from sympy import Matrix, Symbol
import sympy
from IPython.display import display, Markdown

B_CAL = Matrix([
    [Symbol("B11", complex=True, commutative = True), Symbol("B12", complex=True, commutative = True), Symbol("B13", complex=True, commutative = True)],
    [Symbol("B21", complex=True, commutative = True), Symbol("B22", complex=True, commutative = True), Symbol("B23", complex=True, commutative = True)],
    [Symbol("B31", complex=True, commutative = True), Symbol("B32", complex=True, commutative = True), Symbol("B33", complex=True, commutative = True)]
])

E_CAL = Matrix([
    [Symbol("E11", complex=True, commutative = True), Symbol("E12", complex=True, commutative = True)],
    [Symbol("E21", complex=True, commutative = True), Symbol("E22", complex=True, commutative = True)]
])

display(Markdown('''
# LFR calibration matrices for each frequency bin:
LFR stores two calibration matrices per ASM frequency bin, one matrix for B and one for E.
'''))

display(Markdown("## Magnetic calibration matrice:"))
display(B_CAL) 
display(Markdown("## Electric calibration matrice:"))
display(E_CAL)

LFR calibration matrices for each frequency bin:

LFR stores two calibration matrices per ASM frequency bin, one matrix for B and one for E.

Magnetic calibration matrice:

$\displaystyle \left[\begin{matrix}B_{11} & B_{12} & B_{13}\\B_{21} & B_{22} & B_{23}\\B_{31} & B_{32} & B_{33}\end{matrix}\right]$

Electric calibration matrice:

$\displaystyle \left[\begin{matrix}E_{11} & E_{12}\\E_{21} & E_{22}\end{matrix}\right]$

In memory representation of matrices:

From index 0 to N-1:

Magnetic: [ Real(B₁₁), Imag(B₁₁), Real(B₁₂), Imag(B₁₂), Real(B₁₃), Imag(B₁₃), ... , Real(B₃₁), Imag(B₃₁), Real(B₃₂), Imag(B₃₂), Real(B₃₃), Imag(B₃₃)]

Electric: [ Real(E₁₁), Imag(E₁₁), Real(E₁₂), Imag(E₁₂), Real(E₂₁), Imag(E₂₁), Real(E₂₂), Imag(E₂₂)]

This representation is used in all the following packets descriptions.

TC LOAD KCOEF format:

To set all calibration matrices we need to send 36 TC with 0 <= sy_lfr_kcoeff_frequency <= 35, and they must be sent in order from sy_lfr_kcoeff_frequency=0 to sy_lfr_kcoeff_frequency=35

Since 36 packets are not enough to fill all calibration matrices for F0,F1 and F2 we set one matrice each 8 frequency bins then we interpolate them.

In the following description B_F0_Bin_16 means B calibration matrice at F0 for the frequency bin 16.

offset = 0
for s,f,c in ((16,0,11), (5,1,13), (6,2,12)):  
    display(Markdown(f"## F{f}"))
    for i in range(c):
        fbin= s+i*8
        if i<3:
            extra = f', B_F{f}_Bin_{s+c*8}_Line{i+1}'
        elif i<5:
            extra = f', E_F{f}_Bin_{s+c*8}_Line{i-2}'
        else:
            extra = ''
        display(Markdown(f'''
- sy_lfr_kcoeff_frequency = {offset+i}:
    F{f} calibration matrix bin {fbin} 

    `LFR_KCOEFFICIENTS_PARAMETERS` = `[ B_F{f}_Bin_{fbin}, E_F{f}_Bin_{fbin}{extra} ]`
'''))
    offset += c

F0

• sy_lfr_kcoeff_frequency = 0: F0 calibration matrix bin 16

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F0_Bin_16, E_F0_Bin_16, B_F0_Bin_104_Line1 ]

• sy_lfr_kcoeff_frequency = 1: F0 calibration matrix bin 24

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F0_Bin_24, E_F0_Bin_24, B_F0_Bin_104_Line2 ]

• sy_lfr_kcoeff_frequency = 2: F0 calibration matrix bin 32

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F0_Bin_32, E_F0_Bin_32, B_F0_Bin_104_Line3 ]

