def cirDist(k2s):
'''
circle distortion
'''
norder = 7
# slow but general ---
sext = nsls2.ring.getElements('sext','sh1')[0]
sext.put('K2',k2s[0])
sext = nsls2.ring.getElements('sext','sh3')[0]
sext.put('K2',k2s[1])
sext = nsls2.ring.getElements('sext','sh4')[0]
sext.put('K2',k2s[2])
sext = nsls2.ring.getElements('sext','sl3')[0]
sext.put('K2',k2s[3])
sext = nsls2.ring.getElements('sext','sl2')[0]
sext.put('K2',k2s[4])
sext = nsls2.ring.getElements('sext','sl1')[0]
sext.put('K2',k2s[5])
K2 = [nsls2.ring.bl[k].K2 for k in nsls2.ring.klist]
temp = [CTPS(0,i) for i in xrange(1,nv+1)]
for i,k in enumerate(nsls2.ring.klist):
temp = sm.lmPass(nsls2.ring.mlist[i][:nv,:nv],temp)
temp = sm.thickSextPass(L[i],K2[i],2,temp)
# --- attach thin octupole to sext
temp = sm.thinOctPass(K2[i]/abs(K2[i])*10.,temp)
temp = sm.lmPass(nsls2.ring.mlist[-1][:nv,:nv],temp)
mf = np.array([[temp[i].element(jj) for jj in xrange(mlen)] for i in xrange(nv)])
#mf = np.array([sm.aline(temp[i],powerindex) for i in xrange(nv)])
elemtx = mf[:,1:5]
#6. Derive normalized map M=(BK)^(-1).mm.BK, see my notes 'Relation to Normal Form' of Wednesday, March 30, 2011 10:34 PM
# here #mfbk is the first 4 rows of M, it is
mfbk = jfdf.d3(bKi[1:5,1:5],mf,bK)
mfbk,scalemf,As,Asm = scalingmf(mfbk,powerindex)
Ms = sqdf.squarematrix(mfbk,norder,powerindex,sequencenumber,tol)
try:
#print Ms[-1],Ms.shape,phix0,1,powerindex,scalemf,sequencenumber[1,0,0,0],norder
ux1,uxbar,Jx,scalex,Msx,As2x,Asm2x = \
jfdf.UMsUbarexpJ(Ms,phix0,1,powerindex,scalemf,sequencenumber[1,0,0,0],ypowerorder=norder)
uy1,uybar,Jy,scaley,Msy,As2y,Asm2y = \
jfdf.UMsUbarexpJ(Ms,phiy0,1,powerindex,scalemf,sequencenumber[0,0,1,0],ypowerorder=norder)
except:
return [1.0e8]*12
# --- particle one by one
zx,zy = [],[]
for xy in xylist:
#11. Prepare data for |wx|,thetax,|wy|,thetay to plot Poincare section of thetax,|wy|,thetay
section1 = [] #section1 is without joined blocks
for row in xy:
row1 = row+(ux1,uy1)
section1.append(tuneshift(row1[0],row1[1],row1[2],row1[3],row1[4],row1[5],
bKi4b4,scalex,scaley,powerindex,norder))
st1 = zip(*section1)
#print 'K2s = %.2f:'%k2s
zmax = max(st1[0])
zmin = min(st1[0])
zav = np.mean(st1[0])
zx1 = (zmax-zmin)/zav
#print "for wx1 without resonance block, (zmax-zmin)/zmean = ", zx1
zmax = max(st1[1])
zmin = min(st1[1])
zav = np.mean(st1[1])
zy1 = (zmax-zmin)/zav
#print "for wy1 without resonance block, (zmax-zmin)/zmean = ", zy1
#print ''
zx.append(zx1)
zy.append(zy1)
xlist = np.linspace(-3e-2, 3e-2,30) # a list of x
ylist = np.linspace( 1e-6, 1e-2,10) # a list of y
xyplane = [[i,j] for i in xlist for j in ylist]
nu,da = [],[]
for x,y in xyplane:
t1,t2,t3,t4,t5,t6,t7,t8 = tuneshift(x,0,y,0,ux1,uy1,
bKi4b4,scalex,scaley,powerindex,norder)
nu.append([t5,t6])
da.append([t7,t8])
da = np.array(da)
nux = [i[0].real/2/np.pi for i in nu]
