import jax.numpy as jnp
from jax import Array

from ..._problem import AbstractNonlinearEquations


class LINVERSENE(AbstractNonlinearEquations):
    """
    The problem is to find the positive definite lower bidiagonal
    matrix L such that the matrix L(inv)L(inv-transp) best approximates,
    in the Frobenius norm, a given symmetric target matrix T.
    More precisely, one is interested in the positive definite lower
    bidiagonal L such that

         || L T L(transp) - I ||     is minimum.
                                F

    The positive definite character of L is imposed by requiring
    that all its diagonal entries to be at least equal to EPSILON,
    a strictly positive real number.

    Many variants of the problem can be obtained by varying the target
    matrix T and the scalar EPSILON. In the present problem,
    a) T is chosen to be pentadiagonal with T(i,j) = sin(i)cos(j) (j .leq. i)
    b) EPSILON = 1.D-8

    Source:
    Ph. Toint, private communication, 1991.

    SIF input: Ph. Toint, March 1991.
    Bound-constrained nonlinear equations version: Nick Gould, June 2019.

    classification NOR2-AN-V-V
    """

    n: int = 1000  # Dimension of the matrix
    epsilon: float = 1.0e-8
    y0_iD: int = 0
    provided_y0s: frozenset = frozenset({0})

    def num_residuals(self) -> int:
        """Number of residuals."""
        # The number of groups O(i,j) equals n + (n-1) + (n-2) = 3n - 3
        return 3 * self.n - 3

    def _get_target_matrix_element(self, i: int, j: int):
        """Compute T(i,j) = sin(i)cos(j) for pentadiagonal matrix."""
        if abs(i - j) > 2:
            return 0.0
        return jnp.sin(float(i)) * jnp.cos(float(j))

    def residual(self, y: Array, args) -> Array:
        """Compute the residual vector.

        Variables are organized as: A(1), B(1), A(2), B(2), ..., A(N-1), B(N-1), A(N)
        """
        n = self.n
        rootp5 = jnp.sqrt(0.5)

        # Extract A and B from the variable vector using vectorized operations
        # Create indices for a and b extraction
        a_indices = jnp.concatenate([jnp.arange(n - 1) * 2, jnp.array([2 * (n - 1)])])
        b_indices = jnp.arange(n - 1) * 2 + 1

        a = y[a_indices]
        b = y[b_indices]

        # Initialize residuals array
        num_res = self.num_residuals()
        residuals = jnp.zeros(num_res, dtype=jnp.float64)

        # O(1,1) group
        t_11 = self._get_target_matrix_element(1, 1)
        residuals = residuals.at[0].set(t_11 * a[0] * a[0] - 1.0)

        # O(2,1) group
        t_21 = self._get_target_matrix_element(2, 1)
        t_11 = self._get_target_matrix_element(1, 1)
        residuals = residuals.at[1].set(
            rootp5 * (t_21 * a[1] * a[0] + t_11 * b[0] * a[0])
        )

        # O(3,1) group
        t_31 = self._get_target_matrix_element(3, 1)
        t_21 = self._get_target_matrix_element(2, 1)
        residuals = residuals.at[2].set(
            rootp5 * (t_31 * a[2] * a[0] + t_21 * b[1] * a[0])
        )

        # O(2,2) group
        t_22 = self._get_target_matrix_element(2, 2)
        t_12 = self._get_target_matrix_element(1, 2)
        residuals = residuals.at[3].set(
            t_22 * a[1] * a[1]
            + 2.0 * t_12 * a[1] * b[0]
            + t_12 * a[1] * b[0]
            + t_12 * b[0] * b[0]
            - 1.0
        )

        # TODO: Human review needed
        # Attempts made: Partial implementation exists but is incomplete
        # Suspected issues: Complex group structure with many cases
        # Resources needed: Complete implementation of all O(i,j) groups
        # This is a simplified implementation focusing on the structure
        # Full implementation would require all group contributions

        return residuals

    @property
    def y0(self) -> Array:
        num_vars = 2 * self.n - 1  # Variables are A(1)..A(N) and B(1)..B(N-1)
        return jnp.full(num_vars, -1.0, dtype=jnp.float64)

    @property
    def args(self):
        """Additional arguments for the residual function."""
        return None

    @property
    def expected_result(self) -> Array:
        """Expected result of the optimization problem."""
        # Not explicitly given
        num_vars = 2 * self.n - 1
        return jnp.zeros(num_vars, dtype=jnp.float64)

    @property
    def expected_objective_value(self) -> Array:
        """Expected value of the objective at the solution."""
        # For nonlinear equations with pycutest formulation, this is always zero
        return jnp.array(0.0)

    def constraint(self, y):
        """Returns the residuals as equality constraints."""
        return self.residual(y, self.args), None

    @property
    def bounds(self) -> tuple[Array, Array] | None:
        """Bounds for variables - A(i) >= epsilon, B(i) free."""
        num_vars = 2 * self.n - 1
        lower = jnp.full(num_vars, -jnp.inf, dtype=jnp.float64)
        upper = jnp.full(num_vars, jnp.inf, dtype=jnp.float64)

        # Set lower bounds for A(i) variables using vectorized operations
        # A(i) variables are at positions 0, 2, 4, ..., 2*(n-1)
        a_indices = jnp.concatenate(
            [jnp.arange(self.n - 1) * 2, jnp.array([2 * (self.n - 1)])]
        )
        lower = lower.at[a_indices].set(self.epsilon)

        return lower, upper
