Skip to content
This repository has been archived by the owner on Dec 3, 2019. It is now read-only.

Amino-acid models not implemented correctly? #130

Closed
bredelings opened this issue Jul 20, 2018 · 4 comments
Closed

Amino-acid models not implemented correctly? #130

bredelings opened this issue Jul 20, 2018 · 4 comments
Assignees
@hoehna

Comments

@bredelings
Copy link
Contributor

Hi,

It looks like the fnWAG and fnLG models returns symmetric matrices. However, the Q matrix for the WAG isn't symmetric. Am I missing some kind of function that combines the WAG S-matrix with frequencies to get a Q matrix?

-BenRI
@bredelings
Copy link
Contributor Author

Yeah, so the WAG model basically specifies a symmetric matrix for use in the GTR. Just like the GTR, you need to add amino-acid frequencies to get a rate matrix: Q(i,j) = symmetric(i,j)*pi[j].

I believe the WAG matrix comes with a set of frequencies -- so you could use those.
People also often estimate the frequencies from the data set that they are analyzing.

But using the symmetric matrix as the Q matrix is only right if the amino acids have equal frequencies, which they don't. So, it looks like the WAG model is not implemented correctly. It should be pretty easy to fix, though.

@bredelings
Copy link
Contributor Author

@mlandis Michael, am I right that you coded up the WAG and LG functions? Would you be interested in working on this during the hackathon?

@bredelings
Copy link
Contributor Author

Looking at revbayes/src/core/datatypes/phylogenetics/ratematrix/RateMatrix_Wag.cpp, it looks like the matrix m[i][j] simply needs to be multiplied by stationary_freqs[j] before the call to setDiagonal(). And, I think similarly for all the other empirical rate matrices?

@bredelings bredelings assigned hoehna and unassigned mlandis Jul 23, 2018
@mlandis
Copy link
Member

mlandis commented Jul 31, 2018

Hey @bredelings, sorry to be slow to reply. I was out of town this past week.

Thanks for identifying this mistake -- a good catch! Empirical rate matrices were not correctly multiplying state columns by the stationary frequencies. This appears to have been an old bug that was propagated into newer empirical matrices. Commit 5e5c494 should fix this issue for the following classes:

RateMatrix_Blosum62
RateMatrix_CpRev
RateMatrix_Dayhoff
RateMatrix_Jones
RateMatrix_LG
RateMatrix_MtMam
RateMatrix_MtRev24
RateMatrix_RtRev24
RateMatrix_Vt
RateMatrix_Wag

For cleanliness and consistency, we should assign values to exchangeability_rates then call TimeReversibleRateMatrix::computeOffDiagonal() to populate m. For now, I am manually multiplying stationary_frequencies through the columns of m as a temporary fix.

I'll close this issue. We can open a new one if needed.

Here are the new rate matrix values:

