def testqr(a, eps):
q,r = qr_decomposition(a,mode='e')
q,r = qr_decomposition(a,mode='r')
q,r = qr_decomposition(a,mode='full')
res = num.matrixmultiply(q,r)
b = num.ravel( num.abs(res - a) )
if num.maximum.reduce(b) > eps:
raise SelftestFailure
else:
print "OK"
def testqr(a, eps):
q, r = qr_decomposition(a, mode='e')
q, r = qr_decomposition(a, mode='r')
q, r = qr_decomposition(a, mode='full')
res = num.matrixmultiply(q, r)
b = num.ravel(num.abs(res - a))
if num.maximum.reduce(b) > eps:
raise SelftestFailure
else:
print "OK"
def linear_least_squares(a, b, rcond=1.e-10):
"""solveLinearLeastSquares(a,b) returns x,resids,rank,s
where x minimizes 2-norm(|b - Ax|)
resids is the sum square residuals
rank is the rank of A
s is an rank of the singual values of A in desending order
If b is a matrix then x is also a matrix with corresponding columns.
If the rank of A is less than the number of columns of A or greater than
the numer of rows, then residuals will be returned as an empty array
otherwise resids = sum((b-dot(A,x)**2).
Singular values less than s[0]*rcond are treated as zero.
"""
one_eq = len(b.getshape()) == 1
if one_eq:
b = b[:, num.NewAxis]
_assertRank2(a, b)
m = a.getshape()[0]
n = a.getshape()[1]
n_rhs = b.getshape()[1]
ldb = max(n,m)
if m != b.getshape()[0]:
raise LinAlgError, 'Incompatible dimensions'
t =_commonType(a, b)
real_t = _array_type[0][_array_precision[t]]
bstar = num.zeros((ldb,n_rhs),t)
bstar[:b.getshape()[0],:n_rhs] = copy.copy(b)
a,bstar = _castCopyAndTranspose(t, a, bstar)
s = num.zeros((min(m,n),),real_t)
nlvl = max( 0, int( math.log( float(min( m,n ))/2. ) ) + 1 )
iwork = num.zeros((3*min(m,n)*nlvl+11*min(m,n),), 'l')
if _array_kind[t] == 1: # Complex routines take different arguments
lapack_routine = lapack_lite2.zgelsd
lwork = 1
rwork = num.zeros((lwork,), real_t)
work = num.zeros((lwork,),t)
results = lapack_routine( m, n, n_rhs, a, m, bstar,ldb , s, rcond,
0,work,-1,rwork,iwork,0 )
lwork = int(abs(work[0]))
rwork = num.zeros((lwork,),real_t)
a_real = num.zeros((m,n),real_t)
bstar_real = num.zeros((ldb,n_rhs,),real_t)
results = lapack_lite2.dgelsd( m, n, n_rhs, a_real, m, bstar_real,ldb , s, rcond,
0,rwork,-1,iwork,0 )
lrwork = int(rwork[0])
work = num.zeros((lwork,), t)
rwork = num.zeros((lrwork,), real_t)
results = lapack_routine( m, n, n_rhs, a, m, bstar,ldb , s, rcond,
0,work,lwork,rwork,iwork,0 )
else:
lapack_routine = lapack_lite2.dgelsd
lwork = 1
work = num.zeros((lwork,), t)
results = lapack_routine( m, n, n_rhs, a, m, bstar,ldb , s, rcond,
0,work,-1,iwork,0 )
lwork = int(work[0])
work = num.zeros((lwork,), t)
results = lapack_routine( m, n, n_rhs, a, m, bstar,ldb , s, rcond,
0,work,lwork,iwork,0 )
if results['info'] > 0:
raise LinAlgError, 'SVD did not converge in Linear Least Squares'
resids = num.array([],type=t)
if one_eq:
x = copy.copy(num.ravel(bstar)[:n])
if (results['rank']==n) and (m>n):
resids = num.array([num.sum((num.ravel(bstar)[n:])**2)])
else:
x = copy.copy(num.transpose(bstar)[:n,:])
if (results['rank']==n) and (m>n):
resids = copy.copy(num.sum((num.transpose(bstar)[n:,:])**2))
return x,resids,results['rank'],copy.copy(s[:min(n,m)])