def lsq(self, A, b, reg=0.0, radius=None, **kwargs):
"""
Solve the linear least-squares problem in the variable x
minimize |Ax - b| + reg * |x|
in the Euclidian norm with LSQR. Optionally, x may be
subject to a Euclidian-norm trust-region constraint
|x| <= radius. This function returns (x, xNorm, status).
"""
LSQR = LSQRFramework(A)
LSQR.solve(b, radius=radius, damp=reg, show=False)
return (LSQR.x, LSQR.xnorm, LSQR.status)
def lsq(self, A, b, reg=0.0, radius=None, **kwargs):
"""
Solve the linear least-squares problem in the variable x
minimize |Ax - b| + reg * |x|
in the Euclidian norm with LSQR. Optionally, x may be
subject to a Euclidian-norm trust-region constraint
|x| <= radius. This function returns (x, xNorm, status).
"""
LSQR = LSQRFramework(A)
LSQR.solve(b, radius=radius, damp=reg, show=False)
return (LSQR.x, LSQR.xnorm, LSQR.status)
print 'op.T(e1) = ', op.T(e1)
print 'op.T.T is op : ', (op.T.T is op)
print
print 'Testing SimpleLinearOperator:'
op = SimpleLinearOperator(J.shape[1],
J.shape[0],
lambda v: J * v,
matvec_transp=lambda u: u * J)
print 'op.shape = ', op.shape
print 'op.T.shape = ', op.T.shape
print 'op * e2 = ', op * e2
print 'e1.shape = ', e1.shape
print 'op.T * e1 = ', op.T * e1
print 'op.T.T * e2 = ', op.T.T * e2
print 'op(e2) = ', op(e2)
print 'op.T(e1) = ', op.T(e1)
print 'op.T.T is op : ', (op.T.T is op)
print
print 'Solving a constrained least-squares problem with LSQR:'
lsqr = LSQRFramework(op)
lsqr.solve(np.random.random(nlp.m), show=True)
print
print 'Building a SquaredLinearOperator:'
op2 = SquaredLinearOperator(J, log=True)
print 'op2 * e2 = ', op2 * e2
print 'op.T * (op * e2) = ', op.T * (op * e2)
op3 = SquaredLinearOperator(J, transposed=True, log=True)
print 'op3 * e1 = ', op3 * e1
print 'op * (op.T * e1) = ', op * (op.T * e1)
print 'op3 is symmetric: ', op3.check_symmetric()
print 'op(e2) = ', op(e2)
print 'op.T(e1) = ', op.T(e1)
print 'op.T.T is op : ', (op.T.T is op)
print
print 'Testing SimpleLinearOperator:'
op = SimpleLinearOperator(J.shape[1], J.shape[0],
lambda v: J*v,
matvec_transp=lambda u: u*J)
print 'op.shape = ', op.shape
print 'op.T.shape = ', op.T.shape
print 'op * e2 = ', op * e2
print 'e1.shape = ', e1.shape
print 'op.T * e1 = ', op.T * e1
print 'op.T.T * e2 = ', op.T.T * e2
print 'op(e2) = ', op(e2)
print 'op.T(e1) = ', op.T(e1)
print 'op.T.T is op : ', (op.T.T is op)
print
print 'Solving a constrained least-squares problem with LSQR:'
lsqr = LSQRFramework(op)
lsqr.solve(np.random.random(nlp.m), show=True)
print
print 'Building a SquaredLinearOperator:'
op2 = SquaredLinearOperator(J, log=True)
print 'op2 * e2 = ', op2 * e2
print 'op.T * (op * e2) = ', op.T * (op * e2)
op3 = SquaredLinearOperator(J, transposed=True, log=True)
print 'op3 * e1 = ', op3 * e1
print 'op * (op.T * e1) = ', op * (op.T * e1)
print 'op3 is symmetric: ', op3.check_symmetric()