numpy中的matrix类
numpy提供了一个专门的矩阵处理模块：numpy.matlib。
1、矩阵创建函数。
2、矩阵的特殊属性。
3、矩阵的特殊函数。
备注：
( 1 ) 矩阵创建函数在numpy.matlib模块下，不过函数也有numpy命名空间，可以在numpy模块名下使用。
( 2 ) 矩阵类是：numpy.matrices
一、矩阵创建函数
numpy命名空间中的函数
创建函数
函数说明
mat(data[, dtype])
Interpret the input as a matrix.
matrix(data[, dtype, copy])
Returns a matrix from an array-like object, or from a string of data.
asmatrix(data[, dtype])
Interpret the input as a matrix.
bmat(obj[, ldict, gdict])
Build a matrix object from a string, nested sequence, or array.matlib命名空间中的函数
创建函数
函数说明
empty(shape[, dtype, order])
Return a new matrix of given shape and type, without initializing entries.
zeros(shape[, dtype, order])
Return a matrix of given shape and type, filled with zeros.
ones(shape[, dtype, order])
Matrix of ones.
eye(n[, M, k, dtype, order])
Return a matrix with ones on the diagonal and zeros elsewhere.
identity(n[, dtype])
Returns the square identity matrix of given size.
repmat(a, m, n)
Repeat a 0-D to 2-D array or matrix MxN times.
rand(*args)
Return a matrix of random values with given shape.
randn(*args)
Return a random matrix with data from the “standard normal” distribution.注意：上述函数在新的版本中，为了方便，在numpy于numpy.matlib都有定义。如果在numpy中无效，则说明版本是老板，可以使用numpy.matlib
1. 创建矩阵函数的模块matlib
import numpy as np
m=np.mat ( [
[ 1, 2, 3],
[ 4, 5, 6]
] )
print ( m )
[[1 2 3]
[4 5 6]]
import numpy.matlib as mb
m=mb.empty( (2, 3 ) )
print ( m )
import numpy as np
m=mb.empty( (2, 3 ) )
print ( m )
#mat在numpy也定义。
m=mb.mat ( [
[ 1, 2, 3],
[ 4, 5, 6]
] )
print ( m )
[[4.9e-324 9.9e-324 1.5e-323]
[2.0e-323 2.5e-323 3.0e-323]]
[[4.9e-324 9.9e-324 1.5e-323]
[2.0e-323 2.5e-323 3.0e-323]]
[[1 2 3]
[4 5 6]]2. matrix类
矩阵创建函数中matrix实际是类，定义如下：
class numpy.matrix(data, dtype=None, copy=True)[source]
其中data可是是字符串。
#下面输出的矩阵类型是matrix
mb.matrix ( [
[ 1, 2, 3],
[ 4, 5, 6]
] )
matrix([[1, 2, 3],
[4, 5, 6]])
# data可以是字符串：逗号表示列，分号表示行
data = '[ [ 1, 2, 3 ]; [ 4, 5, 6] ]'
mb.matrix ( data )
matrix([[1, 2, 3],
[4, 5, 6]])
# mat返回的都是矩阵类型
mb.mat ( [
[ 1, 2, 3],
[ 4, 5, 6]
] )
matrix([[1, 2, 3],
[4, 5, 6]])二、matrix的特殊属性
下面是matrxi新增属性属性
矩阵的属性
属性说明
A
Return self as an ndarray object.
A1
Return self as a flattened ndarray.
H
Returns the (complex) conjugate transpose of self.
I
Returns the (multiplicative) inverse of invertible self.下面是从nadarray继承的属性
矩阵的属性
属性说明
T
Returns the transpose of the matrix.
base
Base object if memory is from some other object.
ctypes
An object to simplify the interaction of the array with the ctypes module.
data
Python buffer object pointing to the start of the array’s data.
dtype
Data-type of the array’s elements.
flags
Information about the memory layout of the array.
flat
A 1-D iterator over the array.
imag
The imaginary part of the array.
itemsize
Length of one array element in bytes.
nbytes
Total bytes consumed by the elements of the array.
ndim
Number of array dimensions.
real
The real part of the array.
shape
Tuple of array dimensions.
size
Number of elements in the array.
