np.meshgrid()

Love The Way You Lie 2022-12-23 07:20 105阅读 0赞

### 目录 ###

*  1.meshgrid函数介绍
 *  2.meshgrid函数官方说明

# 1.meshgrid函数介绍 #

**参数：**  
\*xi，也就是x1，x2，…，xn ：表示网格坐标的一维数组。  
copy：默认为True，如果为False，就返回原始数组以节省内存。  
sparse：默认值为False如果为True，则返回一个稀疏网格以节省内存。  
indexing：输出的笛卡尔（默认为“ xy”）或矩阵（“ ij”）索引。（后面有例子介绍该参数）

**return** ：返回网格坐标矩阵（返回值为list,list中包含各个方向的坐标矩阵）

看到这可能还不是很理解，举个例子就很明白了，如下图所示，下图二维平面中有6个网格坐标，可以看出他们的横坐标为\[0, 1, 2\]，纵坐标为\[0, 1\]，倘若只知道他们的横坐标和纵坐标的一维数组，怎么构建这6个网格坐标，meshgrid的作用就是这个。  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM4MDQ4NzU2_size_16_color_FFFFFF_t_70]

>>> a = [0, 1, 2]
    >>> b = [0, 1]
    >>> np.meshgrid(a,b)
    [array([[0, 1, 2],[0, 1, 2]]), array([[0, 0, 0],[1, 1, 1]])]
    >>>

返回的结果现在还不是6个点的坐标，但是将a中的元素与b中的每个元素一一对应就得到了上述6个点的坐标。

那么indexing的作用是什么呢？

>>> np.meshgrid(a,b,indexing = 'ij')
    [array([[0, 0], [1, 1],[2, 2]]), array([[0, 1],[0, 1], [0, 1]])]
    >>>

也就是若indexing = ‘xy’，返回的矩阵形状为(N2, N1, N3,…Nn)，其中Ni = len(xi)。若indexing = ‘ij’，则返回的矩阵形状为(N1, N2, N3,…Nn)。具体的影响就是处理数据时，读取数据方式不同。

xv, yv = np.meshgrid(x, y, sparse=False, indexing='ij')
            for i in range(nx):
                for j in range(ny):
                    # treat xv[i,j], yv[i,j]
    
            xv, yv = np.meshgrid(x, y, sparse=False, indexing='xy')
            for i in range(nx):
                for j in range(ny):
                    # treat xv[j,i], yv[j,i]

sparse为True时，返回稀疏的网格（为了节省内存），也就是该坐标矩阵下的元素有哪些（由于每行/列下的元素都一样，所以返回一行或一列就可以知道该坐标矩阵下的元素）。

>>> x = np.meshgrid(a,b,sparse= True)
    >>> x
    [array([[0, 1, 2]]), array([[0],
           [1]])]
    >>>

接下来把meshgrid的结果变为最终的坐标点：

>>> a = [0, 1, 2]
    >>> b = [0, 1]
    >>> np.meshgrid(a,b)
    [array([[0, 1, 2],[0, 1, 2]]), array([[0, 0, 0],[1, 1, 1]])]
    >>> x, y = np.meshgrid(a,b)
    >>> x.flatten()[:, np.newaxis]
    array([[0],
           [1],
           [2],
           [0],
           [1],
           [2]])
    >>> y.flatten()[:, np.newaxis]
    array([[0],
           [0],
           [0],
           [1],
           [1],
           [1]])
    >>> xx = x.flatten()[:, np.newaxis]
    >>> yy = y.flatten()[:, np.newaxis]
    >>> np.c_[xx, yy]
    array([[0, 0],
           [1, 0],
           [2, 0],
           [0, 1],
           [1, 1],
           [2, 1]])
    >>>

--------------------

**np.newaxis介绍**：可以在数组索引中使用np.newaxis对象添加大小为1的新尺寸，如：

>>> a.shape
    (5, 7)
    >>> a[:,np.newaxis,:].shape
    (5, 1, 7)
    
    >>> x = np.arange(5)
    >>> x[:, np.newaxis]
    array([[0],
           [1],
           [2],
           [3],
           [4]])
    >>>

