m^t C^-1 m, vary C3 from e-08 to e-12, hold C3

gistfile1.txt

Same as https://gist.github.com/evanbiederstedt/72b0035ca4b9fce830c3
except vary C3, hold sigma^2 fixed

FIRST, NO PEAK CODE, i.e. scale covariance matrix by e+21
CODE
""""
#
# Hold sigma^2 constant, vary C3
#
vary_x_samples125 = np.logspace(-8, -12, num=40) # C3 parameter, vary from e-08 to e-12
sigma125 = 5e-22 # chose this sigma^2 parameter, hold constant

Sij = vary_x_samples125[:, None, None] * norm_matrix[1][None, :, :]
newSij = (1e21)*Sij   # multiply S_ij by 1e12
Nij = sigma125 * id_mat[None, :, :]
newNij = (1e21)*Nij
# Format 7/4pi * param * P_3(M) where param is the parameter we vary, C_l
# Sij.shape = (40, 3072, 3072)
Cij = newSij + newNij
#invCij = np.linalg.inv(Cij)
logdetC = np.linalg.slogdet(Cij)  # returns sign and determinant; use logdetC[1]
# model_fit_terms = m^T C^-1 m
#
# model_fit_terms = np.array([np.dot(tempval.T , np.dot(invCij[i] , tempval) ) 
# for i in range(invCij.shape[0])])
#
model_fit_terms = np.array([np.dot(tempp.T , np.linalg.solve(Cij[i], tempp) ) for i in range(Cij.shape[0]) ]) 
print "m^T c^-1 m terms are"
print model_fit_terms 
print "******************"
print "logdetC terms are"
print logdetC[1] 
print "******************"
print "Npix2pi term is"
print Npix2pi
""""

OUTPUT:


m^T c^-1 m terms are
[ 17424944.59432721  25431124.82535299  20988175.41728179  18788639.9688897
  17380549.27187007  16487860.85815524  15909766.35792065
  15497517.16395973  15189182.91137147  14972008.39197645
  14793336.73669815  14664017.69568876  14568322.70447167  14492458.7918589
  14433833.23682215  14389138.7429928   14352751.6784684   14325011.10904521
  14302605.58943325  14285747.28930357  14272097.84990945
  14261432.05420008  14253089.98221404  14246570.26856775
  14241465.54843466  14237157.87713204  14234018.59879179
  14231438.17048982  14229450.48704928  14227802.58328702
  14226586.63568589  14225606.63455151  14224772.51924103
  14224178.22232257  14223689.86871848  14223295.19405429
  14222996.47245571  14222746.69923505  14222557.92339739
  14222409.72199761]
******************
logdetC terms are
[-1910.79269502 -1899.49346143 -1894.31400072 -1893.9865907  -1890.0321336
 -1889.55785882 -1889.79498435 -1890.52858638 -1891.04930553 -1892.56437866
 -1893.64297778 -1895.06109716 -1896.61902812 -1898.36601353 -1899.78459156
 -1901.39518245 -1903.05163531 -1904.67733691 -1906.32176722 -1907.95386497
 -1909.59522293 -1911.21625436 -1912.86998408 -1914.50988852 -1916.15690315
 -1917.81120861 -1919.462296   -1921.10832586 -1922.76238417 -1924.41349353
 -1926.06744684 -1927.71856858 -1929.37104233 -1931.02466563 -1932.67642731
 -1934.32805631 -1935.98147704 -1937.63429343 -1939.28755537 -1940.94054106]
******************
Npix2pi term is
19301.9452637

**************************************
*************************************
SECOND, THERE IS A PEAK CODE, i.e. scale covariance matrix by e+22
CODE
""""
#
# Hold sigma^2 constant, vary C3
#
vary_x_samples123 = np.logspace(-8, -12, num=40) # C3 parameter, vary from e-08 to e-12
sigma123 = 5e-22 # chose this sigma^2 parameter, hold constant
#
# Plot noise sigma from e-22 to e-24
#