> Q_Blosum62 <- fnBlosum62()
> Q_Blosum62
   [ [ -1.0826, 0.0342, 0.0195, 0.0262, 0.0326, 0.0364, 0.0565, 0.1292, 0.0166, 0.0368, 0.0707,
   0.0671, 0.0280, 0.0207, 0.0409, 0.2201, 0.0787, 0.0054, 0.0205, 0.1426 ] ,
     0.0486, -0.9041, 0.0521, 0.0242, 0.0051, 0.0917, 0.0656, 0.0277, 0.0338, 0.0141, 0.0550,
   0.2802, 0.0220, 0.0156, 0.0156, 0.0571, 0.0416, 0.0049, 0.0206, 0.0286 ] ,
     0.0321, 0.0602, -0.9530, 0.1533, 0.0089, 0.0558, 0.0598, 0.0896, 0.0560, 0.0172, 0.0187,
   0.0825, 0.0145, 0.0149, 0.0172, 0.1478, 0.0864, 0.0022, 0.0154, 0.0204 ] ,
     0.0359, 0.0233, 0.1278, -0.7701, 0.0054, 0.0362, 0.1814, 0.0528, 0.0181, 0.0254, 0.0193,
   0.0535, 0.0050, 0.0118, 0.0254, 0.0805, 0.0425, 0.0017, 0.0075, 0.0168 ] ,
     0.0965, 0.0106, 0.0160, 0.0116, -0.5749, 0.0100, 0.0068, 0.0276, 0.0082, 0.0470, 0.0735,
   0.0148, 0.0171, 0.0185, 0.0124, 0.0609, 0.0510, 0.0061, 0.0134, 0.0728 ] ,
     0.0793, 0.1402, 0.0739, 0.0574, 0.0074, -1.3106, 0.2666, 0.0403, 0.0565, 0.0143, 0.0513,
   0.2043, 0.0557, 0.0061, 0.0299, 0.0985, 0.0582, 0.0088, 0.0274, 0.0346 ] ,
     0.0774, 0.0632, 0.0498, 0.1814, 0.0031, 0.1678, -1.0495, 0.0280, 0.0378, 0.0113, 0.0329,
   0.1451, 0.0124, 0.0122, 0.0323, 0.0901, 0.0488, 0.0047, 0.0170, 0.0342 ] ,
     0.1292, 0.0194, 0.0545, 0.0385, 0.0093, 0.0185, 0.0204, -0.5526, 0.0125, 0.0115, 0.0192,
   0.0389, 0.0103, 0.0154, 0.0176, 0.0768, 0.0292, 0.0059, 0.0088, 0.0165 ] ,
     0.0473, 0.0676, 0.0970, 0.0375, 0.0079, 0.0739, 0.0784, 0.0357, -0.8354, 0.0153, 0.0308,
   0.0529, 0.0220, 0.0300, 0.0184, 0.0568, 0.0267, 0.0035, 0.1205, 0.0131 ] ,
     0.0400, 0.0108, 0.0114, 0.0202, 0.0173, 0.0072, 0.0090, 0.0125, 0.0059, -1.2883, 0.3439,
   0.0210, 0.0751, 0.0637, 0.0135, 0.0182, 0.0537, 0.0040, 0.0193, 0.5417 ] ,
     0.0529, 0.0289, 0.0085, 0.0105, 0.0186, 0.0176, 0.0180, 0.0144, 0.0081, 0.2362, -0.9073,
   0.0231, 0.1346, 0.0866, 0.0130, 0.0180, 0.0417, 0.0080, 0.0232, 0.1454 ] ,
     0.0856, 0.2512, 0.0640, 0.0498, 0.0064, 0.1198, 0.1351, 0.0497, 0.0237, 0.0247, 0.0394,
   -1.1263, 0.0240, 0.0112, 0.0365, 0.0892, 0.0594, 0.0039, 0.0205, 0.0325 ] ,
     0.0828, 0.0457, 0.0261, 0.0107, 0.0171, 0.0757, 0.0268, 0.0304, 0.0228, 0.2043, 0.5330, 0.0556,
   -1.5412, 0.0744, 0.0158, 0.0468, 0.0678, 0.0103, 0.0272, 0.1679 ] ,
     0.0326, 0.0173, 0.0143, 0.0136, 0.0099, 0.0044, 0.0140, 0.0243, 0.0166, 0.0921, 0.1825, 0.0138,
   0.0396, -0.8042, 0.0081, 0.0275, 0.0222, 0.0241, 0.1928, 0.0546 ] ,
     0.0775, 0.0208, 0.0199, 0.0352, 0.0079, 0.0261, 0.0447, 0.0333, 0.0122, 0.0236, 0.0331, 0.0542,
   0.0101, 0.0098, -0.5597, 0.0595, 0.0458, 0.0029, 0.0106, 0.0324 ] ,
     0.2858, 0.0521, 0.1167, 0.0763, 0.0267, 0.0587, 0.0853, 0.0997, 0.0259, 0.0217, 0.0312, 0.0907,
   0.0205, 0.0227, 0.0407, -1.3533, 0.2346, 0.0045, 0.0228, 0.0366 ] ,
     0.1142, 0.0425, 0.0763, 0.0450, 0.0250, 0.0388, 0.0516, 0.0424, 0.0136, 0.0716, 0.0809, 0.0675,
   0.0332, 0.0205, 0.0350, 0.2622, -1.1960, 0.0060, 0.0229, 0.1468 ] ,
     0.0308, 0.0198, 0.0077, 0.0070, 0.0118, 0.0230, 0.0197, 0.0336, 0.0070, 0.0208, 0.0611, 0.0172,
   0.0198, 0.0870, 0.0088, 0.0197, 0.0234, -0.5514, 0.1158, 0.0174 ] ,
     0.0475, 0.0335, 0.0216, 0.0126, 0.0105, 0.0291, 0.0288, 0.0204, 0.0979, 0.0410, 0.0717, 0.0372,
   0.0212, 0.2831, 0.0129, 0.0405, 0.0365, 0.0471, -0.9581, 0.0652 ] ,
     0.1445, 0.0204, 0.0126, 0.0124, 0.0249, 0.0161, 0.0253, 0.0167, 0.0047, 0.5046, 0.1972, 0.0258,
   0.0575, 0.0352, 0.0173, 0.0286, 0.1026, 0.0031, 0.0286, -1.2781 ] ]
>
> Q_CpRev <- fnCpRev()
> Q_CpRev
   [ [ -0.9154, 0.0125, 0.0178, 0.0124, 0.0115, 0.0114, 0.0468, 0.1070, 0.0032, 0.0225, 0.0381,
   0.0226, 0.0078, 0.0066, 0.0404, 0.2898, 0.1386, 0.0005, 0.0033, 0.1224 ] ,
     0.0153, -0.8995, 0.0280, 0.0030, 0.0142, 0.1270, 0.0143, 0.0391, 0.0342, 0.0211, 0.0393,
   0.4293, 0.0053, 0.0052, 0.0072, 0.0457, 0.0325, 0.0079, 0.0192, 0.0116 ] ,
     0.0331, 0.0424, -1.4819, 0.3144, 0.0093, 0.0559, 0.0990, 0.1051, 0.0673, 0.0261, 0.0219,
   0.2328, 0.0026, 0.0095, 0.0143, 0.2477, 0.1441, 0.0014, 0.0448, 0.0105 ] ,
     0.0255, 0.0051, 0.3484, -1.0254, 0.0002, 0.0291, 0.3465, 0.0694, 0.0159, 0.0016, 0.0019,
   0.0395, 0.0020, 0.0021, 0.0140, 0.0701, 0.0275, 0.0006, 0.0167, 0.0095 ] ,
     0.0974, 0.0978, 0.0423, 0.0007, -1.0489, 0.0007, 0.0009, 0.0488, 0.0211, 0.0435, 0.0766,
   0.0046, 0.0067, 0.0709, 0.0235, 0.2769, 0.0596, 0.0150, 0.0871, 0.0749 ] ,
     0.0229, 0.2073, 0.0603, 0.0284, 0.0002, -1.2212, 0.2931, 0.0214, 0.0608, 0.0143, 0.0553,
   0.3174, 0.0085, 0.0010, 0.0266, 0.0470, 0.0249, 0.0018, 0.0232, 0.0068 ] ,
     0.0727, 0.0181, 0.0829, 0.2616, 0.0002, 0.2273, -1.1978, 0.0610, 0.0078, 0.0230, 0.0159,
   0.2518, 0.0048, 0.0142, 0.0152, 0.0675, 0.0382, 0.0022, 0.0084, 0.0253 ] ,
     0.0968, 0.0289, 0.0513, 0.0306, 0.0052, 0.0097, 0.0356, -0.4064, 0.0009, 0.0062, 0.0039,
   0.0252, 0.0009, 0.0024, 0.0023, 0.0821, 0.0095, 0.0028, 0.0006, 0.0115 ] ,
     0.0096, 0.0849, 0.1104, 0.0235, 0.0076, 0.0924, 0.0152, 0.0031, -0.5804, 0.0045, 0.0128,
