diff options
Diffstat (limited to 'packages/base/src/Numeric')
-rw-r--r-- | packages/base/src/Numeric/LinearAlgebra/Algorithms.hs | 26 |
1 files changed, 22 insertions, 4 deletions
diff --git a/packages/base/src/Numeric/LinearAlgebra/Algorithms.hs b/packages/base/src/Numeric/LinearAlgebra/Algorithms.hs index 7e36978..fd9177c 100644 --- a/packages/base/src/Numeric/LinearAlgebra/Algorithms.hs +++ b/packages/base/src/Numeric/LinearAlgebra/Algorithms.hs | |||
@@ -64,6 +64,7 @@ module Numeric.LinearAlgebra.Algorithms ( | |||
64 | nullspacePrec, | 64 | nullspacePrec, |
65 | nullVector, | 65 | nullVector, |
66 | nullspaceSVD, | 66 | nullspaceSVD, |
67 | orthSVD, | ||
67 | orth, | 68 | orth, |
68 | -- * Norms | 69 | -- * Norms |
69 | Normed(..), NormType(..), | 70 | Normed(..), NormType(..), |
@@ -463,7 +464,7 @@ nullspaceSVD :: Field t | |||
463 | -- or Right \"theoretical\" matrix rank. | 464 | -- or Right \"theoretical\" matrix rank. |
464 | -> Matrix t -- ^ input matrix m | 465 | -> Matrix t -- ^ input matrix m |
465 | -> (Vector Double, Matrix t) -- ^ 'rightSV' of m | 466 | -> (Vector Double, Matrix t) -- ^ 'rightSV' of m |
466 | -> [Vector t] -- ^ list of unitary vectors spanning the nullspace | 467 | -> Matrix t -- ^ nullspace |
467 | nullspaceSVD hint a (s,v) = vs where | 468 | nullspaceSVD hint a (s,v) = vs where |
468 | tol = case hint of | 469 | tol = case hint of |
469 | Left t -> t | 470 | Left t -> t |
@@ -471,7 +472,7 @@ nullspaceSVD hint a (s,v) = vs where | |||
471 | k = case hint of | 472 | k = case hint of |
472 | Right t -> t | 473 | Right t -> t |
473 | _ -> rankSVD tol a s | 474 | _ -> rankSVD tol a s |
474 | vs = drop k $ toRows $ ctrans v | 475 | vs = dropColumns k v |
475 | 476 | ||
476 | 477 | ||
477 | -- | The nullspace of a matrix. See also 'nullspaceSVD'. | 478 | -- | The nullspace of a matrix. See also 'nullspaceSVD'. |
@@ -479,12 +480,29 @@ nullspacePrec :: Field t | |||
479 | => Double -- ^ relative tolerance in 'eps' units (e.g., use 3 to get 3*'eps') | 480 | => Double -- ^ relative tolerance in 'eps' units (e.g., use 3 to get 3*'eps') |
480 | -> Matrix t -- ^ input matrix | 481 | -> Matrix t -- ^ input matrix |
481 | -> [Vector t] -- ^ list of unitary vectors spanning the nullspace | 482 | -> [Vector t] -- ^ list of unitary vectors spanning the nullspace |
482 | nullspacePrec t m = nullspaceSVD (Left (t*eps)) m (rightSV m) | 483 | nullspacePrec t m = toColumns $ nullspaceSVD (Left (t*eps)) m (rightSV m) |
483 | 484 | ||
484 | -- | The nullspace of a matrix, assumed to be one-dimensional, with machine precision. | 485 | -- | The nullspace of a matrix, assumed to be one-dimensional, with machine precision. |
485 | nullVector :: Field t => Matrix t -> Vector t | 486 | nullVector :: Field t => Matrix t -> Vector t |
486 | nullVector = last . nullspacePrec 1 | 487 | nullVector = last . nullspacePrec 1 |
487 | 488 | ||
489 | -- | The range space a matrix from its precomputed SVD decomposition. | ||
490 | orthSVD :: Field t | ||
491 | => Either Double Int -- ^ Left \"numeric\" zero (eg. 1*'eps'), | ||
492 | -- or Right \"theoretical\" matrix rank. | ||
493 | -> Matrix t -- ^ input matrix m | ||
494 | -> (Matrix t, Vector Double) -- ^ 'leftSV' of m | ||
495 | -> Matrix t -- ^ orth | ||
496 | orthSVD hint a (v,s) = vs where | ||
497 | tol = case hint of | ||
498 | Left t -> t | ||
499 | _ -> eps | ||
500 | k = case hint of | ||
501 | Right t -> t | ||
502 | _ -> rankSVD tol a s | ||
503 | vs = takeColumns k v | ||
504 | |||
505 | |||
488 | orth :: Field t => Matrix t -> [Vector t] | 506 | orth :: Field t => Matrix t -> [Vector t] |
489 | -- ^ Return an orthonormal basis of the range space of a matrix | 507 | -- ^ Return an orthonormal basis of the range space of a matrix |
490 | orth m = take r $ toColumns u | 508 | orth m = take r $ toColumns u |
@@ -541,7 +559,7 @@ rcond :: Field t => Matrix t -> Double | |||
541 | rcond m = last s / head s | 559 | rcond m = last s / head s |
542 | where s = toList (singularValues m) | 560 | where s = toList (singularValues m) |
543 | 561 | ||
544 | -- | Number of linearly independent rows or columns. | 562 | -- | Number of linearly independent rows or columns. See also 'ranksv' |
545 | rank :: Field t => Matrix t -> Int | 563 | rank :: Field t => Matrix t -> Int |
546 | rank m = rankSVD eps m (singularValues m) | 564 | rank m = rankSVD eps m (singularValues m) |
547 | 565 | ||