Sij = vary_x_samples123 [:, None, None] * norm_matrix[1][None, :, :]
newSij = (1e22)*Sij   # multiply S_ij by 1e12
Nij = sigma123 * id_mat[None, :, :]
newNij = (1e22)*Nij
# Format 7/4pi * param * P_3(M) where param is the parameter we vary, C_l
# Sij.shape = (40, 3072, 3072)
Cij = newSij + newNij
#invCij = np.linalg.inv(Cij)
logdetC = np.linalg.slogdet(Cij)  # returns sign and determinant; use logdetC[1]
# model_fit_terms = m^T C^-1 m
#
# model_fit_terms = np.array([np.dot(tempval.T , np.dot(invCij[i] , tempval) ) 
# for i in range(invCij.shape[0])])
#
model_fit_terms = np.array([np.dot(tempp.T , np.linalg.solve(Cij[i], tempp) ) for i in range(Cij.shape[0]) ]) 

print "m^T c^-1 m terms are"
print model_fit_terms 
print "******************"
print "logdetC terms are"
print logdetC[1] 
print "******************"
print "Npix2pi term is"
print Npix2pi
""""

OUTPUT
m^T c^-1 m terms are
[ 2931868.99027531  2561423.09736563  2092876.99077943  1876397.00384942
  1740382.76555146  1650113.62054166  1589940.751404    1549446.41704495
  1519557.92056381  1496555.37291566  1479682.09032262  1466653.76019673
  1456837.51067493  1449220.46772181  1443528.73129329  1438909.39635894
  1435211.46326468  1432468.39780895  1430277.65089106  1428567.73979521
  1427238.59379346  1426165.74999515  1425328.54426065  1424671.52510419
  1424138.61076047  1423723.85218339  1423394.01406752  1423137.00097182
  1422944.56767479  1422779.35144192  1422656.21763844  1422559.03605542
  1422480.3001671   1422414.48572627  1422367.35435307  1422328.77614777
  1422298.52139999  1422275.64094104  1422255.88586292  1422241.38234343]
******************
logdetC terms are
[ 5162.11916985  5174.89668376  5179.54501215  5178.57071109  5182.81051551
  5184.46873299  5183.19398907  5183.19703352  5182.37013867  5181.01067721
  5179.97913256  5178.52226416  5176.80653401  5175.16623507  5173.76193185
  5172.11691893  5170.45643259  5168.87473124  5167.23262542  5165.6055479
  5163.95696043  5162.3116691   5160.67301514  5159.02720484  5157.37926926
  5155.73010752  5154.07978174  5152.43292945  5150.77874406  5149.12856074
  5147.47438028  5145.82296635  5144.17003878  5142.51772009  5140.86502619
  5139.21290009  5137.56004832  5135.9069266   5134.25393896  5132.60101615]
******************
Npix2pi term is
19301.9452637

We can do the same tests with holding C3 and varying the sigma^2 noise parameter:

First use C3 = 5e-10, and then try 10% less, i.e. C3=4.5e-10

FIRST CODE, fix C3 = 5e-10
""""

Hold C3 fixed, then do test again with 10% less C3 value

We use C3 = 5e-10

vary_x_samples125 = 5e-10
sigma125 = np.logspace(-21, -23, num=40)

Sij = vary_x_samples125 * norm_matrix[1][None, :, :]
newSij = (1e21)_Sij # multiply S_ij by 1e12
Nij = sigma125[:, None, None] * id_mat[None, :, :]
newNij = (1e21)_Nij

Format 7/4pi * param * P_3(M) where param is the parameter we vary, C_l

Sij.shape = (40, 3072, 3072)

