def cvx():
# Figures 6.8-10, pages 313-314
# Quadratic smoothing.
from math import pi
from cvxopt import blas, lapack, matrix, sin, mul, normal
n = 4000
t = matrix(list(range(n)), tc='d')
ex = 0.5 * mul(sin(2 * pi / n * t), sin(0.01 * t))
corr = ex + 0.05 * normal(n, 1)
# A = D'*D is an n by n tridiagonal matrix with -1.0 on the
# upper/lower diagonal and 1, 2, 2, ..., 2, 2, 1 on the diagonal.
Ad = matrix([1.0] + (n - 2) * [2.0] + [1.0])
As = matrix(-1.0, (n - 1, 1))
nopts = 50
deltas = -10.0 + 20.0 / (nopts - 1) * matrix(list(range(nopts)))
cost1, cost2 = [], []
for delta in deltas:
xr = +corr
lapack.ptsv(1.0 + 10 ** delta * Ad, 10 ** delta * As, xr)
cost1 += [blas.nrm2(xr - corr)]
cost2 += [blas.nrm2(xr[1:] - xr[:-1])]
# Find solutions with ||xhat - xcorr || roughly equal to 8.0, 3.1, 1.0.
time.sleep(1)
mv1, k1 = min(zip([abs(c - 8.0) for c in cost1], range(nopts)))
xr1 = +corr
lapack.ptsv(1.0 + 10 ** deltas[k1] * Ad, 10 ** deltas[k1] * As, xr1)
mv2, k2 = min(zip([abs(c - 3.1) for c in cost1], range(nopts)))
xr2 = +corr
lapack.ptsv(1.0 + 10 ** deltas[k2] * Ad, 10 ** deltas[k2] * As, xr2)
mv3, k3 = min(zip([abs(c - 1.0) for c in cost1], range(nopts)))
xr3 = +corr
lapack.ptsv(1.0 + 10 ** deltas[k3] * Ad, 10 ** deltas[k3] * As, xr3)
pylab.plot(t, corr)
pylab.ylabel('xcor[i]')
pylab.xlabel('i')
# A = D'*D is an n by n tridiagonal matrix with -1.0 on the
# upper/lower diagonal and 1, 2, 2, ..., 2, 2, 1 on the diagonal.
Ad = matrix([1.0] + (n-2)*[2.0] + [1.0])
As = matrix(-1.0, (n-1,1))
nopts = 50
deltas = -10.0 + 20.0/(nopts-1) * matrix(list(range(nopts)))
cost1, cost2 = [], []
for delta in deltas:
xr = +corr
lapack.ptsv(1.0 + 10**delta * Ad, 10**delta *As, xr)
cost1 += [blas.nrm2(xr - corr)]
cost2 += [blas.nrm2(xr[1:] - xr[:-1])]
# Find solutions with ||xhat - xcorr || roughly equal to 8.0, 3.1, 1.0.
mv1, k1 = min(zip([abs(c - 8.0) for c in cost1], range(nopts)))
xr1 = +corr
lapack.ptsv(1.0 + 10**deltas[k1] * Ad, 10**deltas[k1] *As, xr1)
mv2, k2 = min(zip([abs(c - 3.1) for c in cost1], range(nopts)))
xr2 = +corr
lapack.ptsv(1.0 + 10**deltas[k2] * Ad, 10**deltas[k2] *As, xr2)
mv3, k3 = min(zip([abs(c - 1.0) for c in cost1], range(nopts)))
xr3 = +corr
lapack.ptsv(1.0 + 10**deltas[k3] * Ad, 10**deltas[k3] *As, xr3)
if pylab_installed:
pylab.subplot(212)
pylab.plot(t, corr)
pylab.ylabel('xcor[i]')
pylab.xlabel('i')
# A = D'*D is an n by n tridiagonal matrix with -1.0 on the
# upper/lower diagonal and 1, 2, 2, ..., 2, 2, 1 on the diagonal.
Ad = matrix([1.0] + (n - 2) * [2.0] + [1.0])
As = matrix(-1.0, (n - 1, 1))
nopts = 50
deltas = -10.0 + 20.0 / (nopts - 1) * matrix(list(range(nopts)))
cost1, cost2 = [], []
for delta in deltas:
xr = +corr
lapack.ptsv(1.0 + 10**delta * Ad, 10**delta * As, xr)
cost1 += [blas.nrm2(xr - corr)]
cost2 += [blas.nrm2(xr[1:] - xr[:-1])]
# Find solutions with ||xhat - xcorr || roughly equal to 8.0, 3.1, 1.0.
mv1, k1 = min(zip([abs(c - 8.0) for c in cost1], range(nopts)))
xr1 = +corr
lapack.ptsv(1.0 + 10**deltas[k1] * Ad, 10**deltas[k1] * As, xr1)
mv2, k2 = min(zip([abs(c - 3.1) for c in cost1], range(nopts)))
xr2 = +corr
lapack.ptsv(1.0 + 10**deltas[k2] * Ad, 10**deltas[k2] * As, xr2)
mv3, k3 = min(zip([abs(c - 1.0) for c in cost1], range(nopts)))
xr3 = +corr
lapack.ptsv(1.0 + 10**deltas[k3] * Ad, 10**deltas[k3] * As, xr3)
if pylab_installed: