Python numpy.sum() Examples

def iter_apply(Xs, Ms, Ys):
    # fns = [lambda x: np.concatenate(x, 0), lambda x: float(np.sum(x))]
    logits = []
    cost = 0
    with chainer.using_config('train', False), \
            chainer.using_config('enable_backprop', False):
        for xmb, mmb, ymb in iter_data(
                Xs, Ms, Ys, n_batch=n_batch_train, truncate=False, verbose=True):
            n = len(xmb)
            XMB = model.xp.asarray(xmb)
            YMB = model.xp.asarray(ymb)
            MMB = model.xp.asarray(mmb)
            h = model(XMB)
            clf_logits = clf_head(h, XMB)
            clf_logits *= n
            clf_losses = compute_loss_fct(
                XMB, YMB, MMB, clf_logits, only_return_losses=True)
            clf_losses *= n
            logits.append(cuda.to_cpu(clf_logits.array))
            cost += cuda.to_cpu(F.sum(clf_losses).array)
        logits = np.concatenate(logits, 0)
    return logits, cost 

def community_density(community, co_graph, density_prop, fill=0):
    """community_density
    Calculate the density of a clique based on the number of occurrences
    and coocurrences of the terms within it. Based on Callon et al. 1991.

    Parameters
    ----------
        community : :obj:`iter` of :obj:`int`: 
            A set of terms that comprise a single clique.
        g : :obj:`graph_tool.Graph` 
            The coocurrence graph from which the clique originated
        fill :obj:`float`: 
            A number to fill in for the cooccurrence value if none exists.
    Returns
    -------
        density :obj:`float`: The density of the clique.
    """
    card = len(community)
    densities = density_prop.a[community]
    density = 1 / card * np.sum(densities)
    return density 

def make_initial_P_d_K(
        init_name,
        prng=np.random,
        alpha_K=None,
        init_P_d_K_list=None):
    K = alpha_K.size

    if init_name.count('warm'):
        return init_P_d_K_list.pop()
    elif init_name.count('uniform_sample'):
        return prng.dirichlet(np.ones(K))
    elif init_name.count('prior_sample'):
        return prng.dirichlet(alpha_K)
    elif init_name.count("prior_mean"):
        return alpha_K / np.sum(alpha_K) #np.zeros(K, dtype=alpha_K.dtype)
    else:
        raise ValueError("Unrecognized vb lstep_init_name: " + init_name) 

def evaluate_frame(gt_labels, pred_labels):
    assert np.all(np.isin(pred_labels, (0, 1))), \
        'Invalid values: pred labels value should be either 0 or 1, got {}'.format(set(pred_labels))

    correct_predictions = gt_labels == pred_labels
    positive_predictions = pred_labels == 1

    # correct, positive prediction -> True positive
    tp = np.sum(correct_predictions & positive_predictions)

    # incorrect, negative prediction (using De Morgan's law) -> False negative
    fn = np.sum(np.logical_not(correct_predictions | positive_predictions))

    # incorrect, positive prediction -> False positive
    fp = np.sum(np.logical_not(correct_predictions) & positive_predictions)

    return tp, fn, fp 

def solve_modal(model,k:int):
    """
    Solve eigen mode of the MDOF system
    
    params:
        model: FEModel.
        k: number of modes to extract.
    """
    K_,M_=model.K_,model.M_
    if k>model.DOF:
        logger.info('Warning: the modal number to extract is larger than the system DOFs, only %d modes are available'%model.DOF)
        k=model.DOF
    omega2s,modes = sl.eigsh(K_,k,M_,sigma=0,which='LM')
    delta = modes/np.sum(modes,axis=0)
    model.is_solved=True
    model.mode_=delta
    model.omega_=np.sqrt(omega2s).reshape((k,1)) 

def found_search(self, x, y):
        '''
        This function is applied when the lane lines have been detected in the previous frame.
        It uses a sliding window to search for lane pixels in close proximity (+/- 25 pixels in the x direction)
        around the previous detected polynomial.
        '''
        xvals = []
        yvals = []
        if self.found == True:
            i = 720
            j = 630
            while j >= 0:
                yval = np.mean([i,j])
                xval = (np.mean(self.fit0))*yval**2 + (np.mean(self.fit1))*yval + (np.mean(self.fit2))
                x_idx = np.where((((xval - 25) < x)&(x < (xval + 25))&((y > j) & (y < i))))
                x_window, y_window = x[x_idx], y[x_idx]
                if np.sum(x_window) != 0:
                    np.append(xvals, x_window)
                    np.append(yvals, y_window)
                i -= 90
                j -= 90
        if np.sum(xvals) == 0:
            self.found = False # If no lane pixels were detected then perform blind search
        return xvals, yvals, self.found 

def test(model, data):
    x_test, y_test = data
    y_pred, x_recon = model.predict(x_test, batch_size=100)
    print('-'*50)
    print('Test acc:', np.sum(np.argmax(y_pred, 1) == np.argmax(y_test, 1))/y_test.shape[0])

    import matplotlib.pyplot as plt
    from utils import combine_images
    from PIL import Image

    img = combine_images(np.concatenate([x_test[:50],x_recon[:50]]))
    image = img * 255
    Image.fromarray(image.astype(np.uint8)).save("real_and_recon.png")
    print()
    print('Reconstructed images are saved to ./real_and_recon.png')
    print('-'*50)
    plt.imshow(plt.imread("real_and_recon.png", ))
    plt.show() 

def test(model, data):
    x_test, y_test = data
    y_pred, x_recon = model.predict(x_test, batch_size=100)
    print('-'*50)
    print('Test acc:', np.sum(np.argmax(y_pred, 1) == np.argmax(y_test, 1))/y_test.shape[0])

    import matplotlib.pyplot as plt
    from utils import combine_images
    from PIL import Image

    img = combine_images(np.concatenate([x_test[:50],x_recon[:50]]))
    image = img * 255
    Image.fromarray(image.astype(np.uint8)).save("real_and_recon.png")
    print()
    print('Reconstructed images are saved to ./real_and_recon.png')
    print('-'*50)
    plt.imshow(plt.imread("real_and_recon.png", ))
    plt.show() 

def test_evaluate(sess, unary_score, test_sequence_length, transMatrix, inp_char, inp_pinyin, inp_wubi, tX_char, tX_pinyin, tX_wubi, tY):
    totalEqual = 0
    batchSize = FLAGS.batch_size
    totalLen = tX_char.shape[0]
    numBatch = int((tX_char.shape[0] - 1) / batchSize) + 1
    correct_labels = 0
    total_labels = 0

    for i in range(numBatch):
        endOff = (i + 1) * batchSize
        if endOff > totalLen:
            endOff = totalLen

        y = tY[i * batchSize:endOff]
        feed_dict = {inp_char: tX_char[i * batchSize:endOff], inp_pinyin:tX_pinyin[i * batchSize:endOff], inp_wubi: tX_wubi[i * batchSize:endOff]}
        #feed_dict_pinyin = {inp_pinyin: tX_pinyin[i * batchSize:endOff]}
        #feed_dict_wubi = {inp_wubi: tX_wubi[i * batchSize:endOff]}
        unary_score_val, test_sequence_length_val = sess.run(
            [unary_score, test_sequence_length], feed_dict)

        for tf_unary_scores_, y_, sequence_length_ in zip(
                unary_score_val, y, test_sequence_length_val):

            tf_unary_scores_ = tf_unary_scores_[:sequence_length_]
            y_ = y_[:sequence_length_]

            viterbi_sequence, _ = tf.contrib.crf.viterbi_decode(
                tf_unary_scores_, transMatrix)

