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5b8ea19d
Commit
5b8ea19d
authored
Aug 24, 2016
by
Victor Poughon
Browse files
DOC: fix math markup
parent
bca81855
Changes
1
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Inline
Side-by-side
Documentation/Cookbook/rst/recipes/sarprocessing.rst
View file @
5b8ea19d
...
...
@@ -149,94 +149,94 @@ For each option parameter, the list below gives the formula used.
#. msinclairtocoherency (SinclairToReciprocalCoherencyMatrixFunctor)
#. :math:`
0.5 . (S_{hh}+S_{vv}).(S_{hh}+S_{vv})^{*}
`
#. :math:`0.5 . (S_{hh}+S_{vv}).(S_{hh}+S_{vv})^{*}`
#. :math:`
0.5 . (S_{hh}+S_{vv}).(S_{hh}-S_{vv})^{*}
`
#. :math:`0.5 . (S_{hh}+S_{vv}).(S_{hh}-S_{vv})^{*}`
#. :math:`
0.5 . (S_{hh}+S_{vv}).(2 S_{hv})^{*}
`
#. :math:`0.5 . (S_{hh}+S_{vv}).(2 S_{hv})^{*}`
#. :math:`
0.5 . (S_{hh}-S_{vv}).(S_{hh}-S_{vv})^{*}
`
#. :math:`0.5 . (S_{hh}-S_{vv}).(S_{hh}-S_{vv})^{*}`
#. :math:`
0.5 . (S_{hh}-S_{vv}).(2 S_{hv})^{*}
`
#. :math:`0.5 . (S_{hh}-S_{vv}).(2 S_{hv})^{*}`
#. :math:`
0.5 . (2 S_{hv}).(2 S_{hv})^{*}
`
#. :math:`0.5 . (2 S_{hv}).(2 S_{hv})^{*}`
#. msinclairtocovariance (SinclairToReciprocalCovarianceMatrixFunctor)
#. :math:`
S_{hh}.S_{hh}^{*}
`
#. :math:`S_{hh}.S_{hh}^{*}`
#. :math:`
\sqrt{2}.S_{hh}.S_{hv}^{*}
`
#. :math:`\sqrt{2}.S_{hh}.S_{hv}^{*}`
#. :math:`
S_{hh}.S_{vv}^{*}
`
#. :math:`S_{hh}.S_{vv}^{*}`
#. :math:`
2.S_{hv}.S_{hv}^{*}
`
#. :math:`2.S_{hv}.S_{hv}^{*}`
#. :math:`
\sqrt{2}.S_{hv}.S_{vv}^{*}
`
#. :math:`\sqrt{2}.S_{hv}.S_{vv}^{*}`
#. :math:`
S_{vv}.S_{vv}^{*}
`
#. :math:`S_{vv}.S_{vv}^{*}`
#. msinclairtocircovariance
(SinclairToReciprocalCircularCovarianceMatrixFunctor)
#. :math:`
S_{ll}.S_{ll}^{*}
`
#. :math:`S_{ll}.S_{ll}^{*}`
#. :math:`
S_{ll}.S_{lr}^{*}
`
#. :math:`S_{ll}.S_{lr}^{*}`
#. :math:`
S_{ll}.S_{rr}^{*}
`
#. :math:`S_{ll}.S_{rr}^{*}`
