def svm_loss(x, y):
"""
Computes the loss and gradient using for multiclass SVM classification.
Inputs:
- x: Input data, of shape (N, C) where x[i, j] is the score for the jth class
for the ith input.
- y: Vector of labels, of shape (N,) where y[i] is the label for x[i] and
0 <= y[i] < C
Returns a tuple of:
- loss: Scalar giving the loss
- dx: Gradient of the loss with respect to x
"""
N = x.shape[0]
correct_class_scores = x[np.arange(N), y]
margins = np.maximum(0, x - correct_class_scores[:, np.newaxis] + 1.0)
margins[np.arange(N), y] = 0
loss = np.sum(margins) / N
num_pos = np.sum(margins > 0, axis=1)
dx = np.zeros_like(x)
dx[margins > 0] = 1
dx[np.arange(N), y] -= num_pos
dx /= N
return loss, dx
python类maximum()的实例源码
def random_hsv_image(bgr_image, delta_hue, delta_sat_scale, delta_val_scale):
hsv_image = cv2.cvtColor(bgr_image, cv2.COLOR_BGR2HSV).astype(np.float32)
# hue
hsv_image[:, :, 0] += int((np.random.rand() * delta_hue * 2 - delta_hue) * 255)
# sat
sat_scale = 1 + np.random.rand() * delta_sat_scale * 2 - delta_sat_scale
hsv_image[:, :, 1] *= sat_scale
# val
val_scale = 1 + np.random.rand() * delta_val_scale * 2 - delta_val_scale
hsv_image[:, :, 2] *= val_scale
hsv_image[hsv_image < 0] = 0
hsv_image[hsv_image > 255] = 255
hsv_image = hsv_image.astype(np.uint8)
bgr_image = cv2.cvtColor(hsv_image, cv2.COLOR_HSV2BGR)
return bgr_image
# non maximum suppression
def reshape_to_yolo_size(img):
input_width, input_height = img.size
min_pixel = 320.0
#max_pixel = 608
max_pixel = 1024.0
min_edge = np.minimum(input_width, input_height)
if min_edge < min_pixel:
input_width *= min_pixel / min_edge
input_height *= min_pixel / min_edge
max_edge = np.maximum(input_width, input_height)
if max_edge > max_pixel:
input_width *= max_pixel / max_edge
input_height *= max_pixel / max_edge
input_width = int(input_width / 32.0 + round(input_width % 32 / 32.0)) * 32
input_height = int(input_height / 32.0 + round(input_height % 32 / 32.0)) * 32
img = img.resize((input_width, input_height))
return img
def test_reduce(self):
dflt = np.typecodes['AllFloat']
dint = np.typecodes['AllInteger']
seq1 = np.arange(11)
seq2 = seq1[::-1]
func = np.maximum.reduce
for dt in dint:
tmp1 = seq1.astype(dt)
tmp2 = seq2.astype(dt)
assert_equal(func(tmp1), 10)
assert_equal(func(tmp2), 10)
for dt in dflt:
tmp1 = seq1.astype(dt)
tmp2 = seq2.astype(dt)
assert_equal(func(tmp1), 10)
assert_equal(func(tmp2), 10)
tmp1[::2] = np.nan
tmp2[::2] = np.nan
assert_equal(func(tmp1), np.nan)
assert_equal(func(tmp2), np.nan)
def test_truth_table_logical(self):
# 2, 3 and 4 serves as true values
input1 = [0, 0, 3, 2]
input2 = [0, 4, 0, 2]
typecodes = (np.typecodes['AllFloat']
+ np.typecodes['AllInteger']
+ '?') # boolean
for dtype in map(np.dtype, typecodes):
arg1 = np.asarray(input1, dtype=dtype)
arg2 = np.asarray(input2, dtype=dtype)
# OR
out = [False, True, True, True]
for func in (np.logical_or, np.maximum):
assert_equal(func(arg1, arg2).astype(bool), out)
# AND
out = [False, False, False, True]
for func in (np.logical_and, np.minimum):
assert_equal(func(arg1, arg2).astype(bool), out)
# XOR
out = [False, True, True, False]
for func in (np.logical_xor, np.not_equal):
assert_equal(func(arg1, arg2).astype(bool), out)
def test_minmax_func(self):
