pycif.plugins.minimizers.congrad — API reference

Configuration reference: congrad plugin

pycif.plugins.minimizers.congrad.check.check_options(self, chi, **kwargs)

Validate CONGRAD parameters and fill missing ones with defaults.

Parameters:

• self (Plugin) – CONGRAD minimizer plugin instance. Reads/sets: zreduc (default 1e-15), pevbnd (default 0.01), kvadim, kverbose (default 1), ldsolve (default True), maxiter (mandatory), knevecout.

• chi (np.ndarray) – initial iterate; used only to read its dimension.

• **kwargs – unused; accepted for interface consistency.

Returns:

self with all resolved parameters written back.

Return type:

Plugin

Raises:

AttributeError – if maxiter is not defined on the plugin.

pycif.plugins.minimizers.congrad.congrad.congrad(self, px, pgrad, planc1, **kwargs)

Execute the CONGRAD Lanczos inner loop.

Builds a Krylov subspace basis via the Lanczos iteration, solves the resulting tridiagonal least-squares problem, and simultaneously accumulates the leading eigenvector estimates (pevecs) of the inverse Hessian.

Parameters:

• self (Plugin) – CONGRAD plugin instance with all parameters already resolved by check_options (zreduc, pevbnd, kvadim, maxiter, kverbose, ldsolve).

• px (np.ndarray) – initial iterate \(\chi_0\), shape (n,).

• pgrad (np.ndarray) – initial gradient \(\nabla J(\chi_0)\), shape (n,).

• planc1 (np.ndarray) – first Lanczos vector (copy of pgrad on entry), shape (n,).

• **kwargs – forwarded to the simulator.

Returns:

(xopt, gradopt, preduc, pevecs, iiter)

• xopt (np.ndarray): optimal iterate.

• gradopt (np.ndarray): gradient at xopt.

• preduc (float): achieved relative gradient-norm reduction.

• pevecs (np.ndarray): estimated leading eigenvectors of \((\mathbf{I} + \mathbf{H}\mathbf{B}\mathbf{H}^\top)^{-1}\), shape (maxiter, n).

• iiter (int): number of Lanczos iterations performed.

Return type:

tuple

pycif.plugins.minimizers.congrad.minimize.minimize(self, finit, gradinit, chi0, **kwargs)

Run the CONGRAD Lanczos minimisation and return the optimal iterate.

Parameters:

• self (Plugin) – CONGRAD minimizer plugin instance.

• finit (float) – initial cost function value \(J(\chi_0)\).

• gradinit (np.ndarray) – initial gradient \(\nabla J(\chi_0)\), shape (n,).

• chi0 (np.ndarray) – initial iterate \(\chi_0\), shape (n,).

• **kwargs – forwarded to the simulator.

Returns:

optimal iterate \(\chi_\mathrm{opt}\), shape (n,).

Return type:

np.ndarray

pycif.plugins.minimizers.congrad.wrevecs.wrevecs(kdprob, knits, kmaxit, kverbose, pevals, pbnds, pblim, pv, plancv, logfile)

Python version of the congrad minimization algorithm

Mike Fisher (ECMWF), April 2002 Frederic Chevallier (LSCE), April 2004, for the Python adaptation verbose from the Fortran subroutine:

WREVECS - Called from CONGRAD. Computes and saves eigenvectors.

Purpose. –

Interface. -

CALL WREVECS (kdprob,knits,kmaxit,pevals,pbnds,pblim,pv,plancv,&

&kngood,ptheta)

Explicit arguments:

Inputs: kdprob – dimension of the problem.

knits – Number of Lanczos vectors. kmaxit – First dimension of ‘pv’. kulout – unit number for information messages (e.g. standard output) kverbose – verbosity (0 => no messages, 1 => taciturn, 2 => verbose) pevals – Approximate eigenvalues (Ritz values). pbnds – Error bounds on eigenvectors. pblim – Error bound below which eigenvector is ‘good’. pv – Eigenvector matrix of tridiagonal problem. plancv – Lanczos vectors

Outputs: kngood – Number of eigenvectors writen.

ptheta – Eigenvalues . pvcglev – Eigenvectors prcglev – Eigenvalues again (originally, this was a file)

Externals. -

Reference. -

None yet!

Author. -

Mike Fisher ECMWF

modifications. –

Original 20/5/94 M. Fisher 01-01-96 : Optionally save vectors in memory M. Fisher 26-11-96 : USE YOM_DISTRIBUTED_VECTORS M. Fisher 31-03-99 : Removed the last vestiges of the MIO package F. Chevallier 04/05: Translate into python