numpy matrix 矩阵对象

https://docs.scipy.org/doc/numpy/reference/generated/numpy.matrix.html#numpy.matrix
1.简介
Matrix类型继承于ndarray类型，因此含有ndarray的所有数据属性和方法。Matrix类型与ndarray类型有六个重要的不同点，当你当Matrix对象当arrays操作时，这些不同点会导致非预期的结果。

1）Matrix对象可以使用一个Matlab风格的字符串来创建，也就是一个以空格分隔列，以分号分隔行的字符串。

2）Matrix对象总是二维的。这包含有深远的影响，比如m.ravel()的返回值是二维的，成员选择的返回值也是二维的，因此序列的行为与array会有本质的不同。

3）Matrix类型的乘法覆盖了array的乘法，使用的是矩阵的乘法运算。当你接收矩阵的返回值的时候，确保你已经理解这些函数的含义。特别地，事实上函数asanyarray(m)会返回一个matrix，如果m是一个matrix。

4）Matrix类型的幂运算也覆盖了之前的幂运算，使用矩阵的幂。根据这个事实，再提醒一下，如果使用一个矩阵的幂作为参数调用asanarray(…)跟上面的相同。

5）矩阵默认的array_priority是10.0，因而ndarray和matrix对象混合的运算总是返回矩阵。

6）矩阵有几个特有的属性使得计算更加容易，这些属性有：

(a) .T －－返回自身的转置

(b) .H －－返回自身的共轭转置

(d) .A －－返回自身数据的2维数组的一个视图（没有做任何的拷贝）

Matrix对象也可以使用其它的Matrix对象，字符串，或者其它的可以转换为一个ndarray的参数来构造。另外，在NumPy里，“mat”是“matrix”的一个别名。
1）通过字符串创建矩阵

>>> a=np.mat('1 2 3; 4 5 3')
>>> print (a*a.T).I
[[ 0.2924 -0.1345]
[-0.1345 0.0819]]

2）通过嵌套列表创建矩阵

>>> mp.mat([[1,5,10],[1.0,3,4j]])
matrix([[ 1.+0.j, 5.+0.j, 10.+0.j],
[ 1.+0.j, 3.+0.j, 0.+4.j]])

3）通过数组创建矩阵

>>> np.mat(random.rand(3,3)).T
matrix([[ 0.7699, 0.7922, 0.3294],
[ 0.2792, 0.0101, 0.9219],
[ 0.3398, 0.7571, 0.8197]])

2.属性与描述

name	descripe
A	返回对应的数组对象 ndarray
A1	返回扁平数组 flattened ndarray.
H	Returns the (complex) conjugate transpose of self.
I	Returns the (multiplicative) inverse of invertible self.
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.

3.方法与描述

name	describe
all([axis, out])	Test whether all matrix elements along a given axis evaluate to True.
any([axis, out])	Test whether any array element along a given axis evaluates to True.
argmax([axis, out])	Indexes of the maximum values along an axis.
argmin([axis, out])	Indexes of the minimum values along an axis.
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 flattened copy of the matrix.
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.
getT()	Returns the transpose of the matrix.
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])	Return the maximum value along an axis.
mean([axis, dtype, out])	Returns the average of the matrix elements along the given axis.
min([axis, out])	Return the minimum value along an 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 prod([axis, dtype, out]) Return the product of the array elements over the given axis.
ptp([axis, out])	Peak-to-peak (maximum - minimum) value along the given axis.
put(indices, values[, mode])	Set a.flat[n] = values[n] for all n in indices.
ravel([order])	Return a flattened matrix.
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, and UPDATEIFCOPY, respectively.
sort([axis, kind, order])	Sort an array, in-place.
squeeze([axis])	Return a possibly reshaped matrix.
std([axis, dtype, out, ddof])	Return the standard deviation of the array elements along the given axis.
sum([axis, dtype, out])	Returns the sum of the matrix elements, along 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 matrix 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])	Returns the variance of the matrix elements, along the given axis.
view([dtype, type])	New view of array with the same data.

http://blog.csdn.net/shuaishuai3409/article/details/50830196

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