   0.0292, 0.0004, 0.0124, 0.0125, 0.0360, 0.0033, 0.0024, 0.1171, 0.0032 ] ,
     0.0211, 0.0162, 0.0132, 0.0007, 0.0048, 0.0067, 0.0139, 0.0064, 0.0014, -1.3304, 0.3377,
   0.0330, 0.0747, 0.0444, 0.0096, 0.0257, 0.1076, 0.0014, 0.0053, 0.6066 ] ,
     0.0287, 0.0241, 0.0089, 0.0007, 0.0068, 0.0208, 0.0077, 0.0032, 0.0032, 0.2708, -0.7982,
   0.0209, 0.0569, 0.1239, 0.0180, 0.0613, 0.0161, 0.0055, 0.0112, 0.1094 ] ,
     0.0344, 0.5324, 0.1909, 0.0292, 0.0008, 0.2412, 0.2468, 0.0423, 0.0146, 0.0535, 0.0422,
   -1.7129, 0.0081, 0.0070, 0.0249, 0.1031, 0.0950, 0.0003, 0.0147, 0.0315 ] ,
     0.0269, 0.0148, 0.0048, 0.0033, 0.0027, 0.0147, 0.0106, 0.0034, 0.0005, 0.2750, 0.2614, 0.0185,
   -0.8305, 0.0320, 0.0082, 0.0110, 0.0667, 0.0030, 0.0128, 0.0601 ] ,
     0.0099, 0.0063, 0.0076, 0.0016, 0.0125, 0.0007, 0.0136, 0.0040, 0.0061, 0.0705, 0.2454, 0.0069,
   0.0138, -0.6725, 0.0035, 0.0578, 0.0153, 0.0161, 0.1408, 0.0401 ] ,
     0.0713, 0.0103, 0.0136, 0.0121, 0.0049, 0.0235, 0.0174, 0.0045, 0.0073, 0.0182, 0.0424, 0.0289,
   0.0042, 0.0042, -0.4553, 0.1428, 0.0269, 0.0017, 0.0058, 0.0154 ] ,
     0.3553, 0.0457, 0.1638, 0.0418, 0.0402, 0.0288, 0.0533, 0.1112, 0.0145, 0.0335, 0.0998, 0.0831,
   0.0039, 0.0476, 0.0990, -1.4989, 0.2225, 0.0025, 0.0310, 0.0211 ] ,
     0.1951, 0.0373, 0.1094, 0.0189, 0.0099, 0.0175, 0.0346, 0.0148, 0.0015, 0.1614, 0.0302, 0.0879,
   0.0272, 0.0145, 0.0214, 0.2555, -1.1385, 0.0010, 0.0042, 0.0961 ] ,
     0.0020, 0.0273, 0.0031, 0.0013, 0.0075, 0.0039, 0.0059, 0.0132, 0.0033, 0.0065, 0.0308, 0.0010,
   0.0036, 0.0457, 0.0040, 0.0087, 0.0030, -0.1927, 0.0205, 0.0013 ] ,
     0.0082, 0.0384, 0.0592, 0.0199, 0.0253, 0.0285, 0.0133, 0.0016, 0.0944, 0.0138, 0.0366, 0.0237,
   0.0091, 0.2316, 0.0080, 0.0620, 0.0073, 0.0119, -0.7077, 0.0150 ] ,
     0.1409, 0.0109, 0.0065, 0.0053, 0.0102, 0.0039, 0.0188, 0.0146, 0.0012, 0.7444, 0.1674, 0.0239,
   0.0200, 0.0310, 0.0101, 0.0198, 0.0786, 0.0003, 0.0071, -1.3150 ] ]
>
> Q_Dayhoff <- fnDayhoff()
> Q_Dayhoff
   [ [ -1.3318, 0.0110, 0.0394, 0.0559, 0.0120, 0.0339, 0.0975, 0.2115, 0.0077, 0.0238, 0.0348,
   0.0208, 0.0106, 0.0071, 0.1260, 0.2829, 0.2159, 0.0000, 0.0071, 0.1338 ] ,
     0.0234, -0.8647, 0.0129, 0.0000, 0.0077, 0.0936, 0.0005, 0.0079, 0.0802, 0.0235, 0.0127,
   0.3713, 0.0132, 0.0055, 0.0519, 0.1065, 0.0151, 0.0210, 0.0024, 0.0154 ] ,
     0.0849, 0.0130, -1.7875, 0.4218, 0.0000, 0.0392, 0.0729, 0.1225, 0.1788, 0.0282, 0.0289,
   0.2545, 0.0001, 0.0055, 0.0212, 0.3424, 0.1333, 0.0024, 0.0283, 0.0097 ] ,
     0.1040, 0.0000, 0.3638, -1.4133, 0.0000, 0.0510, 0.5678, 0.1101, 0.0287, 0.0088, 0.0000,
   0.0568, 0.0000, 0.0000, 0.0066, 0.0657, 0.0384, 0.0000, 0.0000, 0.0116 ] ,
     0.0312, 0.0094, 0.0000, 0.0000, -0.2661, 0.0000, 0.0000, 0.0097, 0.0094, 0.0161, 0.0000,
   0.0000, 0.0000, 0.0000, 0.0096, 0.1114, 0.0093, 0.0000, 0.0286, 0.0315 ] ,
     0.0771, 0.1000, 0.0414, 0.0624, 0.0000, -1.2378, 0.3526, 0.0247, 0.2026, 0.0066, 0.0620,
   0.1224, 0.0167, 0.0000, 0.0771, 0.0387, 0.0308, 0.0000, 0.0000, 0.0225 ] ,
     0.1715, 0.0004, 0.0595, 0.5373, 0.0000, 0.2723, -1.3599, 0.0714, 0.0144, 0.0224, 0.0093,
   0.0664, 0.0044, 0.0000, 0.0257, 0.0547, 0.0198, 0.0000, 0.0065, 0.0238 ] ,
     0.2079, 0.0037, 0.0559, 0.0583, 0.0037, 0.0107, 0.0399, -0.6504, 0.0033, 0.0000, 0.0059,
   0.0216, 0.0025, 0.0059, 0.0171, 0.1619, 0.0175, 0.0000, 0.0000, 0.0347 ] ,
     0.0199, 0.0976, 0.2151, 0.0401, 0.0093, 0.2305, 0.0212, 0.0088, -0.8755, 0.0026, 0.0373,
   0.0208, 0.0000, 0.0190, 0.0474, 0.0242, 0.0128, 0.0028, 0.0378, 0.0283 ] ,
     0.0563, 0.0260, 0.0310, 0.0112, 0.0146, 0.0068, 0.0300, 0.0000, 0.0023, -1.2775, 0.2181,
   0.0368, 0.0493, 0.0775, 0.0060, 0.0166, 0.1118, 0.0000, 0.0110, 0.5721 ] ,
     0.0355, 0.0061, 0.0137, 0.0000, 0.0000, 0.0278, 0.0054, 0.0062, 0.0147, 0.0943, -0.5302,
   0.0144, 0.0773, 0.0621, 0.0161, 0.0118, 0.0192, 0.0048, 0.0083, 0.1126 ] ,
     0.0225, 0.1887, 0.1278, 0.0331, 0.0000, 0.0582, 0.0409, 0.0238, 0.0087, 0.0169, 0.0153,
   -0.7440, 0.0356, 0.0000, 0.0166, 0.0664, 0.0792, 0.0000, 0.0039, 0.0064 ] ,
     0.0624, 0.0366, 0.0004, 0.0000, 0.0000, 0.0434, 0.0148, 0.0150, 0.0000, 0.1232, 0.4473, 0.1945,
   -1.2518, 0.0364, 0.0086, 0.0429, 0.0605, 0.0000, 0.0000, 0.1660 ] ,
     0.0156, 0.0057, 0.0056, 0.0000, 0.0000, 0.0000, 0.0000, 0.0132, 0.0160, 0.0719, 0.1332, 0.0000,
   0.0135, -0.5430, 0.0055, 0.0318, 0.0076, 0.0079, 0.2076, 0.0077 ] ,
     0.2166, 0.0419, 0.0169, 0.0061, 0.0063, 0.0582, 0.0251, 0.0300, 0.0314, 0.0044, 0.0272, 0.0264,
   0.0025, 0.0043, -0.7430, 0.1695, 0.0454, 0.0000, 0.0000, 0.0309 ] ,
     0.3543, 0.0626, 0.1990, 0.0443, 0.0536, 0.0213, 0.0389, 0.2062, 0.0117, 0.0088, 0.0144, 0.0768,
   0.0091, 0.0182, 0.1235, -1.6000, 0.3201, 0.0078, 0.0101, 0.0193 ] ,
     0.3214, 0.0106, 0.0921, 0.0308, 0.0053, 0.0202, 0.0167, 0.0264, 0.0074, 0.0704, 0.0280, 0.1088,
   0.0153, 0.0051, 0.0393, 0.3805, -1.2918, 0.0000, 0.0125, 0.1010 ] ,
     0.0000, 0.0817, 0.0092, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0090, 0.0000, 0.0390, 0.0000,