            # Evaluate word-level accuracy.
            correct_labels += np.sum(np.equal(viterbi_sequence, y_))
            total_labels += sequence_length_

    cl = np.float64(correct_labels)
    tl = np.float64(total_labels)
    accuracy = 100.0 * cl / tl
    print("Accuracy: %.3f%%" % accuracy)
    return accuracy 

def test_evaluate(sess, unary_score, test_sequence_length, transMatrix, inp_char, inp_pinyin, inp_wubi, tX_char, tX_pinyin, tX_wubi, tY):
    totalEqual = 0
    batchSize = FLAGS.batch_size
    totalLen = tX_char.shape[0]
    numBatch = int((tX_char.shape[0] - 1) / batchSize) + 1
    correct_labels = 0
    total_labels = 0

    for i in range(numBatch):
        endOff = (i + 1) * batchSize
        if endOff > totalLen:
            endOff = totalLen

        y = tY[i * batchSize:endOff]
        feed_dict = {inp_char: tX_char[i * batchSize:endOff], inp_pinyin:tX_pinyin[i * batchSize:endOff], inp_wubi: tX_wubi[i * batchSize:endOff]}
        #feed_dict_pinyin = {inp_pinyin: tX_pinyin[i * batchSize:endOff]}
        #feed_dict_wubi = {inp_wubi: tX_wubi[i * batchSize:endOff]}
        unary_score_val, test_sequence_length_val = sess.run(
            [unary_score, test_sequence_length], feed_dict)

        for tf_unary_scores_, y_, sequence_length_ in zip(
                unary_score_val, y, test_sequence_length_val):

            tf_unary_scores_ = tf_unary_scores_[:sequence_length_]
            y_ = y_[:sequence_length_]

            viterbi_sequence, _ = tf.contrib.crf.viterbi_decode(
                tf_unary_scores_, transMatrix)

            # Evaluate word-level accuracy.
            correct_labels += np.sum(np.equal(viterbi_sequence, y_))
            total_labels += sequence_length_

    cl = np.float64(correct_labels)
    tl = np.float64(total_labels)
    accuracy = 100.0 * cl / tl
    print("Accuracy: %.3f%%" % accuracy)
    return accuracy 

def test_evaluate(sess, unary_score, test_sequence_length, inp, tX, tY):
    totalEqual = 0
    batchSize = FLAGS.batch_size
    totalLen = tX.shape[0]
    numBatch = int((tX.shape[0] - 1) / batchSize) + 1
    correct_labels = 0
    total_labels = 0

    for i in range(numBatch):
        endOff = (i + 1) * batchSize
        if endOff > totalLen:
            endOff = totalLen

        y = tY[i * batchSize:endOff]
        feed_dict = {inp: tX[i * batchSize:endOff]}
        unary_score_val, test_sequence_length_val = sess.run(
            [unary_score, test_sequence_length], feed_dict)

        for tf_unary_scores_, y_, sequence_length_ in zip(
                unary_score_val, y, test_sequence_length_val):

            best_sequence = tf_unary_scores_[:sequence_length_]
            y_ = y_[:sequence_length_]

            # Evaluate word-level accuracy.
            correct_labels += np.sum(np.equal(best_sequence, y_))
            total_labels += sequence_length_

    cl = np.float64(correct_labels)
    tl = np.float64(total_labels)
    accuracy = 100.0 * cl / tl

    print("Accuracy: %.3f%%" % accuracy)
    return accuracy 

def test_evaluate(sess, unary_score, test_sequence_length, transMatrix, inp_char, inp_pinyin, inp_wubi, tX_char, tX_pinyin, tX_wubi, tY):
    totalEqual = 0
    batchSize = FLAGS.batch_size
    totalLen = tX_char.shape[0]
    numBatch = int((tX_char.shape[0] - 1) / batchSize) + 1
    correct_labels = 0
    total_labels = 0

    for i in range(numBatch):
        endOff = (i + 1) * batchSize
        if endOff > totalLen:
            endOff = totalLen

        y = tY[i * batchSize:endOff]
        feed_dict = {inp_char: tX_char[i * batchSize:endOff], inp_pinyin:tX_pinyin[i * batchSize:endOff], inp_wubi: tX_wubi[i * batchSize:endOff]}
        #feed_dict_pinyin = {inp_pinyin: tX_pinyin[i * batchSize:endOff]}
        #feed_dict_wubi = {inp_wubi: tX_wubi[i * batchSize:endOff]}
        unary_score_val, test_sequence_length_val = sess.run(
            [unary_score, test_sequence_length], feed_dict)

        for tf_unary_scores_, y_, sequence_length_ in zip(
                unary_score_val, y, test_sequence_length_val):

            tf_unary_scores_ = tf_unary_scores_[:sequence_length_]
            y_ = y_[:sequence_length_]

            viterbi_sequence, _ = tf.contrib.crf.viterbi_decode(
                tf_unary_scores_, transMatrix)

            # Evaluate word-level accuracy.
            correct_labels += np.sum(np.equal(viterbi_sequence, y_))
            total_labels += sequence_length_

    cl = np.float64(correct_labels)
    tl = np.float64(total_labels)
    accuracy = 100.0 * cl / tl
    print("Accuracy: %.3f%%" % accuracy)
    return accuracy 

def test_evaluate(sess, unary_score, test_sequence_length, transMatrix, inp_char, inp_pinyin, inp_wubi,tX_char, tX_pinyin, tX_wubi, tY):
    totalEqual = 0
    batchSize = FLAGS.batch_size
    totalLen = tX_char.shape[0]
    numBatch = int((tX_char.shape[0] - 1) / batchSize) + 1
    correct_labels = 0
    total_labels = 0

    for i in range(numBatch):
        endOff = (i + 1) * batchSize
        if endOff > totalLen:
            endOff = totalLen

        y = tY[i * batchSize:endOff]
        feed_dict = {inp_char: tX_char[i * batchSize:endOff], inp_pinyin:tX_pinyin[i * batchSize:endOff], inp_wubi: tX_wubi[i * batchSize:endOff]}
        unary_score_val, test_sequence_length_val = sess.run(
            [unary_score, test_sequence_length], feed_dict)

        for tf_unary_scores_, y_, sequence_length_ in zip(
                unary_score_val, y, test_sequence_length_val):

            tf_unary_scores_ = tf_unary_scores_[:sequence_length_]
            y_ = y_[:sequence_length_]

            viterbi_sequence, _ = tf.contrib.crf.viterbi_decode(
                tf_unary_scores_, transMatrix)

