2 = c2 - A.basex;

      cu = c2-c1+1;

      Z1 u = new Z1(cu);

      for (j=c1; j<=c2; j++){
         u.put(j-c1, A.re[r][j], A.im[r][j]);
         A.re[r][j] = 0.0;
         A.im[r][j] = 0.0;
      }               

      norm = Norm.fro(u);

      if (c1 == c2 || norm == 0){
         A.re[r][c1] = -u.re[0];
         A.im[r][c1] = -u.im[0];
         u.put(0, Math.sqrt(2), 0);
         return u;
      }

      scale = new Z(1/norm, 0);

      if (u.re[0] != 0 || u.im[0] != 0){
         t = u.get(0);
         scale.Times(scale, Z.Div(t1.Conj(t), t.abs(), 0.0));
      }


      A.put(r+A.basex, c1+A.basex, t.Minus(t.Div(Z.ONE, scale)));

      for (j=0; j<cu; j++){
         u.Times(j, scale);
      }

      u.re[0] = u.re[0] + 1;
      u.im[0] = 0;
      s = Math.sqrt(1/u.re[0]);

      for (j=0; j<cu; j++){
        u.re[j] = s*u.re[j];
        u.im[j] = -s*u.im[j];
      }

      return u;
   }

/**
   Premultiplies the Householder transformation contained in a
   Z1 into a Zmat A[r1:r2,c1:c2] and overwrites
   Zmat A[r1:r2,c1:c2] with the results.  If r1 &gt; r2
   or c1 &gt; c2 the method does nothing.

   @param u    The Householder vector
   @param A    The Zmat to which the transformation
               is to be applied (altered)
   @param r1   The index of the first row to which the transformation
               is to be applied
   @param r2   The index of the last row to which the transformation
               is to be applied
   @param c1   The index of the first column to which the transformation
               is index of the to be applied
   @param c2   The index of the last column to which the transformation
               is to be applied
   @param v    A work array of length at least c2-c1+1
   @return     The transformed Zmat A
   @exception  JampackException
               Thrown if either u or v is too short.
*/
   public static Zmat ua(Z1 u, Zmat A, int r1, int r2, int c1, int c2, Z1 v)
   throws JampackException{

      int i, j, ru;



      if (r2 < r1 || c2 < c1){
         return A;
      }

      if (r2-r1+1 > u.n){
         throw new JampackException
            ("Householder vector too short.");
      }

      if (c2-c1+1 > v.n){
         throw new JampackException
            ("Work vector too short.");
      }

      A.dirty = true;

      r1 = r1 - A.basex;
      r2 = r2 - A.basex;
      c1 = c1 - A.basex;
      c2 = c2 - A.basex;


      for (j=c1; j<=c2; j++){
         v.re[j-c1] = 0;
         v.im[j-c1] = 0;
      }


      for (i=r1; i<=r2; i++){
         for (j=c1; j<=c2; j++){
            v.re[j-c1] = v.re[j-c1] + 
                         u.re[i-r1]*A.re[i][j] + u.im[i-r1]*A.im[i][j];
            v.im[j-c1] = v.im[j-c1] +
                         u.re[i-r1]*A.im[i][j] - u.im[i-r1]*A.re[i][j];
         }
      }


      for (i=r1; i<=r2; i++){
         for (j=c1; j<=c2; j++){
            A.re[i][j] = A.re[i][j] -
                         u.re[i-r1]*v.re[j-c1] + u.im[i-r1]*v.im[j-c1];
            A.im[i][j] = A.im[i][j] -
                         u.re[i-r1]*v.im[j-c1] - u.im[i-r1]*v.re[j-c1];
         }
      }
      return A;
   }

/**
   Premultiplies the Householder transformation contained in a
   Z1 into a Zmat A[r1:r2,c1:c2] and overwrites
   Zmat A[r1:r2,c1:c2] with the results.  If r1 &gt; r2
   or c1 &gt; c2 the method does nothing.

