def call_solver(p,quiet):
"""
Calls solver.
:param p: Convex cvxpy_program.
Assumed to be expanded.
:param quiet: Boolean.
"""
# Set printing format for cvxopt sparse matrices
opt.spmatrix_str = opt.printing.spmatrix_str_triplet
# Expand objects defined via partial minimization
constr_list = cvxpy_list(pm_expand(p.constraints))
# Get variables
variables = constr_list.variables
variables.sort()
# Count variables
n = len(variables)
# Create variable-index map
var_to_index = {}
for i in range(0,n,1):
var_to_index[variables[i]] = i
# Construct objective vector
c = construct_c(p.objective,var_to_index,n,p.action)
# Construct Ax == b
A,b = construct_Ab(constr_list._get_eq(),var_to_index,n)
# Construct Gx <= h
G,h,dim_l,dim_q,dim_s = construct_Gh(constr_list._get_ineq_in(),
var_to_index,n)
# Construct F
F = construct_F(constr_list._get_ineq_in(),var_to_index,n)
# Call cvxopt
solvers.options['maxiters'] = p.options['maxiters']
solvers.options['abstol'] = p.options['abstol']
solvers.options['reltol'] = p.options['reltol']
solvers.options['feastol'] = p.options['feastol']
solvers.options['show_progress'] = not quiet
dims = {'l':dim_l, 'q':dim_q, 's':dim_s}
if F is None:
r = solvers.conelp(c,G,h,dims,A,b)
else:
r = solvers.cpl(c,F,G,h,dims,A,b)
# Store numerical values
if r['status'] != PRIMAL_INFEASIBLE:
for v in variables:
v.value = r['x'][var_to_index[v]]
# Return result
return r
def call_solver(p, quiet):
"""
Calls solver.
:param p: Convex cvxpy_program.
Assumed to be expanded.
:param quiet: Boolean.
"""
# Set printing format for cvxopt sparse matrices
opt.spmatrix_str = opt.printing.spmatrix_str_triplet
# Expand objects defined via partial minimization
constr_list = cvxpy_list(pm_expand(p.constraints))
# Get variables
variables = constr_list.variables
variables.sort()
# Count variables
n = len(variables)
# Create variable-index map
var_to_index = {}
for i in range(0, n, 1):
var_to_index[variables[i]] = i
# Construct objective vector
c = construct_c(p.objective, var_to_index, n, p.action)
# Construct Ax == b
A, b = construct_Ab(constr_list._get_eq(), var_to_index, n)
# Construct Gx <= h
G, h, dim_l, dim_q, dim_s = construct_Gh(constr_list._get_ineq_in(),
var_to_index, n)
# Construct F
F = construct_F(constr_list._get_ineq_in(), var_to_index, n)
# Call cvxopt
solvers.options['maxiters'] = p.options['maxiters']
solvers.options['abstol'] = p.options['abstol']
solvers.options['reltol'] = p.options['reltol']
solvers.options['feastol'] = p.options['feastol']
solvers.options['show_progress'] = not quiet
dims = {'l': dim_l, 'q': dim_q, 's': dim_s}
if F is None:
r = solvers.conelp(c, G, h, dims, A, b)
else:
r = solvers.cpl(c, F, G, h, dims, A, b)
# Store numerical values
if r['status'] != PRIMAL_INFEASIBLE:
for v in variables:
v.value = r['x'][var_to_index[v]]
# Return result
return r
def mean_variance_optimization(covariance,
mean=None,
expected_return=None,
expected_variance=None,
can_short=False):
if expected_return is not None and expected_variance is not None:
raise ValueError('不能同时设定均值与方差!')
A = np.ones((covariance.shape[0], 1))
A = matrix(A.T)
b = np.ones((1, 1))
b = matrix(b)
if expected_variance is not None:
c = -mean.reshape((covariance.shape[0], 1))
def F(x):
return x.dot(covariance).dot(x) - expected_variance
if not can_short:
G = -np.eye(covariance.shape[0])
h = np.zeros_like(mean)
else:
G, h = None, None
c = matrix(c)
G = matrix(G)
h = matrix(h)
result = solvers.cpl(c, F, G, h, A, b)
return np.array(result['x'])
Q = covariance.values
Q = matrix(Q)
p = np.zeros((covariance.shape[0], 1))
p = matrix(p)
if not can_short:
if expected_return is not None:
G = np.vstack([
-mean.values.reshape((1, covariance.shape[0])),
-np.eye(covariance.shape[0])
])
h = np.array([-expected_return].extend([0] * covariance.shape[0]))
else:
G = -np.eye(covariance.shape[0])
h = np.zeros((covariance.shape[0], 1))
else:
if expected_return is not None:
G = -mean.values.reshape((1, covariance.shape[0]))
h = np.array([-expected_return])
else:
G = None
h = None
G = matrix(G)
h = matrix(h)
result = solvers.qp(Q, p, G, h, A, b)
return pd.Series(result['x'],
index=covariance.index), result['primal objective']
def optimize(self, ret, cov):
"""
Max return, constrains on risk
"""
cov = np.matrix(cov)
# positive definite check
if not np.all(np.linalg.eigvals(cov) > 0):
print('Not positive definite.')
