nilmtools/nilmtools/math.py

#!/usr/bin/python

# Miscellaenous useful mathematical functions
from nilmdb.utils.printf import *
from numpy import *
from scipy import *

def sfit4(data, fs):
    """(A, f0, phi, C) = sfit4(data, fs)

    Compute 4-parameter (unknown-frequency) least-squares fit to
    sine-wave data, according to IEEE Std 1241-2010 Annex B

    Input:
      data  vector of input samples
      fs    sampling rate (Hz)

    Output:
      Parameters [A, f0,  phi, C] to fit the equation
        x[n] = A * sin(f0/fs * 2 * pi * n + phi) + C
      where n is sample number.  Or, as a function of time:
        x(t) = A * sin(f0 * 2 * pi * t + phi) + C

    by Jim Paris
    (Verified to match sfit4.m)
    """
    N = len(data)
    t = linspace(0, (N-1) / float(fs), N)

    ## Estimate frequency using FFT (step b)
    Fc = fft(data)
    F = abs(Fc)
    F[0] = 0   # eliminate DC

    # Find pair of spectral lines with largest amplitude:
    # resulting values are in F(i) and F(i+1)
    i = argmax(F[0:int(N/2)] + F[1:int(N/2+1)])

    # Interpolate FFT to get a better result (from Markus [B37])
    try:
        U1 = real(Fc[i])
        U2 = real(Fc[i+1])
        V1 = imag(Fc[i])
        V2 = imag(Fc[i+1])
        n = 2 * pi / N
        ni1 = n * i
        ni2 = n * (i+1)
        K = ((V2-V1)*sin(ni1) + (U2-U1)*cos(ni1)) / (U2-U1)
        Z1 = V1 * (K - cos(ni1)) / sin(ni1) + U1
        Z2 = V2 * (K - cos(ni2)) / sin(ni2) + U2
        i = arccos((Z2*cos(ni2) - Z1*cos(ni1)) / (Z2-Z1)) / n
    except Exception:
        # Just go with the biggest FFT peak
        i = argmax(F[0:int(N/2)])

    # Convert to Hz
    f0 = i * float(fs) / N

    # Fit it.  We'll catch exceptions here and just returns zeros
    # if something fails with the least squares fit, etc.
    try:
        # first guess for A0, B0 using 3-parameter fit (step c)
        s = zeros(3)
        w = 2*pi*f0

        # Now iterate 7 times (step b, plus 6 iterations of step i)
        for idx in range(7):
            D = c_[cos(w*t), sin(w*t), ones(N),
                  -s[0] * t * sin(w*t) + s[1] * t * cos(w*t) ] # eqn B.16
            s = linalg.lstsq(D, data, rcond=None)[0] # eqn B.18
            w = w + s[3]	# update frequency estimate

        ## Extract results
        A = sqrt(s[0]*s[0] + s[1]*s[1]) # eqn B.21
        f0 = w / (2*pi)
        phi = arctan2(s[0], s[1]) # eqn B.22 (flipped for sin instead of cos)
        C = s[2]
        return (A, f0, phi, C)
    except Exception as e:
        # something broke down; just return zeros
        return (0, 0, 0, 0)

def peak_detect(data, delta = 0.1):
    """Simple min/max peak detection algorithm, taken from my code
    in the disagg.m from the 10-8-5 paper.

    Returns an array of peaks: each peak is a tuple
      (n, p, is_max)
    where n is the row number in 'data', and p is 'data[n]',
    and is_max is True if this is a maximum, False if it's a minimum,
    """
    peaks = [];
    cur_min = (None, inf)
    cur_max = (None, -inf)
    lookformax = False
    for (n, p) in enumerate(data):
        if p > cur_max[1]:
            cur_max = (n, p)
        if p < cur_min[1]:
            cur_min = (n, p)
        if lookformax:
            if p < (cur_max[1] - delta):
                peaks.append((cur_max[0], cur_max[1], True))
                cur_min = (n, p)
                lookformax = False
        else:
            if p > (cur_min[1] + delta):
                peaks.append((cur_min[0], cur_min[1], False))
                cur_max = (n, p)
                lookformax = True
    return peaks