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| Data.Packed.Static.Matrix | | Portability | portable | | Stability | experimental | | Maintainer | Reiner Pope <reiner.pope@gmail.com> |
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| Description |
| Statically-dimensioned 2D matrices.
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| Synopsis |
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| data Matrix mn t | | | refineMat :: forall m n t a. Matrix (m, n) t -> (forall m' n'. (PositiveT m', PositiveT n') => Matrix (m', n') t -> a) -> a | | | forgetRowsU :: Matrix (m, n) t -> Matrix (Unknown, n) t | | | forgetColsU :: Matrix (m, n) t -> Matrix (m, Unknown) t | | | atRows :: Matrix (m, n) t -> m -> Matrix (m, n) t | | | atCols :: Matrix (m, n) t -> n -> Matrix (m, n) t | | | withShape :: forall m n t. (PositiveT m, PositiveT n) => (Int -> Int -> Matrix (m, n) t) -> Matrix (m, n) t | | | withRows :: forall m n t. PositiveT m => (Int -> Matrix (m, n) t) -> Matrix (m, n) t | | | withCols :: forall m n t. PositiveT n => (Int -> Matrix (m, n) t) -> Matrix (m, n) t | | | withSquare :: forall n t. PositiveT n => (Int -> Matrix (n, n) t) -> Matrix (n, n) t | | | buildMatrix :: (PositiveT m, PositiveT n, Element a) => ((Int, Int) -> a) -> Matrix (m, n) a | | | (><) :: (PositiveT m, PositiveT n, Element t) => m -> n -> [t] -> Matrix (m, n) t | | | matFromList :: (Element t, PositiveT m, PositiveT n) => [t] -> Matrix (m, n) t | | | fromListsU :: Element t => [[t]] -> Matrix (Unknown, Unknown) t | | | toLists :: Element t => Matrix (m, n) t -> [[t]] | | | fromRowsU :: Element t => [Vector n t] -> Matrix (Unknown, n) t | | | toRows :: Element t => Matrix (m, n) t -> [Vector n t] | | | fromColumnsU :: Element t => [Vector n t] -> Matrix (n, Unknown) t | | | toColumns :: Element t => Matrix (m, n) t -> [Vector m t] | | | fromBlocksU :: Element t => [[Matrix (Unknown, Unknown) t]] -> Matrix (Unknown, Unknown) t | | | asRow :: Element a => Vector n a -> Matrix (D1, n) a | | | asColumn :: Element a => Vector n a -> Matrix (n, D1) a | | | rows :: Matrix (m, n) t -> Int | | | cols :: Matrix (m, n) t -> Int | | | trans :: Matrix (m, n) t -> Matrix (n, m) t | | | reshapeU :: Element t => Int -> Vector n t -> Matrix (Unknown, Unknown) t | | | flatten :: Element t => Matrix (m, n) t -> Vector (m :*: n) t | | | (@@>) :: Storable t => Matrix (m, n) t -> (Int, Int) -> t | | | repmatU :: Element t => Matrix (m, n) t -> Int -> Int -> Matrix (Unknown, Unknown) t | | | flipud :: Element t => Matrix (m, n) t -> Matrix (m, n) t | | | fliprl :: Element t => Matrix (m, n) t -> Matrix (m, n) t | | | subMatrixU :: Element a => (Int, Int) -> (Int, Int) -> Matrix (m, n) a -> Matrix (Unknown, Unknown) a | | | takeRows :: (PositiveT m', Element t, m' :<=: m ~ True) => Matrix (m, n) t -> Matrix (m', n) t | | | dropRows :: (PositiveT m', Element t, m' :<=: m ~ True) => Matrix (m, n) t -> Matrix (m', n) t | | | takeColumns :: (PositiveT n', Element t, n' :<=: n ~ True) => Matrix (m, n) t -> Matrix (m, n') t | | | dropColumns :: (PositiveT n', Element t, n' :<=: n ~ True) => Matrix (m, n) t -> Matrix (m, n') t | | | extractRowsU :: Element t => [Int] -> Matrix (m, n) t -> Matrix (Unknown, n) t | | | ident :: (Element t, PositiveT n) => Matrix (n, n) t | | | diag :: Element a => Vector n a -> Matrix (n, n) a | | | diagRect :: (Element a, PositiveT m, PositiveT n) => Vector (Min m n) a -> Matrix (m, n) a | | | takeDiag :: Element t => Matrix (m, n) t -> Vector (Min m n) t | | | liftMatrix :: (Element a, Element b) => (Vector (m :*: n) a -> Vector (m :*: n) b) -> Matrix (m, n) a -> Matrix (m, n) b | | | format :: Element t => String -> (t -> String) -> Matrix (m, n) t -> String | | | readMatrix :: String -> Matrix (Unknown, Unknown) Double | | | fromFile :: FilePath -> (Int, Int) -> IO (Matrix (Unknown, Unknown) Double) | | | fromArray2D :: Element t => Array (Int, Int) t -> Matrix (Unknown, Unknown) t |
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| Documentation |
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| A matrix with m rows, n columns.