mat = cov * cov.T
w, v = np.linalg.eig(mat)
sqrt_w, v = np.diag(np.sqrt(w)), np.matrix(v)
cov = v * sqrt_w * np.linalg.inv(v)
# positive definite check may yield a plural value matrix
# thus use cov.real, note plural part is tiny e^-10
ret, cov, N = matrix(-ret), matrix(cov.real), len(ret)
## nonlinear constraints
def func(x=None, z=None):
if x is None:
return 1, matrix(1 / N, (N, 1))
# risk constraints and its matrix derivative
f = x.T * cov * x - 0.0064
df = x.T * (cov + cov.T)
if z is None:
return f, df
return f, df, z[0, 0] * (cov + cov.T)
## linear constrains
## note all the constraints are 'less and equal'
# no shortselling
g1 = matrix(np.diag(np.ones(N) * -1))
h1 = matrix(np.zeros(N))
# weights upperlimits
g2 = matrix(np.diag(np.ones(N)))
h2 = matrix(np.ones(N) * 0.05)
g, h = matrix([g1, g2]), matrix([h1, h2])
# weights sum equals 1
a = matrix(np.ones(N)).T
b = matrix(1.0, (1, 1))
## option for solver
# print convergence table
solvers.options['show_progress'] = self.show_progress
# max iteration
solvers.options['maxiters'] = self.maxiter
sol = solvers.cpl(ret, func, g, h, A=a, b=b)
return sol['x']
def model2(sigma2):
r = matrix([-1.0, -1.0, -3.0])
V = matrix(np.diag([1.0, 1.0, 1.0]))
G = matrix(np.diag([-1.0, -1.0, -1.0]))
h = matrix([0.33, 0.33, 0.33])
A = matrix(np.ones(3)).T
b = matrix(0.0, (1, 1))
def F(x=None, z=None):
if x is None:
return 1, matrix([0.0, 0.0, 0.0])
f = x.T * V * x - sigma2
Df = x.T * (V + V.T)
if z is None:
return f, Df
return f, Df, z[0, 0] * (V + V.T)
dims = {'l': h.size[0], 'q': [], 's': []}
sol = solvers.cpl(r, F, G, h, dims, A, b)
return sol['x']
def floorplan(Amin, opts):
# minimize W+H
# subject to Amink / hk <= wk, k = 1,..., 5
# x1 >= 0, x2 >= 0, x4 >= 0
# x1 + w1 + rho <= x3
# x2 + w2 + rho <= x3
# x3 + w3 + rho <= x5
# x4 + w4 + rho <= x5
# x5 + w5 <= W
# y2 >= 0, y3 >= 0, y5 >= 0
# y2 + h2 + rho <= y1
# y1 + h1 + rho <= y4
# y3 + h3 + rho <= y4
# y4 + h4 <= H
# y5 + h5 <= H
# hk/gamma <= wk <= gamma*hk, k = 1, ..., 5
#
# 22 Variables W, H, x (5), y (5), w (5), h (5).
#
# W, H: scalars; bounding box width and height
# x, y: 5-vectors; coordinates of bottom left corners of blocks
# w, h: 5-vectors; widths and heigths of the 5 blocks
rho, gamma = 1.0, 5.0 # min spacing, min aspect ratio
# The objective is to minimize W + H. There are five nonlinear
# constraints
#
# -wk + Amink / hk <= 0, k = 1, ..., 5
c = matrix(2 * [1.0] + 20 * [0.0])
def F(x=None, z=None):
# F0
if x is None:
return 5, matrix(17 * [0.0] + 5 * [1.0])
if min(x[17:]) <= 0.0:
return None
# F1
f = -x[12:17] + div(Amin, x[17:])
Df = matrix(0.0, (5, 22))
Df[:, 12:17] = spmatrix(-1.0, range(5), range(5))
Df[:, 17:] = spmatrix(-div(Amin, x[17:]**2), range(5), range(5))
if z is None:
return f, Df
# F2
H = spmatrix(2.0 * mul(z, div(Amin, x[17::]**3)), range(17, 22),
range(17, 22))
return f, Df, H
G = matrix(0.0, (26, 22))
h = matrix(0.0, (26, 1))
# -x1 <= 0
G[0, 2] = -1.0
# -x2 <= 0
G[1, 3] = -1.0
# -x4 <= 0
G[2, 5] = -1.0
# x1 - x3 + w1 <= -rho
G[3, [2, 4, 12]], h[3] = [1.0, -1.0, 1.0], -rho
# x2 - x3 + w2 <= -rho
G[4, [3, 4, 13]], h[4] = [1.0, -1.0, 1.0], -rho
# x3 - x5 + w3 <= -rho
G[5, [4, 6, 14]], h[5] = [1.0, -1.0, 1.0], -rho
# x4 - x5 + w4 <= -rho
G[6, [5, 6, 15]], h[6] = [1.0, -1.0, 1.0], -rho
# -W + x5 + w5 <= 0
G[7, [0, 6, 16]] = -1.0, 1.0, 1.0
# -y2 <= 0
G[8, 8] = -1.0
# -y3 <= 0
G[9, 9] = -1.0
# -y5 <= 0
G[10, 11] = -1.0
# -y1 + y2 + h2 <= -rho
G[11, [7, 8, 18]], h[11] = [-1.0, 1.0, 1.0], -rho
# y1 - y4 + h1 <= -rho
G[12, [7, 10, 17]], h[12] = [1.0, -1.0, 1.0], -rho
# y3 - y4 + h3 <= -rho
G[13, [9, 10, 19]], h[13] = [1.0, -1.0, 1.0], -rho
# -H + y4 + h4 <= 0
G[14, [1, 10, 20]] = -1.0, 1.0, 1.0
# -H + y5 + h5 <= 0
G[15, [1, 11, 21]] = -1.0, 1.0, 1.0