#. :math:`
S_{lr}.S_{lr}^{*}
`
#. :math:`S_{lr}.S_{lr}^{*}`
#. :math:`
S_{lr}.S_{rr}^{*}
`
#. :math:`S_{lr}.S_{rr}^{*}`
#. :math:`
S_{rr}.S_{rr}^{*}
`
#. :math:`S_{rr}.S_{rr}^{*}`
With:
- :math:`
S_{ll} = 0.5(S_{hh}+2j S_{hv}-S_{vv})
`
- :math:`S_{ll} = 0.5(S_{hh}+2j S_{hv}-S_{vv})`
- :math:`
S_{lr} = 0.5(j S_{hh}+j S_{vv})
`
- :math:`S_{lr} = 0.5(j S_{hh}+j S_{vv})`
- :math:`
S_{rr} = 0.5(-S_{hh}+2j S_{hv}+S_{vv})
`
- :math:`S_{rr} = 0.5(-S_{hh}+2j S_{hv}+S_{vv})`
#. mcoherencytomueller (ReciprocalCoherencyToReciprocalMuellerFunctor)
#. :math:`
0.5*( C_{11}+C_{22}+C_{33} )
`
#. :math:`0.5*( C_{11}+C_{22}+C_{33} )`
#. :math:`
Re(C_{12}) + Im(C_{22})
`
#. :math:`Re(C_{12}) + Im(C_{22})`
#. :math:`
Re(C_{13})
`
#. :math:`Re(C_{13})`
#. :math:`
Im(C_{23})
`
#. :math:`Im(C_{23})`
#. :math:`
Re(C_{12})
`
#. :math:`Re(C_{12})`
#. :math:`
0.5*( C_{11}+C_{22}-C_{33} )
`
#. :math:`0.5*( C_{11}+C_{22}-C_{33} )`
#. :math:`
Re(C_{23})
`
#. :math:`Re(C_{23})`
#. :math:`
Im(C_{13})
`
#. :math:`Im(C_{13})`
#. :math:`
-Re(C_{13})
`
#. :math:`-Re(C_{13})`
#. :math:`
-Re(C_{23})
`
#. :math:`-Re(C_{23})`
#. :math:`
0.5.Re(VAL1)
`
#. :math:`0.5.Re(VAL1)`
#. :math:`
0.5.Im(VAL0)
`
#. :math:`0.5.Im(VAL0)`
#. :math:`
Im(C_{23})
`
#. :math:`Im(C_{23})`
#. :math:`
Im(C_{13})
`
#. :math:`Im(C_{13})`
#. :math:`
0.5.Im(VAL1^{*})
`
#. :math:`0.5.Im(VAL1^{*})`
#. :math:`
0.5.Re(VAL0)
`
#. :math:`0.5.Re(VAL0)`
With:
- :math:`
VAL0 = C_{33}+C_{12}-C_{11}-(C_{12}-C_{22})^{*}
`
- :math:`VAL0 = C_{33}+C_{12}-C_{11}-(C_{12}-C_{22})^{*}`
- :math:`
VAL1 = -C_{33}+C_{12}-C_{11}-(C_{12}-C_{22})^{*}
`
- :math:`VAL1 = -C_{33}+C_{12}-C_{11}-(C_{12}-C_{22})^{*}`
Where :math:`C_{ij}` are related to the elements of the reciprocal
coherence matrix.
...
...
@@ -244,26 +244,26 @@ For each option parameter, the list below gives the formula used.
