mindspore.scipy.sparse.linalg.cg

mindspore.scipy.sparse.linalg.cg(A, b, x0=None, *, tol=1e-05, atol=0.0, maxiter=None, M=None)[source]

Use Conjugate Gradient iteration to solve \(Ax = b\).

The numerics of MindSpore’s cg should exact match SciPy’s cg (up to numerical precision).

Derivatives of cg are implemented via implicit differentiation with another cg solve, rather than by differentiating through the solver. They will be accurate only if both solves converge.

Note

In the future, MindSpore will report the number of iterations when convergence is not achieved, like SciPy. Currently it is None, as a Placeholder. Input A must represent a hermitian, positive definite matrix. If not, the output is wrong and inconsistent with scipy.

Parameters

  • A (Union[Tensor, function]) – 2D Tensor or function that calculates the linear map (matrix-vector product) \(Ax\) when called like \(A(x)\). As function, A must return Tensor with the same structure and shape as its input matrix.

  • b (Tensor) – Right hand side of the linear system representing a single vector. Can be stored as a Tensor.

  • x0 (Tensor) – Starting guess for the solution. Must have the same structure as b. Default: None.

  • tol (float, optional) – Tolerances for convergence, \(norm(residual) <= max(tol*norm(b), atol)\). We do not implement SciPy’s “legacy” behavior, so MindSpore’s tolerance will differ from SciPy unless you explicitly pass atol to SciPy’s cg. Default: 1e-5.

  • atol (float, optional) – The same as tol. Default: 0.0.

  • maxiter (int) – Maximum number of iterations. Iteration will stop after maxiter steps even if the specified tolerance has not been achieved. Default: None.

  • M (Union[Tensor, function]) – Preconditioner for A. The preconditioner should approximate the inverse of A. Effective preconditioning dramatically improves the rate of convergence, which implies that fewer iterations are needed to reach a given error tolerance. Default: None.

Returns

  • Tensor, the converged solution. Has the same structure as b.

  • None, placeholder for convergence information.

Raises

  • ValueError – If x0 and b don’t have the same structure.

  • TypeError – If A, x0 and b don’t have the same float types(mstype.float32 or mstype.float64).

Supported Platforms:

CPU GPU

Examples

>>> import numpy as onp
>>> from mindspore.common import Tensor
>>> from mindspore.scipy.sparse.linalg import cg
>>> A = Tensor(onp.array([[1, 2], [2, 1]], dtype='float32'))
>>> b = Tensor(onp.array([1, -1], dtype='float32'))
>>> result, _ = cg(A, b)
>>> result
Tensor(shape=[2], dtype=Float32, value= [-1.00000000e+00,  1.00000000e+00])