# Tests minimum and maximum.
(x, y, a10, m1, m2, xm, ym, z, zm, xf) = self.d
# max doesn't work if shaped
xr = np.ravel(x)
xmr = ravel(xm)
# following are true because of careful selection of data
assert_equal(max(xr), maximum(xmr))
assert_equal(min(xr), minimum(xmr))
assert_equal(minimum([1, 2, 3], [4, 0, 9]), [1, 0, 3])
assert_equal(maximum([1, 2, 3], [4, 0, 9]), [4, 2, 9])
x = arange(5)
y = arange(5) - 2
x[3] = masked
y[0] = masked
assert_equal(minimum(x, y), where(less(x, y), x, y))
assert_equal(maximum(x, y), where(greater(x, y), x, y))
assert_(minimum(x) == 0)
assert_(maximum(x) == 4)
x = arange(4).reshape(2, 2)
x[-1, -1] = masked
assert_equal(maximum(x), 2)
def applyPadding(inputImg, sampleSizes, receptiveField) :
receptiveField_arr = np.asarray(receptiveField, dtype="int16")
inputImg_arr = np.asarray(inputImg.shape,dtype="int16")
receptiveField = np.array(receptiveField, dtype="int16")
left_padding = (receptiveField - 1) / 2
right_padding = receptiveField - 1 - left_padding
extra_padding = np.maximum(0, np.asarray(sampleSizes,dtype="int16")-(inputImg_arr+left_padding+right_padding))
right_padding += extra_padding
paddingValues = ( (left_padding[0],right_padding[0]),
(left_padding[1],right_padding[1]),
(left_padding[2],right_padding[2]))
paddedImage = lib.pad(inputImg, paddingValues, mode='reflect' )
return [paddedImage, paddingValues]
# ----- Apply unpadding ---------
def _natural_cubic_spline_basis_expansion(xpts,knots):
num_knots = len(knots)
num_pts = len(xpts)
outmat = np.zeros((num_pts,num_knots))
outmat[:,0]= np.ones(num_pts)
outmat[:,1] = xpts
def make_func_H(k):
def make_func_d(k):
def func_d(x):
denom = knots[-1] - knots[k-1]
numer = np.maximum(x-knots[k-1],np.zeros(len(x)))**3 - np.maximum(x-knots[-1],np.zeros(len(x)))**3
return numer/denom
return func_d
def func_H(x):
d_fun_k = make_func_d(k)
d_fun_Km1 = make_func_d(num_knots-1)
return d_fun_k(x) - d_fun_Km1(x)
return func_H
for i in range(1,num_knots-1):
curr_H_fun = make_func_H(i)
outmat[:,i+1] = curr_H_fun(xpts)
return outmat
def batch_iou(proposals, gt):
bboxes = np.transpose(proposals).reshape((4, -1, 1))
bboxes_x1 = bboxes[0]
bboxes_x2 = bboxes[0]+bboxes[2]
bboxes_y1 = bboxes[1]
bboxes_y2 = bboxes[1]+bboxes[3]
gt = np.transpose(gt).reshape((4, 1, -1))
gt_x1 = gt[0]
gt_x2 = gt[0]+gt[2]
gt_y1 = gt[1]
gt_y2 = gt[1]+gt[3]
widths = np.maximum(0, np.minimum(bboxes_x2, gt_x2) -
np.maximum(bboxes_x1, gt_x1))
heights = np.maximum(0, np.minimum(bboxes_y2, gt_y2) -
np.maximum(bboxes_y1, gt_y1))
intersection = widths*heights
union = bboxes[2]*bboxes[3] + gt[2]*gt[3] - intersection
return (intersection / union)
def batch_iou(proposals, gt):
bboxes = np.transpose(proposals).reshape((4, -1, 1))
bboxes_x1 = bboxes[0]
bboxes_x2 = bboxes[0]+bboxes[2]
bboxes_y1 = bboxes[1]
bboxes_y2 = bboxes[1]+bboxes[3]
gt = np.transpose(gt).reshape((4, 1, -1))
