/*
Copyright � 1999 CERN - European Organization for Nuclear Research.
Permission to use, copy, modify, distribute and sell this software and its documentation for any purpose
is hereby granted without fee, provided that the above copyright notice appear in all copies and
that both that copyright notice and this permission notice appear in supporting documentation.
CERN makes no representations about the suitability of this software for any purpose.
It is provided "as is" without expressed or implied warranty.
*/
package cern.colt.matrix.impl;
import cern.colt.matrix.DoubleMatrix1D;
import cern.colt.matrix.DoubleMatrix2D;
/**
Tridiagonal 2-d matrix holding <tt>double</tt> elements.
First see the <a href="package-summary.html">package summary</a> and javadoc <a href="package-tree.html">tree view</a> to get the broad picture.
<p>
<b>Implementation:</b>
TODO.
@author wolfgang.hoschek@cern.ch
@version 0.9, 04/14/2000
*/
class TridiagonalDoubleMatrix2D extends WrapperDoubleMatrix2D {
/*
* The non zero elements of the matrix: {lower, diagonal, upper}.
*/
protected double[] values;
/*
* The startIndexes and number of non zeros: {lowerStart, diagonalStart, upperStart, values.length, lowerNonZeros, diagonalNonZeros, upperNonZeros}.
* lowerStart = 0
* diagonalStart = lowerStart + lower.length
* upperStart = diagonalStart + diagonal.length
*/
protected int[] dims;
protected static final int NONZERO = 4;
//protected double diagonal[];
//protected double lower[];
//protected double upper[];
//protected int diagonalNonZeros;
//protected int lowerNonZeros;
//protected int upperNonZeros;
//protected int N;
/**
* Constructs a matrix with a copy of the given values.
* <tt>values</tt> is required to have the form <tt>values[row][column]</tt>
* and have exactly the same number of columns in every row.
* <p>
* The values are copied. So subsequent changes in <tt>values</tt> are not reflected in the matrix, and vice-versa.
*
* @param values The values to be filled into the new matrix.
* @throws IllegalArgumentException if <tt>for any 1 <= row < values.length: values[row].length != values[row-1].length</tt>.
*/
public TridiagonalDoubleMatrix2D(double[][] values) {
this(values.length, values.length==0 ? 0: values[0].length);
assign(values);
}
/**
* Constructs a matrix with a given number of rows and columns.
* All entries are initially <tt>0</tt>.
* @param rows the number of rows the matrix shall have.
* @param columns the number of columns the matrix shall have.
* @throws IllegalArgumentException if <tt>rows<0 || columns<0 || (double)columns*rows > Integer.MAX_VALUE</tt>.
*/
public TridiagonalDoubleMatrix2D(int rows, int columns) {
super(null);
setUp(rows, columns);
int d = Math.min(rows,columns);
int u = d-1;
int l = d-1;
if (rows>columns) l++;
if (rows<columns) u++;
values = new double[l+d+u]; // {lower, diagonal, upper}
int[] dimensions = { 0, l, l+d, l+d+u, 0, 0, 0}; // {lowerStart, diagonalStart, upperStart, values.length, lowerNonZeros, diagonalNonZeros, upperNonZeros}
dims = dimensions;
//diagonal = new double[d];
//lower = new double[l];
//upper = new double[u];
//diagonalNonZeros = 0;
//lowerNonZeros = 0;
//upperNonZeros = 0;
}
/**
* Sets all cells to the state specified by <tt>value</tt>.
* @param value the value to be filled into the cells.
* @return <tt>this</tt> (for convenience only).
*/
public DoubleMatrix2D assign(double value) {
// overriden for performance only
if (value==0) {
for (int i=values.length; --i >= 0; ) values[i]=0;
for (int i=dims.length; --i >= NONZERO; ) dims[i]=0;
//for (int i=diagonal.length; --i >= 0; ) diagonal[i]=0;
//for (int i=upper.length; --i >= 0; ) upper[i]=0;
//for (int i=lower.length; --i >= 0; ) lower[i]=0;
//diagonalNonZeros = 0;
//lowerNonZeros = 0;
//upperNonZeros = 0;
}
else super.assign(value);
return this;
}
public DoubleMatrix2D assign(final cern.colt.function.DoubleFunction function) {
if (function instanceof cern.jet.math.Mult) { // x[i] = mult*x[i]
final double alpha = ((cern.jet.math.Mult) function).multiplicator;
if (alpha==1) return this;
if (alpha==0) return assign(0);
if (alpha!=alpha) return assign(alpha); // the funny definition of isNaN(). This should better not happen.