strides
Tuple of bytes to step in each dimension when traversing an array.1. matrix独有属性的使用与理解
m= mb.matrix ( [
[ 1, 2, 3 ],
[ 4, 5, 6 ]
] )
#A属性m.A
print ( m.A ) #返回自己，只是类型是ndarray。
#A1属性
print ( m.A1 ) #返回自己，作为1-D数组。
m= mb.matrix ( [
[ 1+3j, 2-5j, 4+7j ],
[ 2+6j, 4+8j, 8-9j ]
] )
#H属性
print ( m.H ) #返回复数的共轭矩阵
[[1 2 3]
[4 5 6]]
[1 2 3 4 5 6]
[[1.-3.j 2.-6.j]
[2.+5.j 4.-8.j]
[4.-7.j 8.+9.j]]2. 矩阵的可逆矩阵
作初等变换，将A化为单位阵E，单位矩阵E就化为可逆矩阵A 。
# I 属性
m= mb.matrix ( [
[ 2, 0, 0 ],
[ 0, 2, 0 ],
[ 0, 0, 2 ]
] )
print ( m.I ) #返回逆矩阵
#如果矩阵不可逆，要计算其可逆矩阵则返回如下错误：LinAlgError: Singular matrix。
#可逆矩阵必须是方阵。
#对非方阵，也能求逆矩阵
m= mb.matrix ( [
[ 1, 2, 3 ],
[ 4, 5, 6 ]
] )
print ( m.I )
print ( m.dot ( m.I ) ) # 接近单位矩阵E。
print ( (m.I).dot ( m ) ) #这个矩阵不是单位矩阵E。
[[0.5 0. 0. ]
[0. 0.5 0. ]
[0. 0. 0.5]]
[[-0.94444444 0.44444444]
[-0.11111111 0.11111111]
[ 0.72222222 -0.22222222]]
[[ 1.00000000e+00 3.60822483e-16]
[-1.11022302e-15 1.00000000e+00]]
[[ 0.83333333 0.33333333 -0.16666667]
[ 0.33333333 0.33333333 0.33333333]
[-0.16666667 0.33333333 0.83333333]]三、 matrix的特殊函数
matrix独有的函数
继承函数
函数说明
getA()
Return self as an ndarray object.
getA1()
Return self as a flattened ndarray.
getH()
Returns the (complex) conjugate transpose of self.
getI()
Returns the (multiplicative) inverse of invertible self.从nadarray继承的函数
继承函数
函数说明
getT()
Returns the transpose of the matrix.
all([axis, out, keepdims])
Returns True if all elements evaluate to True.
any([axis, out, keepdims])
Returns True if any of the elements of a evaluate to True.
argmax([axis, out])
Return indices of the maximum values along the given axis.
argmin([axis, out])
Return indices of the minimum values along the given axis of a.
argpartition(kth[, axis, kind, order])
Returns the indices that would partition this array.
argsort([axis, kind, order])
Returns the indices that would sort this array.
astype(dtype[, order, casting, subok, copy])
Copy of the array, cast to a specified type.
byteswap([inplace])
Swap the bytes of the array elements
choose(choices[, out, mode])
Use an index array to construct a new array from a set of choices.
clip([min, max, out])
Return an array whose values are limited to [min, max].
compress(condition[, axis, out])
Return selected slices of this array along given axis.
conj()
Complex-conjugate all elements.
conjugate()
Return the complex conjugate, element-wise.
copy([order])
Return a copy of the array.
cumprod([axis, dtype, out])
Return the cumulative product of the elements along the given axis.
cumsum([axis, dtype, out])
Return the cumulative sum of the elements along the given axis.
diagonal([offset, axis1, axis2])
Return specified diagonals.
dot(b[, out])
Dot product of two arrays.
dump(file)
Dump a pickle of the array to the specified file.
dumps()
Returns the pickle of the array as a string.
fill(value)
Fill the array with a scalar value.
flatten([order])
Return a copy of the array collapsed into one dimension.
getfield(dtype[, offset])
Returns a field of the given array as a certain type.
item(*args)
Copy an element of an array to a standard Python scalar and return it.
itemset(*args)
Insert scalar into an array (scalar is cast to array’s dtype, if possible)
max([axis, out, keepdims])
Return the maximum along a given axis.
mean([axis, dtype, out, keepdims])
Returns the average of the array elements along given axis.
min([axis, out, keepdims])
Return the minimum along a given axis.
newbyteorder([new_order])
Return the array with the same data viewed with a different byte order.
nonzero()
Return the indices of the elements that are non-zero.
partition(kth[, axis, kind, order])
Rearranges the elements in the array in such a way that value of the element in kth position is in the position it would be in a sorted array.
prod([axis, dtype, out, keepdims])
Return the product of the array elements over the given axis
ptp([axis, out])
Peak to peak (maximum - minimum) value along a given axis.
put(indices, values[, mode])
Set a.flat[n] = values[n] for all n in indices.
ravel([order])
Return a flattened array.
repeat(repeats[, axis])
Repeat elements of an array.
reshape(shape[, order])
Returns an array containing the same data with a new shape.
resize(new_shape[, refcheck])
Change shape and size of array in-place.
round([decimals, out])
Return a with each element rounded to the given number of decimals.
searchsorted(v[, side, sorter])
Find indices where elements of v should be inserted in a to maintain order.
setfield(val, dtype[, offset])
Put a value into a specified place in a field defined by a data-type.
setflags([write, align, uic])
Set array flags WRITEABLE, ALIGNED, (WRITEBACKIFCOPY and UPDATEIFCOPY), respectively.
