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# The user-defined Python class implementing the gradient descent.
from petsc4py import PETSc
class myGradientDescent:
def create(self, tao):
# Create a line search type with constant step size.
self._ls = PETSc.TAOLineSearch().create(comm=PETSc.COMM_SELF)
self._ls.useTAORoutine(tao)
self._ls.setType(PETSc.TAOLineSearch.Type.UNIT)
self._ls.setInitialStepLength(0.2)
def solve(self, tao):
# Get solution and Jacobian vector.
x = tao.getSolution()
gradient = tao.getGradient()[0]
# Prepare search direction for line search.
search_direction = gradient.copy()
# Optimization loop.
for it in range(tao.getMaximumIterations()):
tao.setIterationNumber(it)
# Compute search_direction.
# search_direction = -gradient
tao.computeGradient(x, gradient)
gradient.copy(search_direction)
search_direction.scale(-1)
# Apply line search:
# x += .2 search_direction
f, s, reason = self._ls.apply(x, gradient, search_direction)
if reason < 0:
raise RuntimeError('LS failed.')
# Log and update internal state.
tao.monitor(f=f, res=gradient.norm())
# Convergence check.
if tao.checkConverged() > 0:
break
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