linalg_cond {torch} | R Documentation |
Computes the condition number of a matrix with respect to a matrix norm.
Description
Letting \mathbb{K}
be \mathbb{R}
or \mathbb{C}
,
the condition number \kappa
of a matrix
A \in \mathbb{K}^{n \times n}
is defined as
Usage
linalg_cond(A, p = NULL)
Arguments
A |
(Tensor): tensor of shape |
p |
(int, inf, -inf, 'fro', 'nuc', optional):
the type of the matrix norm to use in the computations (see above). Default: |
Details
Math could not be displayed. Please visit the package website.
The condition number of A
measures the numerical stability of the linear system AX = B
with respect to a matrix norm.
Supports input of float, double, cfloat and cdouble dtypes.
Also supports batches of matrices, and if A
is a batch of matrices then
the output has the same batch dimensions.
p
defines the matrix norm that is computed. See the table in 'Details' to
find the supported norms.
For p
is one of ('fro', 'nuc', inf, -inf, 1, -1)
, this function uses
linalg_norm()
and linalg_inv()
.
As such, in this case, the matrix (or every matrix in the batch) A
has to be square
and invertible.
For p
in (2, -2)
, this function can be computed in terms of the singular values
\sigma_1 \geq \ldots \geq \sigma_n
Math could not be displayed. Please visit the package website.
In these cases, it is computed using linalg_svd()
. For these norms, the matrix
(or every matrix in the batch) A
may have any shape.
p | matrix norm |
NULL | 2 -norm (largest singular value) |
'fro' | Frobenius norm |
'nuc' | nuclear norm |
Inf | max(sum(abs(x), dim=2)) |
-Inf | min(sum(abs(x), dim=2)) |
1 | max(sum(abs(x), dim=1)) |
-1 | min(sum(abs(x), dim=1)) |
2 | largest singular value |
-2 | smallest singular value |
Value
A real-valued tensor, even when A
is complex.
Note
When inputs are on a CUDA device, this function synchronizes that device with the CPU if
if p
is one of ('fro', 'nuc', inf, -inf, 1, -1)
.
Examples
if (torch_is_installed()) {
a <- torch_tensor(rbind(c(1., 0, -1), c(0, 1, 0), c(1, 0, 1)))
linalg_cond(a)
linalg_cond(a, "fro")
}