#. mcovariancetocoherencydegree
(ReciprocalCovarianceToCoherencyDegreeFunctor)
#. :math:`
abs(S_{hh}.S_{vv}^{*}) / sqrt(S_{hh}.S_{hh}^{*}) / sqrt(S_{vv}.S_{vv}^{*})
`
#. :math:`abs(S_{hh}.S_{vv}^{*}) / sqrt(S_{hh}.S_{hh}^{*}) / sqrt(S_{vv}.S_{vv}^{*})`
#. :math:`
abs(S_{hv}.S_{vv}^{*}) / sqrt(S_{hv}.S_{hv}^{*}) / sqrt(S_{vv}.S_{vv}^{*})
`
#. :math:`abs(S_{hv}.S_{vv}^{*}) / sqrt(S_{hv}.S_{hv}^{*}) / sqrt(S_{vv}.S_{vv}^{*})`
#. :math:`
abs(S_{hh}.S_{hv}^{*}) / sqrt(S_{hh}.S_{hh}^{*}) / sqrt(S_{hv}.S_{hv}^{*})
`
#. :math:`abs(S_{hh}.S_{hv}^{*}) / sqrt(S_{hh}.S_{hh}^{*}) / sqrt(S_{hv}.S_{hv}^{*})`
#. mcovariancetocoherency
(ReciprocalCovarianceToReciprocalCoherencyFunctor)
#. :math:`
0.5 . ( C_{33} + C_{13} + C_{13}^{*} + C_{11} )
`
#. :math:`0.5 . ( C_{33} + C_{13} + C_{13}^{*} + C_{11} )`
#. :math:`
0.5 . ( -C_{33} - C_{13} + C_{13}^{*} + C_{11} )
`
#. :math:`0.5 . ( -C_{33} - C_{13} + C_{13}^{*} + C_{11} )`
#. :math:`
0.5 . ( \sqrt{2}.C_{12} + \sqrt{2}.C_{23}^{*} )
`
#. :math:`0.5 . ( \sqrt{2}.C_{12} + \sqrt{2}.C_{23}^{*} )`
#. :math:`
0.5 . ( C_{33} - C_{13} - C_{13}^{*} + C_{11} )
`
#. :math:`0.5 . ( C_{33} - C_{13} - C_{13}^{*} + C_{11} )`
#. :math:`
0.5 . ( \sqrt{2}.C_{12} - \sqrt{2}.C_{23}^{*} )
`
#. :math:`0.5 . ( \sqrt{2}.C_{12} - \sqrt{2}.C_{23}^{*} )`
#. :math:`
0.5 . ( 2 . C_{22} )
`
#. :math:`0.5 . ( 2 . C_{22} )`
Where :math:`C_{ij}` are related to the elements of the reciprocal
linear covariance matrix.
...
...
@@ -271,168 +271,168 @@ For each option parameter, the list below gives the formula used.
#. mlinearcovariancetocircularcovariance
(ReciprocalLinearCovarianceToReciprocalCircularCovarianceFunctor)
#. :math:`
0.25 . ( C_{33}-i.\sqrt{2}.C_{23}-C_{13}+i.\sqrt{2}.C_{23}^{*}-C_{13}^{*}+2.C_{22}-i.\sqrt{2}.C_{12}+i.\sqrt{2}.C_{12}^{*}+C_{11} )
`
#. :math:`0.25 . ( C_{33}-i.\sqrt{2}.C_{23}-C_{13}+i.\sqrt{2}.C_{23}^{*}-C_{13}^{*}+2.C_{22}-i.\sqrt{2}.C_{12}+i.\sqrt{2}.C_{12}^{*}+C_{11} )`
#. :math:`
0.25 . ( i.\sqrt{2}.C_{33}+2.C_{23}-i.\sqrt{2}.C_{13}+i.\sqrt{2}.C_{13}^{*}+2.C_{12}^{*}-i.\sqrt{2}.C_{11} )
`