**np.flatten()介绍:**  
原型声明：`def flatten(self, order='C'):`

**Parameters**：  
**order\{‘C’, ‘F’, ‘A’, ‘K’\}, optional**  
“ C”表示按行优先（C样式）的顺序展平。“ F”表示按列主（Fortran样式）的顺序展平。“ A”表示如果a在内存中是连续的，则按列优先顺序进行展平；否则，按行优先进行展平。“ K”表示按元素在内存中出现的顺序展平 。默认值为“ C”。  
**Returns**  
返回展平为一维的数组副本。

--------------------

# 2.meshgrid函数官方说明 #

[meshgrid的官方api][meshgrid_api]

def meshgrid(*xi, copy=True, sparse=False, indexing='xy'):
        """ Return coordinate matrices from coordinate vectors. Make N-D coordinate arrays for vectorized evaluations of N-D scalar/vector fields over N-D grids, given one-dimensional coordinate arrays x1, x2,..., xn. .. versionchanged:: 1.9 1-D and 0-D cases are allowed. Parameters ---------- x1, x2,..., xn : array_like 1-D arrays representing the coordinates of a grid. indexing : {'xy', 'ij'}, optional Cartesian ('xy', default) or matrix ('ij') indexing of output. See Notes for more details. .. versionadded:: 1.7.0 sparse : bool, optional If True a sparse grid is returned in order to conserve memory. Default is False. .. versionadded:: 1.7.0 copy : bool, optional If False, a view into the original arrays are returned in order to conserve memory. Default is True. Please note that ``sparse=False, copy=False`` will likely return non-contiguous arrays. Furthermore, more than one element of a broadcast array may refer to a single memory location. If you need to write to the arrays, make copies first. .. versionadded:: 1.7.0 Returns ------- X1, X2,..., XN : ndarray For vectors `x1`, `x2`,..., 'xn' with lengths ``Ni=len(xi)`` , return ``(N1, N2, N3,...Nn)`` shaped arrays if indexing='ij' or ``(N2, N1, N3,...Nn)`` shaped arrays if indexing='xy' with the elements of `xi` repeated to fill the matrix along the first dimension for `x1`, the second for `x2` and so on. Notes ----- This function supports both indexing conventions through the indexing keyword argument. Giving the string 'ij' returns a meshgrid with matrix indexing, while 'xy' returns a meshgrid with Cartesian indexing. In the 2-D case with inputs of length M and N, the outputs are of shape (N, M) for 'xy' indexing and (M, N) for 'ij' indexing. In the 3-D case with inputs of length M, N and P, outputs are of shape (N, M, P) for 'xy' indexing and (M, N, P) for 'ij' indexing. The difference is illustrated by the following code snippet:: xv, yv = np.meshgrid(x, y, sparse=False, indexing='ij') for i in range(nx): for j in range(ny): # treat xv[i,j], yv[i,j] xv, yv = np.meshgrid(x, y, sparse=False, indexing='xy') for i in range(nx): for j in range(ny): # treat xv[j,i], yv[j,i] In the 1-D and 0-D case, the indexing and sparse keywords have no effect. See Also -------- index_tricks.mgrid : Construct a multi-dimensional "meshgrid" using indexing notation. index_tricks.ogrid : Construct an open multi-dimensional "meshgrid" using indexing notation. Examples -------- >>> nx, ny = (3, 2) >>> x = np.linspace(0, 1, nx) >>> y = np.linspace(0, 1, ny) >>> xv, yv = np.meshgrid(x, y) >>> xv array([[0. , 0.5, 1. ], [0. , 0.5, 1. ]]) >>> yv array([[0., 0., 0.], [1., 1., 1.]]) >>> xv, yv = np.meshgrid(x, y, sparse=True) # make sparse output arrays >>> xv array([[0. , 0.5, 1. ]]) >>> yv array([[0.], [1.]]) `meshgrid` is very useful to evaluate functions on a grid. >>> import matplotlib.pyplot as plt >>> x = np.arange(-5, 5, 0.1) >>> y = np.arange(-5, 5, 0.1) >>> xx, yy = np.meshgrid(x, y, sparse=True) >>> z = np.sin(xx**2 + yy**2) / (xx**2 + yy**2) >>> h = plt.contourf(x,y,z) >>> plt.show() """

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM4MDQ4NzU2_size_16_color_FFFFFF_t_70]: /images/20221120/68e92ebdfde743c8adeed15b5bd32b87.png
[meshgrid_api]: https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html?highlight=meshgrid#numpy.meshgrid

np.meshgrid()

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