# -w1 + h1/gamma <= 0
G[16, [12, 17]] = -1.0, 1.0 / gamma
# w1 - gamma * h1 <= 0
G[17, [12, 17]] = 1.0, -gamma
# -w2 + h2/gamma <= 0
G[18, [13, 18]] = -1.0, 1.0 / gamma
# w2 - gamma * h2 <= 0
G[19, [13, 18]] = 1.0, -gamma
# -w3 + h3/gamma <= 0
G[20, [14, 18]] = -1.0, 1.0 / gamma
# w3 - gamma * h3 <= 0
G[21, [14, 19]] = 1.0, -gamma
# -w4 + h4/gamma <= 0
G[22, [15, 19]] = -1.0, 1.0 / gamma
# w4 - gamma * h4 <= 0
G[23, [15, 20]] = 1.0, -gamma
# -w5 + h5/gamma <= 0
G[24, [16, 21]] = -1.0, 1.0 / gamma
# w5 - gamma * h5 <= 0.0
G[25, [16, 21]] = 1.0, -gamma
# solve and return W, H, x, y, w, h
solvers.options.update(opts)
sol = solvers.cpl(c, F, G, h)
return sol['x'][0], sol['x'][1], sol['x'][2:7], sol['x'][7:12], \
sol['x'][12:17], sol['x'][17:], sol['x']
def solve_convex(p,mode):
"""
Description
-----------
Solves the convex program p. It assumes p is the convex part
of an expanded and transformed program.
Arguments
---------
p: convex cvxpy_program.
mode: 'rel' (relaxation) or 'scp' (sequential convex programming).
"""
# Select options
if(mode == 'scp'):
options = p.options['SCP_SOL']
else:
options = p.options['REL_SOL']
quiet = p.options['quiet']
# Printing format for cvxopt sparse matrices
opt.spmatrix_str = opt.printing.spmatrix_str_triplet
# Partial minimization expansion
constr_list = pm_expand(p.constr)
# Get variables
variables = constr_list.get_vars()
# Count variables
n = len(variables)
# Create a map (var - pos)
if(options['show steps'] and not quiet):
print '\nCreating variable - index map'
var_to_index = {}
for i in range(0,n,1):
if(options['show steps'] and not quiet):
print variables[i],'<-->',i
var_to_index[variables[i]] = i
# Construct objective vector
c = construct_c(p.obj,var_to_index,n,p.action)
if(options['show steps'] and not quiet):
print '\nConstructing c vector'
print 'c = '
print c
# Construct Ax == b
A,b = construct_Ab(constr_list._get_eq(),var_to_index,n,options)
if(options['show steps'] and not quiet):
print '\nConstructing Ax == b'
print 'A ='
print A
print 'b ='
print b
# Construct Gx <= h
G,h,dim_l,dim_q,dim_s = construct_Gh(constr_list._get_ineq_in(),
var_to_index,n)
if(options['show steps'] and not quiet):
print '\nConstructing Gx <= h'
print 'G ='
print G
print 'h ='
print h
# Construct F
F = construct_F(constr_list._get_ineq_in(),var_to_index,n)
if(options['show steps'] and not quiet):
print '\nConstructing F'
# Call cvxopt
solvers.options['show_progress'] = options['solver progress'] and not quiet
solvers.options['maxiters'] = options['maxiters']
solvers.options['abstol'] = options['abstol']
solvers.options['reltol'] = options['reltol']
solvers.options['feastol'] = options['feastol']
dims = {'l':dim_l, 'q':dim_q, 's':dim_s}
if(F is None):
if(options['show steps'] and not quiet):
print '\nCalling cvxopt conelp solver'
r = solvers.conelp(c,G,h,dims,A,b)
else:
if(options['show steps'] and not quiet):
print '\nCalling cvxopt cpl solver'
r = solvers.cpl(c,F,G,h,dims,A,b)
# Store numerical values
if(r['status'] != 'primal infeasible'):
if(options['show steps'] and not quiet):
print '\nStoring numerical values:'
for v in variables:
value = r['x'][var_to_index[v]]
v.data = value
if(options['show steps']and not quiet):
print v,' <- ', v.data
# Return result
return r
def max_returns(returns, risk_structure, risk, base=None, up=None, eq=None, noeq=None):
"""
给定风险约束，最大化收益的最优投资组合
:param returns: 下一期股票收益
:param risk_structure: 风险结构
:param risk: Double, 风险或是年化跟踪误差的上限
:param base: Vector, 基准组合
:param up: Double, 个股权重的上限
:param eq: list, [A, B], 其余等式约束条件
:param noeq: list, [G, h], 其余不等式约束条件
:return: 最优化的投资组合
"""
assert len(risk_structure) == len(returns), "numbers of companies in risk structure " \