Cij = newSij + newNij

invCij = np.linalg.inv(Cij)

logdetC = np.linalg.slogdet(Cij) # returns sign and determinant; use logdetC[1]

model_fit_terms = m^T C^-1 m

model_fit_terms = np.array([np.dot(tempval.T , np.dot(invCij[i] , tempval) )

for i in range(invCij.shape[0])])

model_fit_terms = np.array([np.dot(tempp.T , np.linalg.solve(Cij[i], tempp) ) for i in range(Cij.shape[0]) ])
print "m^T c^-1 m terms are"
print model_fit_terms
print "_"
print "logdetC terms are"
print logdetC[1]
print "_"
print "Npix2pi term is"
print Npix2pi
""""
OUTPUT

m^T c^-1 m terms are
[ 7.18293292e+06 8.09386470e+06 9.12113596e+06 1.02809343e+07
1.15907061e+07 1.30724929e+07 1.47468537e+07 1.66377572e+07
1.87792946e+07 2.12083991e+07 2.39623566e+07 2.70868218e+07
3.06414381e+07 3.46776845e+07 3.92815846e+07 4.45663590e+07
5.05957546e+07 5.75247398e+07 6.54552543e+07 7.47090796e+07
8.54799215e+07 9.81015899e+07 1.12663772e+08 1.30393234e+08
1.51636111e+08 1.77587337e+08 2.08278721e+08 2.50099439e+08
3.03916267e+08 3.79636875e+08 4.98623636e+08 7.21005423e+08
1.10892079e+09 3.23917412e+09 -3.41985605e+09 -9.80515049e+08
-5.10193129e+08 -2.76047856e+08 -1.17087469e+08 -1.90858052e+07]

---

logdetC terms are
[ 226.9052794 -135.07131727 -496.90121724 -858.84168741
-1220.95683913 -1583.00135661 -1944.915235 -2306.69141473
-2668.93133159 -3030.70976015 -3393.04701702 -3754.86449285
-4117.08237295 -4478.81252165 -4840.70266103 -5203.60698497
-5565.30740991 -5927.80221985 -6289.9127427 -6652.62034049
-7016.06626191 -7378.97770017 -7739.66767859 -8103.60482614
-8468.13642146 -8832.06627575 -9201.75852318 -9558.79338163
-9920.82765381 -10286.47587538 -10655.88535624 -11026.26666575
-11395.66670283 -11762.37585804 -12132.20128441 -12499.66763487
-12883.12465843 -13266.56868972 -13654.89410426 -14040.44010189]

---

Npix2pi term is
19301.9452637

---

---

SECOND CODE, C3 fixed to 4.5e-10
"""""

Hold C3 fixed, then do test again with 10% less C3 value

Now use C3 = 4.5e-10

vary_x_samples125 = 5e-10
sigma125 = np.logspace(-21, -23, num=40)

Sij = vary_x_samples125 * norm_matrix[1][None, :, :]
newSij = (1e21)_Sij # multiply S_ij by 1e12
Nij = sigma125[:, None, None] * id_mat[None, :, :]
newNij = (1e21)_Nij

Format 7/4pi * param * P_3(M) where param is the parameter we vary, C_l

Sij.shape = (40, 3072, 3072)

Cij = newSij + newNij

invCij = np.linalg.inv(Cij)

logdetC = np.linalg.slogdet(Cij) # returns sign and determinant; use logdetC[1]

model_fit_terms = m^T C^-1 m

model_fit_terms = np.array([np.dot(tempval.T , np.dot(invCij[i] , tempval) )

for i in range(invCij.shape[0])])

model_fit_terms = np.array([np.dot(tempp.T , np.linalg.solve(Cij[i], tempp) ) for i in range(Cij.shape[0]) ])
print "m^T c^-1 m terms are"
print model_fit_terms
print "_"
print "logdetC terms are"
print logdetC[1]
print "_"
print "Npix2pi term is"
print Npix2pi
"""""

