智能计算图表刻度位置

Question

无论我使用matplotlib,Open-Flash-Charts还是其他图表框架,我总是需要找到一种方法来设置x/y比例限制和间隔,因为内置的智能不够(或根本没有...)

只是在pylab(ipyhton -pylab)中尝试这个来理解我的意思:

In [1]: a, b, x = np.zeros(10), np.ones(10), np.arange(10)

In [2]: plot(x, a); plot(x, b)

你会看到正好和空的框架网格隐藏在其顶部和底部边框下面的2条水平线.

我想知道是否有一些算法(我可以移植到python)来设置聪明的顶部和底部y限制和步骤,并计算每个显示x厚度的值.

举例来说,假设我有475项措施,(datetime, temperature)如(x, y)用

2011-01-15 10:45:00 < datetime < 2011-01-17 02:20:00

(每5分钟一次)和

26.5 < temperature < 28.3

我对这个特例的建议可能是:

26.4 <= y_scale <= 28.4 每一个都厚 .2

并且x_scale每12个项目(每小时一次)打勾.

但是,如果我在20天内只有20项措施 -21.5 < temperature < 38.7,等等呢？有标准化的方法吗？

Answer 1

以下是我多年来一直使用的简单而且运作良好的内容.请原谅我是C,但转换为Python应该不难.

需要以下功能,来自Graphic Gems第1卷.

double NiceNumber (const double Value, const int Round) {
  int    Exponent;
  double Fraction;
  double NiceFraction;

  Exponent = (int) floor(log10(Value));
  Fraction = Value/pow(10, (double)Exponent);

  if (Round) {
    if (Fraction < 1.5) 
      NiceFraction = 1.0;
    else if (Fraction < 3.0)
      NiceFraction = 2.0;
    else if (Fraction < 7.0)
      NiceFraction = 5.0;
    else
      NiceFraction = 10.0;
   }
  else {
    if (Fraction <= 1.0)
      NiceFraction = 1.0;
    else if (Fraction <= 2.0)
      NiceFraction = 2.0;
    else if (Fraction <= 5.0)
      NiceFraction = 5.0;
    else
      NiceFraction = 10.0;
   }

  return NiceFraction*pow(10, (double)Exponent);
 }

使用它,如下例所示,根据您希望显示的主刻度数选择轴的"漂亮"开始/结束.如果您不关心刻度线,您可以将其设置为常数值(例如:10).

      //Input parameters
  double AxisStart = 26.5;
  double AxisEnd   = 28.3;
  double NumTicks  = 10;

  double AxisWidth;
  double NewAxisStart;
  double NewAxisEnd;
  double NiceRange;
  double NiceTick;

    /* Check for special cases */
  AxisWidth = AxisEnd - AxisStart;
  if (AxisWidth == 0.0) return (0.0);

    /* Compute the new nice range and ticks */
  NiceRange = NiceNumber(AxisEnd - AxisStart, 0);
  NiceTick = NiceNumber(NiceRange/(NumTicks - 1), 1);

    /* Compute the new nice start and end values */
  NewAxisStart = floor(AxisStart/NiceTick)*NiceTick;
  NewAxisEnd = ceil(AxisEnd/NiceTick)*NiceTick;

  AxisStart = NewAxisStart; //26.4
  AxisEnd = NewAxisEnd;     //28.4

Answer 2

如果对某人有任何帮助，我在这里报告我的上述 C 代码的 python 版本：

import math


def nice_number(value, round_=False):
    '''nice_number(value, round_=False) -> float'''
    exponent = math.floor(math.log(value, 10))
    fraction = value / 10 ** exponent

    if round_:
        if fraction < 1.5:
            nice_fraction = 1.
        elif fraction < 3.:
            nice_fraction = 2.
        elif fraction < 7.:
            nice_fraction = 5.
        else:
            nice_fraction = 10.
    else:
        if fraction <= 1:
            nice_fraction = 1.
        elif fraction <= 2:
            nice_fraction = 2.
        elif fraction <= 5:
            nice_fraction = 5.
        else:
            nice_fraction = 10.

    return nice_fraction * 10 ** exponent


def nice_bounds(axis_start, axis_end, num_ticks=10):
    '''
    nice_bounds(axis_start, axis_end, num_ticks=10) -> tuple
    @return: tuple as (nice_axis_start, nice_axis_end, nice_tick_width)
    '''
    axis_width = axis_end - axis_start
    if axis_width == 0:
        nice_tick = 0
    else:
        nice_range = nice_number(axis_width)
        nice_tick = nice_number(nice_range / (num_ticks - 1), round_=True)
        axis_start = math.floor(axis_start / nice_tick) * nice_tick
        axis_end = math.ceil(axis_end / nice_tick) * nice_tick

    return axis_start, axis_end, nice_tick

用于：

>>> nice_bounds(26.5, 28.3)
(26.4, 28.4, 0.2)

还添加一个 javascript 移植：

function nice_number(value, round_){
    //default value for round_ is false
    round_ = round_ || false;
    // :latex: \log_y z = \frac{\log_x z}{\log_x y}
    var exponent = Math.floor(Math.log(value) / Math.log(10));
    var fraction = value / Math.pow(10, exponent);

    if (round_)
        if (fraction < 1.5)
            nice_fraction = 1.
        else if (fraction < 3.)
            nice_fraction = 2.
        else if (fraction < 7.)
            nice_fraction = 5.
        else
            nice_fraction = 10.
    else
        if (fraction <= 1)
            nice_fraction = 1.
        else if (fraction <= 2)
            nice_fraction = 2.
        else if (fraction <= 5)
            nice_fraction = 5.
        else
            nice_fraction = 10.

    return nice_fraction * Math.pow(10, exponent)
}

function nice_bounds(axis_start, axis_end, num_ticks){
    //default value is 10
    num_ticks = num_ticks || 10;
    var axis_width = axis_end - axis_start;

    if (axis_width == 0){
        axis_start -= .5
        axis_end += .5
        axis_width = axis_end - axis_start
    }

    var nice_range = nice_number(axis_width);
    var nice_tick = nice_number(nice_range / (num_ticks -1), true);
    var axis_start = Math.floor(axis_start / nice_tick) * nice_tick;
    var axis_end = Math.ceil(axis_end / nice_tick) * nice_tick;
    return {
        "min": axis_start,
        "max": axis_end,
        "steps": nice_tick
    }
}