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1.簡(jiǎn)介
Matrix類(lèi)型繼承于ndarray類(lèi)型，因此含有ndarray的所有數(shù)據(jù)屬性和方法。Matrix類(lèi)型與ndarray類(lèi)型有六個(gè)重要的不同點(diǎn)，當(dāng)你當(dāng)Matrix對(duì)象當(dāng)arrays操作時(shí)，這些不同點(diǎn)會(huì)導(dǎo)致非預(yù)期的結(jié)果。
1）Matrix對(duì)象可以使用一個(gè)Matlab風(fēng)格的字符串來(lái)創(chuàng)建，也就是一個(gè)以空格分隔列，以分號(hào)分隔行的字符串。
2）Matrix對(duì)象總是二維的。這包含有深遠(yuǎn)的影響，比如m.ravel()的返回值是二維的，成員選擇的返回值也是二維的，因此序列的行為與array會(huì)有本質(zhì)的不同。
3）Matrix類(lèi)型的乘法覆蓋了array的乘法，使用的是矩陣的乘法運(yùn)算。當(dāng)你接收矩陣的返回值的時(shí)候，確保你已經(jīng)理解這些函數(shù)的含義。特別地，事實(shí)上函數(shù)asanyarray(m)會(huì)返回一個(gè)matrix，如果m是一個(gè)matrix。
4）Matrix類(lèi)型的冪運(yùn)算也覆蓋了之前的冪運(yùn)算，使用矩陣的冪。根據(jù)這個(gè)事實(shí)，再提醒一下，如果使用一個(gè)矩陣的冪作為參數(shù)調(diào)用asanarray(…)跟上面的相同。
5）矩陣默認(rèn)的array_priority是10.0，因而ndarray和matrix對(duì)象混合的運(yùn)算總是返回矩陣。
6）矩陣有幾個(gè)特有的屬性使得計(jì)算更加容易，這些屬性有：
(a) .T －－ 返回自身的轉(zhuǎn)置
(b) .H －－ 返回自身的共軛轉(zhuǎn)置
(c) .I －－ 返回自身的逆矩陣
(d) .A －－ 返回自身數(shù)據(jù)的2維數(shù)組的一個(gè)視圖（沒(méi)有做任何的拷貝）
Matrix對(duì)象也可以使用其它的Matrix對(duì)象，字符串，或者其它的可以轉(zhuǎn)換為一個(gè)ndarray的參數(shù)來(lái)構(gòu)造。另外，在NumPy里，“mat”是“matrix”的一個(gè)別名。
1）通過(guò)字符串創(chuàng)建矩陣
重慶分公司
重慶分公司
>>> a=np.mat('1 2 3; 4 5 3')
>>> print (a*a.T).I[[ 0.2924 -0.1345] [-0.1345 0.0819]]2）通過(guò)嵌套列表創(chuàng)建矩陣
>>> 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）通過(guò)數(shù)組創(chuàng)建矩陣
>>> 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.屬性與描述
| name | descripe |
|---|---|
| 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. |
| 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.方法與描述
| 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. |
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