   0.0000, 0.0301, 0.0000, 0.0519, 0.0000, -0.2391, 0.0181, 0.0000 ] ,
     0.0208, 0.0033, 0.0382, 0.0000, 0.0320, 0.0000, 0.0108, 0.0000, 0.0425, 0.0136, 0.0238, 0.0104,
   0.0000, 0.2760, 0.0000, 0.0235, 0.0244, 0.0064, -0.5436, 0.0180 ] ,
     0.1802, 0.0098, 0.0060, 0.0084, 0.0163, 0.0133, 0.0182, 0.0476, 0.0147, 0.3260, 0.1485, 0.0080,
   0.0378, 0.0047, 0.0242, 0.0208, 0.0914, 0.0000, 0.0083, -0.9843 ] ]
>
> Q_Jones <- fnJones()
> Q_Jones
   [ [ -1.2478, 0.0298, 0.0229, 0.0415, 0.0110, 0.0231, 0.0645, 0.1301, 0.0062, 0.0192, 0.0274,
   0.0204, 0.0128, 0.0060, 0.0981, 0.2583, 0.2764, 0.0013, 0.0035, 0.1954 ] ,
     0.0442, -1.0260, 0.0191, 0.0082, 0.0222, 0.1255, 0.0178, 0.0996, 0.0748, 0.0118, 0.0347,
   0.3766, 0.0104, 0.0020, 0.0374, 0.0690, 0.0372, 0.0179, 0.0064, 0.0111 ] ,
     0.0412, 0.0231, -1.2806, 0.2704, 0.0067, 0.0348, 0.0356, 0.0589, 0.0891, 0.0251, 0.0110,
   0.1533, 0.0071, 0.0040, 0.0076, 0.3437, 0.1350, 0.0011, 0.0223, 0.0105 ] ,
     0.0618, 0.0082, 0.2237, -1.0449, 0.0020, 0.0198, 0.4712, 0.0945, 0.0255, 0.0059, 0.0064,
   0.0152, 0.0036, 0.0016, 0.0076, 0.0403, 0.0221, 0.0006, 0.0147, 0.0203 ] ,
     0.0427, 0.0580, 0.0144, 0.0051, -0.5657, 0.0036, 0.0031, 0.0429, 0.0157, 0.0091, 0.0210,
   0.0041, 0.0073, 0.0311, 0.0071, 0.1524, 0.0244, 0.0163, 0.0667, 0.0407 ] ,
     0.0435, 0.1592, 0.0364, 0.0251, 0.0018, -1.0441, 0.1984, 0.0189, 0.1361, 0.0048, 0.0657,
   0.1702, 0.0102, 0.0016, 0.0829, 0.0362, 0.0297, 0.0026, 0.0077, 0.0131 ] ,
     0.0801, 0.0149, 0.0246, 0.3928, 0.0010, 0.1308, -0.9443, 0.0865, 0.0059, 0.0064, 0.0082,
   0.1055, 0.0043, 0.0020, 0.0091, 0.0205, 0.0186, 0.0014, 0.0022, 0.0295 ] ,
     0.1365, 0.0704, 0.0343, 0.0666, 0.0116, 0.0105, 0.0731, -0.6478, 0.0052, 0.0032, 0.0055,
   0.0157, 0.0033, 0.0020, 0.0121, 0.1373, 0.0192, 0.0078, 0.0026, 0.0308 ] ,
     0.0206, 0.1685, 0.1657, 0.0574, 0.0136, 0.2417, 0.0160, 0.0167, -1.1357, 0.0085, 0.0511,
   0.0262, 0.0078, 0.0159, 0.0582, 0.0499, 0.0268, 0.0011, 0.1828, 0.0072 ] ,
     0.0275, 0.0113, 0.0199, 0.0056, 0.0033, 0.0036, 0.0074, 0.0044, 0.0036, -1.2736, 0.2091,
   0.0122, 0.1134, 0.0355, 0.0051, 0.0273, 0.1426, 0.0013, 0.0102, 0.6303 ] ,
     0.0229, 0.0195, 0.0051, 0.0036, 0.0045, 0.0292, 0.0055, 0.0044, 0.0128, 0.1223, -0.6681,
   0.0082, 0.0919, 0.0989, 0.0516, 0.0403, 0.0145, 0.0074, 0.0077, 0.1180 ] ,
     0.0267, 0.3318, 0.1114, 0.0133, 0.0014, 0.1182, 0.1112, 0.0196, 0.0103, 0.0112, 0.0128,
   -0.9007, 0.0154, 0.0016, 0.0106, 0.0321, 0.0599, 0.0014, 0.0026, 0.0092 ] ,
     0.0412, 0.0226, 0.0127, 0.0077, 0.0061, 0.0174, 0.0111, 0.0102, 0.0075, 0.2559, 0.3543, 0.0379,
   -1.1821, 0.0171, 0.0081, 0.0198, 0.1315, 0.0034, 0.0057, 0.2118 ] ,
     0.0114, 0.0026, 0.0042, 0.0020, 0.0153, 0.0016, 0.0031, 0.0036, 0.0091, 0.0475, 0.2265, 0.0023,
   0.0102, -0.6372, 0.0086, 0.0629, 0.0070, 0.0075, 0.1710, 0.0407 ] ,
     0.1479, 0.0380, 0.0064, 0.0077, 0.0028, 0.0664, 0.0111, 0.0174, 0.0262, 0.0053, 0.0931, 0.0122,
   0.0038, 0.0068, -0.7277, 0.1947, 0.0687, 0.0009, 0.0032, 0.0151 ] ,
     0.2883, 0.0519, 0.2131, 0.0302, 0.0439, 0.0215, 0.0184, 0.1461, 0.0166, 0.0214, 0.0539, 0.0274,
   0.0069, 0.0367, 0.1441, -1.4479, 0.2776, 0.0050, 0.0201, 0.0249 ] ,
     0.3622, 0.0329, 0.0983, 0.0195, 0.0083, 0.0207, 0.0197, 0.0240, 0.0105, 0.1309, 0.0228, 0.0601,
   0.0535, 0.0048, 0.0597, 0.3259, -1.3354, 0.0017, 0.0067, 0.0735 ] ,
     0.0069, 0.0647, 0.0034, 0.0020, 0.0226, 0.0073, 0.0061, 0.0400, 0.0018, 0.0048, 0.0475, 0.0058,
   0.0057, 0.0211, 0.0030, 0.0239, 0.0070, -0.3128, 0.0226, 0.0164 ] ,
     0.0084, 0.0103, 0.0297, 0.0236, 0.0411, 0.0097, 0.0043, 0.0058, 0.1306, 0.0171, 0.0219, 0.0047,
   0.0043, 0.2137, 0.0051, 0.0430, 0.0122, 0.0101, -0.6060, 0.0105 ] ,
     0.2272, 0.0087, 0.0068, 0.0159, 0.0122, 0.0081, 0.0276, 0.0342, 0.0025, 0.5133, 0.1644, 0.0082,
   0.0765, 0.0247, 0.0116, 0.0260, 0.0652, 0.0035, 0.0051, -1.2417 ] ]
>
> Q_LG <- fnLG()
> Q_LG
   [ [ -1.0896, 0.0238, 0.0116, 0.0210, 0.0322, 0.0395, 0.0743, 0.1185, 0.0080, 0.0093, 0.0392,
   0.0347, 0.0258, 0.0107, 0.0519, 0.2893, 0.1140, 0.0022, 0.0075, 0.1762 ] ,
     0.0336, -0.8833, 0.0316, 0.0066, 0.0069, 0.1145, 0.0261, 0.0224, 0.0542, 0.0079, 0.0299,
   0.4087, 0.0111, 0.0022, 0.0146, 0.0525, 0.0309, 0.0072, 0.0107, 0.0118 ] ,
     0.0219, 0.0421, -1.1871, 0.2693, 0.0068, 0.0691, 0.0388, 0.0824, 0.1008, 0.0119, 0.0068,
   0.1386, 0.0085, 0.0038, 0.0071, 0.2453, 0.1066, 0.0005, 0.0209, 0.0058 ] ,
     0.0312, 0.0069, 0.2131, -0.8633, 0.0008, 0.0213, 0.3754, 0.0484, 0.0207, 0.0007, 0.0015,
   0.0183, 0.0006, 0.0007, 0.0174, 0.0759, 0.0227, 0.0004, 0.0046, 0.0026 ] ,
     0.1968, 0.0299, 0.0222, 0.0033, -0.8678, 0.0035, 0.0003, 0.0326, 0.0143, 0.0199, 0.0589,
   0.0009, 0.0205, 0.0468, 0.0033, 0.1704, 0.0609, 0.0081, 0.0398, 0.1355 ] ,
     0.0767, 0.1571, 0.0712, 0.0278, 0.0011, -1.2495, 0.2955, 0.0154, 0.1076, 0.0045, 0.0577,
   0.2089, 0.0384, 0.0015, 0.0275, 0.0749, 0.0576, 0.0028, 0.0088, 0.0145 ] ,
     0.0821, 0.0204, 0.0227, 0.2782, 0.0000, 0.1683, -0.8425, 0.0200, 0.0095, 0.0028, 0.0069,
