/** {@inheritDoc} */
public RealVector solve(RealVector b) throws IllegalArgumentException, InvalidMatrixException {
try {
return solve((RealVectorImpl) b);
} catch (ClassCastException cce) {
final int m = lTData.length;
if (b.getDimension() != m) {
throw MathRuntimeException.createIllegalArgumentException(
"vector length mismatch: got {0} but expected {1}", b.getDimension(), m);
}
final double[] x = b.getData();
// Solve LY = b
for (int j = 0; j < m; j++) {
final double[] lJ = lTData[j];
x[j] /= lJ[j];
final double xJ = x[j];
for (int i = j + 1; i < m; i++) {
x[i] -= xJ * lJ[i];
}
}
// Solve LTX = Y
for (int j = m - 1; j >= 0; j--) {
x[j] /= lTData[j][j];
final double xJ = x[j];
for (int i = 0; i < j; i++) {
x[i] -= xJ * lTData[i][j];
}
}
return new RealVectorImpl(x, false);
}
}
/** {@inheritDoc} */
public RealVector solve(RealVector b) {
final int m = pivot.length;
if (b.getDimension() != m) {
throw new DimensionMismatchException(b.getDimension(), m);
}
if (singular) {
throw new SingularMatrixException();
}
final double[] bp = new double[m];
// Apply permutations to b
for (int row = 0; row < m; row++) {
bp[row] = b.getEntry(pivot[row]);
}
// Solve LY = b
for (int col = 0; col < m; col++) {
final double bpCol = bp[col];
for (int i = col + 1; i < m; i++) {
bp[i] -= bpCol * lu[i][col];
}
}
// Solve UX = Y
for (int col = m - 1; col >= 0; col--) {
bp[col] /= lu[col][col];
final double bpCol = bp[col];
for (int i = 0; i < col; i++) {
bp[i] -= bpCol * lu[i][col];
}
}
return new ArrayRealVector(bp, false);
}
/** {@inheritDoc} */
public void setColumnVector(final int column, final RealVector vector) {
MatrixUtils.checkColumnIndex(this, column);
final int nRows = getRowDimension();
if (vector.getDimension() != nRows) {
throw new MatrixDimensionMismatchException(vector.getDimension(), 1, nRows, 1);
}
for (int i = 0; i < nRows; ++i) {
setEntry(i, column, vector.getEntry(i));
}
}
/** {@inheritDoc} */
public void setRowVector(final int row, final RealVector vector) {
MatrixUtils.checkRowIndex(this, row);
final int nCols = getColumnDimension();
if (vector.getDimension() != nCols) {
throw new MatrixDimensionMismatchException(1, vector.getDimension(), 1, nCols);
}
for (int i = 0; i < nCols; ++i) {
setEntry(row, i, vector.getEntry(i));
}
}
/** {@inheritDoc} */
public OpenMapRealVector add(RealVector v) throws IllegalArgumentException {
checkVectorDimensions(v.getDimension());
if (v instanceof OpenMapRealVector) {
return add((OpenMapRealVector) v);
}
return add(v.getData());
}
/** {@inheritDoc} */
public double getLInfDistance(RealVector v) throws IllegalArgumentException {
checkVectorDimensions(v.getDimension());
if (v instanceof OpenMapRealVector) {
return getLInfDistance((OpenMapRealVector) v);
}
return getLInfDistance(v.getData());
}
@Override
public Label predict(Instance instance) {
Label l = null;
if (instance.getLabel() instanceof ClassificationLabel || instance.getLabel() == null) {
// ----------------- declare variables ------------------
double lambda = 0.0;
RealVector x_instance = new ArrayRealVector(matrixX.getColumnDimension(), 0);
double result = 0.0;
// -------------------------- initialize xi -------------------------
for (int idx = 0; idx < matrixX.getColumnDimension(); idx++) {
x_instance.setEntry(idx, instance.getFeatureVector().get(idx + 1));
}
// ------------------ get lambda -----------------------
for (int j = 0; j < alpha.getDimension(); j++) {
lambda += alpha.getEntry(j) * kernelFunction(matrixX.getRowVector(j), x_instance);
}
// ----------------- make prediction -----------------
Sigmoid g = new Sigmoid(); // helper function
result = g.value(lambda);
l = new ClassificationLabel(result < 0.5 ? 0 : 1);
} else {
System.out.println("label type error!");
}
return l;
}
/**
* Performs all dimension checks on the parameters of {@link #solve(RealLinearOperator,
* RealVector, RealVector) solve} and {@link #solveInPlace(RealLinearOperator, RealVector,
* RealVector) solveInPlace}, and throws an exception if one of the checks fails.
