A (Tensor) – the input tensor of size ( ∗ , m , m ) (*, m, m) (∗,m,m)
B (Tensor, optional) – the input tensor of size ( ∗ , m , m ) (*, m, m) (∗,m,m). When not specified, B is interpreted as identity matrix.
X (tensor, optional) – the input tensor of size ( ∗ , m , n ) (*, m, n) (∗,m,n) where k <= n <= m. When specified, it is used as initial approximation of eigenvectors. X must be a dense tensor.
iK (tensor, optional) – the input tensor of size ( ∗ , m , m ) (*, m, m) (∗,m,m). When specified, it will be used as preconditioner.
k (integer, optional) – the number of requested eigenpairs. Default is the number of X X X columns (when specified) or 1.
n (integer, optional) – if X X X is not specified then n specifies the size of the generated random approximation of eigenvectors. Default value for n is k. If X X X is specified, the value of n (when specified) must be the number of X X X columns.
tol (float, optional) – residual tolerance for stopping criterion. Default is feps ** 0.5 where feps is smallest non-zero floating-point number of the given input tensor A data type.
largest (bool, optional) – when True, solve the eigenproblem for the largest eigenvalues. Otherwise, solve the eigenproblem for smallest eigenvalues. Default is True.
method (str, optional) – select LOBPCG method. See the description of the function above. Default is “ortho”.
niter (int, optional) – maximum number of iterations. When reached, the iteration process is hard-stopped and the current approximation of eigenpairs is returned. For infinite iteration but until convergence criteria is met, use -1.
tracker (callable, optional) –
a function for tracing the iteration process. When specified, it is called at each iteration step with LOBPCG instance as an argument. The LOBPCG instance holds the full state of the iteration process in the following attributes:
iparams, fparams, bparams - dictionaries of integer, float, and boolean valued input parameters, respectively
ivars, fvars, bvars, tvars - dictionaries of integer, float, boolean, and Tensor valued iteration variables, respectively.
A, B, iK - input Tensor arguments.
E, X, S, R - iteration Tensor variables.
For instance:
ivars[“istep”] - the current iteration step X - the current approximation of eigenvectors E - the current approximation of eigenvalues R - the current residual ivars[“converged_count”] - the current number of converged eigenpairs tvars[“rerr”] - the current state of convergence criteria
Note that when tracker stores Tensor objects from the LOBPCG instance, it must make copies of these.
If tracker sets bvars[“force_stop”] = True, the iteration process will be hard-stopped.
ortho_iparams (dict, optional) – various parameters to LOBPCG algorithm when using method=”ortho”.
ortho_fparams (dict, optional) – various parameters to LOBPCG algorithm when using method=”ortho”.
ortho_bparams (dict, optional) – various parameters to LOBPCG algorithm when using method=”ortho”.
tensor of eigenvalues of size ( ∗ , k ) (*, k) (∗,k)
X (Tensor): tensor of eigenvectors of size ( ∗ , m , k ) (*, m, k) (∗,m,k)
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