            # Evaluate word-level accuracy.
            correct_labels += np.sum(np.equal(viterbi_sequence, y_))
            total_labels += sequence_length_

    cl = np.float64(correct_labels)
    tl = np.float64(total_labels)
    accuracy = 100.0 * cl / tl
    print("Accuracy: %.3f%%" % accuracy)
    return accuracy 

def test_evaluate(sess, unary_score, test_sequence_length, transMatrix, inp_char, inp_pinyin, inp_wubi, tX_char, tX_pinyin, tX_wubi, tY):
    totalEqual = 0
    batchSize = FLAGS.batch_size
    totalLen = tX_char.shape[0]
    numBatch = int((tX_char.shape[0] - 1) / batchSize) + 1
    correct_labels = 0
    total_labels = 0

    for i in range(numBatch):
        endOff = (i + 1) * batchSize
        if endOff > totalLen:
            endOff = totalLen

        y = tY[i * batchSize:endOff]
        feed_dict = {inp_char: tX_char[i * batchSize:endOff], inp_pinyin:tX_pinyin[i * batchSize:endOff], inp_wubi: tX_wubi[i * batchSize:endOff]}
        #feed_dict_pinyin = {inp_pinyin: tX_pinyin[i * batchSize:endOff]}
        #feed_dict_wubi = {inp_wubi: tX_wubi[i * batchSize:endOff]}
        unary_score_val, test_sequence_length_val = sess.run(
            [unary_score, test_sequence_length], feed_dict)

        for tf_unary_scores_, y_, sequence_length_ in zip(
                unary_score_val, y, test_sequence_length_val):

            tf_unary_scores_ = tf_unary_scores_[:sequence_length_]
            y_ = y_[:sequence_length_]

            viterbi_sequence, _ = tf.contrib.crf.viterbi_decode(
                tf_unary_scores_, transMatrix)

            # Evaluate word-level accuracy.
            correct_labels += np.sum(np.equal(viterbi_sequence, y_))
            total_labels += sequence_length_

    cl = np.float64(correct_labels)
    tl = np.float64(total_labels)
    accuracy = 100.0 * cl / tl
    print("Accuracy: %.3f%%" % accuracy)
    return accuracy 

def test_evaluate(sess, unary_score, test_sequence_length, transMatrix, inp, tX, tY):
    totalEqual = 0
    batchSize = FLAGS.batch_size
    totalLen = tX.shape[0]
    numBatch = int((tX.shape[0] - 1) / batchSize) + 1
    correct_labels = 0
    total_labels = 0

    for i in range(numBatch):
        endOff = (i + 1) * batchSize
        if endOff > totalLen:
            endOff = totalLen

        y = tY[i * batchSize:endOff]
        feed_dict = {inp: tX[i * batchSize:endOff]}
        unary_score_val, test_sequence_length_val = sess.run(
            [unary_score, test_sequence_length], feed_dict)

        for tf_unary_scores_, y_, sequence_length_ in zip(
                unary_score_val, y, test_sequence_length_val):

            tf_unary_scores_ = tf_unary_scores_[:sequence_length_]
            y_ = y_[:sequence_length_]

            viterbi_sequence, _ = tf.contrib.crf.viterbi_decode(
                tf_unary_scores_, transMatrix)

            # Evaluate word-level accuracy.
            correct_labels += np.sum(np.equal(viterbi_sequence, y_))
            total_labels += sequence_length_

    cl = np.float64(correct_labels)
    tl = np.float64(total_labels)
    accuracy = 100.0 * cl / tl
    print("Accuracy: %.3f%%" % accuracy)
    return accuracy 

def test_evaluate(sess, unary_score, test_sequence_length, transMatrix, inp_char, inp_wubi,tX_char, tX_wubi, tY):
    totalEqual = 0
    batchSize = FLAGS.batch_size
    totalLen = tX_char.shape[0]
    numBatch = int((tX_char.shape[0] - 1) / batchSize) + 1
    correct_labels = 0
    total_labels = 0

    for i in range(numBatch):
        endOff = (i + 1) * batchSize
        if endOff > totalLen:
            endOff = totalLen

        y = tY[i * batchSize:endOff]
        feed_dict = {inp_char: tX_char[i * batchSize:endOff], inp_wubi: tX_wubi[i * batchSize:endOff]}
        unary_score_val, test_sequence_length_val = sess.run(
            [unary_score, test_sequence_length], feed_dict)

        for tf_unary_scores_, y_, sequence_length_ in zip(
                unary_score_val, y, test_sequence_length_val):

            tf_unary_scores_ = tf_unary_scores_[:sequence_length_]
            y_ = y_[:sequence_length_]

            viterbi_sequence, _ = tf.contrib.crf.viterbi_decode(
                tf_unary_scores_, transMatrix)

            # Evaluate word-level accuracy.
            correct_labels += np.sum(np.equal(viterbi_sequence, y_))
            total_labels += sequence_length_

    cl = np.float64(correct_labels)
    tl = np.float64(total_labels)
    accuracy = 100.0 * cl / tl
    print("Accuracy: %.3f%%" % accuracy)
    return accuracy 

def test_evaluate(sess, unary_score, test_sequence_length, transMatrix, inp_char, inp_pinyin, inp_wubi, tX_char, tX_pinyin, tX_wubi, tY):
    totalEqual = 0
    batchSize = FLAGS.batch_size
    totalLen = tX_char.shape[0]
    numBatch = int((tX_char.shape[0] - 1) / batchSize) + 1
    correct_labels = 0
    total_labels = 0

    for i in range(numBatch):
        endOff = (i + 1) * batchSize
        if endOff > totalLen:
            endOff = totalLen

        y = tY[i * batchSize:endOff]
        feed_dict = {inp_char: tX_char[i * batchSize:endOff], inp_pinyin:tX_pinyin[i * batchSize:endOff], inp_wubi: tX_wubi[i * batchSize:endOff]}
        #feed_dict_pinyin = {inp_pinyin: tX_pinyin[i * batchSize:endOff]}
        #feed_dict_wubi = {inp_wubi: tX_wubi[i * batchSize:endOff]}
        unary_score_val, test_sequence_length_val = sess.run(
            [unary_score, test_sequence_length], feed_dict)

        for tf_unary_scores_, y_, sequence_length_ in zip(
                unary_score_val, y, test_sequence_length_val):

            tf_unary_scores_ = tf_unary_scores_[:sequence_length_]
            y_ = y_[:sequence_length_]

            viterbi_sequence, _ = tf.contrib.crf.viterbi_decode(
                tf_unary_scores_, transMatrix)

