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Add some commentary to Gauss-Seidel function
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@ -115,7 +115,7 @@ bisect x@( 𝕀 x_inf x_sup )
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where x_mid = midpoint x
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where x_mid = midpoint x
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infixl 6 ⊖
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infixl 6 ⊖
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(⊖) :: ( Ring a, Ord a ) => 𝕀 a -> 𝕀 a -> 𝕀 a
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(⊖) :: ( AbelianGroup a, Ord a ) => 𝕀 a -> 𝕀 a -> 𝕀 a
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(⊖) a@( 𝕀 lo1 hi1 ) b@( 𝕀 lo2 hi2 )
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(⊖) a@( 𝕀 lo1 hi1 ) b@( 𝕀 lo2 hi2 )
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| width a >= width b
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| width a >= width b
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= 𝕀 ( lo1 - lo2 ) ( hi1 - hi2 )
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= 𝕀 ( lo1 - lo2 ) ( hi1 - hi2 )
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@ -202,7 +202,13 @@ gaussSeidelStep
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-> [ ( T ( 𝕀ℝ n ), Bool ) ]
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-> [ ( T ( 𝕀ℝ n ), Bool ) ]
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gaussSeidelStep as b ( T x0 ) = coerce $
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gaussSeidelStep as b ( T x0 ) = coerce $
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forEachCoord @n ( x0, True ) $ \ i ( x, contraction ) -> do
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forEachCoord @n ( x0, True ) $ \ i ( x, contraction ) -> do
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-- For each i, we have an equation: sum_j a_ij * x_j = b_i
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--
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-- Re-arrange this with x_i on the left to get an iteration:
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-- x_i' = ( b_i - sum { j /= i } a_ij * x_j ) / a_ii
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-- x_i' = ( b_i - sum { j /= i } a_ij * x_j ) / a_ii
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--
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-- We perform each iteration in turn (for i = 1, ..., n),
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-- **using the latest updated value of each x_j** in each iteration.
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let s = b `index` i - sum [ ( as ! j ) `index` i * x `index` j
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let s = b `index` i - sum [ ( as ! j ) `index` i * x `index` j
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| j <- toList ( universe @n ), j /= i ]
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| j <- toList ( universe @n ), j /= i ]
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x_i = x `index` i
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x_i = x `index` i
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