   0.1167, 0.0040, 0.0008, 0.0185, 0.0375, 0.0322, 0.0009, 0.0041, 0.0169 ] ,
     0.1634, 0.0218, 0.0603, 0.0448, 0.0074, 0.0109, 0.0250, -0.5041, 0.0070, 0.0005, 0.0044,
   0.0192, 0.0032, 0.0038, 0.0087, 0.1065, 0.0069, 0.0032, 0.0019, 0.0053 ] ,
     0.0284, 0.1357, 0.1893, 0.0492, 0.0083, 0.1962, 0.0303, 0.0179, -1.0932, 0.0068, 0.0363,
   0.0450, 0.0102, 0.0289, 0.0224, 0.0606, 0.0311, 0.0072, 0.1813, 0.0082 ] ,
     0.0118, 0.0071, 0.0080, 0.0006, 0.0041, 0.0030, 0.0032, 0.0005, 0.0024, -1.4150, 0.4107,
   0.0103, 0.0981, 0.0471, 0.0034, 0.0039, 0.0551, 0.0013, 0.0079, 0.7364 ] ,
     0.0313, 0.0169, 0.0029, 0.0008, 0.0077, 0.0237, 0.0050, 0.0025, 0.0082, 0.2576, -0.7938,
   0.0089, 0.1449, 0.1097, 0.0110, 0.0112, 0.0161, 0.0075, 0.0102, 0.1177 ] ,
     0.0424, 0.3539, 0.0900, 0.0150, 0.0002, 0.1319, 0.1294, 0.0170, 0.0156, 0.0099, 0.0136,
   -0.9764, 0.0151, 0.0010, 0.0172, 0.0458, 0.0606, 0.0006, 0.0045, 0.0128 ] ,
     0.0889, 0.0271, 0.0156, 0.0014, 0.0116, 0.0682, 0.0124, 0.0080, 0.0099, 0.2656, 0.6254, 0.0424,
   -1.5420, 0.0761, 0.0044, 0.0212, 0.1077, 0.0084, 0.0164, 0.1313 ] ,
     0.0201, 0.0029, 0.0038, 0.0009, 0.0143, 0.0015, 0.0013, 0.0051, 0.0152, 0.0692, 0.2569, 0.0015,
   0.0413, -0.8106, 0.0042, 0.0221, 0.0088, 0.0296, 0.2665, 0.0453 ] ,
     0.0931, 0.0186, 0.0068, 0.0209, 0.0010, 0.0255, 0.0300, 0.0113, 0.0114, 0.0049, 0.0247, 0.0252,
   0.0023, 0.0040, -0.4166, 0.0819, 0.0305, 0.0011, 0.0031, 0.0205 ] ,
     0.3738, 0.0480, 0.1683, 0.0658, 0.0360, 0.0499, 0.0438, 0.0998, 0.0221, 0.0040, 0.0181, 0.0484,
   0.0080, 0.0153, 0.0589, -1.4284, 0.3449, 0.0030, 0.0137, 0.0068 ] ,
     0.1692, 0.0324, 0.0840, 0.0226, 0.0148, 0.0440, 0.0433, 0.0074, 0.0131, 0.0643, 0.0300, 0.0734,
   0.0464, 0.0070, 0.0252, 0.3961, -1.2344, 0.0017, 0.0084, 0.1513 ] ,
     0.0143, 0.0332, 0.0019, 0.0016, 0.0087, 0.0096, 0.0056, 0.0154, 0.0133, 0.0069, 0.0614, 0.0032,
   0.0160, 0.1039, 0.0042, 0.0152, 0.0075, -0.4428, 0.1076, 0.0131 ] ,
     0.0173, 0.0176, 0.0257, 0.0072, 0.0151, 0.0105, 0.0086, 0.0031, 0.1186, 0.0145, 0.0297, 0.0085,
   0.0110, 0.3301, 0.0039, 0.0245, 0.0131, 0.0380, -0.7144, 0.0172 ] ,
     0.2014, 0.0096, 0.0035, 0.0020, 0.0253, 0.0086, 0.0175, 0.0044, 0.0027, 0.6619, 0.1687, 0.0120,
   0.0436, 0.0277, 0.0131, 0.0060, 0.1166, 0.0023, 0.0085, -1.3354 ] ]
>
> Q_MtMam <- fnMtMam()
> Q_MtMam
   [ [ -1.0484, 0.0050, 0.0007, 0.0017, 0.0000, 0.0000, 0.0000, 0.0367, 0.0019, 0.0574, 0.0297,
   0.0000, 0.0360, 0.0000, 0.0240, 0.2095, 0.5006, 0.0012, 0.0000, 0.1439 ] ,
     0.0187, -0.1702, 0.0014, 0.0000, 0.0102, 0.0495, 0.0000, 0.0085, 0.0543, 0.0000, 0.0085,
   0.0093, 0.0000, 0.0000, 0.0041, 0.0018, 0.0000, 0.0040, 0.0000, 0.0000 ] ,
     0.0012, 0.0006, -0.7876, 0.1358, 0.0000, 0.0016, 0.0000, 0.0221, 0.1072, 0.0145, 0.0000,
   0.0762, 0.0100, 0.0031, 0.0149, 0.2732, 0.0809, 0.0015, 0.0448, 0.0000 ] ,
     0.0064, 0.0000, 0.2920, -0.4784, 0.0000, 0.0099, 0.1135, 0.0372, 0.0026, 0.0000, 0.0000,
   0.0000, 0.0000, 0.0026, 0.0009, 0.0098, 0.0000, 0.0000, 0.0000, 0.0036 ] ,
     0.0000, 0.0289, 0.0000, 0.0000, -0.6382, 0.0000, 0.0000, 0.0000, 0.0714, 0.0314, 0.0382,
   0.0000, 0.0000, 0.0036, 0.0000, 0.2126, 0.0838, 0.0161, 0.1523, 0.0000 ] ,
     0.0000, 0.0382, 0.0027, 0.0077, 0.0000, -0.3849, 0.0546, 0.0000, 0.1287, 0.0000, 0.0283,
   0.0452, 0.0104, 0.0000, 0.0231, 0.0184, 0.0000, 0.0000, 0.0155, 0.0119 ] ,
     0.0000, 0.0000, 0.0000, 0.0894, 0.0000, 0.0551, -0.2232, 0.0104, 0.0051, 0.0000, 0.0000,
   0.0401, 0.0000, 0.0000, 0.0000, 0.0129, 0.0029, 0.0000, 0.0000, 0.0072 ] ,
     0.0456, 0.0028, 0.0159, 0.0124, 0.0000, 0.0000, 0.0044, -0.1518, 0.0000, 0.0000, 0.0000,
   0.0000, 0.0000, 0.0000, 0.0000, 0.0686, 0.0000, 0.0000, 0.0003, 0.0018 ] ,
     0.0047, 0.0361, 0.1548, 0.0017, 0.0168, 0.1106, 0.0044, 0.0000, -0.8409, 0.0000, 0.0368,
   0.0000, 0.0000, 0.0000, 0.0240, 0.0123, 0.0007, 0.0000, 0.4381, 0.0000 ] ,
     0.0439, 0.0000, 0.0064, 0.0000, 0.0023, 0.0000, 0.0000, 0.0000, 0.0000, -1.6650, 0.3284,
   0.0011, 0.1792, 0.0294, 0.0023, 0.0000, 0.2646, 0.0000, 0.0046, 0.8029 ] ,
     0.0123, 0.0009, 0.0000, 0.0000, 0.0015, 0.0040, 0.0000, 0.0000, 0.0061, 0.1774, -0.7548,
   0.0007, 0.2887, 0.1270, 0.0195, 0.0453, 0.0250, 0.0030, 0.0072, 0.0362 ] ,
     0.0000, 0.0078, 0.1379, 0.0000, 0.0000, 0.0487, 0.0429, 0.0000, 0.0000, 0.0046, 0.0057,
   -0.3794, 0.0280, 0.0000, 0.0082, 0.0398, 0.0368, 0.0000, 0.0192, 0.0000 ] ,
     0.0444, 0.0000, 0.0071, 0.0000, 0.0000, 0.0044, 0.0000, 0.0000, 0.0000, 0.2891, 0.8619, 0.0110,
   -2.0645, 0.0057, 0.0000, 0.0288, 0.5080, 0.0032, 0.0000, 0.3009 ] ,
     0.0000, 0.0000, 0.0020, 0.0008, 0.0004, 0.0000, 0.0000, 0.0000, 0.0000, 0.0436, 0.3482, 0.0000,
   0.0052, -0.6670, 0.0077, 0.0551, 0.0059, 0.0000, 0.1959, 0.0022 ] ,
     0.0310, 0.0014, 0.0112, 0.0003, 0.0000, 0.0103, 0.0000, 0.0000, 0.0124, 0.0038, 0.0609, 0.0034,
   0.0000, 0.0088, -0.3285, 0.1237, 0.0573, 0.0017, 0.0023, 0.0000 ] ,
     0.2000, 0.0005, 0.1507, 0.0025, 0.0191, 0.0060, 0.0042, 0.0527, 0.0047, 0.0000, 0.1047, 0.0121,