/*
double[] vals = values.elements();
for (int j=values.size(); --j >= 0; ) {
vals[j] *= alpha;
}
*/
forEachNonZero(
new cern.colt.function.IntIntDoubleFunction() {
public double apply(int i, int j, double value) {
return function.apply(value);
}
}
);
}
else {
super.assign(function);
}
return this;
}
/**
* Replaces all cell values of the receiver with the values of another matrix.
* Both matrices must have the same number of rows and columns.
* If both matrices share the same cells (as is the case if they are views derived from the same matrix) and intersect in an ambiguous way, then replaces <i>as if</i> using an intermediate auxiliary deep copy of <tt>other</tt>.
*
* @param source the source matrix to copy from (may be identical to the receiver).
* @return <tt>this</tt> (for convenience only).
* @throws IllegalArgumentException if <tt>columns() != source.columns() || rows() != source.rows()</tt>
*/
public DoubleMatrix2D assign(DoubleMatrix2D source) {
// overriden for performance only
if (source==this) return this; // nothing to do
checkShape(source);
if (source instanceof TridiagonalDoubleMatrix2D) {
// quickest
TridiagonalDoubleMatrix2D other = (TridiagonalDoubleMatrix2D) source;
System.arraycopy(other.values, 0, this.values, 0, this.values.length);
System.arraycopy(other.dims, 0, this.dims, 0, this.dims.length);
return this;
}
if (source instanceof RCDoubleMatrix2D || source instanceof SparseDoubleMatrix2D) {
assign(0);
source.forEachNonZero(
new cern.colt.function.IntIntDoubleFunction() {
public double apply(int i, int j, double value) {
setQuick(i,j,value);
return value;
}
}
);
return this;
}
return super.assign(source);
}
public DoubleMatrix2D assign(final DoubleMatrix2D y, cern.colt.function.DoubleDoubleFunction function) {
checkShape(y);
if (function instanceof cern.jet.math.PlusMult) { // x[i] = x[i] + alpha*y[i]
final double alpha = ((cern.jet.math.PlusMult) function).multiplicator;
if (alpha==0) return this; // nothing to do
y.forEachNonZero(
new cern.colt.function.IntIntDoubleFunction() {
public double apply(int i, int j, double value) {
setQuick(i,j,getQuick(i,j) + alpha*value);
return value;
}
}
);
return this;
}
if (function==cern.jet.math.Functions.mult) { // x[i] = x[i] * y[i]
forEachNonZero(
new cern.colt.function.IntIntDoubleFunction() {
public double apply(int i, int j, double value) {
setQuick(i,j,getQuick(i,j) * y.getQuick(i,j));
return value;
}
}
);
return this;
}
if (function==cern.jet.math.Functions.div) { // x[i] = x[i] / y[i]
forEachNonZero(
new cern.colt.function.IntIntDoubleFunction() {
public double apply(int i, int j, double value) {
setQuick(i,j,getQuick(i,j) / y.getQuick(i,j));
return value;
}
}
);
return this;
}
return super.assign(y,function);
}
public DoubleMatrix2D forEachNonZero(final cern.colt.function.IntIntDoubleFunction function) {
for (int kind=0; kind<=2; kind++) {
int i=0,j=0;
switch (kind) {
case 0: { i=1; } // lower
// case 1: { } // diagonal
case 2: { j=1; } // upper
}
int low = dims[kind];
int high = dims[kind+1];
for (int k=low; k < high; k++, i++, j++) {
double value = values[k];
if (value!=0) {
double r = function.apply(i,j,value);
if (r!=value) {
if (r==0) dims[kind+NONZERO]++; // one non zero more
values[k] = r;
}
}
}
}
return this;
}
/**
* Returns the content of this matrix if it is a wrapper; or <tt>this</tt> otherwise.
* Override this method in wrappers.
*/
protected DoubleMatrix2D getContent() {
return this;
}
/**
* Returns the matrix cell value at coordinate <tt>[row,column]</tt>.
*
* <p>Provided with invalid parameters this method may return invalid objects without throwing any exception.
