Python autograd.numpy.minimum() Examples

def is_a_scores_vector_batch(self, K, parent_vectors, other_vectors, rel_reversed):
        norm_parents = np.linalg.norm(parent_vectors, axis=1)
        norms_other = np.linalg.norm(other_vectors, axis=1)
        euclidean_dists = np.maximum(np.linalg.norm(parent_vectors - other_vectors, axis=1), 1e-6) # To avoid the fact that parent can be equal to child for the reconstruction experiment

        if not rel_reversed:
            cos_angles_child = (norms_other**2 - norm_parents**2 - euclidean_dists**2) / (2 * euclidean_dists * norm_parents) # 1 + neg_size
            angles_psi_parent = np.arcsin(K / norm_parents) # scalar
        else:
            cos_angles_child = (norm_parents**2 - norms_other**2 - euclidean_dists**2) / (2 * euclidean_dists * norms_other) # 1 + neg_size
            angles_psi_parent = np.arcsin(K / norms_other) # 1 + neg_size

        assert not np.isnan(cos_angles_child).any()
        clipped_cos_angle_child = np.maximum(cos_angles_child, -1 + EPS)
        clipped_cos_angle_child = np.minimum(clipped_cos_angle_child, 1 - EPS)
        angles_child = np.arccos(clipped_cos_angle_child)  # (1 + neg_size, batch_size)

        return np.maximum(0, angles_child - angles_psi_parent) 

def bound_by_data(Z, Data):
    """
    Determine lower and upper bound for each dimension from the Data, and project 
    Z so that all points in Z live in the bounds.

    Z: m x d 
    Data: n x d

    Return a projected Z of size m x d.
    """
    n, d = Z.shape
    Low = np.min(Data, 0)
    Up = np.max(Data, 0)
    LowMat = np.repeat(Low[np.newaxis, :], n, axis=0)
    UpMat = np.repeat(Up[np.newaxis, :], n, axis=0)

    Z = np.maximum(LowMat, Z)
    Z = np.minimum(UpMat, Z)
    return Z 

def constraint_c2(f, r):
    n_obj = f.shape[1]

    v1 = anp.inf * anp.ones(f.shape[0])

    for i in range(n_obj):
        temp = (f[:, i] - 1) ** 2 + (anp.sum(f ** 2, axis=1) - f[:, i] ** 2) - r ** 2
        v1 = anp.minimum(temp.flatten(), v1)

    a = 1 / anp.sqrt(n_obj)
    v2 = anp.sum((f - a) ** 2, axis=1) - r ** 2
    g = anp.minimum(v1, v2.flatten())

    return g 

def _compute_loss(self):
        """Compute and store loss value for the given batch of examples."""
        if self._loss_computed:
            return
        self._loss_computed = True

        self.euclidean_dists = np.linalg.norm(self.vectors_u - self.vectors_v, axis=1)  # (1 + neg_size, batch_size)
        euclidean_dists_sq = self.euclidean_dists ** 2

        if not self.rels_reversed:
            # (1 + neg_size, batch_size)
            child_numerator = self.norms_v_sq - self.norms_u_sq - euclidean_dists_sq
            self.child_numitor = 2 * self.euclidean_dists * self.norms_u
            self.angles_psi_parent = np.arcsin(self.K / self.norms_u) # (1, batch_size)

        else:
            # (1 + neg_size, batch_size)
            child_numerator = self.norms_u_sq - self.norms_v_sq - euclidean_dists_sq
            self.child_numitor = 2 * self.euclidean_dists * self.norms_v
            self.angles_psi_parent = np.arcsin(self.K / self.norms_v) # (1 + neg_size, batch_size)

        self.cos_angles_child = child_numerator / self.child_numitor
        # To avoid numerical errors
        self.clipped_cos_angle_child = np.maximum(self.cos_angles_child, -1 + EPS)
        self.clipped_cos_angle_child = np.minimum(self.clipped_cos_angle_child, 1 - EPS)
        self.angles_child = np.arccos(self.clipped_cos_angle_child)  # (1 + neg_size, batch_size)