nuy = [i[1].real/2/np.pi for i in nu]
#nux = [i[0].imag/2/np.pi for i in nu]
#nuy = [i[1].imag/2/np.pi for i in nu]
dnuxda = np.max(np.abs(nux))
dnuyda = np.max(np.abs(nuy))
dax = np.max(np.abs(da[:,0]))
day = np.max(np.abs(da[:,1]))
#k2c = [sc.K2 for sc in chsext]
return zx+zy+[dnuxda,dnuyda,dax,day]#+k2c
def cirDist():
'''
circle distortion
'''
norder = 7
K2 = [nsls2.ring.bl[k].K2 for k in nsls2.ring.klist]
temp = [CTPS(0, i) for i in xrange(1, nv + 1)]
for i, k in enumerate(nsls2.ring.klist):
temp = sm.lmPass(nsls2.ring.mlist[i][:nv, :nv], temp)
temp = sm.thickSextPass(L[i], K2[i], 1, temp)
temp = sm.lmPass(nsls2.ring.mlist[-1][:nv, :nv], temp)
mf = np.array([[temp[i].element(jj) for jj in xrange(mlen)]
for i in xrange(nv)])
#mf = np.array([sm.aline(temp[i],powerindex) for i in xrange(nv)])
elemtx = mf[:, 1:5]
#6. Derive normalized map M=(BK)^(-1).mm.BK, see my notes 'Relation to Normal Form' of Wednesday, March 30, 2011 10:34 PM
# here #mfbk is the first 4 rows of M, it is
mfbk = jfdf.d3(bKi[1:5, 1:5], mf, bK)
mfbk, scalemf, As, Asm = scalingmf(mfbk, powerindex)
Ms = sqdf.squarematrix(mfbk, norder, powerindex, sequencenumber, tol)
try:
#print Ms[-1],Ms.shape,phix0,1,powerindex,scalemf,sequencenumber[1,0,0,0],norder
ux1,uxbar,Jx,scalex,Msx,As2x,Asm2x = \
jfdf.UMsUbarexpJ(Ms,phix0,1,powerindex,scalemf,sequencenumber[1,0,0,0],ypowerorder=norder)
uy1,uybar,Jy,scaley,Msy,As2y,Asm2y = \
jfdf.UMsUbarexpJ(Ms,phiy0,1,powerindex,scalemf,sequencenumber[0,0,1,0],ypowerorder=norder)
except:
return [1.0e8] * 12
# --- particle one by one
zxy = []
for xy in xylist:
#11. Prepare data for |wx|,thetax,|wy|,thetay to plot Poincare section of thetax,|wy|,thetay
section1 = [] #section1 is without joined blocks
for row in xy:
row1 = row + (ux1, uy1)
section1.append(
tuneshift(row1[0], row1[1], row1[2], row1[3], row1[4], row1[5],
bKi4b4, scalex, scaley, powerindex, norder))
st1 = zip(*section1)
#print 'K2s = %.2f:'%k2s
#zmax = max(st1[0])
#zmin = min(st1[0])
#zav = np.mean(st1[0])
#zx1 = (zmax-zmin)/zav
#print "for wx1 without resonance block, (zmax-zmin)/zmean = ", zx1
#zmax = max(st1[1])
#zmin = min(st1[1])
#zav = np.mean(st1[1])
#zy1 = (zmax-zmin)/zav
#print "for wy1 without resonance block, (zmax-zmin)/zmean = ", zy1
#print ''
zxy.append(st1)
return zxy
def cirDist(k2s):
'''
circle distortion
'''
npass = 64
norder = 7
tol = 1e-12
sexts = ring.matchElements('sh1.*')
for s in sexts:
ring[s,'K2'] = k2s[0]
sexts = ring.matchElements('sh3.*')
for s in sexts:
ring[s,'K2'] = k2s[1]
sexts = ring.matchElements('sh4.*')
for s in sexts:
ring[s,'K2'] = k2s[2]
sexts = ring.matchElements('sl3.*')
for s in sexts:
ring[s,'K2'] = k2s[3]
sexts = ring.matchElements('sl2.*')
for s in sexts:
ring[s,'K2'] = k2s[4]
sexts = ring.matchElements('sl1.*')
for s in sexts:
ring[s,'K2'] = k2s[5]