   0.0223, 0.0465, 0.0915, -1.2038, 0.4514, 0.0042, 0.0307, 0.0000 ] ,
     0.3982, 0.0000, 0.0372, 0.0000, 0.0063, 0.0000, 0.0008, 0.0000, 0.0002, 0.2753, 0.0481, 0.0093,
   0.3276, 0.0041, 0.0353, 0.3761, -1.6043, 0.0000, 0.0000, 0.0857 ] ,
     0.0029, 0.0025, 0.0020, 0.0000, 0.0036, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0170, 0.0000,
   0.0062, 0.0000, 0.0032, 0.0104, 0.0000, -0.0518, 0.0040, 0.0000 ] ,
     0.0000, 0.0000, 0.0527, 0.0000, 0.0291, 0.0109, 0.0000, 0.0005, 0.3569, 0.0122, 0.0354, 0.0125,
   0.0000, 0.3521, 0.0036, 0.0655, 0.0000, 0.0035, -0.9350, 0.0000 ] ,
     0.2327, 0.0000, 0.0000, 0.0016, 0.0000, 0.0066, 0.0040, 0.0024, 0.0000, 1.6976, 0.1415, 0.0000,
   0.3944, 0.0031, 0.0000, 0.0000, 0.1742, 0.0000, 0.0000, -2.6582 ] ]
>
> Q_MtRev <- fnMtRev()
> Q_MtRev
   [ [ -0.9586, 0.0038, 0.0090, 0.0029, 0.0031, 0.0004, 0.0020, 0.0581, 0.0033, 0.0730, 0.0368,
   0.0017, 0.0659, 0.0033, 0.0252, 0.2401, 0.3555, 0.0005, 0.0018, 0.0721 ] ,
     0.0143, -0.2035, 0.0044, 0.0003, 0.0053, 0.0475, 0.0004, 0.0111, 0.0398, 0.0014, 0.0225,
   0.0280, 0.0009, 0.0025, 0.0110, 0.0037, 0.0015, 0.0055, 0.0005, 0.0028 ] ,
     0.0167, 0.0022, -1.1223, 0.1298, 0.0030, 0.0373, 0.0130, 0.0257, 0.1194, 0.0205, 0.0219,
   0.1204, 0.0304, 0.0080, 0.0340, 0.3061, 0.1763, 0.0027, 0.0543, 0.0007 ] ,
     0.0109, 0.0003, 0.2664, -0.5561, 0.0001, 0.0119, 0.1204, 0.0273, 0.0274, 0.0033, 0.0027,
   0.0005, 0.0009, 0.0026, 0.0062, 0.0427, 0.0207, 0.0050, 0.0060, 0.0007 ] ,
     0.0371, 0.0169, 0.0198, 0.0003, -0.6648, 0.0162, 0.0004, 0.0148, 0.0341, 0.0475, 0.0371,
   0.0004, 0.0029, 0.0371, 0.0145, 0.1715, 0.1331, 0.0084, 0.0723, 0.0007 ] ,
     0.0012, 0.0361, 0.0582, 0.0090, 0.0039, -0.6902, 0.0647, 0.0033, 0.1402, 0.0063, 0.0573,
   0.0921, 0.0220, 0.0100, 0.0637, 0.0335, 0.0702, 0.0005, 0.0110, 0.0070 ] ,
     0.0060, 0.0003, 0.0211, 0.0953, 0.0001, 0.0674, -0.3482, 0.0136, 0.0118, 0.0025, 0.0027,
   0.0621, 0.0009, 0.0014, 0.0060, 0.0339, 0.0110, 0.0005, 0.0037, 0.0078 ] ,
     0.0747, 0.0038, 0.0179, 0.0093, 0.0016, 0.0015, 0.0058, -0.2210, 0.0005, 0.0045, 0.0035,
   0.0045, 0.0009, 0.0010, 0.0009, 0.0780, 0.0083, 0.0027, 0.0009, 0.0009 ] ,
     0.0086, 0.0270, 0.1664, 0.0186, 0.0073, 0.1252, 0.0101, 0.0009, -0.7480, 0.0093, 0.0166,
   0.0252, 0.0056, 0.0253, 0.0283, 0.0480, 0.0331, 0.0018, 0.1901, 0.0007 ] ,
     0.0597, 0.0003, 0.0091, 0.0007, 0.0032, 0.0018, 0.0007, 0.0029, 0.0030, -1.6168, 0.4754,
   0.0039, 0.2405, 0.0444, 0.0096, 0.0295, 0.2724, 0.0005, 0.0071, 0.4521 ] ,
     0.0158, 0.0025, 0.0051, 0.0003, 0.0013, 0.0085, 0.0004, 0.0012, 0.0028, 0.2490, -0.8649,
   0.0029, 0.2496, 0.1133, 0.0186, 0.0456, 0.0935, 0.0081, 0.0125, 0.0339 ] ,
     0.0052, 0.0231, 0.2041, 0.0004, 0.0001, 0.1001, 0.0648, 0.0109, 0.0307, 0.0148, 0.0215,
   -0.7323, 0.0424, 0.0034, 0.0233, 0.0655, 0.1008, 0.0060, 0.0145, 0.0007 ] ,
     0.0878, 0.0003, 0.0219, 0.0003, 0.0003, 0.0102, 0.0004, 0.0009, 0.0029, 0.3919, 0.7765, 0.0181,
   -1.9873, 0.0476, 0.0087, 0.0688, 0.3905, 0.0054, 0.0113, 0.1433 ] ,
     0.0039, 0.0008, 0.0051, 0.0008, 0.0037, 0.0041, 0.0006, 0.0009, 0.0116, 0.0641, 0.3121, 0.0013,
   0.0422, -0.6603, 0.0080, 0.0398, 0.0250, 0.0020, 0.1321, 0.0023 ] ,
     0.0336, 0.0039, 0.0246, 0.0022, 0.0016, 0.0295, 0.0026, 0.0009, 0.0147, 0.0156, 0.0579, 0.0099,
   0.0087, 0.0091, -0.4236, 0.1052, 0.0948, 0.0010, 0.0046, 0.0030 ] ,
     0.2401, 0.0010, 0.1658, 0.0113, 0.0143, 0.0116, 0.0113, 0.0606, 0.0186, 0.0361, 0.1063, 0.0209,
   0.0516, 0.0337, 0.0789, -1.3325, 0.4416, 0.0096, 0.0184, 0.0007 ] ,
     0.2976, 0.0003, 0.0800, 0.0046, 0.0093, 0.0204, 0.0031, 0.0054, 0.0108, 0.2788, 0.1826, 0.0270,
   0.2452, 0.0178, 0.0595, 0.3697, -1.7010, 0.0025, 0.0110, 0.0756 ] ,
     0.0012, 0.0036, 0.0036, 0.0032, 0.0017, 0.0004, 0.0004, 0.0053, 0.0017, 0.0014, 0.0469, 0.0047,
   0.0101, 0.0041, 0.0020, 0.0239, 0.0074, -0.1310, 0.0074, 0.0020 ] ,
     0.0040, 0.0003, 0.0642, 0.0035, 0.0131, 0.0083, 0.0027, 0.0015, 0.1613, 0.0189, 0.0638, 0.0101,
   0.0186, 0.2442, 0.0075, 0.0402, 0.0286, 0.0065, -0.6982, 0.0007 ] ,
     0.1208, 0.0012, 0.0006, 0.0003, 0.0001, 0.0041, 0.0044, 0.0012, 0.0005, 0.9253, 0.1324, 0.0004,
   0.1799, 0.0033, 0.0038, 0.0012, 0.1512, 0.0013, 0.0005, -1.5327 ] ]
>
> Q_RtRev <- fnRtRev()
> Q_RtRev
   [ [ -1.1713, 0.0181, 0.0271, 0.0053, 0.2333, 0.0170, 0.0430, 0.0717, 0.0159, 0.0005, 0.0239,
   0.0202, 0.1249, 0.0005, 0.0516, 0.2445, 0.1371, 0.0027, 0.0292, 0.1047 ] ,
     0.0181, -0.8136, 0.0186, 0.0159, 0.0489, 0.1174, 0.0053, 0.0218, 0.0478, 0.0128, 0.0096,
   0.3151, 0.0303, 0.0037, 0.0128, 0.0542, 0.0340, 0.0069, 0.0250, 0.0154 ] ,
     0.0271, 0.0186, -1.1107, 0.2041, 0.0680, 0.1254, 0.0420, 0.0500, 0.1701, 0.0186, 0.0080,
   0.0654, 0.0005, 0.0260, 0.0175, 0.1562, 0.0787, 0.0085, 0.0149, 0.0112 ] ,
     0.0053, 0.0159, 0.2041, -0.7860, 0.0005, 0.0415, 0.2880, 0.0324, 0.0484, 0.0005, 0.0027,
   0.0106, 0.0005, 0.0005, 0.0292, 0.0723, 0.0292, 0.0005, 0.0005, 0.0032 ] ,