|  Instances | | ShapedContainer Matrix | | JoinableH (Matrix ((,) m n)) (Vector m) | | JoinableH (Matrix ((,) m n)) (Matrix ((,) m p)) | | JoinableH (Vector m) (Matrix ((,) m n)) | | JoinableV (Matrix ((,) m n)) (Vector n) | | JoinableV (Matrix ((,) m n)) (Matrix ((,) p n)) | | JoinableV (Vector n) (Matrix ((,) m n)) | | n ~ n' => Mul (Matrix ((,) m n)) (Vector n') | | n ~ n' => Mul (Matrix ((,) m n)) (Matrix ((,) n' p)) | | m ~ m' => Mul (Vector m) (Matrix ((,) m' n)) | | (Element e, Show e) => Show (Matrix ((,) m n) e) |
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| Shaping
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Fixes a matrix's static row length.
Essentially a mechanism for partial type signatures:
you can specify the row length without specifying the
rest of matrix's type.
>ident `atRows` d5
[$mat| 1.0, 0.0, 0.0, 0.0, 0.0;
0.0, 1.0, 0.0, 0.0, 0.0;
0.0, 0.0, 1.0, 0.0, 0.0;
0.0, 0.0, 0.0, 1.0, 0.0;
0.0, 0.0, 0.0, 0.0, 1.0 |] |
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Fixes a matrix's static column length.
> ident `atCols` d4
[$mat| 1.0, 0.0, 0.0, 0.0;
0.0, 1.0, 0.0, 0.0;
0.0, 0.0, 1.0, 0.0;
0.0, 0.0, 0.0, 1.0 |] |
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| By-index construction
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Constructs a matrix using the function from row/column index. The first of the pair is the row; the second is the column. Indexing is 0-based.
> buildMatrix (fromIntegral . uncurry (^)) `atShape` (d3,d4)
[$mat| 1.0, 0.0, 0.0, 0.0;
1.0, 1.0, 1.0, 1.0;
1.0, 2.0, 4.0, 8.0 |] |
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| To/from lists
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Constructs a matrix from a list. The size
in the matrix's type and the list's length must agree or
else a runtime error will be raised.
> (d2 >< d3)[1,2,3,4,5,6]
[$mat| 1.0, 2.0, 3.0;
4.0, 5.0, 6.0 |] |
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Constructs a matrix from a list. The size
in the matrix's type and the list's length must agree or
else a runtime error will be raised.
> matFromList [1,2,3,4,5,6] `atShape` (d2,d3)
[$mat| 1.0, 2.0, 3.0;
4.0, 5.0, 6.0 |] |
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Constructs a matrix from a list of lists of elements.
Each sublist must be of equal size or a runtime error
will be raised.
> fromListsU [[1,2,3],[4,5,6]]
[$mat| 1.0, 2.0, 3.0;
4.0, 5.0, 6.0 |] |
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Converts a matrix to a list of its rows, each as
a list.
> toLists [$mat|1,2,3;4,5,6|]
[[1.0,2.0,3.0],[4.0,5.0,6.0]] |
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| Tofrom rowscolumn vectors
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Constructs a matrix from a list of rows.
> fromRowsU [[$vec|1,2,3|],[$vec|4,5,6|]]
[$mat| 1.0, 2.0, 3.0;
4.0, 5.0, 6.0 |] |
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Converts a matrix to a list of its rows.
> toRows [$mat|1,2,3;4,5,6|]
[[$vec| 1.0, 2.0, 3.0 |],[$vec| 4.0, 5.0, 6.0 |]] |
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Constructs a matrix from a list of columns.
> fromColumnsU [[$vec|1,2,3|],[$vec|4,5,6|]]
[$mat| 1.0, 4.0;
2.0, 5.0;
3.0, 6.0 |] |
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Converts a matrix to a list of its columns.
> toColumns [$mat|1,2,3;4,5,6|]
[[$vec| 1.0, 4.0 |],[$vec| 2.0, 5.0 |],[$vec| 3.0, 6.0 |]] |
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Constructs a matrix from blocks.
> fromBlocksU [[[$matU|1,2,3;4,5,6|], [$matU|7,8,9;10,11,12|]],
[[$matU|11,12,13;14,15,16|],[$matU|21,22,23;24,25,26|]]]
[$mat| 1.0, 2.0, 3.0, 7.0, 8.0, 9.0;
4.0, 5.0, 6.0, 10.0, 11.0, 12.0;
11.0, 12.0, 13.0, 21.0, 22.0, 23.0;
14.0, 15.0, 16.0, 24.0, 25.0, 26.0 |] |
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Interprets a vector as a 1-row matrix.
