Question

我在查看scipy cookbook implementation of the Savitzky-Golay algorithm：

#!python
def savitzky_golay(y, window_size, order, deriv=0, rate=1):
    r"""Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
    The Savitzky-Golay filter removes high frequency noise from data.
    It has the advantage of preserving the original shape and
    features of the signal better than other types of filtering
    approaches, such as moving averages techniques.
    Parameters
    ----------
    y : array_like, shape (N,)
        the values of the time history of the signal.
    window_size : int
        the length of the window. Must be an odd integer number.
    order : int
        the order of the polynomial used in the filtering.
        Must be less then `window_size` - 1.
    deriv: int
        the order of the derivative to compute (default = 0 means only smoothing)
    Returns
    -------
    ys : ndarray, shape (N)
        the smoothed signal (or it's n-th derivative).
    Notes
    -----
    The Savitzky-Golay is a type of low-pass filter, particularly
    suited for smoothing noisy data. The main idea behind this
    approach is to make for each point a least-square fit with a
    polynomial of high order over a odd-sized window centered at
    the point.
    Examples
    --------
    t = np.linspace(-4, 4, 500)
    y = np.exp( -t**2 ) + np.random.normal(0, 0.05, t.shape)
    ysg = savitzky_golay(y, window_size=31, order=4)
    import matplotlib.pyplot as plt
    plt.plot(t, y, label='Noisy signal')
    plt.plot(t, np.exp(-t**2), 'k', lw=1.5, label='Original signal')
    plt.plot(t, ysg, 'r', label='Filtered signal')
    plt.legend()
    plt.show()
    References
    ----------
    .. [1] A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of
       Data by Simplified Least Squares Procedures. Analytical
       Chemistry, 1964, 36 (8), pp 1627-1639.
    .. [2] Numerical Recipes 3rd Edition: The Art of Scientific Computing
       W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery
       Cambridge University Press ISBN-13: 9780521880688
    """
    import numpy as np
    from math import factorial

    try:
        window_size = np.abs(np.int(window_size))
        order = np.abs(np.int(order))
    except ValueError, msg:
        raise ValueError("window_size and order have to be of type int")
    if window_size % 2 != 1 or window_size < 1:
        raise TypeError("window_size size must be a positive odd number")
    if window_size < order + 2:
        raise TypeError("window_size is too small for the polynomials order")
    order_range = range(order+1)
    half_window = (window_size -1) // 2
    # precompute coefficients
    b = np.mat([[k**i for i in order_range] for k in range(-half_window, half_window+1)])
    m = np.linalg.pinv(b).A[deriv] * rate**deriv * factorial(deriv)
    # pad the signal at the extremes with
    # values taken from the signal itself
    firstvals = y[0] - np.abs( y[1:half_window+1][::-1] - y[0] )
    lastvals = y[-1] + np.abs(y[-half_window-1:-1][::-1] - y[-1])
    y = np.concatenate((firstvals, y, lastvals))
    return np.convolve( m[::-1], y, mode='valid')

这是令我困惑的部分：

firstvals = y[0] - np.abs( y[1:half_window+1][::-1] - y[0] )
lastvals = y[-1] + np.abs(y[-half_window-1:-1][::-1] - y[-1])
y = np.concatenate((firstvals, y, lastvals))

我知道我们需要'填充'y，否则会排除第一个window_size/2点，但我没有看到用{{减去特定值的绝对差值的重点1}}来自y[0]。

我不认为绝对值应该存在，否则，如果趋势从增加开始，趋势会被水平镜像，而如果从趋势开始减少则趋势是垂直的。

正如@ImportanceOfBeingErnest指出的那样，这可能是代码中的拼写错误，可以通过查看我链接到的页面中的绘图的左侧看到。

Answer 1

实际上，这种逻辑是不正确的，通过考虑y [0]和y [-1]为0的情况可以最好地看出这一点。我认为目的是实现奇数反射，以便一阶导数会在反射点连续。正确的形式是

<!-- your.component.html -->
<button (click)="openPdf();">Open Pdf</button>

<!-- Please note, you need a copy of https://github.com/intbot/ng2-pdfjs-viewer/tree/master/pdfjs for some of the below features to work -->
<ng2-pdfjs-viewer #pdfViewer style="width: 800px; height: 400px"
  [pdfJsFolder]="'pdfjs'"
  [externalWindow]="true"
  [downloadFileName]="'mytestfile.pdf'"
  [openFile]="false"
  [viewBookmark]="false"
  [download]="false">
</ng2-pdfjs-viewer>

<!-- your.component.ts-->
export class RateCardComponent implements OnInit {
  @ViewChild('pdfViewer') pdfViewer;
  ...

  private downloadFile(url: string): any {
    return this.http.get(url, { responseType: ResponseContentType.Blob }).map(
      (res) => {
        return new Blob([res.blob()], { type: "application/pdf" });
      });
  }

  public openPdf() {
    let url = "url to fetch pdf as byte array";
    // url can be local url or remote http request to an api/pdf file. 
    // E.g: let url = "assets/pdf-sample.pdf";
    // E.g: https://github.com/intbot/ng2-pdfjs-viewer/tree/master/sampledoc/pdf-sample.pdf
    // E.g: http://localhost:3000/api/GetMyPdf
    // Please note, for remote urls to work, CORS should be enabled at the server. Read: https://enable-cors.org/server.html

    this.downloadFile(url).subscribe(
      (res) => {
        this.pdfViewer.pdfSrc = res; // pdfSrc can be Blob or Uint8Array
      }
    );
  }

或者，在一步中结合反转和切片，

firstvals = 2*y[0] - y[1:half_window+1][::-1]
lastvals = 2*y[-1] - y[-half_window-1:-1][::-1]

我应该强调这只是用户贡献的一些代码。实际Scipy implementation of Savitzky-Golay filter完全不同。

Scipy实现了Savitzky-Golay过滤器

1 个答案: