"""Test simple iteration."""
from functools import partial
import numpy as np
from numpy.testing import TestCase

import pyamg
from pyamg.krylov import minimal_residual, steepest_descent
from pyamg.util.linalg import norm


class TestSimpleIterations(TestCase):
    def setUp(self):
        self.definite_cases = []
        self.spd_cases = []

        # 1x1
        A = np.array([[1.2]])
        b = np.array([3.9]).reshape(-1, 1)
        x0 = np.zeros((1, 1))
        self.definite_cases.append({'A': A, 'b': b, 'x0': x0, 'maxiter': 1,
                                    'reduction_factor': 1e-10})
        self.spd_cases.append({'A': A, 'b': b, 'x0': x0, 'maxiter': 1,
                               'reduction_factor': 1e-10})

        # 2x2
        A = np.array([[4.5, -1.2],
                      [3.4, 6.7]])
        b = np.array([-3.2, 5.6]).reshape(-1, 1)
        x0 = np.zeros((2, 1))
        self.definite_cases.append({'A': A, 'b': b, 'x0': x0, 'maxiter': 4,
                                    'reduction_factor': 0.1})
        self.spd_cases.append({'A': A.T.dot(A), 'b': b, 'x0': x0, 'maxiter': 4,
                               'reduction_factor': 0.1})

        # 2x2 Imaginary
        A = np.array([[4.5, -1.2j],
                      [3.4+1.2j, 6.7]])
        b = np.array([-3.2, 5.6]).reshape(-1, 1)
        x0 = np.zeros((2, 1))
        self.spd_cases.append({'A': A.T.dot(A), 'b': b, 'x0': x0, 'maxiter': 4,
                               'reduction_factor': 0.1})

        # 4x4
        A = np.array([[1.2, 0., 0., 0.],
                      [0., 10., 2., 6.],
                      [0., 0., 9.3, -2.31],
                      [-4., 0., 0., 11.]])
        b = np.array([1., 3.9, 0., -1.23]).reshape(-1, 1)
        x0 = np.zeros((4, 1))
        self.definite_cases.append({'A': A, 'b': b, 'x0': x0, 'maxiter': 4,
                                    'reduction_factor': 0.3})
        self.spd_cases.append({'A': A.T.dot(A), 'b': b, 'x0': x0, 'maxiter': 4,
                               'reduction_factor': 0.3})

        # 4x4 Imaginary
        A = np.array(A, dtype=complex)
        A[0, 0] += 3.1j
        A[3, 3] -= 1.34j
        A[1, 3] *= 1.0j
        A[1, 2] += 1.0j
        b = np.array([1. - 1.0j, 2.0 - 3.9j, 0., -1.23]).reshape(-1, 1)
        x0 = np.ones((4, 1))
        self.spd_cases.append({'A': A.conj().T.dot(A), 'b': b, 'x0': x0, 'maxiter': 4,
                               'reduction_factor': 0.3})

        # 10x10
        A = np.array([[91.1, 0., 0., 0., 3.9, 0., 0., 11., -1., 0.],
                      [0., 45., 2.9, 0., 0., 6.8, 0., 0., 0., 0.],
                      [0., 0., 19.0, 0., 0., 0.8, 1., -2.2, 0., 9.],
                      [-4., 0., 0.0, 4., 0., 0.0, 2., 2.2, 0., 0.],
                      [0., 0., 0.0, 21., 30., 0.1, 0., 0., 0., 0.],
                      [0., 0., 0.0, 0., -4.7, 7.0, 0., 0., 0., 0.],
                      [2.1, 7., 2.0, 0., 0., 0.0, 8., 0., 0., 0.],
                      [0., 0., 0.0, 34., 0., 0.0, 0., 87.1, -12.3, 0.],
                      [0., 3.4, 0.0, 0., 0., -0.3, 0., 0., 7., 0.],
                      [9., 0., 0.0, 0., 8.7, 0.0, 0., 0., 0., 11.2]])
        b = np.array([1., 0., 0.2, 8., 0., -1.9,
                      11.3, 0.0, 0.1, 0.0]).reshape(-1, 1)
        x0 = np.zeros((10, 1))
        x0[4] = 11.1
        x0[7] = -2.1
        self.definite_cases.append({'A': A, 'b': b, 'x0': x0, 'maxiter': 2,
                                    'reduction_factor': 0.98})
        self.spd_cases.append({'A':
                               pyamg.gallery.poisson((10,)).toarray(),
                               'b': b, 'x0': x0, 'maxiter': 2,
                               'reduction_factor': 0.5})

    def test_steepest_descent(self):
        # Ensure repeatability
        np.random.seed(0)

        def cb(x, A, b):
            fvals.append(0.5*np.dot(x.ravel(), np.ravel(A @ x))
                         - np.dot(b.ravel(), x.ravel()))

        for case in self.spd_cases:
            A = case['A']
            b = case['b']
            x0 = case['x0']
            maxiter = case['maxiter']
            reduction_factor = case['reduction_factor']

            # This function should always decrease
            fvals = []

            callback = partial(cb, A=A, b=b)

            x, _ = steepest_descent(A, b, x0=x0, tol=1e-16,
                                    maxiter=maxiter, callback=callback)
            norm1 = norm(np.ravel(b) - np.ravel(A.dot(x.reshape(-1, 1))))
            norm2 = norm(np.ravel(b) - np.ravel(A.dot(x0.reshape(-1, 1))))
            actual_factor = norm1 / norm2
            assert actual_factor < reduction_factor

            if A.dtype != complex:
                for i in range(len(fvals)-1):
                    assert fvals[i+1] <= fvals[i]

        # Test preconditioning
        A = pyamg.gallery.poisson((10, 10), format='csr')
        b = np.random.rand(A.shape[0], 1)
        x0 = np.random.rand(A.shape[0], 1)
        fvals = []

        callback = partial(cb, A=A, b=b)

        resvec = []
        sa = pyamg.smoothed_aggregation_solver(A)
        x, _ = steepest_descent(A, b, x0, tol=1e-8, maxiter=20,
                                residuals=resvec, M=sa.aspreconditioner(),
                                callback=callback)
        assert resvec[-1]/resvec[0] < 1e-8
        for i in range(len(fvals)-1):
            assert fvals[i+1] <= fvals[i]

    def test_minimal_residual(self):
        # Ensure repeatability
        np.random.seed(0)

        self.definite_cases.extend(self.spd_cases)

        def cb(x, A):
            fvals.append(np.sqrt(np.dot(x.ravel(), np.ravel(A @ x))))

        for case in self.definite_cases:
            A = case['A']
            maxiter = case['maxiter']
            x0 = np.random.rand(A.shape[0],)
            b = np.zeros_like(x0)
            reduction_factor = case['reduction_factor']
            if A.dtype != complex:

                # This function should always decrease (assuming zero RHS)
                fvals = []

                callback = partial(cb, A=A)
                x, _ = minimal_residual(A, b, x0=x0,
                                        tol=1e-16, maxiter=maxiter,
                                        callback=callback)
                norm1 = norm(np.ravel(b) - np.ravel(A.dot(x.reshape(-1, 1))))
                norm2 = norm(np.ravel(b) - np.ravel(A.dot(x0.reshape(-1, 1))))
                actual_factor = norm1 / norm2
                assert actual_factor < reduction_factor
                if A.dtype != complex:
                    for i in range(len(fvals)-1):
                        assert fvals[i+1] <= fvals[i]

        # Test preconditioning
        A = pyamg.gallery.poisson((10, 10), format='csr')
        x0 = np.random.rand(A.shape[0], 1)
        b = np.zeros_like(x0)
        fvals = []

        callback = partial(cb, A=A)
        resvec = []
        sa = pyamg.smoothed_aggregation_solver(A)
        x, _ = minimal_residual(A, b, x0, tol=1e-8, maxiter=20,
                                residuals=resvec, M=sa.aspreconditioner(),
                                callback=callback)
        assert resvec[-1]/resvec[0] < 1e-8
        for i in range(len(fvals)-1):
            assert fvals[i+1] <= fvals[i]