• sy_lfr_kcoeff_frequency = 3: F0 calibration matrix bin 40

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F0_Bin_40, E_F0_Bin_40, E_F0_Bin_104_Line1 ]

• sy_lfr_kcoeff_frequency = 4: F0 calibration matrix bin 48

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F0_Bin_48, E_F0_Bin_48, E_F0_Bin_104_Line2 ]

• sy_lfr_kcoeff_frequency = 5: F0 calibration matrix bin 56

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F0_Bin_56, E_F0_Bin_56 ]

• sy_lfr_kcoeff_frequency = 6: F0 calibration matrix bin 64

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F0_Bin_64, E_F0_Bin_64 ]

• sy_lfr_kcoeff_frequency = 7: F0 calibration matrix bin 72

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F0_Bin_72, E_F0_Bin_72 ]

• sy_lfr_kcoeff_frequency = 8: F0 calibration matrix bin 80

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F0_Bin_80, E_F0_Bin_80 ]

• sy_lfr_kcoeff_frequency = 9: F0 calibration matrix bin 88

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F0_Bin_88, E_F0_Bin_88 ]

• sy_lfr_kcoeff_frequency = 10: F0 calibration matrix bin 96

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F0_Bin_96, E_F0_Bin_96 ]

F1

• sy_lfr_kcoeff_frequency = 11: F1 calibration matrix bin 5

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F1_Bin_5, E_F1_Bin_5, B_F1_Bin_109_Line1 ]

• sy_lfr_kcoeff_frequency = 12: F1 calibration matrix bin 13

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F1_Bin_13, E_F1_Bin_13, B_F1_Bin_109_Line2 ]

• sy_lfr_kcoeff_frequency = 13: F1 calibration matrix bin 21

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F1_Bin_21, E_F1_Bin_21, B_F1_Bin_109_Line3 ]

• sy_lfr_kcoeff_frequency = 14: F1 calibration matrix bin 29

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F1_Bin_29, E_F1_Bin_29, E_F1_Bin_109_Line1 ]

• sy_lfr_kcoeff_frequency = 15: F1 calibration matrix bin 37

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F1_Bin_37, E_F1_Bin_37, E_F1_Bin_109_Line2 ]

• sy_lfr_kcoeff_frequency = 16: F1 calibration matrix bin 45

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F1_Bin_45, E_F1_Bin_45 ]

• sy_lfr_kcoeff_frequency = 17: F1 calibration matrix bin 53

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F1_Bin_53, E_F1_Bin_53 ]

• sy_lfr_kcoeff_frequency = 18: F1 calibration matrix bin 61

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F1_Bin_61, E_F1_Bin_61 ]

• sy_lfr_kcoeff_frequency = 19: F1 calibration matrix bin 69

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F1_Bin_69, E_F1_Bin_69 ]

• sy_lfr_kcoeff_frequency = 20: F1 calibration matrix bin 77

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F1_Bin_77, E_F1_Bin_77 ]

• sy_lfr_kcoeff_frequency = 21: F1 calibration matrix bin 85

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F1_Bin_85, E_F1_Bin_85 ]

• sy_lfr_kcoeff_frequency = 22: F1 calibration matrix bin 93

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F1_Bin_93, E_F1_Bin_93 ]

• sy_lfr_kcoeff_frequency = 23: F1 calibration matrix bin 101

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F1_Bin_101, E_F1_Bin_101 ]

F2

• sy_lfr_kcoeff_frequency = 24: F2 calibration matrix bin 6

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F2_Bin_6, E_F2_Bin_6, B_F2_Bin_102_Line1 ]

• sy_lfr_kcoeff_frequency = 25: F2 calibration matrix bin 14

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F2_Bin_14, E_F2_Bin_14, B_F2_Bin_102_Line2 ]

• sy_lfr_kcoeff_frequency = 26: F2 calibration matrix bin 22

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F2_Bin_22, E_F2_Bin_22, B_F2_Bin_102_Line3 ]

• sy_lfr_kcoeff_frequency = 27: F2 calibration matrix bin 30

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F2_Bin_30, E_F2_Bin_30, E_F2_Bin_102_Line1 ]

• sy_lfr_kcoeff_frequency = 28: F2 calibration matrix bin 38

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F2_Bin_38, E_F2_Bin_38, E_F2_Bin_102_Line2 ]