"and returns vector are not the same"
if base is not None:
assert len(base) == len(returns), "numbers of companies in base vector and returns vector are not the same"
if up is None:
up = np.ones(len(returns)) # 默认取值为1
else:
up = np.ones(len(returns)) * up # up 既可以为值也可以为列向量
r, v = matrix(np.asarray(returns)) * -1, matrix(np.asarray(risk_structure))
num = len(returns)
base = matrix(np.asarray(base if base is not None else np.zeros(num))) * 1.0 # base 默认为0
def func(x=None, z=None):
if x is None:
return 1, matrix(0.0, (len(r), 1))
f = x.T * v * x - risk ** 2 / 12
df = x.T * (v + v.T)
if z is None:
return f, df
return f, df, z[0, 0] * (v + v.T)
# 不能卖空
g1 = matrix(np.diag(np.ones(num) * -1))
h1 = base
# 个股上限
g2 = matrix(np.diag(np.ones(num)))
h2 = matrix(up) - base
g, h = matrix([g1, g2]), matrix([h1, h2])
# 控制权重和
# 0.0 if sum(base) > 0 else 1.0 在没有基准（即基准为 0.0）时为1.0，有基准时为0.0
a = matrix(np.ones(num)).T
b = matrix(0.0 if sum(base) > 0 else 1.0, (1, 1))
if noeq is not None:
assert type(noeq) == list and len(noeq) == 2, "不等式约束条件为形如 [G, H] 的列表"
g3, h3 = matrix(noeq[0]), matrix(noeq[1])
g, h = matrix([g, g3]), matrix([h, h3])
if eq is not None:
assert type(eq) == list and len(eq) == 2, "等式约束条件为形如 [A, B] 的列表"
a1, b1 = matrix(eq[0]), matrix(eq[1])
a, b = matrix([a, a1]), matrix([b, b1])
solvers.options['show_progress'] = show_progress
solvers.options['maxiters'] = 1000
sol = solvers.cpl(r, func, g, h, A=a, b=b)
return sol['x']
def max_returns(returns,
risk_structure,
risk,
base=None,
up=None,
industry=None,
deviate=None,
factor=None,
xk=None):
"""
给定风险约束，最大化收益的最优投资组合
:param returns: 下一期股票收益
:param risk_structure: 风险结构
:param risk: Double, 风险或是年化跟踪误差的上限
:param base: Vector, 基准组合
:param up: Double, 个股权重的上限
:param industry: DataFrame, 行业哑变量矩阵
:param deviate: Double, 行业偏离
:param factor: DataFrame, 因子暴露
:param xk: Double, 因子风险的上限
:return: 最优化的投资组合
"""
assert len(risk_structure) == len(returns), "numbers of companies in risk structure " \
"and returns vector are not the same"
if industry is not None:
assert len(industry) == len(returns), "numbers of companies in industry dummy matrix " \
"not equals to it in returns vector"
if base is not None:
assert len(base) == len(
returns
), "numbers of companies in base vector and returns vector are not the same"
if up is None:
up = np.ones(len(returns))
else:
up = np.ones(len(returns)) * up
r, v = matrix(np.asarray(returns)) * -1, matrix(np.asarray(risk_structure))
num = len(returns)
base = matrix(
np.asarray(base if base is not None else np.zeros(num))) * 1.0
def func(x=None, z=None):
if x is None:
return 1, matrix(0.0, (len(r), 1))
f = x.T * v * x - risk**2 / 12
df = x.T * (v + v.T)
if z is None:
return f, df
return f, df, z[0, 0] * (v + v.T)
# 不能卖空
g1 = matrix(np.diag(np.ones(num) * -1))
h1 = base
# 个股上限
g2 = matrix(np.diag(np.ones(num)))
h2 = matrix(up) - base
g, h = matrix([g1, g2]), matrix([h1, h2])
# 控制权重和
# 0.0 if sum(base) > 0 else 1.0 在没有基准（即基准为 0.0）时为1.0，有基准时为0.0
a = matrix(np.ones(num)).T
b = matrix(0.0 if sum(base) > 0 else 1.0, (1, 1))
# 因子风险约束
if factor is not None:
g3 = matrix(np.asarray(factor)).T
h3 = matrix(xk, (len(factor.columns), 1))
g, h = matrix([g, g3]), matrix([h, h3])
# 对冲行业风险
if industry is not None:
m = matrix(np.asarray(industry) * 1.0).T
c = matrix(deviate, (len(industry.columns), 1))
if deviate == 0.0:
a, base = m, c
elif deviate > 0.0:
g, h = matrix([matrix([g, m]), -m]), matrix([matrix([h, c]), c])
solvers.options['show_progress'] = show_progress
solvers.options['maxiters'] = 1000
sol = solvers.cpl(r, func, g, h, A=a, b=b)
return sol['x']
def solve_convex(p, mode):
"""
Description
-----------
Solves the convex program p. It assumes p is the convex part
of an expanded and transformed program.