sort([axis, kind, order])
Sort an array, in-place.
squeeze([axis])
Remove single-dimensional entries from the shape of a.
std([axis, dtype, out, ddof, keepdims])
Returns the standard deviation of the array elements along given axis.
sum([axis, dtype, out, keepdims])
Return the sum of the array elements over the given axis.
swapaxes(axis1, axis2)
Return a view of the array with axis1 and axis2 interchanged.
take(indices[, axis, out, mode])
Return an array formed from the elements of a at the given indices.
tobytes([order])
Construct Python bytes containing the raw data bytes in the array.
tofile(fid[, sep, format])
Write array to a file as text or binary (default).
tolist()
Return the array as a (possibly nested) list.
tostring([order])
Construct Python bytes containing the raw data bytes in the array.
trace([offset, axis1, axis2, dtype, out])
Return the sum along diagonals of the array.
transpose(*axes)
Returns a view of the array with axes transposed.
var([axis, dtype, out, ddof, keepdims])
Returns the variance of the array elements, along given axis.
view([dtype, type])
New view of array with the same data.
1. matrix 独有方法的使用
#matrix都有的几个函数都对应着属性。
m= mb.matrix ( [
[ 1, 2, 3 ],
[ 4, 5, 6 ]
] )
print ( m.getI ( ) )
[[-0.94444444 0.44444444]
[-0.11111111 0.11111111]
[ 0.72222222 -0.22222222]]2. ndarray几个函数使用的补充
clip函数
ndarray.clip(min=None, max=None, out=None)
返回一个数组，数组的值限制在 [min, max]. 比min下的都设置为min，比max大的都设置为max。
m= mb.matrix ( [
[ 7, 4, 3, 6, 5, 1 ],
[ 2, 5, 9, 7, 1, 8 ]
] )
print ( m.clip ( min = 3, max = 6 ) )
[[6 4 3 6 5 3]
[3 5 6 6 3 6]]conj函数与conjugate函数
ndarray.conj()
ndarray.conjugate()
都是返回复数共轭矩阵
m= mb.matrix ( [
[ 1+3j, 2-5j, 4+7j ],
[ 2+6j, 4+8j, 8-9j ]
] )
print ( m.conj ( ) )
print ( m.conjugate ( ) )
print ( m.H )
print ( m.getH ( ) )
[[1.-3.j 2.+5.j 4.-7.j]
[2.-6.j 4.-8.j 8.+9.j]]
[[1.-3.j 2.+5.j 4.-7.j]
[2.-6.j 4.-8.j 8.+9.j]]
[[1.-3.j 2.-6.j]
[2.+5.j 4.-8.j]
[4.-7.j 8.+9.j]]
[[1.-3.j 2.-6.j]
[2.+5.j 4.-8.j]
[4.-7.j 8.+9.j]]dot函数
ndarray.dot(b, out=None)
计算内积(内积必须满足条件：mxn nxk，返回mxk的矩阵)
A = mb.matrix ( [
[ 1, 2, 3 ],
[ 4, 5, 6 ]
] )
B = mb.matrix ( [
[ 1, 2],
[ 4, 5],
[ 7, 8]
] )
print ( A.dot( B ) )
print ( A @ B )
print ( B.dot( A ) )
print ( B @ A )
[[30 36]
[66 81]]
[[30 36]
[66 81]]
[[ 9 12 15]
[24 33 42]
[39 54 69]]
[[ 9 12 15]
[24 33 42]
[39 54 69]]ptp函数
ndarray.ptp(axis=None, out=None)
最大值与最小值只差(maximum - minimum)
ptp是peak to peak缩写(峰到峰)
A = mb.matrix ( [
[ 1, 2, 3 ],
[ 4, 5, 6 ]
] )
print ( A.ptp ( ) )
print ( A.ptp ( axis=0 ) )
print ( A.ptp ( axis=1 ) )
5
[[3 3 3]]
[[2]
[2]]round函数
ndarray.round(decimals=0, out=None)
返回四舍五入矩阵
decimals=0 设置精度(小数点位数)
A = mb.matrix ( [
[ 1.4, 2.9, 3.5 ],
[ 4.49, 5.51, 6.3 ]
] )
print ( A.round ( ) )
print ( A.round ( decimals =1 ) )
[[1. 3. 4.]
[4. 6. 6.]]
[[1.4 2.9 3.5]
[4.5 5.5 6.3]]
swapaxes函数
ndarray.swapaxes(axis1, axis2)
交换坐标轴
A = mb.matrix ( [
[ 1.4, 2.9, 3.5 ],
[ 4.49, 5.51, 6.3 ]
] )print ( A.swapaxes ( 0, 1 ) ) #对2-D矩阵来说就是转置。
[[1.4 4.49]
[2.9 5.51]
[3.5 6.3 ]]【资源】
本文使用ipython notebook格式编辑，文件下载：
【ndarray_matrix.ipynb】
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