forked from mindspore-Ecosystem/mindspore
fix doc string
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zhujingxuan
parent
99d8425d3b
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434947f8fc
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@ -496,9 +496,9 @@ def lu(a, permute_l=False, overwrite_a=False, check_finite=True):
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diagonal elements, and U upper triangular.
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Args:
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a (Tensor): a (M, N) matrix to decompose
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permute_l (bool, optional): Perform the multiplication P*L (Default: do not permute)
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overwrite_a (bool, optional): Whether to overwrite data in a (may improve performance)
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a (Tensor): a (M, N) matrix to decompose.
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permute_l (bool, optional): Perform the multiplication P*L (Default: do not permute).
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overwrite_a (bool, optional): Whether to overwrite data in a (may improve performance).
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check_finite (bool, optional): Whether to check that the input matrix contains
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only finite numbers. Disabling may give a performance gain, but may result
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in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.
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@ -506,14 +506,14 @@ def lu(a, permute_l=False, overwrite_a=False, check_finite=True):
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Returns:
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**(If permute_l == False)**
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- Tensor, (M, M) Permutation matrix
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- Tensor, (M, K) Lower triangular or trapezoidal matrix with unit diagonal. K = min(M, N)
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- Tensor, (K, N) Upper triangular or trapezoidal matrix
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- Tensor, (M, M) Permutation matrix.
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- Tensor, (M, K) Lower triangular or trapezoidal matrix with unit diagonal. K = min(M, N).
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- Tensor, (K, N) Upper triangular or trapezoidal matrix.
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**(If permute_l == True)**
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- Tensor, (M, K) Permuted L matrix. K = min(M, N)
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- Tensor, (K, N) Upper triangular or trapezoidal matrix
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- Tensor, (M, K) Permuted L matrix. K = min(M, N).
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- Tensor, (K, N) Upper triangular or trapezoidal matrix.
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Supported Platforms:
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``CPU`` ``GPU``
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@ -302,7 +302,7 @@ class LineSearch(nn.Cell):
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return state
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def line_search(f, xk, pk, old_fval=None, old_old_fval=None, gfk=None, c1=1e-4,
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def line_search(f, xk, pk, gfk=None, old_fval=None, old_old_fval=None, c1=1e-4,
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c2=0.9, maxiter=20):
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"""Inexact line search that satisfies strong Wolfe conditions.
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@ -311,12 +311,14 @@ def line_search(f, xk, pk, old_fval=None, old_old_fval=None, gfk=None, c1=1e-4,
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Args:
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fun (function): function of the form f(x) where x is a flat Tensor and returns a real
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scalar. The function should be composed of operations with vjp defined.
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x0 (Tensor): initial guess.
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xk (Tensor): initial guess.
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pk (Tensor): direction to search in. Assumes the direction is a descent direction.
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old_fval, gfk (Tensor): initial value of value_and_gradient as position.
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gfk (Tensor): initial value of value_and_gradient as position.
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old_fval (Tensor): The same as gfk.
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old_old_fval (Tensor): unused argument, only for scipy API compliance.
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c1 (float): Wolfe criteria constant, see ref.
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c2 (float): The same as c1.
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maxiter (int): maximum number of iterations to search
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c1, c2 (float): Wolfe criteria constant, see ref.
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Returns:
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LineSearchResults
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@ -192,17 +192,18 @@ def gmres(A, b, x0=None, *, tol=1e-5, atol=0.0, restart=20, maxiter=None,
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is not achieved, like SciPy. Currently it is None, as a Placeholder.
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Args:
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A (Tensor or function): 2D Tensor or function that calculates the linear
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A (Union[Tensor, function]): 2D Tensor or function that calculates the linear
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map (matrix-vector product) ``Ax`` when called like ``A(x)``.
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``A`` must return Tensor with the same structure and shape as its argument.
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b (Tensor): Right hand side of the linear system representing a single vector.
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Can be stored as a Tensor
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x0 (Tensor, optional): Starting guess for the solution. Must have the same structure
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as ``b``. If this is unspecified, zeroes are used.