# six phase space varialbe, 4 independent, expand to n'rd order.
m = tesla.TPSMap(6,4,norder)
m.c = [0, 0, 0, 0, 0, 0]
m.m = [[1,0,0,0], [0,1,0,0], [0,0,1,0], [0,0,0,1], [0,0,0,0],[0,0,0,0]]
ms = ring.trackTPSMaps(m, 0, ring.elements()) #ms has the maps of all elements around the ring, m is one turn map
tw, ml = tesla.calcLinearTwiss(ring)
#4. Construct map matrix mm
mf,powerindex = sqdf.mfunction(m,norder) # m is one turn map
#This program only applies when x[0]=0,xp[0]=0,y[0]=0, yp[0]=0. If not, then the map matrix mm is no longer semi-triangular
mf[0][0] = 0
mf[1][0] = 0
mf[2][0] = 0
mf[3][0] = 0
mf = np.array(mf)
mlen=len(powerindex)
# sequencenumber[i1,i2,i3,i4] gives the sequence number in power index for power of x^i1*xp^i2*y^i3*yp^i4
sequencenumber = np.zeros((norder+1,norder+1,norder+1,norder+1),'i')
powerindex = sqdf.powerindex4(norder)
powerindex = np.array(powerindex,'i')
mlen = len(powerindex)
for i in range(mlen):
ip = powerindex[i]
sequencenumber[ip[0]][ip[1]][ip[2]][ip[3]] = i
betax0,phix0,alphax0,betay0,phiy0,alphay0 = sqdf.extracttwiss(mf)
gammax0 = (1+alphax0**2)/betax0
mlix = [np.cos(phix0)+alphax0*np.sin(phix0), betax0*np.sin(phix0)],\
[-gammax0*np.sin(phix0), np.cos(phix0)-alphax0*np.sin(phix0)]
gammay0 = (1+alphay0**2)/betay0
mliy = [np.cos(phiy0)+alphay0*np.sin(phiy0), betay0*np.sin(phiy0)],\
[-gammay0*np.sin(phiy0), np.cos(phiy0)-alphay0*np.sin(phiy0)]
elemtx = np.zeros((4,4))
elemtx[0:2,0:2] = mlix #Replace linear part of elegant, which is accurate only to 8 digits,
#by the twiss matrix obtained from the twiss parameters extract from the tpsa linear part of matrix
elemtx[2:4,2:4] = mliy #Notice that mlix and mliy is accurate simplex to machine precision, so their determinantes are closer to zero.
mf[:,1:5] = elemtx #Now replace the linear part of map matrix by the more accurate twiss matrix
sqrtbetax = np.sqrt(betax0)
sqrtbetay = np.sqrt(betay0)
#5. Construct the BK square matrix using the first 5 rows.