gt_x1 = gt[0]
gt_x2 = gt[0]+gt[2]
gt_y1 = gt[1]
gt_y2 = gt[1]+gt[3]
widths = np.maximum(0, np.minimum(bboxes_x2, gt_x2) -
np.maximum(bboxes_x1, gt_x1))
heights = np.maximum(0, np.minimum(bboxes_y2, gt_y2) -
np.maximum(bboxes_y1, gt_y1))
intersection = widths*heights
union = bboxes[2]*bboxes[3] + gt[2]*gt[3] - intersection
return (intersection / union)
def decode_bboxes(tcoords, anchors):
var_x, var_y, var_w, var_h = config['prior_variance']
t_x = tcoords[:, 0]*var_x
t_y = tcoords[:, 1]*var_y
t_w = tcoords[:, 2]*var_w
t_h = tcoords[:, 3]*var_h
a_w = anchors[:, 2]
a_h = anchors[:, 3]
a_x = anchors[:, 0]+a_w/2
a_y = anchors[:, 1]+a_h/2
x = t_x*a_w + a_x
y = t_y*a_h + a_y
w = tf.exp(t_w)*a_w
h = tf.exp(t_h)*a_h
x1 = tf.maximum(0., x - w/2)
y1 = tf.maximum(0., y - h/2)
x2 = tf.minimum(1., w + x1)
y2 = tf.minimum(1., h + y1)
return tf.stack([y1, x1, y2, x2], axis=1)
def plot(self, image, filename, save_sample):
""" Plot an image."""
image = np.minimum(image, 1)
image = np.maximum(image, -1)
image = np.squeeze(image)
# Scale to 0..255.
imin, imax = image.min(), image.max()
image = (image - imin) * 255. / (imax - imin) + .5
image = image.astype(np.uint8)
if save_sample:
try:
Image.fromarray(image).save(filename)
except Exception as e:
print("Warning: could not sample to ", filename, ". Please check permissions and make sure the path exists")
print(e)
GlobalViewer.update(image)
def sample_output(self, val):
vocabulary = self.get_vocabulary()
if self.one_hot:
vals = [ np.argmax(r) for r in val ]
ox_val = [vocabulary[obj] for obj in list(vals)]
string = "".join(ox_val)
return string
else:
val = np.reshape(val, [-1])
val *= len(vocabulary)/2.0
val += len(vocabulary)/2.0
val = np.round(val)
val = np.maximum(0, val)
val = np.minimum(len(vocabulary)-1, val)
ox_val = [self.get_character(obj) for obj in list(val)]
string = "".join(ox_val)
return string
def get_union_sets(lang_codes, feature_set_str):
feature_set_parts = feature_set_str.split("|")
feature_names, feature_values = get_named_set(lang_codes, feature_set_parts[0])
for feature_set_part in feature_set_parts[1:]:
more_feature_names, more_feature_values = get_named_set(lang_codes, feature_set_part)
if len(feature_names) != len(more_feature_names):
print("ERROR: Cannot perform elementwise union on feature sets of different size")
sys.exit(0)
feature_values = np.maximum(feature_values, more_feature_values)
return feature_names, feature_values
def prewhiten(x):
mean = np.mean(x)
std = np.std(x)
std_adj = np.maximum(std, 1.0/np.sqrt(x.size))
y = np.multiply(np.subtract(x, mean), 1/std_adj)
return y
def get_precision(self):
"""Compute data precision matrix with the generative model.
Equals the inverse of the covariance but computed with
the matrix inversion lemma for efficiency.
Returns
-------
precision : array, shape=(n_features, n_features)
Estimated precision of data.