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tol, atol (float, optional): Tolerances for convergence,
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tol (float, optional): Tolerances for convergence,
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``norm(residual) <= max(tol*norm(b), atol)``. We do not implement SciPy's
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"legacy" behavior, so MindSpore's tolerance will differ from SciPy unless you
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explicitly pass ``atol`` to SciPy's ``gmres``.
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atol (float, optional): The same as tol.
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restart (integer, optional): Size of the Krylov subspace ("number of iterations")
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built between restarts. GMRES works by approximating the true solution x as its
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projection into a Krylov space of this dimension - this parameter
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@ -215,22 +216,21 @@ def gmres(A, b, x0=None, *, tol=1e-5, atol=0.0, restart=20, maxiter=None,
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Krylov space starting from the solution found at the last iteration. If GMRES
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halts or is very slow, decreasing this parameter may help.
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Default is infinite.
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M (Tensor or function): Preconditioner for A. The preconditioner should approximate the
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M (Union[Tensor, function]): Preconditioner for A. The preconditioner should approximate the
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inverse of A. Effective preconditioning dramatically improves the
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rate of convergence, which implies that fewer iterations are needed
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to reach a given error tolerance.
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solve_method ('incremental' or 'batched'): The 'incremental' solve method
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builds a QR decomposition for the Krylov subspace incrementally during
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the GMRES process using Givens rotations.
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This improves numerical stability and gives a free estimate of the
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residual norm that allows for early termination within a single "restart".
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In contrast, the 'batched' solve method solves the least squares problem
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from scratch at the end of each GMRES iteration. It does not allow for
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early termination, but has much less overhead on GPUs.
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solve_method (str): There are two kinds of solve methods,'incremental' or 'batched'. Default: "batched".
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- incremental: builds a QR decomposition for the Krylov subspace incrementally during
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the GMRES process using Givens rotations. This improves numerical stability and gives
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a free estimate of the residual norm that allows for early termination within a single "restart".
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- batched: solve the least squares problem from scratch at the end of each GMRES
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iteration. It does not allow for early termination, but has much less overhead on GPUs.
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Returns:
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- Tensor, The converged solution. Has the same structure as ``b``.
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- None, Placeholder for convergence information.
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- Tensor, The converged solution. Has the same structure as ``b``.
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- None, Placeholder for convergence information.
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Supported Platforms:
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``CPU`` ``GPU``
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@ -332,25 +332,26 @@ def cg(A, b, x0=None, *, tol=1e-5, atol=0.0, maxiter=None, M=None):
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is not achieved, like SciPy. Currently it is None, as a Placeholder.
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Args:
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A (Tensor or function): 2D Tensor or function that calculates the linear
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A (Union[Tensor, function]): 2D Tensor or function that calculates the linear
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map (matrix-vector product) ``Ax`` when called like ``A(x)``.
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``A`` must return Tensor with the same structure and shape as its argument.
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b (Tensor): Right hand side of the linear system representing a single vector. Can be
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stored as a Tensor.
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x0 (Tensor): Starting guess for the solution. Must have the same structure as ``b``.
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tol, atol (float, optional): Tolerances for convergence, ``norm(residual) <= max(tol*norm(b), atol)``.
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tol (float, optional): Tolerances for convergence, ``norm(residual) <= max(tol*norm(b), atol)``.
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We do not implement SciPy's "legacy" behavior, so MindSpore's tolerance will
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differ from SciPy unless you explicitly pass ``atol`` to SciPy's ``cg``.
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atol (float, optional): The same as tol.
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maxiter (int): Maximum number of iterations. Iteration will stop after maxiter
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steps even if the specified tolerance has not been achieved.
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M (Tensor or function): Preconditioner for A. The preconditioner should approximate the
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M (Union[Tensor, function]): Preconditioner for A. The preconditioner should approximate the
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inverse of A. Effective preconditioning dramatically improves the
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rate of convergence, which implies that fewer iterations are needed
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to reach a given error tolerance.
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Returns:
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- Tensor, The converged solution. Has the same structure as ``b``.
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- None, Placeholder for convergence information.
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- Tensor, The converged solution. Has the same structure as ``b``.
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- None, Placeholder for convergence information.
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Supported Platforms:
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``CPU`` ``GPU``
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