bK,bKi = sqdf.BKmatrix(betax0,phix0,alphax0,\
betay0,phiy0,alphay0,
0,0,norder,powerindex,sequencenumber,tol)
#6. Derive normalized map M=(BK)^(-1).mm.BK, see my notes 'Relation to Normal Form' of Wednesday, March 30, 2011 10:34 PM
# here #mfbk is the first 4 rows of M, it is
mfbk = jfdf.d3(bKi[1:5,1:5],mf,bK)
mfbk,scalemf,As,Asm = scalingmf(mfbk,powerindex)
Ms = sqdf.squarematrix(mfbk,norder,powerindex,sequencenumber,tol)
Bi = np.array([[1/sqrtbetax,0,0,0],[alphax0/sqrtbetax,sqrtbetax,0,0],
[0,0,1/sqrtbetay,0],[0,0,alphay0/sqrtbetay,sqrtbetay]])
Ki = np.array([[1,-1j,0,0],[1,1j,0,0],[0,0,1,-1j],[0,0,1,1j]])
bKi4b4 = np.dot(Ki,Bi)
try:
ux1,uxbar,Jx,scalex,Msx,As2x,Asm2x = \
jfdf.UMsUbarexpJ(Ms,phix0,1,powerindex,scalemf,sequencenumber[1,0,0,0],ypowerorder=norder)
uy1,uybar,Jy,scaley,Msy,As2y,Asm2y = \
jfdf.UMsUbarexpJ(Ms,phiy0,1,powerindex,scalemf,sequencenumber[0,0,1,0],ypowerorder=norder)
except:
return [1e8]*8
# --- particle 1
x0 = 2.5e-2
y0 = 5e-3
xxpyyp = np.zeros((4,npass+1))
xxpyyp[:,0] = np.array([x0,0,y0,0])
for i in xrange(1,npass+1):
xxpyyp[:,i] = np.dot(elemtx,xxpyyp[:,i-1])
xybar = np.dot(Bi,xxpyyp)
xy = zip(*xybar)
section = []
for row in xy:
section.append(normalcoordinate(*row))
st = zip(*section)
#11. Prepare data for |wx|,thetax,|wy|,thetay to plot Poincare section of thetax,|wy|,thetay
section1 = [] #section1 is without joined blocks
xy = zip(*xxpyyp)
for row in xy:
row1 = row+(ux1,uy1)
section1.append(tuneshift(row1[0],row1[1],row1[2],row1[3],row1[4],row1[5],
bKi4b4,scalex,scaley,powerindex,norder))
st1 = zip(*section1)
#print 'K2s = %.2f:'%k2s
zmax = max(st1[0])
zmin = min(st1[0])
zav = np.mean(st1[0])
zx1 = (zmax-zmin)/zav
#print "for wx1 without resonance block, (zmax-zmin)/zmean = ", zx1
zmax = max(st1[1])
zmin = min(st1[1])
zav = np.mean(st1[1])
zy1 = (zmax-zmin)/zav
#print "for wy1 without resonance block, (zmax-zmin)/zmean = ", zy1
#print ''
# --- particle 2
x0 = 1.0e-2
y0 = 2e-3
xxpyyp = np.zeros((4,npass+1))
xxpyyp[:,0] = np.array([x0,0,y0,0])
for i in xrange(1,npass+1):
xxpyyp[:,i] = np.dot(elemtx,xxpyyp[:,i-1])
xybar = np.dot(Bi,xxpyyp)
xy = zip(*xybar)
section = []
for row in xy:
section.append(normalcoordinate(*row))
st = zip(*section)
#11. Prepare data for |wx|,thetax,|wy|,thetay to plot Poincare section of thetax,|wy|,thetay
section1 = [] #section1 is without joined blocks
xy = zip(*xxpyyp)
for row in xy:
row1 = row+(ux1,uy1)
section1.append(tuneshift(row1[0],row1[1],row1[2],row1[3],row1[4],row1[5],
bKi4b4,scalex,scaley,powerindex,norder))
st1 = zip(*section1)
#print 'K2s = %.2f:'%k2s
zmax = max(st1[0])
zmin = min(st1[0])
zav = np.mean(st1[0])
zx2 = (zmax-zmin)/zav
#print "for wx1 without resonance block, (zmax-zmin)/zmean = ", zx1
zmax = max(st1[1])
zmin = min(st1[1])
zav = np.mean(st1[1])
zy2 = (zmax-zmin)/zav
#print "for wy1 without resonance block, (zmax-zmin)/zmean = ", zy1