*
* @param a the linear operator A of the system
* @param b the right-hand side vector
* @param x0 the initial guess of the solution
* @throws NullArgumentException if one of the parameters is {@code null}
* @throws NonSquareOperatorException if {@code a} is not square
* @throws DimensionMismatchException if {@code b} or {@code x0} have dimensions inconsistent with
* {@code a}
*/
protected static void checkParameters(
final RealLinearOperator a, final RealVector b, final RealVector x0)
throws NullArgumentException, NonSquareOperatorException, DimensionMismatchException {
MathUtils.checkNotNull(a);
MathUtils.checkNotNull(b);
MathUtils.checkNotNull(x0);
if (a.getRowDimension() != a.getColumnDimension()) {
throw new NonSquareOperatorException(a.getRowDimension(), a.getColumnDimension());
}
if (b.getDimension() != a.getRowDimension()) {
throw new DimensionMismatchException(b.getDimension(), a.getRowDimension());
}
if (x0.getDimension() != a.getColumnDimension()) {
throw new DimensionMismatchException(x0.getDimension(), a.getColumnDimension());
}
}
/**
* Serialize a {@link RealVector}.
*
* <p>This method is intended to be called from within a private <code>writeObject</code> method
* (after a call to <code>oos.defaultWriteObject()</code>) in a class that has a {@link
* RealVector} field, which should be declared <code>transient</code>. This way, the default
* handling does not serialize the vector (the {@link RealVector} interface is not serializable by
* default) but this method does serialize it specifically.
*
* <p>The following example shows how a simple class with a name and a real vector should be
* written:
*
* <pre><code>
* public class NamedVector implements Serializable {
*
* private final String name;
* private final transient RealVector coefficients;
*
* // omitted constructors, getters ...
*
* private void writeObject(ObjectOutputStream oos) throws IOException {
* oos.defaultWriteObject(); // takes care of name field
* MatrixUtils.serializeRealVector(coefficients, oos);
* }
*
* private void readObject(ObjectInputStream ois) throws ClassNotFoundException, IOException {
* ois.defaultReadObject(); // takes care of name field
* MatrixUtils.deserializeRealVector(this, "coefficients", ois);
* }
*
* }
* </code></pre>
*
* @param vector real vector to serialize
* @param oos stream where the real vector should be written
* @exception IOException if object cannot be written to stream
* @see #deserializeRealVector(Object, String, ObjectInputStream)
*/
public static void serializeRealVector(final RealVector vector, final ObjectOutputStream oos)
throws IOException {
final int n = vector.getDimension();
oos.writeInt(n);
for (int i = 0; i < n; ++i) {
oos.writeDouble(vector.getEntry(i));
}
}
/**
* Solve the linear equation A × X = B in least square sense.
*
* <p>The m×n matrix A may not be square, the solution X is such that ||A × X - B||
* is minimal.
*
* @param b right-hand side of the equation A × X = B
* @return a vector X that minimizes the two norm of A × X - B
* @exception IllegalArgumentException if matrices dimensions don't match
* @exception InvalidMatrixException if decomposed matrix is singular
*/
public RealVector solve(final RealVector b)
throws IllegalArgumentException, InvalidMatrixException {
if (b.getDimension() != uT.getColumnDimension()) {
throw MathRuntimeException.createIllegalArgumentException(
"vector length mismatch: got {0} but expected {1}",
b.getDimension(), uT.getColumnDimension());
}
final RealVector w = uT.operate(b);
for (int i = 0; i < singularValues.length; ++i) {
final double si = singularValues[i];
if (si == 0) {
throw new SingularMatrixException();
}
w.setEntry(i, w.getEntry(i) / si);
}
return v.operate(w);
}
/** {@inheritDoc} */
public OpenMapRealVector ebeMultiply(RealVector v) throws IllegalArgumentException {
checkVectorDimensions(v.getDimension());
OpenMapRealVector res = new OpenMapRealVector(this);
Iterator iter = res.entries.iterator();
while (iter.hasNext()) {
iter.advance();
res.setEntry(iter.key(), iter.value() * v.getEntry(iter.key()));
}
return res;
}
/** {@inheritDoc} */
public double dotProduct(RealVector v) throws IllegalArgumentException {
checkVectorDimensions(v.getDimension());
double res = 0;
Iterator iter = entries.iterator();
while (iter.hasNext()) {
iter.advance();
res += v.getEntry(iter.key()) * iter.value();
}
return res;
}
/**
* Generic copy constructor.