* <b>You should only use this method when you are absolutely sure that the coordinate is within bounds.</b>
* Precondition (unchecked): <tt>0 <= column < columns() && 0 <= row < rows()</tt>.
*
* @param row the index of the row-coordinate.
* @param column the index of the column-coordinate.
* @return the value at the specified coordinate.
*/
public double getQuick(int row, int column) {
int i = row;
int j = column;
int k = j-i+1;
int q = i;
if (k==0) q=j; // lower diagonal
if (k>=0 && k<=2) {
return values[dims[k]+q];
}
return 0;
//int k = -1;
//int q = 0;
//if (i==j) { k=0; q=i; }
//if (i==j+1) { k=1; q=j; }
//if (i==j-1) { k=2; q=i; }
//if (k<0) return 0;
//return values[dims[k]+q];
//if (i==j) return diagonal[i];
//if (i==j+1) return lower[j];
//if (i==j-1) return upper[i];
//return 0;
}
/**
* Construct and returns a new empty matrix <i>of the same dynamic type</i> as the receiver, having the specified number of rows and columns.
* For example, if the receiver is an instance of type <tt>DenseDoubleMatrix2D</tt> the new matrix must also be of type <tt>DenseDoubleMatrix2D</tt>,
* if the receiver is an instance of type <tt>SparseDoubleMatrix2D</tt> the new matrix must also be of type <tt>SparseDoubleMatrix2D</tt>, etc.
* In general, the new matrix should have internal parametrization as similar as possible.
*
* @param rows the number of rows the matrix shall have.
* @param columns the number of columns the matrix shall have.
* @return a new empty matrix of the same dynamic type.
*/
public DoubleMatrix2D like(int rows, int columns) {
return new TridiagonalDoubleMatrix2D(rows,columns);
}
/**
* Construct and returns a new 1-d matrix <i>of the corresponding dynamic type</i>, entirelly independent of the receiver.
* For example, if the receiver is an instance of type <tt>DenseDoubleMatrix2D</tt> the new matrix must be of type <tt>DenseDoubleMatrix1D</tt>,
* if the receiver is an instance of type <tt>SparseDoubleMatrix2D</tt> the new matrix must be of type <tt>SparseDoubleMatrix1D</tt>, etc.
*
* @param size the number of cells the matrix shall have.
* @return a new matrix of the corresponding dynamic type.
*/
public DoubleMatrix1D like1D(int size) {
return new SparseDoubleMatrix1D(size);
}
/**
* Sets the matrix cell at coordinate <tt>[row,column]</tt> to the specified value.
*
* <p>Provided with invalid parameters this method may access illegal indexes without throwing any exception.
* <b>You should only use this method when you are absolutely sure that the coordinate is within bounds.</b>
* Precondition (unchecked): <tt>0 <= column < columns() && 0 <= row < rows()</tt>.
*
* @param row the index of the row-coordinate.
* @param column the index of the column-coordinate.
* @param value the value to be filled into the specified cell.
*/
public void setQuick(int row, int column, double value) {
int i = row;
int j = column;
boolean isZero = (value==0);
int k = j-i+1;
int q = i;
if (k==0) q=j; // lower diagonal
if (k>=0 && k<=2) {
int index = dims[k]+q;
if (values[index]!=0) {
if (isZero) dims[k+NONZERO]--; // one nonZero less
}
else {
if (!isZero) dims[k+NONZERO]++; // one nonZero more
}
values[index] = value;
return;
}
if (!isZero) throw new IllegalArgumentException("Can't store non-zero value to non-tridiagonal coordinate: row="+row+", column="+column+", value="+value);
//int k = -1;
//int q = 0;
//if (i==j) { k=0; q=i; } // diagonal
//if (i==j+1) { k=1; q=j; } // lower diagonal
//if (i==j-1) { k=2; q=i; } // upper diagonal
//if (k>0) {
//int index = dims[k]+q;
//if (values[index]!=0) {
//if (isZero) dims[k+NONZERO]--; // one nonZero less
//}
//else {
//if (!isZero) dims[k+NONZERO]++; // one nonZero more
//}
//values[index] = value;