     0.2333, 0.0489, 0.0680, 0.0005, -1.0804, 0.0372, 0.0005, 0.0255, 0.0659, 0.0553, 0.0585,
   0.0085, 0.0829, 0.0372, 0.0005, 0.0399, 0.0622, 0.0292, 0.0696, 0.1568 ] ,
     0.0170, 0.1174, 0.1254, 0.0415, 0.0372, -1.3281, 0.1977, 0.0096, 0.2057, 0.0175, 0.0287,
   0.1642, 0.0840, 0.0005, 0.0361, 0.1196, 0.0776, 0.0053, 0.0239, 0.0191 ] ,
     0.0430, 0.0053, 0.0420, 0.2880, 0.0005, 0.1977, -0.8694, 0.0372, 0.0181, 0.0005, 0.0112,
   0.0749, 0.0005, 0.0005, 0.0276, 0.0505, 0.0436, 0.0090, 0.0005, 0.0186 ] ,
     0.0717, 0.0218, 0.0500, 0.0324, 0.0255, 0.0096, 0.0372, -0.4443, 0.0361, 0.0005, 0.0016,
   0.0159, 0.0197, 0.0037, 0.0090, 0.0808, 0.0037, 0.0122, 0.0112, 0.0016 ] ,
     0.0159, 0.0478, 0.1701, 0.0484, 0.0659, 0.2057, 0.0181, 0.0361, -1.1660, 0.0181, 0.0271,
   0.0404, 0.0616, 0.0749, 0.0234, 0.0973, 0.0260, 0.0255, 0.1632, 0.0005 ] ,
     0.0005, 0.0128, 0.0186, 0.0005, 0.0553, 0.0175, 0.0005, 0.0005, 0.0181, -1.2175, 0.2046,
   0.0181, 0.1993, 0.0340, 0.0053, 0.0021, 0.0383, 0.0207, 0.0138, 0.5570 ] ,
     0.0239, 0.0096, 0.0080, 0.0027, 0.0585, 0.0287, 0.0112, 0.0016, 0.0271, 0.2046, -0.9481,
   0.0122, 0.3088, 0.0951, 0.0117, 0.0128, 0.0133, 0.0250, 0.0340, 0.0595 ] ,
     0.0202, 0.3151, 0.0654, 0.0106, 0.0085, 0.1642, 0.0749, 0.0159, 0.0404, 0.0181, 0.0122,
   -0.9603, 0.0712, 0.0074, 0.0229, 0.0409, 0.0585, 0.0032, 0.0005, 0.0101 ] ,
     0.1249, 0.0303, 0.0005, 0.0005, 0.0829, 0.0840, 0.0005, 0.0197, 0.0616, 0.1993, 0.3088, 0.0712,
   -1.4099, 0.1313, 0.0005, 0.0005, 0.0696, 0.0590, 0.0393, 0.1254 ] ,
     0.0005, 0.0037, 0.0260, 0.0005, 0.0372, 0.0005, 0.0005, 0.0037, 0.0749, 0.0340, 0.0951, 0.0074,
   0.1313, -1.1548, 0.0058, 0.0106, 0.0367, 0.0967, 0.5405, 0.0489 ] ,
     0.0516, 0.0128, 0.0175, 0.0292, 0.0005, 0.0361, 0.0276, 0.0090, 0.0234, 0.0053, 0.0117, 0.0229,
   0.0005, 0.0058, -0.3837, 0.0712, 0.0329, 0.0048, 0.0074, 0.0133 ] ,
     0.2445, 0.0542, 0.1562, 0.0723, 0.0399, 0.1196, 0.0505, 0.0808, 0.0973, 0.0021, 0.0128, 0.0409,
   0.0005, 0.0106, 0.0712, -1.4546, 0.3566, 0.0074, 0.0165, 0.0207 ] ,
     0.1371, 0.0340, 0.0787, 0.0292, 0.0622, 0.0776, 0.0436, 0.0037, 0.0260, 0.0383, 0.0133, 0.0585,
   0.0696, 0.0367, 0.0329, 0.3566, -1.2207, 0.0005, 0.0181, 0.1042 ] ,
     0.0027, 0.0069, 0.0085, 0.0005, 0.0292, 0.0053, 0.0090, 0.0122, 0.0255, 0.0207, 0.0250, 0.0032,
   0.0590, 0.0967, 0.0048, 0.0074, 0.0005, -0.4246, 0.0935, 0.0138 ] ,
     0.0292, 0.0250, 0.0149, 0.0005, 0.0696, 0.0239, 0.0005, 0.0112, 0.1632, 0.0138, 0.0340, 0.0005,
   0.0393, 0.5405, 0.0074, 0.0165, 0.0181, 0.0935, -1.1330, 0.0314 ] ,
     0.1047, 0.0154, 0.0112, 0.0032, 0.1568, 0.0191, 0.0186, 0.0016, 0.0005, 0.5570, 0.0595, 0.0101,
   0.1254, 0.0489, 0.0133, 0.0207, 0.1042, 0.0138, 0.0314, -1.3153 ] ]
>
> Q_VT <- fnVT()
> Q_VT
   [ [ -1.4603, 0.0341, 0.0241, 0.0402, 0.0099, 0.0325, 0.1005, 0.1774, 0.0052, 0.0395, 0.1170,
   0.0644, 0.0144, 0.0144, 0.0501, 0.3293, 0.1403, 0.0011, 0.0086, 0.2572 ] ,
     0.0525, -0.7412, 0.0255, 0.0160, 0.0014, 0.0518, 0.0452, 0.0318, 0.0141, 0.0145, 0.0530,
   0.2877, 0.0060, 0.0053, 0.0161, 0.0530, 0.0326, 0.0018, 0.0095, 0.0236 ] ,
     0.0449, 0.0309, -0.7652, 0.1340, 0.0012, 0.0289, 0.0479, 0.0733, 0.0191, 0.0155, 0.0191,
   0.0824, 0.0039, 0.0049, 0.0105, 0.1535, 0.0753, 0.0004, 0.0092, 0.0104 ] ,
     0.0597, 0.0154, 0.1068, -0.7715, 0.0004, 0.0216, 0.2831, 0.0631, 0.0089, 0.0021, 0.0168,
   0.0428, 0.0008, 0.0021, 0.0201, 0.0836, 0.0285, 0.0004, 0.0051, 0.0102 ] ,
     0.0512, 0.0046, 0.0033, 0.0016, -0.2002, 0.0005, 0.0009, 0.0103, 0.0011, 0.0082, 0.0253,
   0.0007, 0.0016, 0.0063, 0.0014, 0.0318, 0.0127, 0.0003, 0.0042, 0.0342 ] ,
     0.0699, 0.0723, 0.0333, 0.0312, 0.0002, -0.7877, 0.1701, 0.0261, 0.0208, 0.0097, 0.0671,
   0.1209, 0.0082, 0.0032, 0.0197, 0.0649, 0.0398, 0.0008, 0.0061, 0.0234 ] ,
     0.1280, 0.0374, 0.0327, 0.2426, 0.0002, 0.1008, -1.0023, 0.0507, 0.0069, 0.0083, 0.0418,
   0.1456, 0.0040, 0.0035, 0.0257, 0.0736, 0.0513, 0.0007, 0.0054, 0.0430 ] ,
     0.1974, 0.0230, 0.0438, 0.0473, 0.0022, 0.0135, 0.0443, -0.6197, 0.0038, 0.0091, 0.0240,
   0.0317, 0.0032, 0.0062, 0.0156, 0.1111, 0.0218, 0.0009, 0.0037, 0.0173 ] ,
     0.0177, 0.0312, 0.0351, 0.0204, 0.0007, 0.0331, 0.0185, 0.0118, -0.3366, 0.0036, 0.0285,
   0.0251, 0.0014, 0.0099, 0.0099, 0.0303, 0.0162, 0.0008, 0.0281, 0.0143 ] ,
     0.0502, 0.0119, 0.0105, 0.0018, 0.0020, 0.0057, 0.0082, 0.0103, 0.0013, -1.6215, 0.5756,
   0.0153, 0.0336, 0.0397, 0.0069, 0.0148, 0.0602, 0.0013, 0.0085, 0.7635 ] ,
     0.0957, 0.0282, 0.0084, 0.0092, 0.0040, 0.0256, 0.0269, 0.0176, 0.0068, 0.3707, -1.2186,
   0.0330, 0.0751, 0.1171, 0.0213, 0.0390, 0.0389, 0.0032, 0.0187, 0.2795 ] ,
     0.0886, 0.2571, 0.0608, 0.0396, 0.0002, 0.0775, 0.1573, 0.0391, 0.0101, 0.0165, 0.0554,
   -1.0219, 0.0066, 0.0047, 0.0266, 0.0725, 0.0714, 0.0009, 0.0068, 0.0302 ] ,
     0.0477, 0.0129, 0.0069, 0.0018, 0.0010, 0.0127, 0.0104, 0.0094, 0.0014, 0.0876, 0.3045, 0.0158,
   -0.6530, 0.0214, 0.0013, 0.0164, 0.0295, 0.0008, 0.0072, 0.0642 ] ,