Arguments
---------
p: convex cvxpy_program.
mode: 'rel' (relaxation) or 'scp' (sequential convex programming).
"""
# Select options
if (mode == 'scp'):
options = p.options['SCP_SOL']
else:
options = p.options['REL_SOL']
quiet = p.options['quiet']
# Printing format for cvxopt sparse matrices
opt.spmatrix_str = opt.printing.spmatrix_str_triplet
# Partial minimization expansion
constr_list = pm_expand(p.constr)
# Get variables
variables = constr_list.get_vars()
# Count variables
n = len(variables)
# Create a map (var - pos)
if (options['show steps'] and not quiet):
print '\nCreating variable - index map'
var_to_index = {}
for i in range(0, n, 1):
if (options['show steps'] and not quiet):
print variables[i], '<-->', i
var_to_index[variables[i]] = i
# Construct objective vector
c = construct_c(p.obj, var_to_index, n, p.action)
if (options['show steps'] and not quiet):
print '\nConstructing c vector'
print 'c = '
print c
# Construct Ax == b
A, b = construct_Ab(constr_list._get_eq(), var_to_index, n, options)
if (options['show steps'] and not quiet):
print '\nConstructing Ax == b'
print 'A ='
print A
print 'b ='
print b
# Construct Gx <= h
G, h, dim_l, dim_q, dim_s = construct_Gh(constr_list._get_ineq_in(),
var_to_index, n)
if (options['show steps'] and not quiet):
print '\nConstructing Gx <= h'
print 'G ='
print G
print 'h ='
print h
# Construct F
F = construct_F(constr_list._get_ineq_in(), var_to_index, n)
if (options['show steps'] and not quiet):
print '\nConstructing F'
# Call cvxopt
solvers.options['show_progress'] = options['solver progress'] and not quiet
solvers.options['maxiters'] = options['maxiters']
solvers.options['abstol'] = options['abstol']
solvers.options['reltol'] = options['reltol']
solvers.options['feastol'] = options['feastol']
dims = {'l': dim_l, 'q': dim_q, 's': dim_s}
if (F is None):
if (options['show steps'] and not quiet):
print '\nCalling cvxopt conelp solver'
r = solvers.conelp(c, G, h, dims, A, b)
else:
if (options['show steps'] and not quiet):
print '\nCalling cvxopt cpl solver'
r = solvers.cpl(c, F, G, h, dims, A, b)
# Store numerical values
if (r['status'] != 'primal infeasible'):
if (options['show steps'] and not quiet):
print '\nStoring numerical values:'
for v in variables:
value = r['x'][var_to_index[v]]
v.data = value
if (options['show steps'] and not quiet):
print v, ' <- ', v.data
# Return result
return r
def floorplan(Amin):
