matplotlib quiver箭图绘制案例

quiver绘制表示梯度变化非常有用，下面是学习过程中给出的两个例子，可以很好理解quiver的用法

from pylab import *
close()

## example 1

x = linspace(0,10,40)
y = x**2*exp(-x)

u = array([x[i+1]-x[i] for i in range(len(x)-1)])
v = array([y[i+1]-y[i] for i in range(len(x)-1)])

x = x[:len(u)] # 使得维数和u,v一致
y = y[:len(v)]

c = randn(len(u)) # arrow颜色

figure()
quiver(x,y,u,v,c, angles='xy', scale_units='xy', scale=1) # 注意参数的赋值

## example 2

x = linspace(0,20,30)
y = sin(x)

u = array([x[i+1]-x[i] for i in range(len(x)-1)])
v = array([y[i+1]-y[i] for i in range(len(x)-1)])

x = x[:len(u)] # 使得维数和u,v一致
y = y[:len(v)]

c = randn(len(u)) # arrow颜色

figure()
quiver(x,y,u,v,c, angles='xy', scale_units='xy', scale=1) # 注意参数的赋值
show()

结果如下：

补充知识：Matlab矢量图图例函数quiverkey

Matlab自带函数中不包含构造 quiver 函数注释过程，本文参照 matplotlib 中 quiverkey 函数，构造类似函数为 Matlab 中 quiver 矢量场进行标注。

quiverkey函数

首先看 matplotlib 中 quiverkey 如何定义的

quiverkey(*args, **kw)
Add a key to a quiver plot.

Call signature::

 quiverkey(Q, X, Y, U, label, **kw)

Arguments:

 *Q*:
 The Quiver instance returned by a call to quiver.

 *X*, *Y*:
 The location of the key; additional explanation follows.

 *U*:
 The length of the key

 *label*:
 A string with the length and units of the key

Keyword arguments:

 *coordinates* = [ 'axes' | 'figure' | 'data' | 'inches' ]
 Coordinate system and units for *X*, *Y*: 'axes' and 'figure' are
 normalized coordinate systems with 0,0 in the lower left and 1,1
 in the upper right; 'data' are the axes data coordinates (used for
 the locations of the vectors in the quiver plot itself); 'inches'
 is position in the figure in inches, with 0,0 at the lower left
 corner.

 *color*:
 overrides face and edge colors from *Q*.

 *labelpos* = [ 'N' | 'S' | 'E' | 'W' ]
 Position the label above, below, to the right, to the left of the
 arrow, respectively.

 *labelsep*:
 Distance in inches between the arrow and the label. Default is
 0.1

 *labelcolor*:
 defaults to default :class:`~matplotlib.text.Text` color.

 *fontproperties*:
 A dictionary with keyword arguments accepted by the
 :class:`~matplotlib.font_manager.FontProperties` initializer:
 *family*, *style*, *variant*, *size*, *weight*

Any additional keyword arguments are used to override vector
properties taken from *Q*.

The positioning of the key depends on *X*, *Y*, *coordinates*, and
*labelpos*. If *labelpos* is 'N' or 'S', *X*, *Y* give the position
of the middle of the key arrow. If *labelpos* is 'E', *X*, *Y*
positions the head, and if *labelpos* is 'W', *X*, *Y* positions the
tail; in either of these two cases, *X*, *Y* is somewhere in the
middle of the arrow+label key object.


Additional kwargs: hold = [True|False] overrides default hold state

可以看到主要参数有这么些个

quiver绘图指针

图例位置 X, Y

标注大小 U

标注单位字符

其他参数

1）. 输入坐标 X, Y 单位
2）. （文字）标注在图例哪个位置
3）. 标注与图例相对距离
4）. 标注字体颜色

使用方法：

对应Matlab函数也应该使用这么个流程

使用quiver绘图

将quiver返回指针与图例位置坐标和大小等作为参数传入

示例

[x,y] = meshgrid(0:0.2:2,0:0.2:2);
u = cos(x).*y;
v = sin(x).*y;

figure; 
Qh = quiver(x,y,u,v);

quiverkey(Qh, 0.5, 2.5, 1, 'm/s', 'Color', 'r', 'Coordinates', 'data')

最终效果图

代码

function Q = quiverkey(Q, X, Y, U, label, varargin)
%QUIVERKEY legend for quiver
%
% QUIVERKEY(Q, X, Y, U, label) 
% 
% Arguments:
%  Q :  The quiver handle returned by a call to quiver
%  X,Y : The location of the legend
%  U :  The unit length. If U<0, the arrow will be reversed
%  label : The string with the length and units of the key
% 
% Addition arguments:
%  Coordinates = [ 'axes' | 'data'(default) ]
% 
%   'axes' & 'figure' : 'axes' and 'figure' are normalized 
%      coordinate systems with 0,0 in the lower left 
%      and 1,1 in the upper right;
%   'data' : use the axes data coordinates
% 
%  LabelDistance : Distance in 'coordinates' between the arrow and the
%     label. Deauft is 0.1 (units 'axes').
% 
%  Color : overrides face and edge colors from Q.
% 
%  LabelPosition = [ 'N' | 'S'(default) | 'E' | 'W' ]
% 
%    Position the label above, below, to the right, 
%    to the left of the arrow, respectively.
% 
%  LabelColor : defaults to black
%  
% Examples: 
% 
% [x,y] = meshgrid(0:0.2:2,0:0.2:2);
% u = cos(x).*y;
% v = sin(x).*y;
% figure; Qh = quiver(x,y,u,v);
% quiverkey(Qh, 0.5, 2.5, 1, 'm/s', 'Color', 'r', 'Coordinates', 'data')
% 
% Author:
% li12242 - Department of Civil Engineering in Tianjin University
% Email:
% li12242@tju.edu.cn
% 

%% get input argument
if nargin < 5 
 error('Input arguments" Number incorrect!')
end

if isempty(varargin) && mod(length(varargin), 2) ~= 0
 error('Input arguments donot pairs!')
else
 [CoorUnit, LabelDist, Color, LabelPosition, LabelColor] = getInput(varargin);
end


%% add legend arrow

% get original data
xData = get(Q, 'XData'); yData = get(Q, 'YData');
uData = get(Q, 'UData'); vData = get(Q, 'VData');

% get axes properties
haxes = get(Q, 'Parent');
xLim = get(haxes, 'XLim'); yLim = get(haxes, 'YLim');
NextPlot = get(haxes, 'NextPlot');

% set axes properties
set(haxes, 'NextPlot', 'add')

if strcmp(CoorUnit, 'axes')
 % position of legend arrow
 xa = xLim(1) + X*(xLim(2) - xLim(1));
 ya = yLim(1) + Y*(yLim(2) - yLim(1));
else
 xa = X; ya = Y;
end

% add legend arrow into data vector
xData = [xData(:); xa]; yData = [yData(:); ya];
uData = [uData(:); U]; vData = [vData(:); 0];

% reset data
set(Q, 'XData', xData, 'YData', yData, 'UData', uData, 'VData', vData);
set(Q, 'Color', Color)

%% add text
dx = LabelDist*(xLim(2) - xLim(1));
dy = LabelDist*(yLim(2) - yLim(1));

% set position of label
switch LabelPosition
 case 'N'
  xl = xa; yl = ya + dy;
 case 'S'
  xl = xa; yl = ya - dy;
 case 'E'
  xl = xa + dx; yl = ya;
 case 'W'
  xl = xa - dx; yl = ya;
end% switch

th = text(xl, yl, [num2str(U), ' ', label]);
set(th, 'Color', LabelColor);

% turn axes properties to original
set(haxes, 'NextPlot', NextPlot)

end% func

%% sub function

function [CoorUnit, LabelDist, Color, LabelPosition, LabelColor] = getInput(varcell)
% Input:
% varcell - cell variable
% Output:
% 
nargin = numel(varcell);

%% set default arguments

CoorUnit = 'data';
LabelDist = 0.05; % units 'axes'
Color = 'k';
LabelPosition = 'S';
LabelColor = 'k';

%% get input arguments
contour = 1;
while contour < nargin
 switch varcell{contour}
  case 'Coordinates'
   CoorUnit = varcell{contour+ 1};
  case 'LabelDistance'
   LabelDist = varcell{contour+ 1};
  case 'Color'
   Color = varcell{contour+ 1};
  case 'LabelPosition'
   LabelPosition = varcell{contour+ 1};
  case 'LabelColor'
   LabelColor = varcell{contour+ 1};
  otherwise
   error('Unknown input argument.')
 end% switch
 contour = contour + 2;
end% while

end% fun

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