#. :math:`0.25 . ( i.\sqrt{2}.C_{33}+2.C_{23}-i.\sqrt{2}.C_{13}+i.\sqrt{2}.C_{13}^{*}+2.C_{12}^{*}-i.\sqrt{2}.C_{11} )`
#. :math:`
0.25 . ( -C_{33}+i.\sqrt{2}.C_{23}+C_{13}+i.\sqrt{2}.C_{23}^{*}+C_{13}^{*}+2.C_{22}-i.\sqrt{2}.C_{12}-i.\sqrt{2}.C_{12}^{*}-C_{11} )
`
#. :math:`0.25 . ( -C_{33}+i.\sqrt{2}.C_{23}+C_{13}+i.\sqrt{2}.C_{23}^{*}+C_{13}^{*}+2.C_{22}-i.\sqrt{2}.C_{12}-i.\sqrt{2}.C_{12}^{*}-C_{11} )`
#. :math:`
0.25 . ( 2.C_{33}+2.C_{13}+2.C_{13}^{*}+2.C_{11} )
`
#. :math:`0.25 . ( 2.C_{33}+2.C_{13}+2.C_{13}^{*}+2.C_{11} )`
#. :math:`
0.25 . ( i.\sqrt{2}.C_{33}+i.\sqrt{2}.C_{13}+2.C_{23}^{*}-i.\sqrt{2}.C_{13}^{*}+2.C_{12}-i.\sqrt{2}.C_{11} )
`
#. :math:`0.25 . ( i.\sqrt{2}.C_{33}+i.\sqrt{2}.C_{13}+2.C_{23}^{*}-i.\sqrt{2}.C_{13}^{*}+2.C_{12}-i.\sqrt{2}.C_{11} )`
#. :math:`
0.25 . ( C_{33}+i.\sqrt{2}.C_{23}-C_{13}-i.\sqrt{2}.C_{23}^{*}-C_{13}^{*}+2.C_{22}+i.\sqrt{2}.C_{12}-i.\sqrt{2}.C_{12}^{*}+C_{11} )
`
#. :math:`0.25 . ( C_{33}+i.\sqrt{2}.C_{23}-C_{13}-i.\sqrt{2}.C_{23}^{*}-C_{13}^{*}+2.C_{22}+i.\sqrt{2}.C_{12}-i.\sqrt{2}.C_{12}^{*}+C_{11} )`
Where :math:`C_{ij}` are related to the elements of the reciprocal
linear covariance matrix.
#. muellertomcovariance (MuellerToReciprocalCovarianceFunctor)
#. :math:`
0.5.(M_{11}+M_{22}+2.M_{12})
`
#. :math:`0.5.(M_{11}+M_{22}+2.M_{12})`
#. :math:`
0.5.\sqrt{2}.[(M_{13}+M_{23}) + j.(M_{14}+M_{24})]
`
#. :math:`0.5.\sqrt{2}.[(M_{13}+M_{23}) + j.(M_{14}+M_{24})]`
#. :math:`
-0.5.(M_{33}+M_{44}) - j.M_{34}
`
#. :math:`-0.5.(M_{33}+M_{44}) - j.M_{34}`
#. :math:`
M_{11}-M_{22}
`
#. :math:`M_{11}-M_{22}`
#. :math:`
0.5.\sqrt{2}.[(M_{13}-M_{23}) + j.(M_{14}-M_{24})]
`
#. :math:`0.5.\sqrt{2}.[(M_{13}-M_{23}) + j.(M_{14}-M_{24})]`
#. :math:`
0.5.(M_{11}+M_{22}-2.M_{12})
`
#. :math:`0.5.(M_{11}+M_{22}-2.M_{12})`
— Bistatic case —
#. bsinclairtocoherency (SinclairToCoherencyMatrixFunctor)
#. :math:`
(S_{hh}+S_{vv}).(S_{hh}+S_{vv})^{*}
`
#. :math:`(S_{hh}+S_{vv}).(S_{hh}+S_{vv})^{*}`
#. :math:`
(S_{hh}+S_{vv}).(S_{hh}-S_{vv})^{*}
`
#. :math:`(S_{hh}+S_{vv}).(S_{hh}-S_{vv})^{*}`
#. :math:`
(S_{hh}+S_{vv}).(S_{hv}+S_{vh})^{*}
`
#. :math:`(S_{hh}+S_{vv}).(S_{hv}+S_{vh})^{*}`
#. :math:`
