prbnmcn-linalg 0.0.1 · OCaml Package

Module type of matrices.

type 'a k

type 'a m

type base_index

type 'a shape

type index := base_index * base_index

include Vec
  with type 'a k := 'a k
   and type 'a m := 'a m
   and type 'a shape := 'a shape

type ('a, 'b) morphism

Type of shape morphisms.

type elt

Type of elements.

type 'i t = ('i shape, 'i m, elt m) vec

type 'i out = ('i shape, 'i m, elt m, unit m) ovec

val idim : 'i t -> 'i shape

Dimensions of an input vector.

val odim : 'i out -> 'i shape

Dimensions of an output vector.

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

Creates an input vector from a dimension and a function.

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

Pullback a vector along a shape morphism.

val 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.

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

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

val 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.

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

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

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

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

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

val zero : 'i shape -> 'i t

Everywhere zero vector.

val one : 'i shape -> 'i t

Everywhere one vector.

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

Constant vector.

val 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.

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

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

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

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

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

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

val neg : 'i t -> 'i t

Pointwise negation.

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

Multiplication by a scalar.

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

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

val iter : ('i shape, 'i m, unit m) vec -> unit m

iter v iterates the effectful computation at each index

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

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

Vector assignement.

raises Dimensions_mismatch
if the size of operands are not equal.

val 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.

val 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.

val 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.

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

Dot product.

raises Dimensions_mismatch
if the size of operands are not equal.

module Infix : sig ... end

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

Indexing

val cols : index t -> base_index shape

cols m returns the shape of the columns of m.

val rows : index t -> base_index shape

rows m returns the shape of the rows of m

val identity : base_index shape -> index t

Identity matrix

val diagonal : (base_index shape, base_index m, elt m) vec -> index t

Square matrix with given vector on diagonal

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

Get a column.

raises Out_of_bounds
if given indices are invalid.

val of_col : (base_index shape, base_index m, elt m) vec -> index t

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

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

Get a row.

raises Out_of_bounds
if given indices are invalid.

val of_row : (base_index shape, base_index m, elt m) vec -> index t

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

val 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.

val 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.

val 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.

val 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.

val 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.

package prbnmcn-linalg