Package org.ejml.dense.row.mult

Class VectorVectorMult_DDRM

java.lang.Object

org.ejml.dense.row.mult.VectorVectorMult_DDRM

public class VectorVectorMult_DDRM
extends Object

Operations that involve multiplication of two vectors.

Constructor Summary

Constructors

Constructor	Description
VectorVectorMult_DDRM()

Method Summary

Modifier and Type	Method	Description
static void	addOuterProd(double gamma, DMatrixD1 x, DMatrixD1 y, DMatrix1Row A)	Adds to A ∈ ℜ m × n the results of an outer product multiplication of the two vectors.
static void	householder(double gamma, DMatrixD1 u, DMatrixD1 x, DMatrixD1 y)	Multiplies a householder reflection against a vector: y = (I + γ u uT)x
static double	innerProd(DMatrixD1 x, DMatrixD1 y)	Computes the inner product of the two vectors.
static double	innerProdA(DMatrixD1 x, DMatrixD1 A, DMatrixD1 y)	return = xT*A*y
static double	innerProdTranA(DMatrixD1 x, DMatrixD1 A, DMatrixD1 y)	xTATy
static void	outerProd(DMatrixD1 x, DMatrixD1 y, DMatrix1Row A)	Sets A ∈ ℜ m × n equal to an outer product multiplication of the two vectors.
static void	rank1Update(double gamma, DMatrixRMaj A, DMatrixRMaj u, DMatrixRMaj w)	Performs a rank one update on matrix A using vectors u and w.
static void	rank1Update(double gamma, DMatrixRMaj A, DMatrixRMaj u, DMatrixRMaj w, DMatrixRMaj B)	Performs a rank one update on matrix A using vectors u and w.

Methods inherited from class java.lang.Object

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

Constructor Details

VectorVectorMult_DDRM

public VectorVectorMult_DDRM()

Method Details

innerProd

public static double innerProd(DMatrixD1 x,
 DMatrixD1 y)

Computes the inner product of the two vectors. In geometry this is known as the dot product.

∑_k=1:n x_k * y_k
where x and y are vectors with n elements.

These functions are often used inside of highly optimized code and therefor sanity checks are kept to a minimum. It is not recommended that any of these functions be used directly.

Parameters:

x - A vector with n elements. Not modified.

y - A vector with n elements. Not modified.

Returns:

The inner product of the two vectors.

innerProdA

public static double innerProdA(DMatrixD1 x,
 DMatrixD1 A,
 DMatrixD1 y)

return = x^T*A*y

Parameters:

x - A vector with n elements. Not modified.

A - A matrix with n by m elements. Not modified.

y - A vector with m elements. Not modified.

Returns:

The results.

innerProdTranA

public static double innerProdTranA(DMatrixD1 x,
 DMatrixD1 A,
 DMatrixD1 y)

x^TA^Ty

Parameters:

x - A vector with n elements. Not modified.

A - A matrix with n by n elements. Not modified.

y - A vector with n elements. Not modified.

Returns:

The results.

outerProd

public static void outerProd(DMatrixD1 x,
 DMatrixD1 y,
 DMatrix1Row A)

Sets A ∈ ℜ ^{m × n} equal to an outer product multiplication of the two vectors. This is also known as a rank-1 operation.

A = x * y' where x ∈ ℜ ^m and y ∈ ℜ ⁿ are vectors.

Which is equivalent to: A_ij = x_i*y_j

These functions are often used inside of highly optimized code and therefor sanity checks are kept to a minimum. It is not recommended that any of these functions be used directly.

Parameters:

x - A vector with m elements. Not modified.

y - A vector with n elements. Not modified.

A - A Matrix with m by n elements. Modified.

addOuterProd

public static void addOuterProd(double gamma,
 DMatrixD1 x,
 DMatrixD1 y,
 DMatrix1Row A)

Adds to A ∈ ℜ ^{m × n} the results of an outer product multiplication of the two vectors. This is also known as a rank 1 update.

A = A + γ x * y^T where x ∈ ℜ ^m and y ∈ ℜ ⁿ are vectors.

Which is equivalent to: A_ij = A_ij + γ x_i*y_j

These functions are often used inside of highly optimized code and therefor sanity checks are kept to a minimum. It is not recommended that any of these functions be used directly.

Parameters:

gamma - A multiplication factor for the outer product.

x - A vector with m elements. Not modified.

y - A vector with n elements. Not modified.

A - A Matrix with m by n elements. Modified.

householder

public static void householder(double gamma,
 DMatrixD1 u,
 DMatrixD1 x,
 DMatrixD1 y)

Multiplies a householder reflection against a vector:

y = (I + γ u u^T)x

The Householder reflection is used in some implementations of QR decomposition.

Parameters:

u - A vector. Not modified.

x - a vector. Not modified.

y - Vector where the result are written to.

rank1Update

public static void rank1Update(double gamma,
 DMatrixRMaj A,
 DMatrixRMaj u,
 DMatrixRMaj w,
 DMatrixRMaj B)

Performs a rank one update on matrix A using vectors u and w. The results are stored in B.

B = A + γ u w^T

This is called a rank1 update because the matrix u w^T has a rank of 1. Both A and B can be the same matrix instance, but there is a special rank1Update for that.

Parameters:

gamma - A scalar.

A - A m by m matrix. Not modified.

u - A vector with m elements. Not modified.

w - A vector with m elements. Not modified.

B - A m by m matrix where the results are stored. Modified.

rank1Update

public static void rank1Update(double gamma,
 DMatrixRMaj A,
 DMatrixRMaj u,
 DMatrixRMaj w)

Performs a rank one update on matrix A using vectors u and w. The results are stored in A.

A = A + γ u w^T

This is called a rank1 update because the matrix u w^T has a rank of 1.

Parameters:

gamma - A scalar.

A - A m by m matrix. Modified.

u - A vector with m elements. Not modified.