(S_{hh}+S_{vv}).( j (S_{hv}-S_{vh}))^{*}
`
#. :math:`(S_{hh}+S_{vv}).( j (S_{hv}-S_{vh}))^{*}`
#. :math:`
(S_{hh}-S_{vv}).(S_{hh}-S_{vv})^{*}
`
#. :math:`(S_{hh}-S_{vv}).(S_{hh}-S_{vv})^{*}`
#. :math:`
(S_{hh}-S_{vv}).(S_{hv}+S_{vh})^{*}
`
#. :math:`(S_{hh}-S_{vv}).(S_{hv}+S_{vh})^{*}`
#. :math:`
(S_{hh}-S_{vv}).( j (S_{hv}-S_{vh}))^{*}
`
#. :math:`(S_{hh}-S_{vv}).( j (S_{hv}-S_{vh}))^{*}`
#. :math:`
(S_{hv}+S_{vh}).(S_{hv}+S_{vh})^{*}
`
#. :math:`(S_{hv}+S_{vh}).(S_{hv}+S_{vh})^{*}`
#. :math:`
(S_{hv}+S_{vh}).( j (S_{hv}-S_{vh}))^{*}
`
#. :math:`(S_{hv}+S_{vh}).( j (S_{hv}-S_{vh}))^{*}`
#. :math:`
j (S_{hv}-S_{vh}).( j (S_{hv}-S_{vh}))^{*}
`
#. :math:`j (S_{hv}-S_{vh}).( j (S_{hv}-S_{vh}))^{*}`
#. bsinclairtocovariance (SinclairToCovarianceMatrixFunctor)
#. :math:`
S_{hh}.S_{hh}^{*}
`
#. :math:`S_{hh}.S_{hh}^{*}`
#. :math:`
S_{hh}.S_{hv}^{*}
`
#. :math:`S_{hh}.S_{hv}^{*}`
#. :math:`
S_{hh}.S_{vh}^{*}
`
#. :math:`S_{hh}.S_{vh}^{*}`
#. :math:`
S_{hh}.S_{vv}^{*}
`
#. :math:`S_{hh}.S_{vv}^{*}`
#. :math:`
S_{hv}.S_{hv}^{*}
`
#. :math:`S_{hv}.S_{hv}^{*}`
#. :math:`
S_{hv}.S_{vh}^{*}
`
#. :math:`S_{hv}.S_{vh}^{*}`
#. :math:`
S_{hv}.S_{vv}^{*}
`
#. :math:`S_{hv}.S_{vv}^{*}`
#. :math:`
S_{vh}.S_{vh}^{*}
`
#. :math:`S_{vh}.S_{vh}^{*}`
#. :math:`
S_{vh}.S_{vv}^{*}
`
#. :math:`S_{vh}.S_{vv}^{*}`
#. :math:`
S_{vv}.S_{vv}^{*}
`
#. :math:`S_{vv}.S_{vv}^{*}`
#. bsinclairtocircovariance (SinclairToCircularCovarianceMatrixFunctor)
#. :math:`
S_{ll}.S_{ll}^{*}
`
#. :math:`S_{ll}.S_{ll}^{*}`
#. :math:`
S_{ll}.S_{lr}^{*}
`
#. :math:`S_{ll}.S_{lr}^{*}`
#. :math:`
S_{ll}.S_{rl}^{*}
`
#. :math:`S_{ll}.S_{rl}^{*}`
#. :math:`
S_{ll}.S_{rr}^{*}
`
#. :math:`S_{ll}.S_{rr}^{*}`
#. :math:`
S_{lr}.S_{lr}^{*}
`
#. :math:`S_{lr}.S_{lr}^{*}`
#. :math:`
S_{lr}.S_{rl}^{*}
`
#. :math:`S_{lr}.S_{rl}^{*}`
#. :math:`
S_{lr}.S_{rr}^{*}
`
#. :math:`S_{lr}.S_{rr}^{*}`
#. :math:`
S_{rl}.S_{rl}^{*}
`
#. :math:`S_{rl}.S_{rl}^{*}`
#. :math:`
S_{rl}.S_{rr}^{*}
`
#. :math:`S_{rl}.S_{rr}^{*}`
#. :math:`
S_{rr}.S_{rr}^{*}
`
#. :math:`S_{rr}.S_{rr}^{*}`
With:
- :math:`
S_{ll} = 0.5(S_{hh}+j S_{hv}+j S_{vh}-S_{vv})
