SVD

fact_mult(A::SVD, B::SVD) -> SVD

Stabilized multiplication of two SVD decompositions. Returns a SVD factorization object.

Same as gesdd but saves space by overwriting the input matrix.

Calculates the SVD deomposition of a matrix by employing a divide and conquer approach. Returns a SVD factorization object.

Same as gesvd but saves space by overwriting the input matrix.

Calculates the SVD deomposition of a matrix. Returns a SVD factorization object.

inv_one_plus!(res, A::SVD, B::SVD) -> res

Stabilized calculation of [1 + UlDlVtlUrDrVtr]^(-1). Writes the result into res.

See svd_inv_one_plus for preallocation options.

inv_one_plus!(res, F::SVD) -> res

Stabilized calculation of [1 + USVt]^(-1):

• Use one intermediate SVD decomposition.

Writes the result into res.

See svd_inv_one_plus for preallocation options.

inv_one_plus(A::SVD, B::SVD) -> AbstractMatrix

Stabilized calculation of [1 + UlDlTlUrDrTr]^(-1).

See svd_inv_one_plus for preallocation options.

inv_one_plus(F::SVD) -> AbstractMatrix

Stabilized calculation of [1 + USVt]^(-1):

• Use one intermediate SVD decomposition.

See svd_inv_one_plus for preallocation options.

invoneplus_loh!(res, F::SVD) -> res

Stabilized calculation of [1 + USVt]^(-1):

• Separate scales larger and smaller than unity
• Use two intermediate SVD decompositions.

Writes the result into res.

See svd_inv_one_plus_loh for preallocation options.

invoneplus_loh(F::SVD) -> AbstractMatrix

Stabilized calculation of [1 + USVt]^(-1):

• Separate scales larger and smaller than unity
• Use two intermediate SVD decompositions.

See svd_inv_one_plus_loh for preallocation options.

inv_sum!(res, A::SVD, B::SVD) -> res

Stabilized calculation of [UaSaVta + UbSbVtb]^(-1):

• Use one intermediate SVD decompositions.

Writes the result into res.

See svd_inv_sum for preallocation options.

inv_sum(A::SVD, B::SVD) -> res

Stabilized calculation of [UaSaVta + UbSbVtb]^(-1):

• Use one intermediate SVD decompositions.

See svd_inv_sum for preallocation options.

inv_sum_loh!(res, A::SVD, B::SVD) -> res

Stabilized calculation of [UaSaVta + UbSbVtb]^(-1):

• Separate scales larger and smaller than unity
• Use two intermediate SVD decompositions.

Writes the result into res.

See svd_inv_sum_loh for preallocation options.

inv_sum_loh(A::SVD, B::SVD) -> res

Stabilized calculation of [UaSaVta + UbSbVtb]^(-1):

• Separate scales larger and smaller than unity
• Use two intermediate SVD decompositions.

See svd_inv_sum_loh for preallocation options.

svd_inv_one_plus(A::SVD, B::SVD) -> SVD

Stabilized calculation of [1 + UlDlVtlUrDrVtr]^(-1). Returns and SVD factorization object.

Optional preallocations via keyword arguments:

• tmp = similar(A.U)
• tmp2 = similar(A.U)
• tmp3 = similar(A.U)

svd_inv_one_plus(F::SVD) -> SVD

Stabilized calculation of [1 + USVt]^(-1):

• Use one intermediate SVD decomposition.

Options for preallocation via keyword arguments:

• t = similar(F.U)
• a = similar(F.U)
• c = similar(F.U)

svd_inv_one_plus_loh(F::SVD) -> SVD

Stabilized calculation of [1 + USVt]^(-1):

• Separate scales larger and smaller than unity
• Use two intermediate SVD decompositions.

Options for preallocation via keyword arguments:

• l = similar(F.U)
• r = similar(F.U)
• Dp = similar(F.D)
• Dm = similar(F.D)

svd_inv_sum(A::SVD, B::SVD) -> SVD

Stabilized calculation of [UaSaVta + UbSbVtb]^(-1):

• Use one intermediate SVD decompositions.

Options for preallocations via keyword arguments:

• m1 = similar(A.U)
• m2 = similar(A.U)

svd_inv_sum_loh(A::SVD, B::SVD) -> SVD

Stabilized calculation of [UaSaVta + UbSbVtb]^(-1):

• Separate scales larger and smaller than unity
• Use two intermediate SVD decompositions.

Options for preallocations via keyword arguments:

• None (yet)