            # Evaluate word-level accuracy.
            correct_labels += np.sum(np.equal(viterbi_sequence, y_))
            total_labels += sequence_length_

    cl = np.float64(correct_labels)
    tl = np.float64(total_labels)
    accuracy = 100.0 * cl / tl
    print("Accuracy: %.3f%%" % accuracy)
    return accuracy 

def test_evaluate(sess, unary_score, test_sequence_length, transMatrix, inp_char, inp_pinyin,tX_char, tX_pinyin, tY):
    totalEqual = 0
    batchSize = FLAGS.batch_size
    totalLen = tX_char.shape[0]
    numBatch = int((tX_char.shape[0] - 1) / batchSize) + 1
    correct_labels = 0
    total_labels = 0

    for i in range(numBatch):
        endOff = (i + 1) * batchSize
        if endOff > totalLen:
            endOff = totalLen

        y = tY[i * batchSize:endOff]
        feed_dict = {inp_char: tX_char[i * batchSize:endOff], inp_pinyin:tX_pinyin[i * batchSize:endOff]}
        unary_score_val, test_sequence_length_val = sess.run(
            [unary_score, test_sequence_length], feed_dict)

        for tf_unary_scores_, y_, sequence_length_ in zip(
                unary_score_val, y, test_sequence_length_val):

            tf_unary_scores_ = tf_unary_scores_[:sequence_length_]
            y_ = y_[:sequence_length_]

            viterbi_sequence, _ = tf.contrib.crf.viterbi_decode(
                tf_unary_scores_, transMatrix)

            # Evaluate word-level accuracy.
            correct_labels += np.sum(np.equal(viterbi_sequence, y_))
            total_labels += sequence_length_

    cl = np.float64(correct_labels)
    tl = np.float64(total_labels)
    accuracy = 100.0 * cl / tl
    print("Accuracy: %.3f%%" % accuracy)
    return accuracy 

def test_evaluate(sess, unary_score, test_sequence_length, transMatrix, inp_char, inp_pinyin, inp_wubi, tX_char, tX_pinyin, tX_wubi, tY):
    totalEqual = 0
    batchSize = FLAGS.batch_size
    totalLen = tX_char.shape[0]
    numBatch = int((tX_char.shape[0] - 1) / batchSize) + 1
    correct_labels = 0
    total_labels = 0

    for i in range(numBatch):
        endOff = (i + 1) * batchSize
        if endOff > totalLen:
            endOff = totalLen

        y = tY[i * batchSize:endOff]
        feed_dict = {inp_char: tX_char[i * batchSize:endOff], inp_pinyin:tX_pinyin[i * batchSize:endOff], inp_wubi: tX_wubi[i * batchSize:endOff]}
        #feed_dict_pinyin = {inp_pinyin: tX_pinyin[i * batchSize:endOff]}
        #feed_dict_wubi = {inp_wubi: tX_wubi[i * batchSize:endOff]}
        unary_score_val, test_sequence_length_val = sess.run(
            [unary_score, test_sequence_length], feed_dict)

        for tf_unary_scores_, y_, sequence_length_ in zip(
                unary_score_val, y, test_sequence_length_val):

            tf_unary_scores_ = tf_unary_scores_[:sequence_length_]
            y_ = y_[:sequence_length_]

            viterbi_sequence, _ = tf.contrib.crf.viterbi_decode(
                tf_unary_scores_, transMatrix)

            # Evaluate word-level accuracy.
            correct_labels += np.sum(np.equal(viterbi_sequence, y_))
            total_labels += sequence_length_

    cl = np.float64(correct_labels)
    tl = np.float64(total_labels)
    accuracy = 100.0 * cl / tl
    print("Accuracy: %.3f%%" % accuracy)
    return accuracy 

def test_evaluate(sess, unary_score, test_sequence_length, transMatrix, inp_char, inp_pinyin, inp_wubi,tX_char, tX_pinyin, tX_wubi, tY):
    totalEqual = 0
    batchSize = FLAGS.batch_size
    totalLen = tX_char.shape[0]
    numBatch = int((tX_char.shape[0] - 1) / batchSize) + 1
    correct_labels = 0
    total_labels = 0

    for i in range(numBatch):
        endOff = (i + 1) * batchSize
        if endOff > totalLen:
            endOff = totalLen

        y = tY[i * batchSize:endOff]
        feed_dict = {inp_char: tX_char[i * batchSize:endOff], inp_pinyin:tX_pinyin[i * batchSize:endOff], inp_wubi: tX_wubi[i * batchSize:endOff]}
        unary_score_val, test_sequence_length_val = sess.run(
            [unary_score, test_sequence_length], feed_dict)

        for tf_unary_scores_, y_, sequence_length_ in zip(
                unary_score_val, y, test_sequence_length_val):

            tf_unary_scores_ = tf_unary_scores_[:sequence_length_]
            y_ = y_[:sequence_length_]

            viterbi_sequence, _ = tf.contrib.crf.viterbi_decode(
                tf_unary_scores_, transMatrix)

            # Evaluate word-level accuracy.
            correct_labels += np.sum(np.equal(viterbi_sequence, y_))
            total_labels += sequence_length_

    cl = np.float64(correct_labels)
    tl = np.float64(total_labels)
    accuracy = 100.0 * cl / tl
    print("Accuracy: %.3f%%" % accuracy)
    return accuracy 

def test_evaluate(sess, unary_score, test_sequence_length, transMatrix, inp, tX, tY):
    totalEqual = 0
    batchSize = FLAGS.batch_size
    totalLen = tX.shape[0]
    numBatch = int((tX.shape[0] - 1) / batchSize) + 1
    correct_labels = 0
    total_labels = 0

    for i in range(numBatch):
        endOff = (i + 1) * batchSize
        if endOff > totalLen:
            endOff = totalLen

        y = tY[i * batchSize:endOff]
        feed_dict = {inp: tX[i * batchSize:endOff]}
        unary_score_val, test_sequence_length_val = sess.run(
            [unary_score, test_sequence_length], feed_dict)

        for tf_unary_scores_, y_, sequence_length_ in zip(
                unary_score_val, y, test_sequence_length_val):

            tf_unary_scores_ = tf_unary_scores_[:sequence_length_]
            y_ = y_[:sequence_length_]

            viterbi_sequence, _ = tf.contrib.crf.viterbi_decode(
                tf_unary_scores_, transMatrix)

