Value parameters
- a
-
the m-by-n matrix to factor/decompose (requires m >= n)
Attributes
- Companion
- object
- Graph
-
- Supertypes
Members list
Value members
Concrete methods
Compute the condition number of 'this' matrix, i.e., the ratio of the largest singular value to the smallest. Note, if not of full rank, it will be infinity.
Compute the condition number of 'this' matrix, i.e., the ratio of the largest singular value to the smallest. Note, if not of full rank, it will be infinity.
Attributes
Factor/deflate the matrix by iteratively turning elements not in the main diagonal to zero. Save factorization result in mat3.
Factor/deflate the matrix by iteratively turning elements not in the main diagonal to zero. Save factorization result in mat3.
Attributes
Factor matrix a into the product of a matrix of left singular vectors u, a vector of singular values q and a matrix of right singular vectors v such that a = u *~ q * v.t.
Factor matrix a into the product of a matrix of left singular vectors u, a vector of singular values q and a matrix of right singular vectors v such that a = u *~ q * v.t.
Attributes
Return the two factored matrices.
Return the two factored matrices.
Attributes
Flip negative singular values to positive and set singular values close to zero to zero.
Flip negative singular values to positive and set singular values close to zero to zero.
Value parameters
- s
-
the vector of singular values
- u
-
the left orthongonal matrix
Attributes
Flip negative main diagonal elements in the singular vectors to positive.
Flip negative main diagonal elements in the singular vectors to positive.
Value parameters
- u
-
the left orthongonal matrix
- v
-
the right orthongonal matrix
Attributes
Efficient calculation of inverse matrix a^-1 from existing factorization. a * a^-1 = I
Efficient calculation of inverse matrix a^-1 from existing factorization. a * a^-1 = I
Attributes
Calculate the reciprocal of the given vector avoiding divide by zero. To handle the problem of a singular matrix, the singular values which are zero are left zero. (This function is similar to 'VectorD.recip ()' except for the zeros part.)
Calculate the reciprocal of the given vector avoiding divide by zero. To handle the problem of a singular matrix, the singular values which are zero are left zero. (This function is similar to 'VectorD.recip ()' except for the zeros part.)
Value parameters
- d
-
the vector of singular values
Attributes
- See also
Reorder the singular values to be in non-increasing order. Must swap singular vectors in lock step with singular values. To minimize the number of swaps, selection sort is used.
Reorder the singular values to be in non-increasing order. Must swap singular vectors in lock step with singular values. To minimize the number of swaps, selection sort is used.
Value parameters
- ft
-
the factored matrix (u, s, v)
Attributes
Solve for x in a^tax = b using Fac_SVD.
Solve for x in a^tax = b using Fac_SVD.
Value parameters
- b
-
the constant vector
Attributes
Test super-diagonal element e(l) and main diagonal element q(l-1) to set the lower index l.
Test super-diagonal element e(l) and main diagonal element q(l-1) to set the lower index l.
Value parameters
- e
-
the super-diagonal
- k
-
the upper index
- q
-
the main diagonal
Attributes
Inherited methods
Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the first matrix.
Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the first matrix.
Attributes
- Inherited from:
- Factorization
Factor a matrix into the product of two matrices, e.g., 'a = l * l.t' or a = q * r, returning both the first and second matrices.
Factor a matrix into the product of two matrices, e.g., 'a = l * l.t' or a = q * r, returning both the first and second matrices.
Attributes
- Inherited from:
- Factorization
Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the second matrix.
Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the second matrix.
Attributes
- Inherited from:
- Factorization
Return whether the matrix has been factored has aleady been factored.
Return whether the matrix has been factored has aleady been factored.
Attributes
- Inherited from:
- Factorization
Reset by setting factored to false.
Inherited fields
Flag indicating whether the matrix has been factored