#print ''
# --- particle 3
x0 = 3.5e-2
y0 = 3.0e-3
xxpyyp = np.zeros((4,npass+1))
xxpyyp[:,0] = np.array([x0,0,y0,0])
for i in xrange(1,npass+1):
xxpyyp[:,i] = np.dot(elemtx,xxpyyp[:,i-1])
xybar = np.dot(Bi,xxpyyp)
xy = zip(*xybar)
section = []
for row in xy:
section.append(normalcoordinate(*row))
st = zip(*section)
#11. Prepare data for |wx|,thetax,|wy|,thetay to plot Poincare section of thetax,|wy|,thetay
section1 = [] #section1 is without joined blocks
xy = zip(*xxpyyp)
for row in xy:
row1 = row+(ux1,uy1)
section1.append(tuneshift(row1[0],row1[1],row1[2],row1[3],row1[4],row1[5],
bKi4b4,scalex,scaley,powerindex,norder))
st1 = zip(*section1)
#print 'K2s = %.2f:'%k2s
zmax = max(st1[0])
zmin = min(st1[0])
zav = np.mean(st1[0])
zx3 = (zmax-zmin)/zav
#print "for wx1 without resonance block, (zmax-zmin)/zmean = ", zx1
zmax = max(st1[1])
zmin = min(st1[1])
zav = np.mean(st1[1])
zy3 = (zmax-zmin)/zav
#print "for wy1 without resonance block, (zmax-zmin)/zmean = ", zy1
#print ''
xlist = np.linspace(-3e-2,3e-2,30) #a list of theta0
ylist = np.arange(1e-6,1.0e-2,10) #a list of theta0
xyplane = [[i,j] for i in xlist for j in ylist]
nu,da = [],[]
for x,y in xyplane:
t1,t2,t3,t4,t5,t6,t7,t8 = tuneshift(x,0,y,0,ux1,uy1,
bKi4b4,scalex,scaley,powerindex,norder)
nu.append([t5,t6])
da.append([t7,t8])
da = np.array(da)
nux = [i[0].real/2/np.pi for i in nu]
nuy = [i[1].real/2/np.pi for i in nu]
dnuxda = np.max(np.abs(nux))
dnuyda = np.max(np.abs(nuy))
dax = np.max(np.abs(da[:,0]))
day = np.max(np.abs(da[:,1]))
return [zx1,zy1,zx2,zy2,zx3,zy3,dnuxda,dnuyda,dax,day]
def cirDist(k2s):
'''
circle distortion
'''
npass = 64
norder = 7
# slow but general ---
'''
sext = nsls2.ring.getElements('sext','sh1')[0]
sext.put('K2',k2s[0])
sext = nsls2.ring.getElements('sext','sh3')[0]
sext.put('K2',k2s[1])
sext = nsls2.ring.getElements('sext','sh4')[0]
sext.put('K2',k2s[2])
sext = nsls2.ring.getElements('sext','sl3')[0]
sext.put('K2',k2s[3])
sext = nsls2.ring.getElements('sext','sl2')[0]
sext.put('K2',k2s[4])
sext = nsls2.ring.getElements('sext','sl1')[0]
sext.put('K2',k2s[5])
K2 = [nsls2.ring.bl[k].K2 for k in nsls2.ring.klist]
'''
# ---fast but not general, only for nsls2-II chrom+7/+7
sm12 = [-26.21867845, 30.69679902, -28.01658206]
K2 = np.hstack((k2s[:3], sm12, k2s[3:], k2s[-1:-4:-1], sm12, k2s[-4::-1]))
temp = copy.deepcopy(unit)
for i, k in enumerate(nsls2.ring.klist):
temp = sm.lmPass(nsls2.ring.mlist[i][:nv, :nv], temp)
temp = sm.thickSextPass(L[i], K2[i], 1, temp, truncate=norder)
temp = sm.lmPass(nsls2.ring.mlist[-1][:nv, :nv], temp)
mf = np.array([sm.aline(temp[i], powerindex) for i in xrange(nv)])
elemtx = mf[:, 1:5]
#6. Derive normalized map M=(BK)^(-1).mm.BK, see my notes 'Relation to Normal Form' of Wednesday, March 30, 2011 10:34 PM
# here #mfbk is the first 4 rows of M, it is
mfbk = jfdf.d3(bKi[1:5, 1:5], mf, bK)
