numpy 可用的常规函数 numpy 广播

该部分位于numpy - ref - 1.14.5中的2.8 available ufuncs

1 数学运算

加法规则：

numpy.add(x1, x2, /, out=None, *, where=True, casting=’same_kind’, order=’K’, dtype=None, subok=True[, signature, extobj]) = <ufunc 'add'>

x1 ，x2 - number，ndarray，Iterable 均可，实际上一般为ndarray。

out - 存储结果的位置，如果提供，其必须事具有输入广播的形状，如果无或者不提供，则返回新分配的数组；元组（可能仅作为关键字参数）的长度必须等于输出的数量。

余下参数略，不做说明，实际上记住 numpy.add(x1, x2） 即可，余下参数用的不多

示例一：一个ndarray + 数字

将数字与ndarray中的每一个元素相加

a = np.arange(1,5).reshape(2,2)
print(a)
# [[1 2]
#  [3 4]]
b = np.add(a,2)
print(b)
# [[3 4]
#  [5 6]]

示例二：两个同shape的ndarray相加

对应元素相加

a = np.arange(1,5).reshape(2,2)
print(a)
# [[1 2]
#  [3 4]]
b = np.arange(0,4).reshape(2,2)
print(b)
# [[0 1]
#  [2 3]]
c = np.add(a,b)
print(c)
# [[1 3]
#  [5 7]]

示例三：两个shape不全相等的ndarray相加

此时相当于 广播

a = np.arange(1,5).reshape(2,2)
print(a)
# [[1 2]
#  [3 4]]
b = np.arange(0,2)
print(b)
# [0 1]
c = np.add(a,b)
print(c)
# [[1 3]
#  [3 5]]

示例四：两个shape不全相等的ndarray相加

此时 与 广播 等价

a = np.arange(1,5).reshape(2,2)
print(a)
# [[1 2]
#  [3 4]]
b = np.arange(0,2).reshape(-1,1)
print(b)
# [[0]
#  [1]]
c = np.add(a,b)
print(c)
# [[1 2]
#  [4 5]]

示例五：两个shape不全相等的ndarray相加

此时相当于广播

a = np.arange(1,5).reshape(2,2)
print(a)
# [[1 2]
#  [3 4]]
b = np.arange(0,4).reshape(1,2,2)
print(b)
# [[[0 1]
#   [2 3]]]
c = np.add(a,b)
print(c)
# [[[1 3]
#   [5 7]]]

示例六：x1 x2的shape值不符合广播规则时，无法add

numpy 广播

a = np.arange(1,5).reshape(2,2)
print(a)
# [[1 2]
#  [3 4]]
b = np.arange(0,4)
print(b)
# [0 1 2 3]
c = np.add(a,b)
print(c)
# ValueError: operands could not be broadcast together with shapes (2,2) (4,) 

a = np.arange(1,7).reshape(2,3)
print(a)
# [[1 2 3]
#  [4 5 6]]
b = np.arange(0,4).reshape(2,2)
print(b)
# [[0 1]
#  [2 3]]
c = np.add(a,b)
print(c)
# ValueError: operands could not be broadcast together with shapes (2,3) (2,2) 

综上：当x1.shape != x2.shape 时，x1 x2 必须可广播到一个通用形状（可能是其中一个或另一个形状shape）they must be broadcastable to a common shape (which may be the shape of one or the other)。