*
* @param v The instance to copy from
*/
public OpenMapRealVector(RealVector v) {
virtualSize = v.getDimension();
entries = new OpenIntToDoubleHashMap(0.0);
epsilon = DEFAULT_ZERO_TOLERANCE;
for (int key = 0; key < virtualSize; key++) {
double value = v.getEntry(key);
if (!isZero(value)) {
entries.put(key, value);
}
}
}
@Test
public void testGenreVector() {
double[] testVec1 = {0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
double[] testVec2 = {0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
RealVector testRealVector1 = MatrixUtils.createRealVector(testVec1);
RealVector testRealVector2 = MatrixUtils.createRealVector(testVec2);
assertThat(gdao.getItemGenre(0), equalTo(testRealVector1));
assertThat(gdao.getItemGenre(5), equalTo(testRealVector2));
assertThat(testRealVector1.getDimension(), equalTo(gdao.getGenreSize()));
assertThat(gdao.getItemGenre(0).getDimension(), equalTo(gdao.getGenreSize()));
assertThat(testVec1.length, equalTo(gdao.getGenreSize()));
}
/** {@inheritDoc} */
public RealVector preMultiply(final RealVector v) throws DimensionMismatchException {
try {
return new ArrayRealVector(preMultiply(((ArrayRealVector) v).getDataRef()), false);
} catch (ClassCastException cce) {
final int nRows = getRowDimension();
final int nCols = getColumnDimension();
if (v.getDimension() != nRows) {
throw new DimensionMismatchException(v.getDimension(), nRows);
}
final double[] out = new double[nCols];
for (int col = 0; col < nCols; ++col) {
double sum = 0;
for (int i = 0; i < nRows; ++i) {
sum += getEntry(i, col) * v.getEntry(i);
}
out[col] = sum;
}
return new ArrayRealVector(out, false);
}
}
/** {@inheritDoc} */
@Override
public RealVector operate(final RealVector v) throws DimensionMismatchException {
try {
return new ArrayRealVector(operate(((ArrayRealVector) v).getDataRef()), false);
} catch (ClassCastException cce) {
final int nRows = getRowDimension();
final int nCols = getColumnDimension();
if (v.getDimension() != nCols) {
throw new DimensionMismatchException(v.getDimension(), nCols);
}
final double[] out = new double[nRows];
for (int row = 0; row < nRows; ++row) {
double sum = 0;
for (int i = 0; i < nCols; ++i) {
sum += getEntry(row, i) * v.getEntry(i);
}
out[row] = sum;
}
return new ArrayRealVector(out, false);
}
}
/** {@inheritDoc} */
public RealMatrix outerProduct(RealVector v) throws IllegalArgumentException {
checkVectorDimensions(v.getDimension());
if (v instanceof OpenMapRealVector) {
return outerproduct((OpenMapRealVector) v);
}
RealMatrix res = new OpenMapRealMatrix(virtualSize, virtualSize);
Iterator iter = entries.iterator();
while (iter.hasNext()) {
iter.advance();
int row = iter.key();
for (int col = 0; col < virtualSize; col++) {
res.setEntry(row, col, iter.value() * v.getEntry(col));
}
}
return res;
}
@Test
public void testConstructors() {
OpenMapRealVector v0 = new OpenMapRealVector();
Assert.assertEquals("testData len", 0, v0.getDimension());
OpenMapRealVector v1 = new OpenMapRealVector(7);
Assert.assertEquals("testData len", 7, v1.getDimension());
Assert.assertEquals("testData is 0.0 ", 0.0, v1.getEntry(6), 0);
OpenMapRealVector v3 = new OpenMapRealVector(vec1);
Assert.assertEquals("testData len", 3, v3.getDimension());
Assert.assertEquals("testData is 2.0 ", 2.0, v3.getEntry(1), 0);
// SparseRealVector v4 = new SparseRealVector(vec4, 3, 2);
// Assert.assertEquals("testData len", 2, v4.getDimension());
// Assert.assertEquals("testData is 4.0 ", 4.0, v4.getEntry(0));
// try {
// new SparseRealVector(vec4, 8, 3);
// Assert.fail("MathIllegalArgumentException expected");
// } catch (MathIllegalArgumentException ex) {
// expected behavior
// }
RealVector v5_i = new OpenMapRealVector(dvec1);
Assert.assertEquals("testData len", 9, v5_i.getDimension());
Assert.assertEquals("testData is 9.0 ", 9.0, v5_i.getEntry(8), 0);
OpenMapRealVector v5 = new OpenMapRealVector(dvec1);
Assert.assertEquals("testData len", 9, v5.getDimension());
Assert.assertEquals("testData is 9.0 ", 9.0, v5.getEntry(8), 0);
OpenMapRealVector v7 = new OpenMapRealVector(v1);
Assert.assertEquals("testData len", 7, v7.getDimension());
Assert.assertEquals("testData is 0.0 ", 0.0, v7.getEntry(6), 0);
SparseRealVectorTestImpl v7_i = new SparseRealVectorTestImpl(vec1);
OpenMapRealVector v7_2 = new OpenMapRealVector(v7_i);
Assert.assertEquals("testData len", 3, v7_2.getDimension());
Assert.assertEquals("testData is 0.0 ", 2.0d, v7_2.getEntry(1), 0);
OpenMapRealVector v8 = new OpenMapRealVector(v1);
Assert.assertEquals("testData len", 7, v8.getDimension());
Assert.assertEquals("testData is 0.0 ", 0.0, v8.getEntry(6), 0);
}
/** {@inheritDoc} */
public RealVector projection(RealVector v) throws IllegalArgumentException {
checkVectorDimensions(v.getDimension());
return v.mapMultiply(dotProduct(v) / v.dotProduct(v));
}
/** {@inheritDoc} */
public void setSubVector(int index, RealVector v) throws MatrixIndexException {
checkIndex(index);
checkIndex(index + v.getDimension() - 1);
setSubVector(index, v.getData());
}