Class VectorVectorMult_FDRM

Constructor Summary

Method Summary
Modifier and TypeMethodDescriptionstatic 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})xstatic float
Computes the inner product of the two vectors.static float
innerProdA
(FMatrixD1 x, FMatrixD1 A, FMatrixD1 y) return = x^{T}*A*ystatic float
innerProdTranA
(FMatrixD1 x, FMatrixD1 A, FMatrixD1 y) x^{T}A^{T}ystatic 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.

Constructor Details

VectorVectorMult_FDRM
public VectorVectorMult_FDRM()


Method Details

innerProd
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
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
x^{T}A^{T}y
 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
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.
 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
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
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(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.
 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
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.