`
- :math:`S_{ll} = 0.5(S_{hh}+j S_{hv}+j S_{vh}-S_{vv})`
- :math:`
S_{lr} = 0.5(j S_{hh}+S_{hv}-S_{vh}+j S_{vv})
`
- :math:`S_{lr} = 0.5(j S_{hh}+S_{hv}-S_{vh}+j S_{vv})`
- :math:`
S_{rl} = 0.5(j S_{hh}-S_{hv}+ S_{vh}+j S_{vv})
`
- :math:`S_{rl} = 0.5(j S_{hh}-S_{hv}+ S_{vh}+j S_{vv})`
- :math:`
S_{rr} = 0.5(-S_{hh}+j S_{hv}+j S_{vh}+S_{vv})
`
- :math:`S_{rr} = 0.5(-S_{hh}+j S_{hv}+j S_{vh}+S_{vv})`
— Both cases —
#. sinclairtomueller (SinclairToMueller)
#. :math:`
0.5 Re( T_{xx}.T_{xx}^{*} + T_{xy}.T_{xy}^{*} + T_{yx}.T_{yx}^{*} + T_{yy}.T_{yy}^{*} )
`
#. :math:`0.5 Re( T_{xx}.T_{xx}^{*} + T_{xy}.T_{xy}^{*} + T_{yx}.T_{yx}^{*} + T_{yy}.T_{yy}^{*} )`
#. :math:`
0.5 Re( T_{xx}.T_{xx}^{*} - T_{xy}.T_{xy}^{*} + T_{yx}.T_{yx}^{*} - T_{yy}.T_{yy}^{*} )
`
#. :math:`0.5 Re( T_{xx}.T_{xx}^{*} - T_{xy}.T_{xy}^{*} + T_{yx}.T_{yx}^{*} - T_{yy}.T_{yy}^{*} )`
#. :math:`
Re( T_{xx}.T_{xy}^{*} + T_{yx}.T_{yy}^{*} )
`
#. :math:`Re( T_{xx}.T_{xy}^{*} + T_{yx}.T_{yy}^{*} )`
#. :math:`
Im( T_{xx}.T_{xy}^{*} + T_{yx}.T_{yy}^{*} )
`
#. :math:`Im( T_{xx}.T_{xy}^{*} + T_{yx}.T_{yy}^{*} )`
#. :math:`
0.5 Re( T_{xx}.T_{xx}^{*} + T_{xy}.T_{xy}^{*} - T_{yx}.T_{yx}^{*} - T_{yy}.T_{yy}^{*} )
`
#. :math:`0.5 Re( T_{xx}.T_{xx}^{*} + T_{xy}.T_{xy}^{*} - T_{yx}.T_{yx}^{*} - T_{yy}.T_{yy}^{*} )`
#. :math:`
0.5 Re( T_{xx}.T_{xx}^{*} - T_{xy}.T_{xy}^{*} - T_{yx}.T_{yx}^{*} + T_{yy}.T_{yy}^{*} )
`
#. :math:`0.5 Re( T_{xx}.T_{xx}^{*} - T_{xy}.T_{xy}^{*} - T_{yx}.T_{yx}^{*} + T_{yy}.T_{yy}^{*} )`
#. :math:`
Re( T_{xx}.T_{xy}^{*} - T_{yx}.T_{yy}^{*} )
`
#. :math:`Re( T_{xx}.T_{xy}^{*} - T_{yx}.T_{yy}^{*} )`
#. :math:`
Im( T_{xx}.T_{xy}^{*} - T_{yx}.T_{yy}^{*} )
`
#. :math:`Im( T_{xx}.T_{xy}^{*} - T_{yx}.T_{yy}^{*} )`
#. :math:`
Re( T_{xx}.T_{yx}^{*} + T_{xy}.T_{yy}^{*} )
`
#. :math:`Re( T_{xx}.T_{yx}^{*} + T_{xy}.T_{yy}^{*} )`
#. :math:`
Im( T_{xx}.T_{yx}^{*} - T_{xy}.T_{yy}^{*} )
`
#. :math:`Im( T_{xx}.T_{yx}^{*} - T_{xy}.T_{yy}^{*} )`
#. :math:`
Re( T_{xx}.T_{yy}^{*} + T_{xy}.T_{yx}^{*} )
`
#. :math:`Re( T_{xx}.T_{yy}^{*} + T_{xy}.T_{yx}^{*} )`
#. :math:`
Im( T_{xx}.T_{yy}^{*} - T_{xy}.T_{yx}^{*} )