OUTPUT
m^T c^-1 m terms are
[ 7.18293292e+06 8.09386470e+06 9.12113596e+06 1.02809343e+07
1.15907061e+07 1.30724929e+07 1.47468537e+07 1.66377572e+07
1.87792946e+07 2.12083991e+07 2.39623566e+07 2.70868218e+07
3.06414381e+07 3.46776845e+07 3.92815846e+07 4.45663590e+07
5.05957546e+07 5.75247398e+07 6.54552543e+07 7.47090796e+07
8.54799215e+07 9.81015899e+07 1.12663772e+08 1.30393234e+08
1.51636111e+08 1.77587337e+08 2.08278721e+08 2.50099439e+08
3.03916267e+08 3.79636875e+08 4.98623636e+08 7.21005423e+08
1.10892079e+09 3.23917412e+09 -3.41985605e+09 -9.80515049e+08
-5.10193129e+08 -2.76047856e+08 -1.17087469e+08 -1.90858052e+07]

---

logdetC terms are
[ 226.9052794 -135.07131727 -496.90121724 -858.84168741
-1220.95683913 -1583.00135661 -1944.915235 -2306.69141473
-2668.93133159 -3030.70976015 -3393.04701702 -3754.86449285
-4117.08237295 -4478.81252165 -4840.70266103 -5203.60698497
-5565.30740991 -5927.80221985 -6289.9127427 -6652.62034049
-7016.06626191 -7378.97770017 -7739.66767859 -8103.60482614
-8468.13642146 -8832.06627575 -9201.75852318 -9558.79338163
-9920.82765381 -10286.47587538 -10655.88535624 -11026.26666575
-11395.66670283 -11762.37585804 -12132.20128441 -12499.66763487
-12883.12465843 -13266.56868972 -13654.89410426 -14040.44010189]

---

Npix2pi term is
19301.9452637

FIRST, FIND NO PEAK IN LF, NOISE PARAMETERS E-22 TO E-24

CODE, C3 = 5e-10:
""""

Hold C3 fixed, then do test again with 10% less C3 value

Use C3=5e-10

Noise is now varied from e-22 to e-24

vary_x_samples123 = 5e-10
sigma123 = np.logspace(-22, -24, num=40)

Sij = vary_x_samples123 * norm_matrix[1][None, :, :]
newSij = (1e22)_Sij # multiply S_ij by 1e12
Nij = sigma123[:, None, None] * id_mat[None, :, :]
newNij = (1e22)_Nij

Format 7/4pi * param * P_3(M) where param is the parameter we vary, C_l

Sij.shape = (40, 3072, 3072)

Cij = newSij + newNij

invCij = np.linalg.inv(Cij)

logdetC = np.linalg.slogdet(Cij) # returns sign and determinant; use logdetC[1]

model_fit_terms = m^T C^-1 m

model_fit_terms = np.array([np.dot(tempval.T , np.dot(invCij[i] , tempval) )

for i in range(invCij.shape[0])])

model_fit_terms = np.array([np.dot(tempp.T , np.linalg.solve(Cij[i], tempp) ) for i in range(Cij.shape[0]) ])

print "m^T c^-1 m terms are"
print model_fit_terms
print "_"
print "logdetC terms are"
print logdetC[1]
print "_"
print "Npix2pi term is"
print Npix2pi
""""

OUTPUT
m^T c^-1 m terms are
[ 7.99112774e+06 9.15862622e+06 1.05174464e+07 1.21218540e+07
1.40481199e+07 1.63849383e+07 1.94345938e+07 2.28107290e+07
2.75426116e+07 3.39869501e+07 4.30589812e+07 5.86874289e+07
8.17059720e+07 1.64401397e+08 -3.15809360e+10 -1.55530576e+08
-7.00025652e+07 -3.69097741e+07 -2.01136741e+07 5.33705542e+06
4.54644402e+06 1.50969154e+07 3.64295994e+07 7.59843057e+07
-5.50891593e+07 1.77650620e+07 5.68860609e+07 1.24610626e+08
-1.18748462e+08 1.00196018e+08 3.26506311e+07 -5.96827008e+06
-9.43865379e+07 -2.91770949e+07 1.05304583e+08 -4.74799471e+07
-1.85701131e+07 1.86812899e+07 -4.27639327e+07 -5.13285598e+07]