mfbk, scalemf, As, Asm = scalingmf(mfbk, powerindex)
Ms = sqdf.squarematrix(mfbk, norder, powerindex, sequencenumber, tol)
'''
Bi = np.array([[1/sqrtbetax,0,0,0],[alphax0/sqrtbetax,sqrtbetax,0,0],
[0,0,1/sqrtbetay,0],[0,0,alphay0/sqrtbetay,sqrtbetay]])
Ki = np.array([[1,-1j,0,0],[1,1j,0,0],[0,0,1,-1j],[0,0,1,1j]])
bKi4b4 = np.dot(Ki,Bi)
'''
try:
#print Ms[-1],Ms.shape,phix0,1,powerindex,scalemf,sequencenumber[1,0,0,0],norder
ux1,uxbar,Jx,scalex,Msx,As2x,Asm2x = \
jfdf.UMsUbarexpJ(Ms,phix0,1,powerindex,scalemf,sequencenumber[1,0,0,0],ypowerorder=norder)
uy1,uybar,Jy,scaley,Msy,As2y,Asm2y = \
jfdf.UMsUbarexpJ(Ms,phiy0,1,powerindex,scalemf,sequencenumber[0,0,1,0],ypowerorder=norder)
except:
return [1e8] * 8
# --- particle 1
x0 = 2.5e-2
y0 = 5e-3
xxpyyp = np.zeros((4, npass + 1))
xxpyyp[:, 0] = np.array([x0, 0, y0, 0])
for i in xrange(1, npass + 1):
xxpyyp[:, i] = np.dot(elemtx, xxpyyp[:, i - 1])
xybar = np.dot(Bi, xxpyyp)
xy = zip(*xybar)
section = []
for row in xy:
section.append(normalcoordinate(*row))
st = zip(*section)
#11. Prepare data for |wx|,thetax,|wy|,thetay to plot Poincare section of thetax,|wy|,thetay
section1 = [] #section1 is without joined blocks
xy = zip(*xxpyyp)
for row in xy:
row1 = row + (ux1, uy1)
section1.append(
tuneshift(row1[0], row1[1], row1[2], row1[3], row1[4], row1[5],
bKi4b4, scalex, scaley, powerindex, norder))
st1 = zip(*section1)
#print 'K2s = %.2f:'%k2s
zmax = max(st1[0])
zmin = min(st1[0])
zav = np.mean(st1[0])
zx1 = (zmax - zmin) / zav
#print "for wx1 without resonance block, (zmax-zmin)/zmean = ", zx1
zmax = max(st1[1])
zmin = min(st1[1])
zav = np.mean(st1[1])
zy1 = (zmax - zmin) / zav
#print "for wy1 without resonance block, (zmax-zmin)/zmean = ", zy1
#print ''
# --- particle 2
x0 = 1.0e-2
y0 = 2e-3
xxpyyp = np.zeros((4, npass + 1))
xxpyyp[:, 0] = np.array([x0, 0, y0, 0])
for i in xrange(1, npass + 1):
xxpyyp[:, i] = np.dot(elemtx, xxpyyp[:, i - 1])
xybar = np.dot(Bi, xxpyyp)
xy = zip(*xybar)
section = []
for row in xy:
section.append(normalcoordinate(*row))
st = zip(*section)
#11. Prepare data for |wx|,thetax,|wy|,thetay to plot Poincare section of thetax,|wy|,thetay
section1 = [] #section1 is without joined blocks
xy = zip(*xxpyyp)
for row in xy:
row1 = row + (ux1, uy1)
section1.append(
tuneshift(row1[0], row1[1], row1[2], row1[3], row1[4], row1[5],
bKi4b4, scalex, scaley, powerindex, norder))
st1 = zip(*section1)
return st1
#print 'K2s = %.2f:'%k2s
zmax = max(st1[0])
zmin = min(st1[0])
zav = np.mean(st1[0])
zx2 = (zmax - zmin) / zav
#print "for wx1 without resonance block, (zmax-zmin)/zmean = ", zx1
zmax = max(st1[1])
zmin = min(st1[1])
zav = np.mean(st1[1])
zy2 = (zmax - zmin) / zav
#print "for wy1 without resonance block, (zmax-zmin)/zmean = ", zy1
#print ''
# --- particle 3
x0 = 3.5e-2
y0 = 3.0e-3
