Module `Mat.Rational`Source

Float allows to manipulate Q.t-valued matrices

Sourcetype 'a k = 'a

Sourcetype 'a m = 'a

Sourcetype base_index = Tensor.Int.pos

Sourcetype 'a shape = 'a Tensor.Int.t

type index := base_index * base_index

include Intf.Vec
  with type 'a k := 'a k
   and type 'a m := 'a m
   and type 'a shape := 'a shape
  with type ('a, 'b) morphism = ('a, 'b) Tensor.Int.Morphism.t
  with type elt = Q.t

Sourcetype ('a, 'b) morphism = ('a, 'b) Tensor.Int.Morphism.t

Type of shape morphisms.

Sourcetype elt = Q.t

Type of elements.

Sourcetype 'i t = ('i shape, 'i m, elt m) Intf.vec

Sourcetype 'i out = ('i shape, 'i m, elt m, unit m) Intf.ovec

Sourceval idim : 'i t -> 'i shape

Dimensions of an input vector.

Sourceval odim : 'i out -> 'i shape

Dimensions of an output vector.

Sourceval make : 'i shape -> ('i m -> elt m) -> 'i t

Creates an input vector from a dimension and a function.

Sourceval pullback : ('j, 'i) morphism -> 'i t -> 'j t k

Pullback a vector along a shape morphism.

Sourceval get : 'i t -> 'i m -> elt m k

Get an elemement of an input vector.

raises Out_of_bounds
if given index is not in the domain of the vector.

Sourceval unsafe_get : 'i t -> 'i m -> elt m

Get an elemement of an input vector. Does not perform bound checking.

Sourceval set : 'i out -> 'i m -> elt m -> unit m k

Set an elemement in an output vector.

raises Out_of_bounds
if given index is not in the domain of the vector.

Source

val map : 
  ('a m -> 'b m) ->
  ('i shape, 'i m, 'a m) Intf.vec ->
  ('i shape, 'i m, 'b m) Intf.vec

Source

val mapi : 
  ('i m -> 'a m -> 'b m) ->
  ('i shape, 'i m, 'a m) Intf.vec ->
  ('i shape, 'i m, 'b m) Intf.vec

Source

val map2 : 
  ('a m -> 'b m -> 'c m) ->
  ('i shape, 'i m, 'a m) Intf.vec ->
  ('i shape, 'i m, 'b m) Intf.vec ->
  ('i shape, 'i m, 'c m) Intf.vec k

Source

val map2i : 
  ('i m -> 'a m -> 'b m -> 'c m) ->
  ('i shape, 'i m, 'a m) Intf.vec ->
  ('i shape, 'i m, 'b m) Intf.vec ->
  ('i shape, 'i m, 'c m) Intf.vec k

Source

val assign : 
  ('i shape, 'i m, 'a m, unit m) Intf.ovec ->
  ('i shape, 'i m, 'a m) Intf.vec ->
  ('i shape, 'i m, unit m) Intf.vec k

Sourceval zero : 'i shape -> 'i t

Everywhere zero vector.

Sourceval one : 'i shape -> 'i t

Everywhere one vector.

Sourceval const : 'i shape -> elt m -> 'i t

Constant vector.

Sourceval basis : 'i shape -> 'i m -> elt m -> 'i t k

basis s i r is the vector of shape s everywhere equal to R.zero except at index i where it is equal to r. Raises Out_of_bounds if i does not belong to s.

Sourceval add : 'i t -> 'i t -> 'i t k

Pointwise addition. Raises Dimensions_mismatch if the shape of operands are not equal.

Sourceval sub : 'i t -> 'i t -> 'i t k

Pointwise subtraction. Raises Dimensions_mismatch if the shape of operands are not equal.

Sourceval mul : 'i t -> 'i t -> 'i t k

Pointwise multiplication. Raises Dimensions_mismatch if the shape of operands are not equal.

Sourceval neg : 'i t -> 'i t

Pointwise negation.

Sourceval smul : elt m -> 'i t -> 'i t

Multiplication by a scalar.

