com.numericalmethod.suanshu.vector.doubles.dense.operation
Class Basis

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.SparseVector
      com.numericalmethod.suanshu.vector.doubles.dense.operation.Basis

All Implemented Interfaces:

DeepCopyable, AbelianGroup<Vector>, BanachSpace<Vector,Real>, HilbertSpace<Vector,Real>, VectorSpace<Vector,Real>, SparseStructure, Vector, java.lang.Iterable<SparseVector.Entry>

public class Basis
extends SparseVector

A basis is a set of linearly independent vectors spanning a vector space. Every element in this space can be uniquely represented by a linear combination of elements in the basis. This implementation is the standard basis of the Euclidean Rⁿ space.

See Also:

Wikipedia: Basis (linear algebra)

Nested Class Summary

Nested classes/interfaces inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.SparseVector

SparseVector.Entry, SparseVector.Iterator

Constructor Summary

Basis(int dim, int i)
Construct a vector that corresponds to the i-th dimension in Rⁿ.

Method Summary

static java.util.List<Vector>	getBasis(int dim) Get the full set of the standard basis vectors.
static java.util.List<Vector>	getBasis(int dim, int nCols) Get a subset of the standard basis vectors.

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.SparseVector

add, add, add, angle, deepCopy, divide, get, innerProduct, innerProduct, iterator, minus, minus, minus, multiply, multiply, nNonZeros, norm, norm, opposite, pow, scaled, scaled, set, size, toArray, toString, ZERO

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

Basis

public Basis(int dim,
             int i)

Construct a vector that corresponds to the i-th dimension in Rⁿ. That is (a 1 in the i-th entry), \[ \begin{bmatrix} 0\\ ...\\ 1\\ ...\\ 0 \end{bmatrix} \]

Parameters:

dim - the dimension

i - the i-th dimension in Rⁿ

Method Detail

getBasis

public static java.util.List<Vector> getBasis(int dim)

Get the full set of the standard basis vectors.

Parameters:

dim - the dimension

Returns:

the basis vectors

getBasis

public static java.util.List<Vector> getBasis(int dim,
                                              int nCols)

Get a subset of the standard basis vectors.

Parameters:

dim - the dimension

nCols - the number of basis vectors requested; it must be smaller than dim

Returns:

the basis vectors

Throws:

java.lang.IllegalArgumentException - if there are more columns requested than the dimension