            # Evaluate word-level accuracy.
            correct_labels += np.sum(np.equal(viterbi_sequence, y_))
            total_labels += sequence_length_

    cl = np.float64(correct_labels)
    tl = np.float64(total_labels)
    accuracy = 100.0 * cl / tl
    print("Accuracy: %.3f%%" % accuracy)
    return accuracy 

def test_evaluate(sess, unary_score, test_sequence_length, transMatrix, inp_char, inp_pinyin, inp_wubi, tX_char, tX_pinyin, tX_wubi, tY):
    totalEqual = 0
    batchSize = FLAGS.batch_size
    totalLen = tX_char.shape[0]
    numBatch = int((tX_char.shape[0] - 1) / batchSize) + 1
    correct_labels = 0
    total_labels = 0

    for i in range(numBatch):
        endOff = (i + 1) * batchSize
        if endOff > totalLen:
            endOff = totalLen

        y = tY[i * batchSize:endOff]
        feed_dict = {inp_char: tX_char[i * batchSize:endOff], inp_pinyin:tX_pinyin[i * batchSize:endOff], inp_wubi: tX_wubi[i * batchSize:endOff]}
        #feed_dict_pinyin = {inp_pinyin: tX_pinyin[i * batchSize:endOff]}
        #feed_dict_wubi = {inp_wubi: tX_wubi[i * batchSize:endOff]}
        unary_score_val, test_sequence_length_val = sess.run(
            [unary_score, test_sequence_length], feed_dict)

        for tf_unary_scores_, y_, sequence_length_ in zip(
                unary_score_val, y, test_sequence_length_val):

            tf_unary_scores_ = tf_unary_scores_[:sequence_length_]
            y_ = y_[:sequence_length_]

            viterbi_sequence, _ = tf.contrib.crf.viterbi_decode(
                tf_unary_scores_, transMatrix)

            # Evaluate word-level accuracy.
            correct_labels += np.sum(np.equal(viterbi_sequence, y_))
            total_labels += sequence_length_

    cl = np.float64(correct_labels)
    tl = np.float64(total_labels)
    accuracy = 100.0 * cl / tl
    print("Accuracy: %.3f%%" % accuracy)
    return accuracy 

def test_evaluate(sess, unary_score, test_sequence_length, transMatrix, inp_char, inp_pinyin, tX_char, tX_pinyin, tY):
    totalEqual = 0
    batchSize = FLAGS.batch_size
    totalLen = tX_char.shape[0]
    numBatch = int((tX_char.shape[0] - 1) / batchSize) + 1
    correct_labels = 0
    total_labels = 0

    for i in range(numBatch):
        endOff = (i + 1) * batchSize
        if endOff > totalLen:
            endOff = totalLen

        y = tY[i * batchSize:endOff]
        feed_dict = {inp_char: tX_char[i * batchSize:endOff], inp_pinyin:tX_pinyin[i * batchSize:endOff]}
        #feed_dict_pinyin = {inp_pinyin: tX_pinyin[i * batchSize:endOff]}
        #feed_dict_wubi = {inp_wubi: tX_wubi[i * batchSize:endOff]}
        unary_score_val, test_sequence_length_val = sess.run(
            [unary_score, test_sequence_length], feed_dict)

        for tf_unary_scores_, y_, sequence_length_ in zip(
                unary_score_val, y, test_sequence_length_val):

            tf_unary_scores_ = tf_unary_scores_[:sequence_length_]
            y_ = y_[:sequence_length_]

            viterbi_sequence, _ = tf.contrib.crf.viterbi_decode(
                tf_unary_scores_, transMatrix)

            # Evaluate word-level accuracy.
            correct_labels += np.sum(np.equal(viterbi_sequence, y_))
            total_labels += sequence_length_

    cl = np.float64(correct_labels)
    tl = np.float64(total_labels)
    accuracy = 100.0 * cl / tl
    print("Accuracy: %.3f%%" % accuracy)
    return accuracy 

def test_evaluate(sess, unary_score, test_sequence_length, transMatrix, inp_char, inp_wubi, tX_char, tX_wubi, tY):
    totalEqual = 0
    batchSize = FLAGS.batch_size
    totalLen = tX_char.shape[0]
    numBatch = int((tX_char.shape[0] - 1) / batchSize) + 1
    correct_labels = 0
    total_labels = 0

    for i in range(numBatch):
        endOff = (i + 1) * batchSize
        if endOff > totalLen:
            endOff = totalLen

        y = tY[i * batchSize:endOff]
        feed_dict = {inp_char: tX_char[i * batchSize:endOff], inp_wubi: tX_wubi[i * batchSize:endOff]}
        #feed_dict_pinyin = {inp_pinyin: tX_pinyin[i * batchSize:endOff]}
        #feed_dict_wubi = {inp_wubi: tX_wubi[i * batchSize:endOff]}
        unary_score_val, test_sequence_length_val = sess.run(
            [unary_score, test_sequence_length], feed_dict)

        for tf_unary_scores_, y_, sequence_length_ in zip(
                unary_score_val, y, test_sequence_length_val):

            tf_unary_scores_ = tf_unary_scores_[:sequence_length_]
            y_ = y_[:sequence_length_]

            viterbi_sequence, _ = tf.contrib.crf.viterbi_decode(
                tf_unary_scores_, transMatrix)

            # Evaluate word-level accuracy.
            correct_labels += np.sum(np.equal(viterbi_sequence, y_))
            total_labels += sequence_length_

    cl = np.float64(correct_labels)
    tl = np.float64(total_labels)
    accuracy = 100.0 * cl / tl
    print("Accuracy: %.3f%%" % accuracy)
    return accuracy 

def test_evaluate(sess, unary_score, test_sequence_length, transMatrix, inp_char, inp_pinyin, inp_wubi,tX_char, tX_pinyin, tX_wubi, tY):
    totalEqual = 0
    batchSize = FLAGS.batch_size
    totalLen = tX_char.shape[0]
    numBatch = int((tX_char.shape[0] - 1) / batchSize) + 1
    correct_labels = 0
    total_labels = 0

    for i in range(numBatch):
        endOff = (i + 1) * batchSize
        if endOff > totalLen:
            endOff = totalLen

        y = tY[i * batchSize:endOff]
        feed_dict = {inp_char: tX_char[i * batchSize:endOff], inp_pinyin:tX_pinyin[i * batchSize:endOff], inp_wubi: tX_wubi[i * batchSize:endOff]}
        unary_score_val, test_sequence_length_val = sess.run(
            [unary_score, test_sequence_length], feed_dict)

        for tf_unary_scores_, y_, sequence_length_ in zip(
                unary_score_val, y, test_sequence_length_val):

            tf_unary_scores_ = tf_unary_scores_[:sequence_length_]
            y_ = y_[:sequence_length_]

            viterbi_sequence, _ = tf.contrib.crf.viterbi_decode(
                tf_unary_scores_, transMatrix)