Sourceval swap : 'i m -> 'i m -> 'i t -> 'i t k

Swapping of indices. Raises Out_of_bounds if given indices are invalid.

Sourceval iter : ('i shape, 'i m, unit m) Intf.vec -> unit m

iter v iterates the effectful computation at each index

Source

val reduce : 
  (elt m -> elt m -> elt m) ->
  elt m ->
  ('i shape, 'i m, elt m) Intf.vec ->
  elt m

reduce op zero v folds the binary, associative operator op over the elements of v with initial value zero. Fold ordering is implementation-dependent: consider using commutative operators.

Source

val (:=) : 
  ('i shape, 'i m, 'a m, unit m) Intf.ovec ->
  ('i shape, 'i m, 'a m) Intf.vec ->
  unit m k

Vector assignement.

raises Dimensions_mismatch
if the size of operands are not equal.

Sourceval add_ : 'i out -> 'i t -> 'i t -> unit m k

Pointwise addition, stores result in first operand.

raises Dimensions_mismatch
if the size of operands are not equal.

Sourceval sub_ : 'i out -> 'i t -> 'i t -> unit m k

Pointwise subtraction, stores result in first operand.

raises Dimensions_mismatch
if the size of operands are not equal.

Sourceval mul_ : 'i out -> 'i t -> 'i t -> unit m k

Pointwise multiplication, stores result in first operand.

raises Dimensions_mismatch
if the size of operands are not equal.

Sourceval dot : 'i t -> 'i t -> elt m k

Dot product.

raises Dimensions_mismatch
if the size of operands are not equal.

Sourcemodule Infix : sig ... end

Sourceval index : c:base_index m -> r:base_index m -> index m

Indexing

Sourceval cols : index t -> base_index shape

cols m returns the shape of the columns of m.

Sourceval rows : index t -> base_index shape

rows m returns the shape of the rows of m

Sourceval identity : base_index shape -> index t

Identity matrix

Sourceval diagonal : (base_index shape, base_index m, elt m) Intf.vec -> index t

Square matrix with given vector on diagonal

Source

val col : 
  index t ->
  base_index m ->
  (base_index shape, base_index m, elt m) Intf.vec k

Get a column.

raises Out_of_bounds
if given indices are invalid.

Sourceval of_col : (base_index shape, base_index m, elt m) Intf.vec -> index t

Convert a vector into a matrix with this vector as single column.

Source

val row : 
  index t ->
  base_index m ->
  (base_index shape, base_index m, elt m) Intf.vec k

Get a row.

raises Out_of_bounds
if given indices are invalid.

Sourceval of_row : (base_index shape, base_index m, elt m) Intf.vec -> index t

Convert a vector into a matrix with this vector as single row.

Sourceval swap_rows : index t -> base_index m -> base_index m -> index t k

Swap two rows.

raises Out_of_bounds
if given indices are invalid.

Sourceval swap_cols : index t -> base_index m -> base_index m -> index t k

Swap two columns.

raises Out_of_bounds
if given indices are invalid.

Sourceval concat_horiz : index t -> index t -> index t k

Concatenate two matrices horizontally, provided they have the same number of rows.

raises Dimensions_mismatch
if this condition is not verified.

Sourceval concat_vert : index t -> index t -> index t k

Concatenate two matrices vertically, provided they have the same number of columns.

raises Dimensions_mismatch
if this condition is not verified.

Sourceval mm : index t -> index t -> index t k

Matrix multiplication.

raises Dimensions_mismatch
if the nummber of columns of the left-hand side is not equal to the number of rows of the right-hand side.

Install

Dune Dependency

Authors

Maintainers

Sources

doc/prbnmcn-linalg/Linalg/Mat/Rational/index.html

Module `Mat.Rational`Source

package prbnmcn-linalg

Install

Dune Dependency

Authors

Maintainers

Sources

doc/prbnmcn-linalg/Linalg/Mat/Rational/index.html

Module Mat.RationalSource

Module `Mat.Rational`Source