//return;
//}
//if (!isZero) throw new IllegalArgumentException("Can't store non-zero value to non-tridiagonal coordinate: row="+row+", column="+column+", value="+value);
//if (i==j) {
//if (diagonal[i]!=0) {
//if (isZero) diagonalNonZeros--;
//}
//else {
//if (!isZero) diagonalNonZeros++;
//}
//diagonal[i] = value;
//return;
//}
//if (i==j+1) {
//if (lower[j]!=0) {
//if (isZero) lowerNonZeros--;
//}
//else {
//if (!isZero) lowerNonZeros++;
//}
//lower[j] = value;
//return;
//}
//if (i==j-1) {
//if (upper[i]!=0) {
//if (isZero) upperNonZeros--;
//}
//else {
//if (!isZero) upperNonZeros++;
//}
//upper[i] = value;
//return;
//}
//if (!isZero) throw new IllegalArgumentException("Can't store non-zero value to non-tridiagonal coordinate: row="+row+", column="+column+", value="+value);
}
public DoubleMatrix1D zMult(DoubleMatrix1D y, DoubleMatrix1D z, double alpha, double beta, final boolean transposeA) {
int m = rows;
int n = columns;
if (transposeA) {
m = columns;
n = rows;
}
boolean ignore = (z==null);
if (z==null) z = new DenseDoubleMatrix1D(m);
if (!(this.isNoView && y instanceof DenseDoubleMatrix1D && z instanceof DenseDoubleMatrix1D)) {
return super.zMult(y,z,alpha,beta,transposeA);
}
if (n != y.size() || m > z.size())
throw new IllegalArgumentException("Incompatible args: "+ ((transposeA ? viewDice() : this).toStringShort()) +", "+y.toStringShort()+", "+z.toStringShort());
if (!ignore) z.assign(cern.jet.math.Functions.mult(beta/alpha));
DenseDoubleMatrix1D zz = (DenseDoubleMatrix1D) z;
final double[] zElements = zz.elements;
final int zStride = zz.stride;
final int zi = z.index(0);
DenseDoubleMatrix1D yy = (DenseDoubleMatrix1D) y;
final double[] yElements = yy.elements;
final int yStride = yy.stride;
final int yi = y.index(0);
if (yElements==null || zElements==null) throw new InternalError();
forEachNonZero(
new cern.colt.function.IntIntDoubleFunction() {
public double apply(int i, int j, double value) {
if (transposeA) { int tmp=i; i=j; j=tmp; }
zElements[zi + zStride*i] += value * yElements[yi + yStride*j];
//z.setQuick(row,z.getQuick(row) + value * y.getQuick(column));
//System.out.println("["+i+","+j+"]-->"+value);
return value;
}
}
);
if (alpha!=1) z.assign(cern.jet.math.Functions.mult(alpha));
return z;
}
public DoubleMatrix2D zMult(DoubleMatrix2D B, DoubleMatrix2D C, final double alpha, double beta, final boolean transposeA, boolean transposeB) {
if (transposeB) B = B.viewDice();
int m = rows;
int n = columns;
if (transposeA) {
m = columns;
n = rows;
}
int p = B.columns;
boolean ignore = (C==null);
if (C==null) C = new DenseDoubleMatrix2D(m,p);
if (B.rows != n)
throw new IllegalArgumentException("Matrix2D inner dimensions must agree:"+toStringShort()+", "+ (transposeB ? B.viewDice() : B).toStringShort());
if (C.rows != m || C.columns != p)
throw new IllegalArgumentException("Incompatibel result matrix: "+toStringShort()+", "+ (transposeB ? B.viewDice() : B).toStringShort()+", "+C.toStringShort());
if (this == C || B == C)
throw new IllegalArgumentException("Matrices must not be identical");
if (!ignore) C.assign(cern.jet.math.Functions.mult(beta));
// cache views
final DoubleMatrix1D[] Brows = new DoubleMatrix1D[n];
for (int i=n; --i>=0; ) Brows[i] = B.viewRow(i);
final DoubleMatrix1D[] Crows = new DoubleMatrix1D[m];
for (int i=m; --i>=0; ) Crows[i] = C.viewRow(i);
final cern.jet.math.PlusMult fun = cern.jet.math.PlusMult.plusMult(0);
forEachNonZero(
new cern.colt.function.IntIntDoubleFunction() {
public double apply(int i, int j, double value) {
fun.multiplicator = value*alpha;
if (!transposeA)
Crows[i].assign(Brows[j],fun);
else
Crows[j].assign(Brows[i],fun);
return value;
}
}
);
return C;
}
}