> asRow [$vec|1,2,3|]
[$mat| 1.0, 2.0, 3.0 |] |
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Interprets a vector as a 1-column matrix.
> asColumn [$vec|1,2,3|]
[$mat| 1.0;
2.0;
3.0 |] |
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| Other operations
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Returns the number of rows of the matrix.
> rows [$mat|1::Double,2,3;4,5,6|]
2 |
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Returns the number of columns of the matrix.
> cols [$mat|1::Double,2,3;4,5,6|]
3 |
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Matrix transpose.
> trans [$mat|1,2,3;4,5,6|]
[$mat| 1.0, 4.0;
2.0, 5.0;
3.0, 6.0 |] |
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Reshapes a vector into a matrix,
with the specified number of columns. If the vector's length
is not a multiple of the required columns,
a runtime error is raised.
> reshapeU 3 [$vecU|1,2,3,4,5,6|]
[$mat| 1.0, 2.0, 3.0;
4.0, 5.0, 6.0 |] |
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Flattens a matrix into a vector.
> flatten [$mat|1,2,3;4,5,6|]
[$vec| 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 |] |
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Indexes a matrix.
> [$mat|1,2,3;4,5,6|] @@> (1,2)
6.0 |
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replicate for matrices.
> repmatU [$mat|1;2|] 2 3
[$mat| 1.0, 1.0, 1.0;
2.0, 2.0, 2.0;
1.0, 1.0, 1.0;
2.0, 2.0, 2.0 |] |
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Vertically flips a matrix.
> flipud [$mat|1,2,3;4,5,6|]
[$mat| 4.0, 5.0, 6.0;
1.0, 2.0, 3.0 |] |
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Horizonatlly flips a matrix.
> fliprl [$mat|1,2,3;4,5,6|]
[$mat| 3.0, 2.0, 1.0;
6.0, 5.0, 4.0 |] |
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Extracts a submatrix.
> subMatrixU (0,1) (2,2) [$mat|1,2,3,4;5,6,7,8;9,10,11,12|]
[$mat| 2.0, 3.0;
6.0, 7.0 |] |
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Takes rows from the top of the matrix
until the required size is reached.
> takeRows [$mat|1,2;3,4;5,6|] `atRows` d2
[$mat| 1.0, 2.0;
3.0, 4.0 |] |
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Takes rows from the bottom of the matrix until
the required size is reached.
> dropRows [$mat|1,2;3,4;5,6|] `atRows` d2
[$mat| 3.0, 4.0;
5.0, 6.0 |] |
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Takes columns from the left of the matrix until
the required size is reached.
> takeColumns [$mat|1,2,3;4,5,6|] `atCols` d2
[$mat| 1.0, 2.0;
4.0, 5.0 |] |
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Takes columns from the right of the matrix
until the required size is reached.
> dropColumns [$mat|1,2,3;4,5,6|] `atCols` d2
[$mat| 2.0, 3.0;
5.0, 6.0 |] |
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Extracts the given rows from a matrix.
> extractRowsU [1,0] [$mat|1,2;3,4;5,6|]
[$mat| 3.0, 4.0;
1.0, 2.0 |] |
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Constructs the identity matrix of any given size.
> ident `atRows` d3
[$mat| 1.0, 0.0, 0.0;
0.0, 1.0, 0.0;
0.0, 0.0, 1.0 |] |
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Constructs a square matrix with the given vector as its diagonal.
> diag (linspace (1,3)) `atRows` d3
[$mat| 1.0, 0.0, 0.0;
0.0, 2.0, 0.0;
0.0, 0.0, 3.0 |] |
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Constructs a rectangular matrix with the given vector as its diagonal.
> diagRect (linspace (1,3)) `atShape` (d3,d4)
[$mat| 1.0, 0.0, 0.0, 0.0;
0.0, 2.0, 0.0, 0.0;
0.0, 0.0, 3.0, 0.0 |]
> diagRect (linspace (1,3)) `atShape` (d4,d3)
[$mat| 1.0, 0.0, 0.0;
0.0, 2.0, 0.0;
0.0, 0.0, 3.0;
0.0, 0.0, 0.0 |] |
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Takes the diagonal from a matrix.
> takeDiag [$mat|1,2,3;4,5,6|]
[$vec| 1.0, 5.0 |] |
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Operations on matrices viewed as operations on the vector of their elements
> liftMatrix (+constant 2) [$mat|1,2,3;4,5,6|]
[$mat| 3.0, 4.0, 5.0;
6.0, 7.0, 8.0 |] |
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| Conversions / file input
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| See hmatrix's format.
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| See hmatrix's readMatrix.
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| See hmatrix's fromFile.
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| See hmatrix's fromArray2D.
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| Produced by Haddock version 2.4.2 |
