public class VectorVectorMult_FDRM
extends java.lang.Object
Constructor and Description 

VectorVectorMult_FDRM() 
Modifier and Type  Method and Description 

static void 
addOuterProd(float gamma,
FMatrixD1 x,
FMatrixD1 y,
FMatrix1Row A)
Adds to A ∈ ℜ ^{m × n} the results of an outer product multiplication
of the two vectors.

static void 
householder(float gamma,
FMatrixD1 u,
FMatrixD1 x,
FMatrixD1 y)
Multiplies a householder reflection against a vector:
y = (I + γ u u^{T})x 
static float 
innerProd(FMatrixD1 x,
FMatrixD1 y)
Computes the inner product of the two vectors.

static float 
innerProdA(FMatrixD1 x,
FMatrixD1 A,
FMatrixD1 y)
return = x^{T}*A*y

static float 
innerProdTranA(FMatrixD1 x,
FMatrixD1 A,
FMatrixD1 y)
x^{T}A^{T}y

static void 
outerProd(FMatrixD1 x,
FMatrixD1 y,
FMatrix1Row A)
Sets A ∈ ℜ ^{m × n} equal to an outer product multiplication of the two
vectors.

static void 
rank1Update(float gamma,
FMatrixRMaj A,
FMatrixRMaj u,
FMatrixRMaj w)
Performs a rank one update on matrix A using vectors u and w.

static void 
rank1Update(float gamma,
FMatrixRMaj A,
FMatrixRMaj u,
FMatrixRMaj w,
FMatrixRMaj B)
Performs a rank one update on matrix A using vectors u and w.

public static float innerProd(FMatrixD1 x, FMatrixD1 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.
x
 A vector with n elements. Not modified.y
 A vector with n elements. Not modified.public static float innerProdA(FMatrixD1 x, FMatrixD1 A, FMatrixD1 y)
return = x^{T}*A*y
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.public static float innerProdTranA(FMatrixD1 x, FMatrixD1 A, FMatrixD1 y)
x^{T}A^{T}y
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.public static void outerProd(FMatrixD1 x, FMatrixD1 y, FMatrix1Row A)
Sets A ∈ ℜ ^{m × n} equal to an outer product multiplication of the two
vectors. This is also known as a rank1 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.
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.public static void addOuterProd(float gamma, FMatrixD1 x, FMatrixD1 y, FMatrix1Row 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.
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.public static void householder(float gamma, FMatrixD1 u, FMatrixD1 x, FMatrixD1 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.
u
 A vector. Not modified.x
 a vector. Not modified.y
 Vector where the result are written to.public static void rank1Update(float gamma, FMatrixRMaj A, FMatrixRMaj u, FMatrixRMaj w, FMatrixRMaj 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.
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.public static void rank1Update(float gamma, FMatrixRMaj A, FMatrixRMaj u, FMatrixRMaj 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.
gamma
 A scalar.A
 A m by m matrix. Modified.u
 A vector with m elements. Not modified.
Copyright © 20092018 Peter Abeles