Computes the solution of a square system of linear equations with a unique solution.
Letting K \mathbb{K} K be R \mathbb{R} R or C \mathbb{C} C, this function computes the solution X ∈ K n × k X \in \mathbb{K}^{n \times k} X∈Kn×k of the linear system associated to A ∈ K n × n , B ∈ K n × k A \in \mathbb{K}^{n \times n}, B \in \mathbb{K}^{n \times k} A∈Kn×n,B∈Kn×k, which is defined as
A X = B AX = B AX=B
If left= False, this function returns the matrix X ∈ K n × k X \in \mathbb{K}^{n \times k} X∈Kn×k that solves the system
X A = B A ∈ K k × k , B ∈ K n × k . XA = B\mathrlap{\qquad A \in \mathbb{K}^{k \times k}, B \in \mathbb{K}^{n \times k}.} XA=BA∈Kk×k,B∈Kn×k.
This system of linear equations has one solution if and only if A A A is invertible. This function assumes that A A A is invertible.
Supports inputs of float, double, cfloat and cdouble dtypes. Also supports batches of matrices, and if the inputs are batches of matrices then the output has the same batch dimensions.
Letting * be zero or more batch dimensions,
If A has shape (*, n, n) and B has shape (*, n) (a batch of vectors) or shape (*, n, k) (a batch of matrices or “multiple right-hand sides”), this function returns X of shape (*, n) or (*, n, k) respectively.
Otherwise, if A has shape (*, n, n) and B has shape (n,) or (n, k), B is broadcasted to have shape (*, n) or (*, n, k) respectively. This function then returns the solution of the resulting batch of systems of linear equations.
Note
This function computes X = A.inverse() @ B in a faster and more numerically stable way than performing the computations separately.
Note
It is possible to compute the solution of the system X A = B XA = B XA=B by passing the inputs A and B transposed and transposing the output returned by this function.
Note
A is allowed to be a non-batched torch.sparse_csr_tensor, but only with left=True.
Note
When inputs are on a CUDA device, this function synchronizes that device with the CPU. For a version of this function that does not synchronize, see torch.linalg.solve_ex().
RuntimeError – if the A matrix is not invertible or any matrix in a batched A is not invertible.
Examples:
>>> A = torch.randn(3, 3) >>> b = torch.randn(3) >>> x = torch.linalg.solve(A, b) >>> torch.allclose(A @ x, b) True >>> A = torch.randn(2, 3, 3) >>> B = torch.randn(2, 3, 4) >>> X = torch.linalg.solve(A, B) >>> X.shape torch.Size([2, 3, 4]) >>> torch.allclose(A @ X, B) True >>> A = torch.randn(2, 3, 3) >>> b = torch.randn(3, 1) >>> x = torch.linalg.solve(A, b) # b is broadcasted to size (2, 3, 1) >>> x.shape torch.Size([2, 3, 1]) >>> torch.allclose(A @ x, b) True >>> b = torch.randn(3) >>> x = torch.linalg.solve(A, b) # b is broadcasted to size (2, 3) >>> x.shape torch.Size([2, 3]) >>> Ax = A @ x.unsqueeze(-1) >>> torch.allclose(Ax, b.unsqueeze(-1).expand_as(Ax)) True
RetroSearch is an open source project built by @garambo | Open a GitHub Issue
Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo
HTML:
3.2
| Encoding:
UTF-8
| Version:
0.7.4