SuanShu, a Java numerical and statistical library

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 Basisextends 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.

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

SuanShu, a Java numerical and statistical library