            # Evaluate word-level accuracy.
            correct_labels += np.sum(np.equal(viterbi_sequence, y_))
            total_labels += sequence_length_

    cl = np.float64(correct_labels)
    tl = np.float64(total_labels)
    accuracy = 100.0 * cl / tl
    print("Accuracy: %.3f%%" % accuracy)
    return accuracy 

def line_distance(coords):
    """Return total road distance in kilometers"""
    dist = []
    for i in range(0, len(coords) - 1):
        dist.append(great_circle_dist(coords[i], coords[i + 1]))
    return np.sum(dist) 

def test_init_collumn():
    test_cols = spatial_pooler_instance.init_collumn(500,600,0.75)

    assert type(test_cols[0]['permanences']) == type(np.array([0.5],dtype=np.float))
    assert np.sum(test_cols[0]['potential_pool'] > 0) > 0.6 # The potential pool should be at least 60 % of all collumns if not more 

def test_run():
    input_sp = np.random.randn(100) > 0
    output_sp = spatial_pooler_instance.run(input_sp)

    # Has the same shape as desired
    assert output_sp.shape[0] == 50

    # Less than 20% of the output_sp is on.
    # Sparsity
    assert np.sum(output_sp)/output_sp.shape[0] < 0.2

    assert type(output_sp) == type(np.array([],dtype=np.bool_)) 

def init_collumn(self,num_collumns,input_size,size_of_potential_pool=0.75):
        collumns = [{} for i in range(num_collumns)]
        for i in range(num_collumns):
            collumns[i]['potential_pool'] = np.random.rand(input_size) > size_of_potential_pool # Create a random potential pool with a certain percantage of potential connections
            collumns[i]['permanences'] = np.random.rand(np.sum(collumns[i]['potential_pool'])) # Random values for the permanence between  0-1
        return collumns 

def activation(self,state):
        """
        Sum state and then compare that to threshhold_activation
        """
        length = state.shape[0]
        return ((np.sum(state)/length) > self.threshhold_activation) 

def np_softmax(x, t=1):
    x = x / t
    x = x - np.max(x, axis=-1, keepdims=True)
    ex = np.exp(x)
    return ex / np.sum(ex, axis=-1, keepdims=True) 

def __call__(
            self,
            X,
            Y,
            M,
            clf_logits,
            lm_logits=None,
            only_return_losses=False):
        # Language modeling loss
        if lm_logits is not None:
            x_shifted = X[:, :, 1:, 0].reshape(-1)           # Shape: 252
            M = M.reshape(-1, M.shape[2])
            lm_losses = self.lm_criterion(lm_logits, x_shifted)
            lm_losses = lm_losses.reshape(
                X.shape[0] * X.shape[1], X.shape[2] - 1)
            lm_losses = lm_losses * M[:, 1:]
            lm_losses = F.sum(lm_losses, axis=1) / F.sum(M[:, 1:], axis=1)
        # Classification loss
        clf_losses = self.clf_criterion(clf_logits, Y)
        if only_return_losses:
            return (
                clf_losses,
                lm_losses) if lm_logits is not None else clf_losses

        if self.lm_coef > 0 and lm_logits is not None:
            train_loss = F.sum(clf_losses) + self.lm_coef * F.sum(lm_losses)
        else:
            train_loss = F.sum(clf_losses)

        if self.opt is not None:
            self.opt.target.cleargrads()
        train_loss.backward()
        if self.opt is not None:
            self.opt.update()
            self.opt.target.cleargrads()
        return train_loss.array 

def compute_all_scores(self):
		self.class_performances = {}
		for i in range(len(self.labels)):
			tp = np.float32(self.matrix[i][i])
			fp_plus_tp = np.float32(np.sum(self.matrix, axis = 0)[i])
			fn_plus_tp = np.float32(np.sum(self.matrix, axis = 1)[i])
			p = tp / fp_plus_tp
			r = tp / fn_plus_tp
			self.class_performances[self.labels[i]] = (p, r, 2*p*r/(p+r))

		self.microf1 = np.float32(np.trace(self.matrix)) / np.sum(self.matrix)
		self.macrof1 = float(sum([x[2] for x in self.class_performances.values()])) / float(len(self.labels))
		self.macroP = float(sum([x[0] for x in self.class_performances.values()])) / float(len(self.labels))
		self.macroR = float(sum([x[1] for x in self.class_performances.values()])) / float(len(self.labels))
		self.accuracy = float(sum([self.matrix[i, i] for i in range(len(self.labels))])) / float(np.sum(self.matrix)) 

def label_new_vertex(g, o_props, label_steps=False):
    '''label_new_vertex

    Parameters
    ----------
    g : :obj:`graph_tool.Graph` 
        A graph.
    o_props : :obj:`dict` 
        A dictionary of vertex property maps containing the vertex occurrence 
        values at each step.
    label_steps : :obj:`bool` 
        If `True`, returns a vertex property map` that indicates the first step
        that each vertex appeared.

    Returns
    -------
        new_vertex_props : :obj:`dict`
        vertex_step_prop : :obj:`graph_tool.PropertyMap`
    '''
    new_vertex_props = {}
    _vertex_tracker = g.new_vertex_property('bool')
    for step, o_prop in o_props.items():
        new_vertex_prop = g.new_vertex_property('bool')
        new_vertex_prop.a = (o_prop.a > 0) & (_vertex_tracker.a == False)
        new_vertex_props[step] = new_vertex_prop
        _vertex_tracker.a = _vertex_tracker.a + new_vertex_prop.a
    if label_steps:
        vertex_step_prop = g.new_vertex_property('int')
        start = 0
        end = np.sum(new_vertex_props[steps[0]].a)
        for i, step in enumerate(steps):
            if i > 0:
                start = int(start + np.sum(new_vertex_props[step - 1].a))
                end = int(end + np.sum(new_vertex_props[step].a))
            vertex_step_prop.a[start:end] = step
        return (new_vertex_props, vertex_step_prop)
    else:
        return new_vertex_props 

def maxlk_sigma(m, xold=None, eps=1e-8, max_iter=100):
    '''Maximum likelihood equation to estimate sigma from gamma distributed values'''

    sum_m2 = np.sum(m**2)
    K = m.size
    sum_log_m2 = np.sum(np.log(m**2))

    def f(sigma):
        return digamma(sum_m2/(2*K*sigma**2)) - sum_log_m2/K + np.log(2*sigma**2)

    def fprime(sigma):
        return -sum_m2 * polygamma(1, sum_m2/(2*K*sigma**2)) / (K*sigma**3) + 2/sigma

    if xold is None:
        xold = m.std()

    for _ in range(max_iter):

        xnew = xold - f(xold) / fprime(xold)

        if np.abs(xold - xnew) < eps:
            break

        xold = xnew

    return xnew 

def _split_channels(total_filters, num_groups):
    split = [total_filters // num_groups for _ in range(num_groups)]
    split[0] += total_filters - sum(split)
    return split