• sy_lfr_kcoeff_frequency = 29: F2 calibration matrix bin 46

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F2_Bin_46, E_F2_Bin_46 ]

• sy_lfr_kcoeff_frequency = 30: F2 calibration matrix bin 54

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F2_Bin_54, E_F2_Bin_54 ]

• sy_lfr_kcoeff_frequency = 31: F2 calibration matrix bin 62

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F2_Bin_62, E_F2_Bin_62 ]

• sy_lfr_kcoeff_frequency = 32: F2 calibration matrix bin 70

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F2_Bin_70, E_F2_Bin_70 ]

• sy_lfr_kcoeff_frequency = 33: F2 calibration matrix bin 78

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F2_Bin_78, E_F2_Bin_78 ]

• sy_lfr_kcoeff_frequency = 34: F2 calibration matrix bin 86

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F2_Bin_86, E_F2_Bin_86 ]

• sy_lfr_kcoeff_frequency = 35: F2 calibration matrix bin 94

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F2_Bin_94, E_F2_Bin_94 ]

TM DUMP KCOEF format:

The TM_LFR_KCOEFFICIENTS_DUMP si splitted into two packets where:

F0=', '.join([f'B_F0_Bin_{i},E_F0_Bin_{i}' for i in range(16,112,8)])
F1=', '.join([f'B_F1_Bin_{i},E_F1_Bin_{i}' for i in range(5,117,8)])
F2=', '.join([f'B_F2_Bin_{i},E_F2_Bin_{i}' for i in range(6,110,8)])

display(Markdown(f'''
- Packet 1 contains:

    `LFR_KCOEFFICIENTS_PARAMETERS` = `[ {F0}, {F1} ]`
    
- Packet 2 contains:

    `LFR_KCOEFFICIENTS_PARAMETERS` = `[ {F2} ]`
'''))

• Packet 1 contains:

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F0_Bin_16,E_F0_Bin_16, B_F0_Bin_24,E_F0_Bin_24, B_F0_Bin_32,E_F0_Bin_32, B_F0_Bin_40,E_F0_Bin_40, B_F0_Bin_48,E_F0_Bin_48, B_F0_Bin_56,E_F0_Bin_56, B_F0_Bin_64,E_F0_Bin_64, B_F0_Bin_72,E_F0_Bin_72, B_F0_Bin_80,E_F0_Bin_80, B_F0_Bin_88,E_F0_Bin_88, B_F0_Bin_96,E_F0_Bin_96, B_F0_Bin_104,E_F0_Bin_104, B_F1_Bin_5,E_F1_Bin_5, B_F1_Bin_13,E_F1_Bin_13, B_F1_Bin_21,E_F1_Bin_21, B_F1_Bin_29,E_F1_Bin_29, B_F1_Bin_37,E_F1_Bin_37, B_F1_Bin_45,E_F1_Bin_45, B_F1_Bin_53,E_F1_Bin_53, B_F1_Bin_61,E_F1_Bin_61, B_F1_Bin_69,E_F1_Bin_69, B_F1_Bin_77,E_F1_Bin_77, B_F1_Bin_85,E_F1_Bin_85, B_F1_Bin_93,E_F1_Bin_93, B_F1_Bin_101,E_F1_Bin_101, B_F1_Bin_109,E_F1_Bin_109 ]

• Packet 2 contains:

  LFR_KCOEFFICIENTS_PARAMETERS = [ B_F2_Bin_6,E_F2_Bin_6, B_F2_Bin_14,E_F2_Bin_14, B_F2_Bin_22,E_F2_Bin_22, B_F2_Bin_30,E_F2_Bin_30, B_F2_Bin_38,E_F2_Bin_38, B_F2_Bin_46,E_F2_Bin_46, B_F2_Bin_54,E_F2_Bin_54, B_F2_Bin_62,E_F2_Bin_62, B_F2_Bin_70,E_F2_Bin_70, B_F2_Bin_78,E_F2_Bin_78, B_F2_Bin_86,E_F2_Bin_86, B_F2_Bin_94,E_F2_Bin_94, B_F2_Bin_102,E_F2_Bin_102 ]