        self.angle_diff = self.angles_child - self.angles_psi_parent
        self.energy_vec = np.maximum(0, self.angle_diff) # (1 + neg_size, batch_size)
        self.pos_loss = self.energy_vec[0].sum()
        self.neg_loss = np.maximum(0, self.margin - self.energy_vec[1:]).sum()
        self.loss = self.pos_loss + self.neg_loss 

def _compute_loss(self):
        """Compute and store loss value for the given batch of examples."""
        if self._loss_computed:
            return
        self._loss_computed = True

        self.euclidean_dists = np.linalg.norm(self.vectors_u - self.vectors_v, axis=1)  # (1 + neg_size, batch_size)
        self.dot_prods = (self.vectors_u * self.vectors_v).sum(axis=1) # (1 + neg, batch_size)

        self.g = 1 + self.norms_v_sq * self.norms_u_sq - 2 * self.dot_prods
        self.g_sqrt = np.sqrt(self.g)

        self.euclidean_times_sqrt_g = self.euclidean_dists * self.g_sqrt

        if not self.rels_reversed:
            # u is x , v is y
            # (1 + neg_size, batch_size)
            child_numerator = self.dot_prods * (1 + self.norms_u_sq) - self.norms_u_sq * (1 + self.norms_v_sq)
            self.child_numitor = self.euclidean_times_sqrt_g * self.norms_u
            self.angles_psi_parent = np.arcsin(self.K * self.one_minus_norms_sq_u / self.norms_u) # (1, batch_size)

        else:
            # v is x , u is y
            # (1 + neg_size, batch_size)
            child_numerator = self.dot_prods * (1 + self.norms_v_sq) - self.norms_v_sq * (1 + self.norms_u_sq)
            self.child_numitor = self.euclidean_times_sqrt_g * self.norms_v
            self.angles_psi_parent = np.arcsin(self.K * self.one_minus_norms_sq_v / self.norms_v) # (1, batch_size)

        self.cos_angles_child = child_numerator / self.child_numitor
        # To avoid numerical errors
        self.clipped_cos_angle_child = np.maximum(self.cos_angles_child, -1 + EPS)
        self.clipped_cos_angle_child = np.minimum(self.clipped_cos_angle_child, 1 - EPS)
        self.angles_child = np.arccos(self.clipped_cos_angle_child)  # (1 + neg_size, batch_size)

        self.angle_diff = self.angles_child - self.angles_psi_parent
        self.energy_vec = np.maximum(0, self.angle_diff) # (1 + neg_size, batch_size)
        self.pos_loss = self.energy_vec[0].sum()
        self.neg_loss = np.maximum(0, self.margin - self.energy_vec[1:]).sum()
        self.loss = self.pos_loss + self.neg_loss 

def plot_gaussian_mixture(params, ax):
    for log_proportion, mean, cov_sqrt in zip(*unpack_gmm_params(params)):
        alpha = np.minimum(1.0, np.exp(log_proportion) * 10)
        plot_ellipse(ax, mean, cov_sqrt, alpha) 

def test_minimum(): combo_check(np.minimum, [0, 1])(
                               [R(1), R(1,4), R(3, 4)],
                               [R(1), R(1,4), R(3, 4)]) 

def constraint_c2(f, r):
    n_obj = f.shape[1]

    v1 = anp.inf * anp.ones(f.shape[0])

    for i in range(n_obj):
        temp = (f[:, i] - 1) ** 2 + (anp.sum(f ** 2, axis=1) - f[:, i] ** 2) - r ** 2
        v1 = anp.minimum(temp.flatten(), v1)

    a = 1 / anp.sqrt(n_obj)
    v2 = anp.sum((f - a) ** 2, axis=1) - r ** 2
    g = anp.minimum(v1, v2.flatten())

    return g 

def _loss_fn(self, matrix, rels_reversed):
        """Given a numpy array with vectors for u, v and negative samples, computes loss value.