# Obtained from https://github.com/tensorflow/tpu/blob/master/models/official/mnasnet/mixnet/mixnet_model.py 

def shared(shape, name):
#{{{
    """
    Create a shared object of a numpy array.
    """ 
    init=initializations.get('glorot_uniform');
    if len(shape) == 1:
        value = np.zeros(shape)  # bias are initialized with zeros
        return theano.shared(value=value.astype(theano.config.floatX), name=name)
    else:
        drange = np.sqrt(6. / (np.sum(shape)))
        value = drange * np.random.uniform(low=-1.0, high=1.0, size=shape)
        return init(shape=shape,name=name);
#}}} 

def voc_ap(rec, prec, use_07_metric=False):
  """ ap = voc_ap(rec, prec, [use_07_metric])
  Compute VOC AP given precision and recall.
  If use_07_metric is true, uses the
  VOC 07 11 point method (default:False).
  """
  if use_07_metric:
    # 11 point metric
    ap = 0.
    for t in np.arange(0., 1.1, 0.1):
      if np.sum(rec >= t) == 0:
        p = 0
      else:
        p = np.max(prec[rec >= t])
      ap = ap + p / 11.
  else:
    # correct AP calculation
    # first append sentinel values at the end
    mrec = np.concatenate(([0.], rec, [1.]))
    mpre = np.concatenate(([0.], prec, [0.]))

    # compute the precision envelope
    for i in range(mpre.size - 1, 0, -1):
      mpre[i - 1] = np.maximum(mpre[i - 1], mpre[i])

    # to calculate area under PR curve, look for points
    # where X axis (recall) changes value
    i = np.where(mrec[1:] != mrec[:-1])[0]

    # and sum (\Delta recall) * prec
    ap = np.sum((mrec[i + 1] - mrec[i]) * mpre[i + 1])
  return ap 

def calc_elbo_for_single_doc__simplified_from_N_d_K(
        word_ct_d_Ud=None,
        log_lik_d_UdK=None,
        alpha_K=None,
        N_d_K=None):
    theta_d_K = N_d_K + alpha_K
    E_log_pi_d_K = digamma(theta_d_K) - digamma(np.sum(theta_d_K))
    log_resp_d_UK = log_lik_d_UdK + E_log_pi_d_K[np.newaxis,:]
    return (
        np.inner(word_ct_d_Ud, logsumexp(log_resp_d_UK, axis=1))
        + c_Dir_1D(alpha_K) - c_Dir_1D(theta_d_K)
        + np.inner(alpha_K - theta_d_K, E_log_pi_d_K)
        ) 

def c_Dir_1D(alpha_K):
    return gammaln(np.sum(alpha_K)) - np.sum(gammaln(alpha_K)) 

def calc_pairwise_cooccurance_counts(
        x_csr_DV=None,
        dataset=None,
        ):
    """ Calculate word cooccurances across a corpus of D documents

    Returns
    -------
    ndocs_V : 1D array, size V
        entry v counts the number of documents that contain v at least once
    ndocs_csc_VV : 2D csc sparse matrix, V x V
        entry v,w counts the number of documents which contain
        the word pair (v, w) at least once

    Examples
    --------
    >>> x_DV = np.arange(6)[:,np.newaxis] * np.hstack([np.eye(6), np.zeros((6, 3))])
    >>> x_DV[:3, :3] += 1
    >>> x_DV[4, 5] += 17
    >>> ndocs_V, ndocs_csc_VV = calc_pairwise_cooccurance_counts(x_csr_DV=x_DV)
    >>> ndocs_V.astype(np.int32).tolist()
    [3, 3, 3, 1, 1, 2, 0, 0, 0]
    >>> ndocs_csc_VV.toarray()[:3, :3]
    array([[ 3.,  3.,  3.],
           [ 3.,  3.,  3.],
           [ 3.,  3.,  3.]])
    """
    if x_csr_DV is None:
        x_csr_DV = dataset['x_csr_DV']
    x_csr_DV = scipy.sparse.csr_matrix(x_csr_DV, dtype=np.float64)

    binx_csr_DV = x_csr_DV.copy()
    binx_csr_DV.data[:] = 1.0

    ndocs_V = np.squeeze(np.asarray(binx_csr_DV.sum(axis=0)))

    ndocs_csc_VV = (binx_csr_DV.T * binx_csr_DV).tocsc()
    return ndocs_V, ndocs_csc_VV 

def calcfrac(bmask):
    return np.sum(bmask) / float(bmask.size) 

def verify_min_examples_per_label(y_NC, min_examples_per_label):
    '''
    
    Examples
    --------
    >>> y_all_0 = np.zeros(10)
    >>> y_all_1 = np.ones(30)
    >>> verify_min_examples_per_label(y_all_0, 3)
    False
    >>> verify_min_examples_per_label(y_all_1, 2)
    False
    >>> verify_min_examples_per_label(np.hstack([y_all_0, y_all_1]), 10)
    True
    >>> verify_min_examples_per_label(np.eye(3), 2)
    False
    '''
    if y_NC.ndim < 2:
        y_NC = np.atleast_2d(y_NC).T
    n_C = np.sum(np.isfinite(y_NC), axis=0)
    n_pos_C = n_C * np.nanmean(y_NC, axis=0)
    min_neg = np.max(n_C - n_pos_C)
    min_pos = np.min(n_pos_C)
    if min_pos < min_examples_per_label:
        return False
    elif min_neg < min_examples_per_label:
        return False
    return True 

def train_test_validation(self, M, train_idx, test_idx, valid_idx, n_steps=100000, result_path='result/'):
        nonzero_user_idx = M.nonzero()[0]
        nonzero_item_idx = M.nonzero()[1]

        trainM = np.zeros(M.shape)
        trainM[nonzero_user_idx[train_idx], nonzero_item_idx[train_idx]] = M[nonzero_user_idx[train_idx], nonzero_item_idx[train_idx]]

        validM = np.zeros(M.shape)
        validM[nonzero_user_idx[valid_idx], nonzero_item_idx[valid_idx]] = M[nonzero_user_idx[valid_idx], nonzero_item_idx[valid_idx]]

        testM = np.zeros(M.shape)
        testM[nonzero_user_idx[test_idx], nonzero_item_idx[test_idx]] = M[nonzero_user_idx[test_idx], nonzero_item_idx[test_idx]]

        for i in range(self.num_user):
            if np.sum(trainM[i]) == 0:
                testM[i] = 0
                validM[i] = 0

        train_writer = tf.summary.FileWriter(
            result_path + '/train', graph=self.sess.graph)

        best_val_rmse = np.inf
        best_test_rmse = 0

        self.sess.run(tf.global_variables_initializer())
        for step in range(1, n_steps):
            feed_dict = {self.user: trainM, self.valid_rating:validM, self.test_rating:testM}