`
#. :math:`Im( T_{xx}.T_{yy}^{*} - T_{xy}.T_{yx}^{*} )`
#. :math:`
Re( T_{xx}.T_{yx}^{*} + T_{xy}.T_{yy}^{*} )
`
#. :math:`Re( T_{xx}.T_{yx}^{*} + T_{xy}.T_{yy}^{*} )`
#. :math:`
Im( T_{xx}.T_{yx}^{*} - T_{xy}.T_{yy}^{*} )
`
#. :math:`Im( T_{xx}.T_{yx}^{*} - T_{xy}.T_{yy}^{*} )`
#. :math:`
Re( T_{xx}.T_{yy}^{*} + T_{xy}.T_{yx}^{*} )
`
#. :math:`Re( T_{xx}.T_{yy}^{*} + T_{xy}.T_{yx}^{*} )`
#. :math:`
Im( T_{xx}.T_{yy}^{*} - T_{xy}.T_{yx}^{*} )
`
#. :math:`Im( T_{xx}.T_{yy}^{*} - T_{xy}.T_{yx}^{*} )`
With :
- :math:`
T_{xx} = -S_{hh}
`
- :math:`T_{xx} = -S_{hh}`
- :math:`
T_{xy} = -S_{hv}
`
- :math:`T_{xy} = -S_{hv}`
- :math:`
T_{yx} = S_{vh}
`
- :math:`T_{yx} = S_{vh}`
- :math:`
T_{yy} = S_{vv}
`
- :math:`T_{yy} = S_{vv}`
#. muellertopoldegandpower (MuellerToPolarisationDegreeAndPowerFunctor)
#. :math:`
P_{min}
`
#. :math:`P_{min}`
#. :math:`
P_{max}
`
#. :math:`P_{max}`
#. :math:`
DegP_{min}
`
#. :math:`DegP_{min}`
#. :math:`
DegP_{max}
`
#. :math:`DegP_{max}`
Examples :
...
...
@@ -549,17 +549,17 @@ Alpha, A(Anisotropy).
Here are the formula used (refer to the previous section about how the
coherence matrix is obtained from the Sinclair one):
#. :math:`
entropy = -\sum_{i=0}^{2} \frac{p[i].\log{p[i]}}{\log{3}}
`
#. :math:`entropy = -\sum_{i=0}^{2} \frac{p[i].\log{p[i]}}{\log{3}}`
#. :math:`
\alpha = \sum_{i=0}^{2} p[i].\alpha_{i}
`
#. :math:`\alpha = \sum_{i=0}^{2} p[i].\alpha_{i}`
#. :math:`
anisotropy = \frac {SortedEigenValues[1] - SortedEigenValues[2]}{SortedEigenValues[1] + SortedEigenValues[2]}
`
#. :math:`anisotropy = \frac {SortedEigenValues[1] - SortedEigenValues[2]}{SortedEigenValues[1] + SortedEigenValues[2]}`
Where:
- :math:`
p[i] = max(SortedEigenValues[i], 0) / \sum_{i=0}^{2, SortedEigenValues[i]>0} SortedEigenValues[i]
`
- :math:`p[i] = max(SortedEigenValues[i], 0) / \sum_{i=0}^{2, SortedEigenValues[i]>0} SortedEigenValues[i]`
- :math:`
\alpha_{i} = \left| SortedEigenVector[i] \right|* \frac{180}{\pi}`
- :math:`\alpha_{i} = \left| SortedEigenVector[i] \right|* \frac{180}{\pi}`
Example :
...
...
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