        Parameters
        ----------
        matrix : numpy.array
            Array containing vectors for u, v and negative samples, of shape (2 + negative_size, dim).
        rels_reversed : bool

        Returns
        -------
        float
            Computed loss value.

        Warnings
        --------
        Only used for autograd gradients, since autograd requires a specific function signature.
        """
        vector_u = matrix[0]
        vectors_v = matrix[1:]

        norm_u = grad_np.linalg.norm(vector_u)
        norms_v = grad_np.linalg.norm(vectors_v, axis=1)
        euclidean_dists = grad_np.linalg.norm(vector_u - vectors_v, axis=1)

        if not rels_reversed:
            # u is x , v is y
            cos_angle_child = (norms_v**2 - norm_u**2 - euclidean_dists**2) / (2 * euclidean_dists * norm_u) # 1 + neg_size
            angles_psi_parent = grad_np.arcsin(self.K / norm_u) # scalar
        else:
            # v is x , u is y
            cos_angle_child = (norm_u**2 - norms_v**2 - euclidean_dists**2) / (2 * euclidean_dists * norms_v) # 1 + neg_size
            angles_psi_parent = grad_np.arcsin(self.K / norms_v) # 1 + neg_size

        # To avoid numerical errors
        clipped_cos_angle_child = grad_np.maximum(cos_angle_child, -1 + EPS)
        clipped_cos_angle_child = grad_np.minimum(clipped_cos_angle_child, 1 - EPS)
        angles_child = grad_np.arccos(clipped_cos_angle_child)  # 1 + neg_size

        energy_vec = grad_np.maximum(0, angles_child - angles_psi_parent)
        positive_term = energy_vec[0]
        negative_terms = energy_vec[1:]
        return positive_term + grad_np.maximum(0, self.margin - negative_terms).sum() 

def _loss_fn(self, matrix, rels_reversed):
        """Given a numpy array with vectors for u, v and negative samples, computes loss value.

        Parameters
        ----------
        matrix : numpy.array
            Array containing vectors for u, v and negative samples, of shape (2 + negative_size, dim).
        rels_reversed : bool

        Returns
        -------
        float
            Computed loss value.

        Warnings
        --------
        Only used for autograd gradients, since autograd requires a specific function signature.
        """
        vector_u = matrix[0]
        vectors_v = matrix[1:]

        norm_u = grad_np.linalg.norm(vector_u)
        norms_v = grad_np.linalg.norm(vectors_v, axis=1)
        euclidean_dists = grad_np.linalg.norm(vector_u - vectors_v, axis=1)
        dot_prod = (vector_u * vectors_v).sum(axis=1)

        if not rels_reversed:
            # u is x , v is y
            cos_angle_child = (dot_prod * (1 + norm_u ** 2) - norm_u ** 2 * (1 + norms_v ** 2)) /\
                              (norm_u * euclidean_dists * grad_np.sqrt(1 + norms_v ** 2 * norm_u ** 2 - 2 * dot_prod))
            angles_psi_parent = grad_np.arcsin(self.K * (1 - norm_u**2) / norm_u) # scalar
        else:
            # v is x , u is y
            cos_angle_child = (dot_prod * (1 + norms_v ** 2) - norms_v **2 * (1 + norm_u ** 2) ) /\
                              (norms_v * euclidean_dists * grad_np.sqrt(1 + norms_v**2 * norm_u**2 - 2 * dot_prod))
            angles_psi_parent = grad_np.arcsin(self.K * (1 - norms_v**2) / norms_v) # 1 + neg_size

        # To avoid numerical errors
        clipped_cos_angle_child = grad_np.maximum(cos_angle_child, -1 + EPS)
        clipped_cos_angle_child = grad_np.minimum(clipped_cos_angle_child, 1 - EPS)
        angles_child = grad_np.arccos(clipped_cos_angle_child)  # 1 + neg_size

        energy_vec = grad_np.maximum(0, angles_child - angles_psi_parent)
        positive_term = energy_vec[0]
        negative_terms = energy_vec[1:]
        return positive_term + grad_np.maximum(0, self.margin - negative_terms).sum()