add(x1, x2, /[, out, where, casting, order, . . . ])   按元素添加参数 Add arguments element-wise.
subtract(x1, x2, /[, out, where, casting, . . . ])     Subtract arguments, element-wise.
multiply(x1, x2, /[, out, where, casting, . . . ]) Multiply arguments element-wise.
divide(x1, x2, /[, out, where, casting, . . . ]) Returns a true division of the inputs, element-wise.
logaddexp(x1, x2, /[, out, where, casting, . . . ]) Logarithm of the sum of exponentiations of the inputs.
logaddexp2(x1, x2, /[, out, where, casting, . . . ]) Logarithm of the sum of exponentiations of the inputs in
base-2.
true_divide(x1, x2, /[, out, where, . . . ]) Returns a true division of the inputs, element-wise.
floor_divide(x1, x2, /[, out, where, . . . ]) Return the largest integer smaller or equal to the division
of the inputs.
negative(x, /[, out, where, casting, order, . . . ]) Numerical negative, element-wise.
positive(x, /[, out, where, casting, order, . . . ]) Numerical positive, element-wise.
power(x1, x2, /[, out, where, casting, . . . ]) First array elements raised to powers from second array,
element-wise.
remainder(x1, x2, /[, out, where, casting, . . . ]) Return element-wise remainder of division.
mod(x1, x2, /[, out, where, casting, order, . . . ]) Return element-wise remainder of division.
fmod(x1, x2, /[, out, where, casting, . . . ]) Return the element-wise remainder of division.
divmod(x1, x2[, out1, out2], / [[, out, . . . ]) Return element-wise quotient and remainder simultane
ously.
absolute(x, /[, out, where, casting, order, . . . ]) Calculate the absolute value element-wise.
fabs(x, /[, out, where, casting, order, . . . ]) Compute the absolute values element-wise.
rint(x, /[, out, where, casting, order, . . . ]) Round elements of the array to the nearest integer.
sign(x, /[, out, where, casting, order, . . . ]) Returns an element-wise indication of the sign of a number.
heaviside(x1, x2, /[, out, where, casting, . . . ]) Compute the Heaviside step function.
conj(x, /[, out, where, casting, order, . . . ]) Return the complex conjugate, element-wise.
exp(x, /[, out, where, casting, order, . . . ]) Calculate the exponential of all elements in the input array.
exp2(x, /[, out, where, casting, order, . . . ]) Calculate 2**p for all p in the input array.
log(x, /[, out, where, casting, order, . . . ]) Natural logarithm, element-wise.

add(x1, x2, /[, out, where, casting, order, . . . ]) Add arguments element-wise.
subtract(x1, x2, /[, out, where, casting, . . . ]) Subtract arguments, element-wise.
multiply(x1, x2, /[, out, where, casting, . . . ]) Multiply arguments element-wise.
divide(x1, x2, /[, out, where, casting, . . . ]) Returns a true division of the inputs, element-wise.
logaddexp(x1, x2, /[, out, where, casting, . . . ]) Logarithm of the sum of exponentiations of the inputs.
logaddexp2(x1, x2, /[, out, where, casting, . . . ]) Logarithm of the sum of exponentiations of the inputs in
base-2.
true_divide(x1, x2, /[, out, where, . . . ]) Returns a true division of the inputs, element-wise.
floor_divide(x1, x2, /[, out, where, . . . ]) Return the largest integer smaller or equal to the division
of the inputs.
negative(x, /[, out, where, casting, order, . . . ]) Numerical negative, element-wise.
positive(x, /[, out, where, casting, order, . . . ]) Numerical positive, element-wise.
power(x1, x2, /[, out, where, casting, . . . ]) First array elements raised to powers from second array,
element-wise.
remainder(x1, x2, /[, out, where, casting, . . . ]) Return element-wise remainder of division.
mod(x1, x2, /[, out, where, casting, order, . . . ]) Return element-wise remainder of division.
fmod(x1, x2, /[, out, where, casting, . . . ]) Return the element-wise remainder of division.
divmod(x1, x2[, out1, out2], / [[, out, . . . ]) Return element-wise quotient and remainder simultane
ously.
absolute(x, /[, out, where, casting, order, . . . ]) Calculate the absolute value element-wise.
fabs(x, /[, out, where, casting, order, . . . ]) Compute the absolute values element-wise.
rint(x, /[, out, where, casting, order, . . . ]) Round elements of the array to the nearest integer.
sign(x, /[, out, where, casting, order, . . . ]) Returns an element-wise indication of the sign of a number.
heaviside(x1, x2, /[, out, where, casting, . . . ]) Compute the Heaviside step function.
conj(x, /[, out, where, casting, order, . . . ]) Return the complex conjugate, element-wise.
exp(x, /[, out, where, casting, order, . . . ]) Calculate the exponential of all elements in the input array.
exp2(x, /[, out, where, casting, order, . . . ]) Calculate 2**p for all p in the input array.
log(x, /[, out, where, casting, order, . . . ]) Natural logarithm, element-wise.