# minimize W+H
# subject to Amin1 / h1 <= w1
# Amin2 / h2 <= w2
# Amin3 / h3 <= w3
# Amin4 / h4 <= w4
# Amin5 / h5 <= w5
# x1 >= 0
# x2 >= 0
# x4 >= 0
# x1 + w1 + rho <= x3
# x2 + w2 + rho <= x3
# x3 + w3 + rho <= x5
# x4 + w4 + rho <= x5
# x5 + w5 <= W
# y2 >= 0
# y3 >= 0
# y5 >= 0
# y2 + h2 + rho <= y1
# y1 + h1 + rho <= y4
# y3 + h3 + rho <= y4
# y4 + h4 <= H
# y5 + h5 <= H
# h1/gamma <= w1 <= gamma*h1
# h2/gamma <= w2 <= gamma*h2
# h3/gamma <= w3 <= gamma*h3
# h4/gamma <= w4 <= gamma*h4
# h5/gamma <= w5 <= gamma*h5
#
# 22 Variables W, H, x (5), y (5), w (5), h (5).
#
# W, H: scalars; bounding box width and height
# x, y: 5-vectors; coordinates of bottom left corners of blocks
# w, h: 5-vectors; widths and heigths of the 5 blocks
rho, gamma = 1.0, 5.0 # min spacing, min aspect ratio
# The objective is to minimize W + H. There are five nonlinear
# constraints
#
# -w1 + Amin1 / h1 <= 0
# -w2 + Amin2 / h2 <= 0
# -w3 + Amin3 / h3 <= 0
# -w4 + Amin4 / h4 <= 0
# -w5 + Amin5 / h5 <= 0.
c = matrix(2*[1.0] + 20*[0.0])
def F(x=None, z=None):
if x is None:
return 5, matrix(17*[0.0] + 5*[1.0])
if min(x[17:]) <= 0.0:
return None
f = -x[12:17] + div(Amin, x[17:])
Df = matrix(0.0, (5,22))
Df[:,12:17] = spmatrix(-1.0, range(5), range(5))
Df[:,17:] = spmatrix(-div(Amin, x[17:]**2), range(5), range(5))
if z is None:
return f, Df
H = spmatrix( 2.0* mul(z, div(Amin, x[17::]**3)), range(17,22),
range(17,22) )
return f, Df, H
# linear inequalities
G = matrix(0.0, (26,22))
h = matrix(0.0, (26,1))
# -x1 <= 0
G[0,2] = -1.0
# -x2 <= 0
G[1,3] = -1.0
# -x4 <= 0
G[2,5] = -1.0
# x1 - x3 + w1 <= -rho
G[3, [2, 4, 12]], h[3] = [1.0, -1.0, 1.0], -rho
# x2 - x3 + w2 <= -rho
G[4, [3, 4, 13]], h[4] = [1.0, -1.0, 1.0], -rho
# x3 - x5 + w3 <= -rho
G[5, [4, 6, 14]], h[5] = [1.0, -1.0, 1.0], -rho
# x4 - x5 + w4 <= -rho
G[6, [5, 6, 15]], h[6] = [1.0, -1.0, 1.0], -rho
# -W + x5 + w5 <= 0
G[7, [0, 6, 16]] = -1.0, 1.0, 1.0
# -y2 <= 0
G[8,8] = -1.0
# -y3 <= 0
G[9,9] = -1.0
# -y5 <= 0
G[10,11] = -1.0
# -y1 + y2 + h2 <= -rho
G[11, [7, 8, 18]], h[11] = [-1.0, 1.0, 1.0], -rho
# y1 - y4 + h1 <= -rho
G[12, [7, 10, 17]], h[12] = [1.0, -1.0, 1.0], -rho
# y3 - y4 + h3 <= -rho
G[13, [9, 10, 19]], h[13] = [1.0, -1.0, 1.0], -rho
# -H + y4 + h4 <= 0
G[14, [1, 10, 20]] = -1.0, 1.0, 1.0
# -H + y5 + h5 <= 0
G[15, [1, 11, 21]] = -1.0, 1.0, 1.0
# -w1 + h1/gamma <= 0
G[16, [12, 17]] = -1.0, 1.0/gamma
# w1 - gamma * h1 <= 0
G[17, [12, 17]] = 1.0, -gamma
# -w2 + h2/gamma <= 0
G[18, [13, 18]] = -1.0, 1.0/gamma
# w2 - gamma * h2 <= 0
G[19, [13, 18]] = 1.0, -gamma
# -w3 + h3/gamma <= 0
G[20, [14, 18]] = -1.0, 1.0/gamma
# w3 - gamma * h3 <= 0
G[21, [14, 19]] = 1.0, -gamma
# -w4 + h4/gamma <= 0
G[22, [15, 19]] = -1.0, 1.0/gamma
# w4 - gamma * h4 <= 0
G[23, [15, 20]] = 1.0, -gamma
# -w5 + h5/gamma <= 0
G[24, [16, 21]] = -1.0, 1.0/gamma
# w5 - gamma * h5 <= 0.0
G[25, [16, 21]] = 1.0, -gamma
# solve and return W, H, x, y, w, h
sol = solvers.cpl(c, F, G, h)
return sol['x'][0], sol['x'][1], sol['x'][2:7], sol['x'][7:12], \
sol['x'][12:17], sol['x'][17:]
G[13, [9, 10, 19]], h[13] = [1.0, -1.0, 1.0], -rho # y3 - y4 + h3 <= -rho
G[14, [1, 10, 20]] = -1.0, 1.0, 1.0 # -H + y4 + h4 <= 0
G[15, [1, 11, 21]] = -1.0, 1.0, 1.0 # -H + y5 + h5 <= 0
G[16, [12, 17]] = -1.0, 1.0/gamma # -w1 + h1/gamma <= 0
G[17, [12, 17]] = 1.0, -gamma # w1 - gamma * h1 <= 0
G[18, [13, 18]] = -1.0, 1.0/gamma # -w2 + h2/gamma <= 0
G[19, [13, 18]] = 1.0, -gamma # w2 - gamma * h2 <= 0
G[20, [14, 19]] = -1.0, 1.0/gamma # -w3 + h3/gamma <= 0
G[21, [14, 19]] = 1.0, -gamma # w3 - gamma * h3 <= 0
G[22, [15, 20]] = -1.0, 1.0/gamma # -w4 + h4/gamma <= 0
G[23, [15, 20]] = 1.0, -gamma # w4 - gamma * h4 <= 0
G[24, [16, 21]] = -1.0, 1.0/gamma # -w5 + h5/gamma <= 0
G[25, [16, 21]] = 1.0, -gamma # w5 - gamma * h5 <= 0.0
# solve and return W, H, x, y, w, h
sol = solvers.cpl(c, F, G, h)
return sol['x'][0], sol['x'][1], sol['x'][2:7], sol['x'][7:12], sol['x'][12:17], sol['x'][17:]
pylab.figure(facecolor='w')
pylab.subplot(221)
Amin = matrix([100., 100., 100., 100., 100.])