     0.0263, 0.0062, 0.0048, 0.0025, 0.0022, 0.0028, 0.0050, 0.0102, 0.0053, 0.0569, 0.2607, 0.0063,
   0.0118, -0.5899, 0.0053, 0.0250, 0.0137, 0.0049, 0.0884, 0.0517 ] ,
     0.0899, 0.0188, 0.0102, 0.0243, 0.0005, 0.0164, 0.0363, 0.0252, 0.0052, 0.0097, 0.0468, 0.0348,
   0.0007, 0.0053, -0.4659, 0.0780, 0.0331, 0.0006, 0.0032, 0.0270 ] ,
     0.4095, 0.0428, 0.1024, 0.0700, 0.0076, 0.0376, 0.0719, 0.1241, 0.0110, 0.0145, 0.0592, 0.0655,
   0.0061, 0.0171, 0.0540, -1.4158, 0.2824, 0.0014, 0.0120, 0.0267 ] ,
     0.1978, 0.0299, 0.0570, 0.0270, 0.0034, 0.0261, 0.0568, 0.0276, 0.0067, 0.0668, 0.0670, 0.0732,
   0.0125, 0.0106, 0.0260, 0.3203, -1.1736, 0.0008, 0.0093, 0.1547 ] ,
     0.0068, 0.0068, 0.0013, 0.0017, 0.0003, 0.0022, 0.0033, 0.0049, 0.0013, 0.0062, 0.0230, 0.0038,
   0.0015, 0.0158, 0.0018, 0.0065, 0.0033, -0.1075, 0.0123, 0.0046 ] ,
     0.0196, 0.0142, 0.0113, 0.0078, 0.0019, 0.0066, 0.0098, 0.0076, 0.0189, 0.0153, 0.0523, 0.0113,
   0.0050, 0.1112, 0.0040, 0.0221, 0.0151, 0.0047, -0.3649, 0.0263 ] ,
     0.2774, 0.0166, 0.0060, 0.0074, 0.0071, 0.0118, 0.0364, 0.0167, 0.0045, 0.6482, 0.3684, 0.0237,
   0.0209, 0.0306, 0.0162, 0.0231, 0.1183, 0.0008, 0.0124, -1.6465 ] ]
>
> Q_WAG <- fnWAG()
> Q_WAG
   [ [ -1.1171, 0.0255, 0.0209, 0.0442, 0.0208, 0.0350, 0.0964, 0.1238, 0.0081, 0.0098, 0.0360,
   0.0590, 0.0183, 0.0085, 0.0691, 0.2459, 0.1358, 0.0017, 0.0089, 0.1493 ] ,
     0.0501, -0.9743, 0.0261, 0.0088, 0.0107, 0.1170, 0.0268, 0.0511, 0.0548, 0.0095, 0.0450,
   0.3484, 0.0140, 0.0041, 0.0326, 0.0893, 0.0355, 0.0176, 0.0141, 0.0187 ] ,
     0.0464, 0.0293, -1.4524, 0.3251, 0.0054, 0.0595, 0.0577, 0.0983, 0.1014, 0.0282, 0.0119,
   0.1961, 0.0041, 0.0039, 0.0094, 0.2900, 0.1300, 0.0011, 0.0402, 0.0146 ] ,
     0.0672, 0.0068, 0.2227, -0.9897, 0.0006, 0.0238, 0.3762, 0.0756, 0.0239, 0.0020, 0.0077,
   0.0312, 0.0021, 0.0019, 0.0204, 0.0782, 0.0240, 0.0020, 0.0121, 0.0113 ] ,
     0.0934, 0.0244, 0.0109, 0.0018, -0.4874, 0.0038, 0.0013, 0.0268, 0.0064, 0.0087, 0.0348,
   0.0048, 0.0080, 0.0161, 0.0053, 0.1027, 0.0328, 0.0108, 0.0201, 0.0746 ] ,
     0.0826, 0.1401, 0.0633, 0.0369, 0.0020, -1.3798, 0.3333, 0.0288, 0.1101, 0.0058, 0.0787,
   0.2536, 0.0316, 0.0040, 0.0448, 0.0751, 0.0549, 0.0033, 0.0084, 0.0224 ] ,
     0.1439, 0.0203, 0.0389, 0.3696, 0.0004, 0.2108, -1.2369, 0.0496, 0.0146, 0.0065, 0.0140,
   0.1682, 0.0065, 0.0033, 0.0328, 0.0514, 0.0527, 0.0024, 0.0073, 0.0438 ] ,
     0.1288, 0.0270, 0.0462, 0.0518, 0.0062, 0.0127, 0.0346, -0.4976, 0.0064, 0.0015, 0.0055,
   0.0243, 0.0036, 0.0020, 0.0117, 0.0979, 0.0145, 0.0051, 0.0038, 0.0139 ] ,
     0.0288, 0.0986, 0.1623, 0.0557, 0.0050, 0.1655, 0.0347, 0.0218, -0.9923, 0.0070, 0.0452,
   0.0580, 0.0083, 0.0274, 0.0334, 0.0540, 0.0303, 0.0040, 0.1434, 0.0088 ] ,
     0.0176, 0.0086, 0.0227, 0.0024, 0.0034, 0.0044, 0.0078, 0.0027, 0.0035, -1.2332, 0.2869,
   0.0211, 0.0871, 0.0427, 0.0048, 0.0233, 0.0934, 0.0032, 0.0156, 0.5820 ] ,
     0.0362, 0.0230, 0.0054, 0.0051, 0.0078, 0.0335, 0.0094, 0.0054, 0.0128, 0.1613, -0.7260,
   0.0168, 0.0994, 0.0853, 0.0200, 0.0252, 0.0209, 0.0100, 0.0148, 0.1340 ] ,
     0.0824, 0.2470, 0.1236, 0.0287, 0.0015, 0.1501, 0.1575, 0.0326, 0.0228, 0.0165, 0.0233,
   -1.1246, 0.0191, 0.0036, 0.0267, 0.0706, 0.0888, 0.0021, 0.0049, 0.0227 ] ,
     0.0812, 0.0315, 0.0081, 0.0062, 0.0079, 0.0596, 0.0192, 0.0152, 0.0104, 0.2166, 0.4392, 0.0608,
   -1.3221, 0.0480, 0.0082, 0.0360, 0.0971, 0.0078, 0.0159, 0.1532 ] ,
     0.0191, 0.0047, 0.0039, 0.0028, 0.0081, 0.0039, 0.0049, 0.0044, 0.0174, 0.0539, 0.1914, 0.0058,
   0.0244, -0.7137, 0.0078, 0.0398, 0.0110, 0.0231, 0.2389, 0.0484 ] ,
     0.1308, 0.0314, 0.0080, 0.0254, 0.0022, 0.0360, 0.0416, 0.0213, 0.0179, 0.0051, 0.0376, 0.0363,
   0.0035, 0.0065, -0.6056, 0.1177, 0.0509, 0.0021, 0.0080, 0.0234 ] ,
     0.3065, 0.0565, 0.1630, 0.0642, 0.0285, 0.0397, 0.0430, 0.1172, 0.0190, 0.0162, 0.0312, 0.0630,
   0.0101, 0.0220, 0.0775, -1.3922, 0.2803, 0.0079, 0.0291, 0.0173 ] ,
     0.1928, 0.0256, 0.0833, 0.0224, 0.0104, 0.0331, 0.0501, 0.0197, 0.0121, 0.0742, 0.0296, 0.0903,
   0.0310, 0.0069, 0.0382, 0.3194, -1.1550, 0.0017, 0.0108, 0.1033 ] ,
     0.0103, 0.0537, 0.0030, 0.0078, 0.0145, 0.0083, 0.0095, 0.0294, 0.0067, 0.0108, 0.0602, 0.0090,
   0.0106, 0.0617, 0.0067, 0.0382, 0.0071, -0.4667, 0.0920, 0.0272 ] ,
     0.0219, 0.0176, 0.0446, 0.0195, 0.0110, 0.0088, 0.0120, 0.0091, 0.0993, 0.0214, 0.0361, 0.0087,
   0.0088, 0.2603, 0.0104, 0.0574, 0.0186, 0.0375, -0.7263, 0.0234 ] ,
     0.1824, 0.0116, 0.0081, 0.0091, 0.0203, 0.0116, 0.0359, 0.0164, 0.0030, 0.3978, 0.1629, 0.0199,
   0.0421, 0.0262, 0.0151, 0.0170, 0.0889, 0.0055, 0.0117, -1.0855 ] ]
>

@mlandis mlandis closed this as completed Jul 31, 2018
@bredelings bredelings mentioned this issue Jul 31, 2018
Open
Sign up for free to subscribe to this conversation on GitHub. Already have an account? Sign in.
Assignees

@hoehna hoehna

Labels
None yet
Projects
None yet
Milestone
No milestone
Development

No branches or pull requests
3 participants
@bredelings @mlandis @hoehna