The Fac_SVD object provides several test matrices as well as methods for making full representations, reducing dimensionality, determining rank and testing SVD factorizations.
Attributes
Members list
Value members
Concrete methods
Convert an SVD factoring to a full matrix representation, returning the result as three matrices having the following dimensions: U (m-by-n), S (n-by-n) and V (n-by-n). This is the compact SVD representation, see the next methods of a full SVD representation.
Convert an SVD factoring to a full matrix representation, returning the result as three matrices having the following dimensions: U (m-by-n), S (n-by-n) and V (n-by-n). This is the compact SVD representation, see the next methods of a full SVD representation.
Value parameters
- u_s_v
-
the 3-way factorization
Attributes
Create a full SVD factorization (rather than a compact one) where the three matrices have the following dimensions: U (m-by-m), S (m-by-n) and V (n-by-n).
Create a full SVD factorization (rather than a compact one) where the three matrices have the following dimensions: U (m-by-m), S (m-by-n) and V (n-by-n).
Value parameters
- a
-
the m-by-n matrix to factor/decompose (requires m >= n)
Attributes
- See also
Return a new normalized m-dimensional vector that is orthogonal to all columns in an orthonormal matrix u of dimension m-by-n (m > n), Use the Gram-Schmidt (SG) Orthogonalization Algorithm. v = a - Σ (a ⋅ uᵢ) * uᵢ
Return a new normalized m-dimensional vector that is orthogonal to all columns in an orthonormal matrix u of dimension m-by-n (m > n), Use the Gram-Schmidt (SG) Orthogonalization Algorithm. v = a - Σ (a ⋅ uᵢ) * uᵢ
Value parameters
- u
-
the given m-by-n orthonormal matrix
Attributes
- See also
Determine the rank of a matrix by counting the number of non-zero singular values. The implementation assumes zero singular values are last in the vector.
Determine the rank of a matrix by counting the number of non-zero singular values. The implementation assumes zero singular values are last in the vector.
Value parameters
- s
-
the vector of singular values for the matrix whose rank is sought
Attributes
Reduce the dimensionality of the u, s and v matrices from n to k. If k = rank, there is no loss of information; when k < rank, multiplying the three matrices results in an approximation (little is lost so long as the singular values set to zero (i.e., clipped) are small).
Reduce the dimensionality of the u, s and v matrices from n to k. If k = rank, there is no loss of information; when k < rank, multiplying the three matrices results in an approximation (little is lost so long as the singular values set to zero (i.e., clipped) are small).
Value parameters
- k
-
the desired dimensionality
- u_s_v
-
the 3-way factorization
Attributes
Test the SVD Factorization algorithm on matrix a by factoring the matrix into a left matrix u, a vector s, and a right matrix v. Then multiply back to recover the original matrix u *~ s * v.t.
Test the SVD Factorization algorithm on matrix a by factoring the matrix into a left matrix u, a vector s, and a right matrix v. Then multiply back to recover the original matrix u *~ s * v.t.
Value parameters
- a
-
the original matrix
- name
-
the name of the test case
- u_s_v
-
the given matrix a factored into three components