W, H, x, y, w, h = floorplan(Amin)
for k in range(5):
pylab.fill([x[k], x[k], x[k]+w[k], x[k]+w[k]],
[y[k], y[k]+h[k], y[k]+h[k], y[k]], facecolor = '#D0D0D0')
pylab.text(x[k]+.5*w[k], y[k]+.5*h[k], "%d" %(k+1))
pylab.axis([-1.0, 26, -1.0, 26])
pylab.xticks([])
pylab.yticks([])
pylab.subplot(222)
def train(self, X, Y, radius, normfac, prevw): solvers.options['show_progress'] = False # Reduce maxiters and tolerance to reasonable levels solvers.options['maxiters'] = 200 solvers.options['abstol'] = 1e-2 solvers.options['feastol'] = 1e-2 row, col = X.shape n = row + self.d prevw = prevw.reshape((self.d, 1)) x_0 = matrix(0.0, (n, 1)) x_0[:row] = 1.0 - Y * dot(X, prevw) / normfac x_0[row:] = prevw # x represents all the variables in an array, the first ones Ei and then each dimenstion of w, updated to 1/row c = matrix(row*[1.0] + self.d*[0.0]) # the objective function represented as a sum of Ei scale_factor = float(dot(c.T, x_0)) if scale_factor > 0.0: c /= scale_factor helper = matrix(array(row*[0.0] + self.d*[1.0]).reshape((n, 1))) r2 = radius**2 def F(x = None, z = None): if x is None: return (2, x_0) # Ei starts from 1 and w starts from 1 w = x[row:] diff = w - prevw f = matrix(0.0, (2, 1)) f[0] = dot(diff.T, diff)[0] - r2 # the first non-linear constraint ||w-w[k-1]||^2 < r[k]^2 f[1] = dot(w.T, w)[0] - 1.0 # the second non-linear constraint ||w||^2 < 1 Df = matrix(0.0, (2, n)) # creating the Df martrix, one row for each non-linear equation with variables as columns Df[0, row:] = 2.0 * diff.T # derivative of first non-linear equation, populates a sparse matrix Df[1, row:] = 2.0 * w.T # derivative of second non-linear equation, populates a sparse matrix if z is None: return f, Df diag_H = 2.0 * z[0] + 2.0 * z[1] * helper # Each nonlinear constraint has second derivative 2I w.r.t. w and 0 w.r.t. eps H = spdiag(diag_H) return f, Df, H # for linear inequalities G = matrix(0.0, (row*2, n)) # there are two linear constaints for Ei, and for each Ei the entire w h = matrix(0.0, (row*2, 1)) for i in range(row): G[i,i] = -1.0 # -Ei <= 0 G[row+i, i] = -1.0 h[row+i] = -1.0 for j in range(self.d): G[row+i, row+j] = (-Y[i][0]/normfac)*X[i,j] # -Ei - yi/Tk(w.xi) <= -1 # solve and return w sol = solvers.cpl(c, F, G, h) self.w = sol['x'][row:] self.w = array(self.w).reshape((self.d,)) #print #print sol['status'] ''' print 'Radius wanted' print radius print 'Output of quadratic solver' print self.w print ' Norm of output of quadratic solver pre-normalization' print sqrt(dot(self.w.T, self.w)) print ' Distance to the previous weight vector pre-normalization' print sqrt(dot((self.w-prevw).T, (self.w-prevw))) ''' self.w = self.w/sqrt(dot(self.w.T,self.w)) # Normalizing the vector output '''
def cc_approx(cep,cov,w_p=1.0,w_q=1.0,init_p=None,init_q=None,show_progress=False,
max_iter=100,exact_p_mask=None,exact_q_mask=None):
""" Computes the power spactra approximatively matching given
cepstral and vovariance coefficients with weights alpha and
beta respectively."""
m = len(cep)
n = len(cov)
# convert initial spectrum, if any, to matrix form
if init_p is not None:
i_p = iter2matrix(init_p/init_p[0])
if init_q is not None:
i_q = iter2matrix(init_q/init_p[0])
# fuction for building weight matrices
def build_inv_weight(w, exact_mask=None):
# as it is this function now if, for a certain k, w[k,k] is zero and
# exact_mask[k] is true at the same time, the first take precedence,
# that is the corresponing parameter will not be matched at all.
I = []
J = []
E = []
kk = 0
for k in range(0,w.size[0]):
if not w[k,k] == 0:
I.append(kk)
J.append(k)
E.append(1.0)
kk += 1
if exact_mask is not None and w[k,k] == 0:
del exact_mask[kk]
I.append(kk-1)
J.append(k)
E.append(0.0)
M = cb.spmatrix(E, I, J)
w_r = M*w*M.T
i_w_r = cb.matrix(linalg.inv(w_r))
if exact_mask is None:
return i_w_r, M
for k in range(0,len(exact_mask)):
if exact_mask[k]:
i_w_r[k,:] = 0.0
i_w_r[:,k] = 0.0
return i_w_r, M
# handle the weight matrices
if type(w_p) is float or type(w_p) is int:
# by default the entropy will not be matched
new_w_p = cb.matrix(0.0, (m,m))
new_w_p[m+1::m+1] = w_p
if type(w_p) is ndarray:
if len(w_p.shape) == 2:
new_w_p = cb.matrix(w_p)
if len(w_p.shape) == 1:
new_w_p = cb.matrix(0.0, (m,m))
new_w_p[m+1::m+1] = w_p[1:m]
if new_w_p[0,0] is not 0.0:
# better avoid match the entropy!
if show_progress:
print "warning: entropy will not be matched"
new_w_p[0,0] = 0.0
i_w_p, Mp = build_inv_weight(new_w_p,exact_p_mask)
rm = Mp.size[0]
if type(w_q) is float or type(w_q) is int:
new_w_q = cb.matrix(0.0, (n,n))
new_w_q[0::n+1] = w_q
if type(w_q) is ndarray:
if len(w_q.shape) == 2:
new_w_q = cb.matrix(w_q)
if len(w_q.shape) == 1:
new_w_q = cb.matrix(0.0, (n,n))
new_w_p[0::n+1] = w_p[:n]
i_w_q, Mq = build_inv_weight(new_w_q,exact_q_mask)
rn = Mq.size[0]
# for debugging purposes
tmp_x = cb.matrix(1.0, (rm+rn+1,1))
def F(x=None,z=None):
if x is None:
x = cb.matrix(0.0, (rm+rn+1,1))
if init_p is None or init_q is None:
x[rm] = 1
else:
x[:rm] = Mp*i_p
x[rm:rm+rn] = Mq*i_q
return 1, x
xp = x[:rm]
p = fromiter(Mp.T*xp, float)
p[0] += 1
xq = x[rm:rm+rn]
q = fromiter(Mq*xq, float)
num = pp2p(p)
den = pp2p(q)
if num is None or den is None:
return None
xcep = cb.matrix( arma2cep(num,den,m-1), (m,1))
xcov = cb.matrix( arma2cov(num,den,n-1), (n,1))
f = 0.5*xp.T*i_w_p*xp + 0.5*xq.T*i_w_q*xq + xp.T*Mp*xcep -1 + xcep[0] - x[rm+rn]
Df = cb.matrix(-1.0, (1,rm+rn+1))
Df[0,0:rm] = (i_w_p*xp + Mp*xcep).T
Df[0,rm:rm+rn] = (i_w_q*xq - Mq*xcov).T
if z is None:
return f, Df
H = cb.matrix(0.0, (rm+rn+1,rm+rn+1))
# evaluate hessian w.r.t p
c_p = arma2cov(ones(1),num,2*m-2)
H_pp = 0.5*toeplitz(c_p[:m]) + 0.5*hankel(c_p[:m], c_p[m-1:])
H[:rm,:rm] = Mp*cb.matrix(H_pp, (m,m))*Mp.T + i_w_p
# evaluate hessian w.r.t q
c_q = arma2cov(num,polymul(den,den),2*n-2)
H_qq = 0.5*toeplitz(c_q[:n]) + 0.5*hankel(c_q[:n], c_q[n-1:])
H[rm:rm+rn,rm:rm+rn] = Mq*cb.matrix(H_qq, (n,n))*Mq.T + i_w_q
# evaluate the mixed part
cc = arma2cov(ones(1),den,n+m-2)
H_pq = -0.5*toeplitz(cc[:m], cc[:n]) - 0.5*hankel(cc[:m],cc[m-1:])
H[:rm,rm:rm+rn] = Mp*cb.matrix(H_pq, (m,n))*Mq.T
H[rm:rm+rn,:rm] = H[:rm,rm:rm+rn].T
# save for debugging purposes
for k in range(0,rm+rn+1):
tmp_x[k] = x[k]
return f, Df, z[0]*H
solvers.options['maxiters'] = max_iter
solvers.options['show_progress']= show_progress
try:
c = cb.matrix(1.0, (rm+rn+1,1))
cep = iter2matrix(cep, (m,1))
c[:rm] = -Mp*cep
cov = iter2matrix(cov, (n,1))
c[rm:rm+rn] = Mq*cov
sol = solvers.cpl(c,F)
except ArithmeticError:
p = fromiter(Mp.T*tmp_x[0:rm], float)
p[0] += 1
q = fromiter(Mq.T*tmp_x[rm:rm+rn], float)
num = pp2p(p)
den = pp2p(q)
if show_progress:
print tmp_x
print abs(roots(num))
print abs(roots(den))
my_plot = plot_spectra()
my_plot.add(p,q)
my_plot.save("debug")
raise
if sol['status'] == 'unknown':
return None, None, sol['status']
x = sol['x'].T
opt_p = fromiter(Mp.T*x[:rm], float)
opt_p[0] += 1
opt_q = fromiter(Mq.T*x[rm:rm+rn], float)
return opt_p/opt_p[0], opt_q/opt_p[0], sol['status']
