def triul(tridmat):
'''
Get the UL decomposition for tridiagonal matrix, A=UL
The complexity of this procedure is n*p^3.
*return*:
A <TLUSystem> instance with order 'UL'.
'''
al=tridmat.lower
bl=tridmat.diagonal
cl=tridmat.upper
ll,ul,hl,invhl=get_tlu_seq(al=al,bl=bl,cl=cl,which='>')
return TLUSystem(ll=ul,ul=ll,hl=hl,invhl=invhl,order='UL')
def triul(tridmat):
'''
Get the UL decomposition for tridiagonal matrix, A=UL
The complexity of this procedure is n*p^3.
*return*:
A <TLUSystem> instance with order 'UL'.
'''
al = tridmat.lower
bl = tridmat.diagonal
cl = tridmat.upper
ll, ul, hl, invhl = get_tlu_seq(al=al, bl=bl, cl=cl, which='>')
return TLUSystem(ll=ul, ul=ll, hl=hl, invhl=invhl, order='UL')
def trilu(tridmat):
'''
Get the LU decomposition for tridiagonal matrix, A=LU
The complexity of this procedure is n*p^3.
trdmat:
A tridiagonal matrix, i.g. an instance of TridMatrix.
*return*:
A <TLUSystem> instance with order 'LU'.
'''
al=tridmat.lower
bl=tridmat.diagonal
cl=tridmat.upper
is_scalar=tridmat.is_scalar
ll,ul,hl,invhl=get_tlu_seq(al=al,bl=bl,cl=cl,which='<')
return TLUSystem(ll=ll,ul=ul,hl=hl,invhl=invhl,order='LU')
def trilu(tridmat):
'''
Get the LU decomposition for tridiagonal matrix, A=LU
The complexity of this procedure is n*p^3.
trdmat:
A tridiagonal matrix, i.g. an instance of TridMatrix.
*return*:
A <TLUSystem> instance with order 'LU'.
'''
al = tridmat.lower
bl = tridmat.diagonal
cl = tridmat.upper
is_scalar = tridmat.is_scalar
ll, ul, hl, invhl = get_tlu_seq(al=al, bl=bl, cl=cl, which='<')
return TLUSystem(ll=ll, ul=ul, hl=hl, invhl=invhl, order='LU')
def get_inv_system(tridmat):
'''
Get the inversion generator for tridiagonal matrix.
The Fortran version and python version are provided for block tridiagonal matrix.
The complexity of this procedure is n*p^3.
However, if you're going to generate the whole inversion elements through STInvSystem instance,
the complexity is n^2*p^3.
Reference -> http://dx.doi.org/10.1016/j.amc.2005.11.098
trdmat:
A tridiagonal matrix, i.g. an instance of TridMatrix.
*return*:
a <BTInvSystem> instance.
'''
ll1,ll2,ll3,ul1,ul2,ul3,hl1,hl2,hl3,invhl1,invhl2,invhl3=get_tlu_seq(al=tridmat.lower,bl=tridmat.diagonal,cl=tridmat.upper)
return BTInvSystem((ll1,hl1,ul1,invhl1),(ll2,hl2,ul2,invhl2),(ll3,hl3,ul3,invhl3))
def get_inv_system(tridmat):
'''
Get the inversion generator for tridiagonal matrix.
The Fortran version and python version are provided for block tridiagonal matrix.
The complexity of this procedure is n*p^3.
However, if you're going to generate the whole inversion elements through STInvSystem instance,
the complexity is n^2*p^3.
Reference -> http://dx.doi.org/10.1016/j.amc.2005.11.098
trdmat:
A tridiagonal matrix, i.g. an instance of TridMatrix.
*return*:
a <BTInvSystem> instance.
'''
ll1, ll2, ll3, ul1, ul2, ul3, hl1, hl2, hl3, invhl1, invhl2, invhl3 = get_tlu_seq(
al=tridmat.lower, bl=tridmat.diagonal, cl=tridmat.upper)
return BTInvSystem((ll1, hl1, ul1, invhl1), (ll2, hl2, ul2, invhl2),
(ll3, hl3, ul3, invhl3))