xxpyyp = np.zeros((4, npass + 1))
xxpyyp[:, 0] = np.array([x0, 0, y0, 0])
for i in xrange(1, npass + 1):
xxpyyp[:, i] = np.dot(elemtx, xxpyyp[:, i - 1])
xybar = np.dot(Bi, xxpyyp)
xy = zip(*xybar)
section = []
for row in xy:
section.append(normalcoordinate(*row))
st = zip(*section)
#11. Prepare data for |wx|,thetax,|wy|,thetay to plot Poincare section of thetax,|wy|,thetay
section1 = [] #section1 is without joined blocks
xy = zip(*xxpyyp)
for row in xy:
row1 = row + (ux1, uy1)
section1.append(
tuneshift(row1[0], row1[1], row1[2], row1[3], row1[4], row1[5],
bKi4b4, scalex, scaley, powerindex, norder))
st1 = zip(*section1)
#print 'K2s = %.2f:'%k2s
zmax = max(st1[0])
zmin = min(st1[0])
zav = np.mean(st1[0])
zx3 = (zmax - zmin) / zav
#print "for wx1 without resonance block, (zmax-zmin)/zmean = ", zx1
zmax = max(st1[1])
zmin = min(st1[1])
zav = np.mean(st1[1])
zy3 = (zmax - zmin) / zav
#print "for wy1 without resonance block, (zmax-zmin)/zmean = ", zy1
#print ''
xlist = np.linspace(-3e-2, 3e-2, 30) #a list of theta0
ylist = np.arange(1e-6, 1.0e-2, 10) #a list of theta0
xyplane = [[i, j] for i in xlist for j in ylist]
nu, da = [], []
for x, y in xyplane:
t1, t2, t3, t4, t5, t6, t7, t8 = tuneshift(x, 0, y, 0, ux1, uy1,
bKi4b4, scalex, scaley,
powerindex, norder)
nu.append([t5, t6])
da.append([t7, t8])
da = np.array(da)
nux = [i[0].real / 2 / np.pi for i in nu]
nuy = [i[1].real / 2 / np.pi for i in nu]
dnuxda = np.max(np.abs(nux))
dnuyda = np.max(np.abs(nuy))
dax = np.max(np.abs(da[:, 0]))
day = np.max(np.abs(da[:, 1]))
return [zx1, zy1, zx2, zy2, zx3, zy3, dnuxda, dnuyda, dax, day]
2:4, 2:
4] = mliy #Notice that mlix and mliy is accurate simplex to machine precision, so their determinantes are closer to zero.
mf[:, 1:
5] = elemtx #Now replace the linear part of map matrix by the more accurate twiss matrix
sqrtbetax = np.sqrt(betax0)
sqrtbetay = np.sqrt(betay0)
#5. Construct the BK square matrix using the first 5 rows.
bK, bKi = sqdf.BKmatrix(betax0, phix0, alphax0, betay0, phiy0, alphay0, 0, 0,
norder, powerindex, sequencenumber, tol)
#6. Derive normalized map M=(BK)^(-1).mm.BK, see my notes 'Relation to Normal Form' of Wednesday, March 30, 2011 10:34 PM
# here #mfbk is the first 4 rows of M, it is
mfbk = jfdf.d3(bKi[1:5, 1:5], mf, bK)
#7. Scale the one turn map in z,z* space
def scalingmf(mf, powerindex):
#Find a scale s so that s x**m and s is on the same scale if the term in M with maximum absolute value has power m
#as described in "M scaling" in "Jordan Form Reformulation.one". mf is the first 4 rows of M so the scaling method is the same.
absM = abs(mf)
i, j = np.unravel_index(absM.argmax(), absM.shape)
power = sum(powerindex[j])
scalex1 = (absM.max())**(-(1. / (power - 1.)))
scalem1 = 1 / scalex1
mlen = len(powerindex)
As = np.identity(mlen)
for i in range(mlen):
As[i, i] = scalem1**sum(powerindex[i])