def givensCoef(x1_in,x2_in):
""" Code adapted from Algorithm 1 of LAPACK working Notes lawn148
"""
if type(x1_in) is int:
x1=float(x1_in)
else:
x1 = x1_in
if type(x2_in) is int:
x2=float(x2_in)
else:
x2 = x2_in
if type(x1) is float and type(x2) is float:
t=pv.vsip_hypot_d(x1,x2)
if x2 == 0.0:
return (1.0,0.0,x1)
elif x1 == 0.0:
return (0.0,sign(x2),t)
else: # return (c,s,r)
sn=sign(x1)
return(pv.vsip_mag_d(x1)/t,sn*x2/t,sn*t)
elif type(x1) is complex or type(x2) is complex:
mx1=pv.vsip_hypot_d(x1.real,x1.imag)
mx2=pv.vsip_hypot_d(x2.real,x2.imag)
if mx2 == 0.0:
return(1.0,0.0,x1)
elif mx1 == 0.0:
return(0,sign(x2.conjugate()),mx2)
else:
t=pv.vsip_hypot_d(mx1,mx2)
c=mx1/t
sn=sign(x1)
s=(sn * x2.conjugate())/t
r=sn * t
return(c,s,r)
else:
print('Type <:'+repr(type(x1)) + ':> or <:'+ \
repr(type(x2))+':> not recognized by givensCoef')
return
def diagPhaseToZero(L,B):
"""
To phase shift the main diagonal entries of a matrix B so entries
are real (imaginary zero) use this routine.
"""
d = B.diagview(0)
for i in range(d.length):
ps=d[i] #phase shift
if ps.imag != 0.0: #ignore if already real
m = pv.vsip_hypot_d(ps.real,ps.imag)
ps /= m
L.colview(i)[:] *= ps
B.rowview(i)[:] *= ps # if B is strictly diagonal don't need this step
d[i] = m
def diagPhaseToZero(L, B):
"""
To phase shift the main diagonal entries of a matrix B so entries
are real (imaginary zero) use this routine.
"""
d = B.diagview(0)
for i in range(d.length):
ps = d[i] # phase shift
if ps.imag != 0.0: # ignore if already real
m = pv.vsip_hypot_d(ps.real, ps.imag)
ps /= m
L.colview(i)[:] *= ps
B.rowview(i)[:] *= ps # if B is strictly diagonal don't need this step
d[i] = m
def givensCoef(x1_in, x2_in):
""" Code adapted from Algorithm 1 of LAPACK working Notes lawn148
"""
if type(x1_in) is int:
x1 = float(x1_in)
else:
x1 = x1_in
if type(x2_in) is int:
x2 = float(x2_in)
else:
x2 = x2_in
if type(x1) is float and type(x2) is float:
t = pv.vsip_hypot_d(x1, x2)
if x2 == 0.0:
return (1.0, 0.0, x1)
elif x1 == 0.0:
return (0.0, sign(x2), t)
else: # return (c,s,r)
sn = sign(x1)
return (pv.vsip_mag_d(x1) / t, sn * x2 / t, sn * t)
elif type(x1) is complex or type(x2) is complex:
mx1 = pv.vsip_hypot_d(x1.real, x1.imag)
mx2 = pv.vsip_hypot_d(x2.real, x2.imag)
if mx2 == 0.0:
return (1.0, 0.0, x1)
elif mx1 == 0.0:
return (0, sign(x2.conjugate()), mx2)
else:
t = pv.vsip_hypot_d(mx1, mx2)
c = mx1 / t
sn = sign(x1)
s = (sn * x2.conjugate()) / t
r = sn * t
return (c, s, r)
else:
print("Type <:" + repr(type(x1)) + ":> or <:" + repr(type(x2)) + ":> not recognized by givensCoef")
return
def sign(a_in): # see LAPACK Working Notes 148 for definition of sign
if type(a_in) is int:
a=float(a_in)
else:
a=a_in
if type(a) is float or type(a) is complex:
t=pv.vsip_hypot_d(a.real,a.imag)
if t == 0.0:
return 1.0
elif a.imag==0.0:
if a.real < 0.0:
return -1.0
else:
return 1.0
else:
return a/t
else:
print('sign function only works on scalars')
return
def biDiagPhaseToZero(L,d,f,R,eps0):
"""
For a Bidiagonal matrix B This routine uses subview vectors
`d=B.diagview(0)`
and
`f=B.diagview(1)`
and phase shifts vectors d and f so that B has zero complex part.
Matrices L and R are update matrices.
eps0 is a small real number used to check for zero. If an element meets a zero
check then that element is set to zero.
"""
for i in range(d.length):
ps=d[i]
if ps.imag == 0.0:
m = ps.real
if m < 0.0:
ps=-1.0
else:
ps= 1.0
m = abs(m)
else:
m=pv.vsip_hypot_d(ps.real,ps.imag)
ps /= m
if m > eps0:
L.colview(i)[:] *= ps
d[i] = m
if i < f.length:
f[i] *= ps.conjugate()
else:
d[i] = 0.0
svdZeroCheckAndSet(eps0,d,f)
for i in range(f.length-1):
j=i+1
ps = f[i]
if ps.imag == 0.0:
m = ps.real
if m < 0.0:
ps=-1.0
else:
ps= 1.0
m = abs(m)
else:
m=pv.vsip_hypot_d(ps.real,ps.imag)
ps /= m
L.colview(j)[:] *= ps.conjugate()
R.rowview(j)[:] *= ps
f[i] = m;
f[j] *= ps
j=f.length
i=j-1
ps=f[i]
if ps.imag == 0.0:
m = ps.real
if m < 0.0:
ps=-1.0
else:
ps= 1.0
m = abs(m)
else:
m=pv.vsip_hypot_d(ps.real,ps.imag)
ps /= m
f[i]=m
L.colview(j)[:] *= ps.conjugate()
R.rowview(j)[:] *= ps
def biDiagPhaseToZero(L, d, f, R, eps0):
"""
For a Bidiagonal matrix B This routine uses subview vectors
`d=B.diagview(0)`
and
`f=B.diagview(1)`
and phase shifts vectors d and f so that B has zero complex part.
Matrices L and R are update matrices.
eps0 is a small real number used to check for zero. If an element meets a zero
check then that element is set to zero.
"""
for i in range(d.length):
ps = d[i]
if ps.imag == 0.0:
m = ps.real
if m < 0.0:
ps = -1.0
else:
ps = 1.0
m = abs(m)
else:
m = pv.vsip_hypot_d(ps.real, ps.imag)
ps /= m
if m > eps0:
L.colview(i)[:] *= ps
d[i] = m
if i < f.length:
f[i] *= ps.conjugate()
else:
d[i] = 0.0
svdZeroCheckAndSet(eps0, d, f)
for i in range(f.length - 1):
j = i + 1
ps = f[i]
if ps.imag == 0.0:
m = ps.real
if m < 0.0:
ps = -1.0
else:
ps = 1.0
m = abs(m)
else:
m = pv.vsip_hypot_d(ps.real, ps.imag)
ps /= m
L.colview(j)[:] *= ps.conjugate()
R.rowview(j)[:] *= ps
f[i] = m
f[j] *= ps
j = f.length
i = j - 1
ps = f[i]
if ps.imag == 0.0:
m = ps.real
if m < 0.0:
ps = -1.0
else:
ps = 1.0
m = abs(m)
else:
m = pv.vsip_hypot_d(ps.real, ps.imag)
ps /= m
f[i] = m
L.colview(j)[:] *= ps.conjugate()
R.rowview(j)[:] *= ps