"""
n_features = self.components_.shape[1]
# handle corner cases first
if self.n_components_ == 0:
return np.eye(n_features) / self.noise_variance_
if self.n_components_ == n_features:
return linalg.inv(self.get_covariance())
# Get precision using matrix inversion lemma
components_ = self.components_
exp_var = self.explained_variance_
exp_var_diff = np.maximum(exp_var - self.noise_variance_, 0.)
precision = np.dot(components_, components_.T) / self.noise_variance_
precision.flat[::len(precision) + 1] += 1. / exp_var_diff
precision = np.dot(components_.T,
np.dot(linalg.inv(precision), components_))
precision /= -(self.noise_variance_ ** 2)
precision.flat[::len(precision) + 1] += 1. / self.noise_variance_
return precision
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 getPosteriorMeanAndVar(self, diagKTestTest, KtrainTest, post, intercept=0):
L = post['L']
if (np.size(L) == 0): raise Exception('L is an empty array') #possible to compute it here
Lchol = np.all((np.all(np.tril(L, -1)==0, axis=0) & (np.diag(L)>0)) & np.isreal(np.diag(L)))
ns = diagKTestTest.shape[0]
nperbatch = 5000
nact = 0
#allocate mem
fmu = np.zeros(ns) #column vector (of length ns) of predictive latent means
fs2 = np.zeros(ns) #column vector (of length ns) of predictive latent variances
while (nact<(ns-1)):
id = np.arange(nact, np.minimum(nact+nperbatch, ns))
kss = diagKTestTest[id]
Ks = KtrainTest[:, id]
if (len(post['alpha'].shape) == 1):
try: Fmu = intercept[id] + Ks.T.dot(post['alpha'])
except: Fmu = intercept + Ks.T.dot(post['alpha'])
fmu[id] = Fmu
else:
try: Fmu = intercept[id][:, np.newaxis] + Ks.T.dot(post['alpha'])
except: Fmu = intercept + Ks.T.dot(post['alpha'])
fmu[id] = Fmu.mean(axis=1)
if Lchol:
V = la.solve_triangular(L, Ks*np.tile(post['sW'], (id.shape[0], 1)).T, trans=1, check_finite=False, overwrite_b=True)
fs2[id] = kss - np.sum(V**2, axis=0) #predictive variances
else:
fs2[id] = kss + np.sum(Ks * (L.dot(Ks)), axis=0) #predictive variances
fs2[id] = np.maximum(fs2[id],0) #remove numerical noise i.e. negative variances
nact = id[-1] #set counter to index of last processed data point
return fmu, fs2
def sq_dist(a, b=None):
#mean-center for numerical stability
D, n = a.shape[0], a.shape[1]
if (b is None):
mu = a.mean(axis=1)
a -= mu[:, np.newaxis]
b = a
m = n
aSq = np.sum(a**2, axis=0)
bSq = aSq
else:
d, m = b.shape[0], b.shape[1]
if (d != D): raise Exception('column lengths must agree')
mu = (float(m)/float(m+n))*b.mean(axis=1) + (float(n)/float(m+n))*a.mean(axis=1)
a -= mu[:, np.newaxis]
b -= mu[:, np.newaxis]
aSq = np.sum(a**2, axis=0)
bSq = np.sum(b**2, axis=0)
C = np.tile(np.column_stack(aSq).T, (1, m)) + np.tile(bSq, (n, 1)) - 2*a.T.dot(b)
C = np.maximum(C, 0) #remove numerical noise
return C
#evaluate 'power sums' of the individual terms in Z
def __init__(self, X):
Kernel.__init__(self)
self.X_scaled = X/np.sqrt(X.shape[1])
if (X.shape[1] >= X.shape[0] or True): self.K_sq = sq_dist(self.X_scaled.T)
else: self.K_sq = None
self.j = np.floor(X.shape[1]/2.0)+self.v+1
self.pp = lambda r,j,v,f: np.maximum(1-r, 0)**(j+v) * self.f(r,j)
self.dpp = lambda r,j,v,f: np.maximum(1-r, 0)**(j+v-1) * r * ((j+v)*f(r,j) - np.maximum(1-r,0)*self.df(r,j))