            _, mse, mae, valid_rmse, test_rmse,  summary_str = self.sess.run(
                [self.train_step, self.MSE, self.MAE, self.valid_RMSE, self.test_RMSE, self.summary_op], feed_dict=feed_dict)
            train_writer.add_summary(summary_str, step)
            print("Iter {0} Train RMSE:{1}, Valid RMSE:{2}, Test RMSE:{3}".format(step, np.sqrt(mse), valid_rmse, test_rmse))

            if best_val_rmse > valid_rmse:
                best_val_rmse = valid_rmse
                best_test_rmse = test_rmse

        self.saver.save(self.sess, result_path + "/model.ckpt")
        return best_test_rmse 

def extract_quaternion(R):
    d = np.diagonal(R)
    t = np.sum(d)
    if t + 1 < 0.25:
        symmetric_mat = R + R.T
        asymmetric_mat = R - R.T
        symmetric_diag = np.diagonal(symmetric_mat)
        i_max = np.argmax(symmetric_diag)
        q = np.empty(4)
        if i_max == 0:
            q[1] = np.sqrt(symmetric_diag[0] - t + 1) / 2
            normalizer = 1 / q[1]
            q[2] = symmetric_mat[1, 0] / 4 * normalizer
            q[3] = symmetric_mat[2, 0] / 4 * normalizer
            q[0] = asymmetric_mat[2, 1] / 4 * normalizer
        elif i_max == 1:
            q[2] = np.sqrt(symmetric_diag[1] - t + 1) / 2
            normalizer = 1 / q[2]
            q[1] = symmetric_mat[1, 0] / 4 * normalizer
            q[3] = symmetric_mat[2, 1] / 4 * normalizer
            q[0] = asymmetric_mat[0, 2] / 4 * normalizer
        elif i_max == 2:
            q[3] = np.sqrt(symmetric_diag[2] - t + 1) / 2
            normalizer = 1 / q[3]
            q[1] = symmetric_mat[2, 0] / 4 * normalizer
            q[2] = symmetric_mat[1, 2] / 4 * normalizer
            q[0] = asymmetric_mat[1, 0] / 4 * normalizer
    else:
        r = np.sqrt(1+t)
        s = 0.5 / r
        q = np.array([0.5*r, (R[2, 1] - R[1, 2])*s, (R[0, 2] - R[2, 0])*s, (R[1, 0] - R[0, 1])*s])

    return q 

def SID(gt, rc):
    N = gt.shape[0]
    err = np.zeros(N)
    for i in range(N):
        err[i] = abs(np.sum(rc[i] * np.log10((rc[i] + 1e-3) / (gt[i] + 1e-3))) +
                        np.sum(gt[i] * np.log10((gt[i] + 1e-3) / (rc[i] + 1e-3))))
    return err.mean() 

def APPSA(gt, rc):
    nom = np.sum(gt * rc, axis=0)
    denom = np.linalg.norm(gt, axis=0) * np.linalg.norm(rc, axis=0)
    
    cos = np.where((nom / (denom + 1e-3)) > 1, 1, (nom / (denom + 1e-3)))
    appsa = np.arccos(cos)
    
    return np.sum(appsa) / (gt.shape[1] * gt.shape[0]) 

def SID(gt, rc):
    N = gt.shape[2]
    err = np.zeros(N)
    for i in range(N):
        err[i] = abs(np.sum(rc[:,:,i] * np.log10((rc[:,:,i] + 1e-3)/(gt[:,:,i] + 1e-3))) +
                     np.sum(gt[:,:,i] * np.log10((gt[:,:,i] + 1e-3)/(rc[:,:,i] + 1e-3))))
    SIDs = err / (gt.shape[1] * gt.shape[0])
    return np.mean(SIDs) 

def APPSA(gt, rc):
    nom = np.sum(gt * rc, axis=0)
    denom = np.linalg.norm(gt, axis=0) * np.linalg.norm(rc, axis=0)
    
    cos = np.where((nom / (denom + 1e-3)) > 1, 1, (nom / (denom + 1e-3)))
    appsa = np.arccos(cos)
    
    return np.sum(appsa) / (gt.shape[1] * gt.shape[0]) 

def possibilities_generator(
        prior, min_pos, max_start_pos, constraint_len, total_filled):
    """
    Given a row prior, a min_pos, max_start_pos, and constraint length,
    yield each potential row

    prior is an array of:
        -1 (unknown),
        0 (definitely empty),
        1 (definitely filled)
    """
    prior_filled = np.zeros(len(prior)).astype(bool)
    prior_filled[prior == 1] = True
    prior_empty = np.zeros(len(prior)).astype(bool)
    prior_empty[prior == 0] = True
    for start_pos in range(min_pos, max_start_pos + 1):
        possible = -1 * np.ones(len(prior))
        possible[start_pos:start_pos + constraint_len] = 1
        if start_pos + constraint_len < len(possible):
            possible[start_pos + constraint_len] = 0
        if start_pos > 0:
            possible[start_pos - 1] = 0

        # add in the prior
        possible[np.logical_and(possible == -1, prior == 0)] = 0
        possible[np.logical_and(possible == -1, prior == 1)] = 1

        # if contradiction with prior, continue
        # 1. possible changes prior = 1 to something else
        # 2. possible changes prior = 0 to something else
        # 3. everything is assigned in possible but there are not
        #    enough filled in
        # 4. possible changes nothing about the prior
        if np.any(possible[np.where(prior == 1)[0]] != 1) or \
                np.any(possible[np.where(prior == 0)[0]] != 0) or \
                np.sum(possible == 1) > total_filled or \
                (np.all(possible >= 0) and np.sum(possible == 1) <
                    total_filled) or \
                np.all(prior == possible):
            continue
        yield possible