"""
z = w'x + b
a = sigmoid(z)
L(a,y) = -(y*log(a) + (1-y)*log(1-a))

    [|  |  | ]
X = [x1 x2 x3]
    [|  |  | ]

[z1 z2 z3 .. zm] = w'*X + [b b b b ] = [w'*x1+b + w'*x2+b ...]
"""


import numpy as np
from .sigmoid import sigmoid


def propagate(w, b, X, Y):
    """
    Implement the cost function and its gradient for the propagation:
    Forward Propagation:
    - You get X
    - You compute $A = \sigma(w^T X + b) = (a^{(0)}, a^{(1)}, ..., a^{(m-1)}, a^{(m)})$
    - You calculate the cost function: $J = -\frac{1}{m}\sum_{i=1}^{m}y^{(i)}\log(a^{(i)})+(1-y^{(i)})\log(1-a^{(i)})$

    Here are the two formulas you will be using:

    $$ \frac{\partial J}{\partial w} = \frac{1}{m}X(A-Y)^T\tag{7}$$
    $$ \frac{\partial J}{\partial b} = \frac{1}{m} \sum_{i=1}^m (a^{(i)}-y^{(i)})\tag{8}$$

    Arguments:
    w -- weights, a numpy array of size (num_px * num_px * 3, 1)
    b -- bias, a scalar
    X -- data of size (num_px * num_px * 3, number of examples)
    Y -- true "label" vector (containing 0 if non-cat, 1 if cat) of size (1, number of examples)

    Return:
    cost -- negative log-likelihood cost for logistic regression
    dw -- gradient of the loss with respect to w, thus same shape as w
    db -- gradient of the loss with respect to b, thus same shape as b

    Tips:
    - Write your code step by step for the propagation. np.log(), np.dot()
    """



    # FORWARD PROPAGATION (FROM X TO COST)
    cost = cost_function(w, b, X, Y)  # compute cost

    # BACKWARD PROPAGATION (TO FIND GRADIENT)
    m = X.shape[1]
    A = sigmoid(np.dot(w.T, X) + b)  # compute activation
    dw = (1./m)*np.dot(X, (A - Y).T)
    db = (1./m)*np.sum(A - Y)

    # sanity check
    assert(A.shape[1] == m)
    assert(dw.shape == w.shape), "dw.shape is {}; w.shape is {}".format(dw.shape, w.shape)
    assert(db.dtype == float)
    cost = np.squeeze(cost)
    assert(cost.shape == ())

    # return gradients
    grads = {"dw": dw,
             "db": db}
    return grads, cost


def cost_function(w, b, X, Y):
    """
    Cost function for binary classification
    yhat = sigmoid(W.T*x + b)
    interpret yhat thhe probably that y=1

    Loss function:
    y log(yhat) + (1 - y) log(1 - yhat)
    """

    m = X.shape[1]
    A = sigmoid(np.dot(w.T, X) + b)
    cost = np.sum(Y*np.log(A) + (1 - Y)*np.log(1 - A))
    return (-1./m)*cost


def optimize(w, b, X, Y, num_iterations, learning_rate, print_cost = False):
    """
    This function optimizes w and b by running a gradient descent algorithm

    Arguments:
    w -- weights, a numpy array of size (num_px * num_px * 3, 1)
    b -- bias, a scalar
    X -- data of shape (num_px * num_px * 3, number of examples)
    Y -- true "label" vector (containing 0 if non-cat, 1 if cat), of shape (1, number of examples)
    num_iterations -- number of iterations of the optimization loop
    learning_rate -- learning rate of the gradient descent update rule
    print_cost -- True to print the loss every 100 steps

    Returns:
    params -- dictionary containing the weights w and bias b
    grads -- dictionary containing the gradients of the weights and bias with respect to the cost function
    costs -- list of all the costs computed during the optimization, this will be used to plot the learning curve.

    Tips:
    You basically need to write down two steps and iterate through them:
        1) Calculate the cost and the gradient for the current parameters. Use propagate().
        2) Update the parameters using gradient descent rule for w and b.
    """

    costs = []

    for i in range(num_iterations):

        # Cost and gradient calculation
        grads, cost = propagate(w, b, X, Y)

        # Retrieve derivatives from grads
        dw = grads["dw"]
        db = grads["db"]

        # gradient descent
        w = w - learning_rate*dw
        b = b - learning_rate*db

        # Record the costs
        if i % 100 == 0:
            costs.append(cost)

        # Print the cost every 100 training examples
        if print_cost and not (i % 100):
            print ("Cost after iteration %i: %f" %(i, cost))

    # package data for return
    params = {"w": w,
              "b": b}
    grads = {"dw": dw,
             "db": db}
    return params, grads, costs