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author | Alberto Ruiz <aruiz@um.es> | 2015-07-12 14:10:51 +0200 |
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committer | Alberto Ruiz <aruiz@um.es> | 2015-07-12 14:10:51 +0200 |
commit | b4873dbd201e0e887fb9cb5b5fe55774fa6fbe78 (patch) | |
tree | 16ae316ab96855c119d1da58d944645033afc1e3 /packages/base/src/Internal/Algorithms.hs | |
parent | b2341058a2214d22dc23f516b6f09d3270faa18d (diff) |
documentation
Diffstat (limited to 'packages/base/src/Internal/Algorithms.hs')
-rw-r--r-- | packages/base/src/Internal/Algorithms.hs | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/packages/base/src/Internal/Algorithms.hs b/packages/base/src/Internal/Algorithms.hs index c8b2d3e..99c90aa 100644 --- a/packages/base/src/Internal/Algorithms.hs +++ b/packages/base/src/Internal/Algorithms.hs | |||
@@ -470,14 +470,14 @@ rq m = {-# SCC "rq" #-} (r,q) where | |||
470 | 470 | ||
471 | -- | Hessenberg factorization. | 471 | -- | Hessenberg factorization. |
472 | -- | 472 | -- |
473 | -- If @(p,h) = hess m@ then @m == p \<> h \<> ctrans p@, where p is unitary | 473 | -- If @(p,h) = hess m@ then @m == p \<> h \<> tr p@, where p is unitary |
474 | -- and h is in upper Hessenberg form (it has zero entries below the first subdiagonal). | 474 | -- and h is in upper Hessenberg form (it has zero entries below the first subdiagonal). |
475 | hess :: Field t => Matrix t -> (Matrix t, Matrix t) | 475 | hess :: Field t => Matrix t -> (Matrix t, Matrix t) |
476 | hess = hess' | 476 | hess = hess' |
477 | 477 | ||
478 | -- | Schur factorization. | 478 | -- | Schur factorization. |
479 | -- | 479 | -- |
480 | -- If @(u,s) = schur m@ then @m == u \<> s \<> ctrans u@, where u is unitary | 480 | -- If @(u,s) = schur m@ then @m == u \<> s \<> tr u@, where u is unitary |
481 | -- and s is a Shur matrix. A complex Schur matrix is upper triangular. A real Schur matrix is | 481 | -- and s is a Shur matrix. A complex Schur matrix is upper triangular. A real Schur matrix is |
482 | -- upper triangular in 2x2 blocks. | 482 | -- upper triangular in 2x2 blocks. |
483 | -- | 483 | -- |
@@ -497,7 +497,7 @@ cholSH = {-# SCC "cholSH" #-} cholSH' | |||
497 | 497 | ||
498 | -- | Cholesky factorization of a positive definite hermitian or symmetric matrix. | 498 | -- | Cholesky factorization of a positive definite hermitian or symmetric matrix. |
499 | -- | 499 | -- |
500 | -- If @c = chol m@ then @c@ is upper triangular and @m == ctrans c \<> c@. | 500 | -- If @c = chol m@ then @c@ is upper triangular and @m == tr c \<> c@. |
501 | chol :: Field t => Matrix t -> Matrix t | 501 | chol :: Field t => Matrix t -> Matrix t |
502 | chol m | exactHermitian m = cholSH m | 502 | chol m | exactHermitian m = cholSH m |
503 | | otherwise = error "chol requires positive definite complex hermitian or real symmetric matrix" | 503 | | otherwise = error "chol requires positive definite complex hermitian or real symmetric matrix" |