   @param u    The Householder vector
   @param A    The Zmat to which the transformation
               is to be applied (altered)
   @param r1   The index of the first row to which the transformation
               is to be applied
   @param r2   The index of the last row to which the transformation
               is to be applied
   @param c1   The index of the first column to which the transformation
               is index of the to be applied
   @param c2   The index of the last column to which the transformation
               is to be applied
   @return     The transformed Zmat A

   @exception  JampackException
               Passed from below.
*/
   public static Zmat ua(Z1 u, Zmat A, int r1, int r2, int c1, int c2)
   throws JampackException{

      if (c1 > c2){
         return A;
      }

      return ua(u, A, r1, r2, c1, c2, new Z1(c2-c1+1));
   }


/**
   Postmultiplies the Householder transformation contained in a
   Z1 into a Zmat A[r1:r2,c1:c2] and overwrites
   Zmat A[r1:r2,c1:c2] with the results.  If r1 &gt; r2
   or c1 &gt; c2 the method does nothing.

   @param u    The Householder vector
   @param A    The Zmat to which the transformation
               is to be applied (altered)
   @param r1   The index of the first row to which the transformation
               is to be applied
   @param r2   The index of the last row to which the transformation
               is to be applied
   @param c1   The index of the first column to which the transformation
               is index of the to be applied
   @param c2   The index of the last column to which the transformation
               is to be applied
   @param v    A work array of length at least c2-c1+1
   @return     The transformed Zmat A
   @exception  JampackException
               Thrown if either u or v is too short.
*/
   public static Zmat au(Zmat A, Z1 u, int r1, int r2, int c1, int c2,  Z1 v)
   throws JampackException{

      int i, j, cu;

      if(r2 < r1 || c2 < c1){
         return A;
      }

      if (c2-c1+1 > u.n){
         throw new JampackException
            ("Householder vector too short.");
      }

      if (r2-r1+1 > v.n){
         throw new JampackException
            ("Work vector too short.");
      }

      A.dirty = true;

      r1 = r1 - A.basex;
      r2 = r2 - A.basex;
      c1 = c1 - A.basex;
      c2 = c2 - A.basex;

      for (i=r1; i<=r2; i++){
         v.put(i-r1, 0, 0);
         for (j=c1; j<=c2; j++){
            v.re[i-r1] = v.re[i-r1] +
                         A.re[i][j]*u.re[j-c1] - A.im[i][j]*u.im[j-c1];
            v.im[i-r1] = v.im[i-r1] +
                         A.re[i][j]*u.im[j-c1] + A.im[i][j]*u.re[j-c1];
            }
         }
      for (i=r1; i<=r2; i++){
         for (j=c1; j<=c2; j++){
            A.re[i][j] = A.re[i][j] -
                         v.re[i-r1]*u.re[j-c1] - v.im[i-r1]*u.im[j-c1];
            A.im[i][j] = A.im[i][j] +
                         v.re[i-r1]*u.im[j-c1] - v.im[i-r1]*u.re[j-c1];
         }
      }
   return A;
   }


/**
   Postmultiplies the Householder transformation contained in a
   Z1 into a Zmat A[r1:r2,c1:c2] and overwrites
   Zmat A[r1:r2,c1:c2] with the results.  If r1 &gt; r2
   or c1 &gt; c2 the method does nothing.

   @param u    The Householder vector
   @param A    The Zmat to which the transformation
               is to be applied (altered)
   @param r1   The index of the first row to which the transformation
               is to be applied
   @param r2   The index of the last row to which the transformation
               is to be applied
   @param c1   The index of the first column to which the transformation
               is index of the to be applied
   @param c2   The index of the last column to which the transformation
               is to be applied
   @return     The transformed Zmat A
   @exception  JampackException  
               Passed from below.
*/

   public static Zmat au(Zmat A, Z1 u, int r1, int r2, int c1, int c2)
   throws JampackException{

      if(r2 < r1){
         return A;
      }

      return au(A, u, r1, r2, c1, c2, new Z1(r2-r1+1));
   }

}