logdetC terms are
[ 239.71699157 -122.71079135 -486.33852385 -849.25504606
-1212.4921126 -1576.26351061 -1944.85327619 -2305.753459
-2669.13822474 -3030.65420367 -3396.41771088 -3763.82736171
-4131.60575246 -4506.35071982 -4889.11466545 -5248.4037388
-5612.4490359 -5995.67825433 -6385.48032885 -6779.9332622
-7172.39370076 -7581.395549 -8041.60387949 -8517.11067861
-9002.83276846 -9446.49442793 -9839.83647962 -10172.92306214
-10420.76829252 -10623.50283171 -10792.24792309 -10928.10844176
-11027.19559602 -11100.06733525 -11170.65063404 -11215.66540551
-11261.93661065 -11284.43614935 -11306.60681018 -11326.08454794]

Npix2pi term is
19301.9452637

SECOND CODE,
C3 = 4.5e-10

Hold C3 fixed, then do test again with 10% less C3 value

Now use C3=4.5e-10

Noise is now varied from e-22 to e-24

vary_x_samples123 = 4.5e-10
sigma123 = np.logspace(-22, -24, num=40)

Sij = vary_x_samples123 * norm_matrix[1][None, :, :]
newSij = (1e22)_Sij # multiply S_ij by 1e12
Nij = sigma123[:, None, None] * id_mat[None, :, :]
newNij = (1e22)_Nij

Format 7/4pi * param * P_3(M) where param is the parameter we vary, C_l

Sij.shape = (40, 3072, 3072)

Cij = newSij + newNij

invCij = np.linalg.inv(Cij)

logdetC = np.linalg.slogdet(Cij) # returns sign and determinant; use logdetC[1]

model_fit_terms = m^T C^-1 m

model_fit_terms = np.array([np.dot(tempval.T , np.dot(invCij[i] , tempval) )

for i in range(invCij.shape[0])])

model_fit_terms = np.array([np.dot(tempp.T , np.linalg.solve(Cij[i], tempp) ) for i in range(Cij.shape[0]) ])

print "m^T c^-1 m terms are"
print model_fit_terms
print "_"
print "logdetC terms are"
print logdetC[1]
print "_"
print "Npix2pi term is"
print Npix2pi

OUTPUT

m^T c^-1 m terms are
[ 7.88230937e+06 9.00401772e+06 1.03091948e+07 1.18496346e+07
1.36733594e+07 1.58717504e+07 1.85223083e+07 2.29277071e+07
2.58774395e+07 3.11601583e+07 3.85718641e+07 4.95209561e+07
6.71862827e+07 9.81421763e+07 2.00515338e+08 1.79149266e+08
-1.57174217e+08 -7.01207170e+07 -3.93179729e+07 -2.01955132e+07
-6.98201421e+06 5.88648498e+06 1.83612716e+07 3.94038299e+07
5.39473080e+07 3.01503865e+07 -3.34339516e+07 -1.31643012e+08
-1.18775863e+08 -8.63387028e+06 2.02255477e+08 -5.89407096e+07
-1.31132724e+08 2.82823527e+07 8.34855351e+06 1.41266857e+08
1.68945314e+08 -8.34350175e+07 -4.03057940e+07 1.36690513e+09]

logdetC terms are
[ 238.87906146 -123.59978549 -486.97635053 -849.54919459
-1212.63010956 -1576.01604717 -1942.33073337 -2309.73321034
-2670.91431763 -3031.09627919 -3396.32588831 -3762.14204865
-4128.07960518 -4502.34341668 -4872.33980536 -5255.02597355
-5607.79232715 -5986.94061374 -6370.62068917 -6753.73665052
-7147.26442618 -7537.878678 -7981.39859695 -8433.45165572
-8907.83987127 -9384.80250567 -9848.92410084 -10252.021386
-10558.32732388 -10804.17249772 -11029.95815536 -11179.59272393
-11324.19494314 -11416.3809462 -11503.90735819 -11568.77486146
-11622.48104156 -11656.23132841 -11687.85082231 -11713.95931238]

Npix2pi term is
19301.9452637