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yap-6.3/packages/python/swig/yap4py/prolog/matrix.yap

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Merge branch 'master' of xato:0517
2017-05-19 10:03:49 +01:00
/*************************************************************************
* *
* YAP Prolog *
* *
* Yap Prolog was developed at NCCUP - Universidade do Porto *
* *
* Copyright L.Damas, V.S.Costa and Universidade do Porto 1985-2006 *
* *
**************************************************************************
* *
* File: matrix.yap *
* Last rev: *
* mods: *
* comments: Have some fun with blobs *
* *
*************************************************************************/
/**
* @file matrix.yap
* @author VITOR SANTOS COSTA <vsc@VITORs-MBP.lan>
* @date Tue Nov 17 22:53:40 2015
*
* @brief Vector, Array and Matrix library
*
*
*/
:- module( matrix,
[(<==)/2, op(800, xfx, <==),
(+=)/2, op(800, xfx, +=),
(-=)/2, op(800, xfx, -=),
op(700, xfx, in),
op(700, xfx, ins),
op(450, xfx, ..), % should bind more tightly than \/
op(710, xfx, of), of/2,
matrix_new/3,
matrix_new/4,
matrix_new_set/4,
matrix_dims/2,
matrix_ndims/2,
matrix_size/2,
matrix_type/2,
matrix_to_list/2,
matrix_to_lists/2,
matrix_get/3,
matrix_set/3,
matrix_set_all/2,
matrix_add/3,
matrix_inc/2,
matrix_dec/2,
matrix_mult/2,
matrix_inc/3,
matrix_dec/3,
matrix_arg_to_offset/3,
matrix_offset_to_arg/3,
matrix_max/2,
matrix_maxarg/2,
matrix_min/2,
matrix_minarg/2,
matrix_sum/2,
matrix_sum_out/3,
matrix_sum_out_several/3,
matrix_sum_logs_out/3,
matrix_sum_logs_out_several/3,
matrix_add_to_all/2,
matrix_agg_lines/3,
matrix_agg_cols/3,
matrix_to_logs/1,
matrix_to_exps/1,
matrix_to_exps2/1,
matrix_to_logs/2,
matrix_to_exps/2,
matrix_op/4,
matrix_op_to_all/4,
matrix_op_to_lines/4,
matrix_op_to_cols/4,
matrix_shuffle/3,
matrix_transpose/2,
matrix_set_all_that_disagree/5,
matrix_expand/3,
matrix_select/4,
matrix_column/3,
matrix_get/2,
matrix_set/2,
foreach/2,
foreach/4,
op(50, yf, []),
op(50, yf, '()'),
op(100, xfy, '.'),
op(100, fy, '.')
]).
/** @defgroup matrix Matrix Library
@ingroup library
@{
This package provides a fast implementation of multi-dimensional
matrices of integers and floats. In contrast to dynamic arrays, these
matrices are multi-dimensional and compact. In contrast to static
arrays. these arrays are allocated in the stack, and disppear in
backtracking. Matrices are available by loading the library
`library(matrix)`. They are multimensional objects of type:
+ <tt>terms</tt>: Prolog terms
+ <tt>ints</tt>: bounded integers, represented as an opaque term. The
maximum integer depends on hardware, but should be obtained from the
natural size of the machine.
+ <tt>floats</tt>: floating-point numbers, represented as an opaque term.
Matrix elements can be accessed through the `matrix_get/2`
predicate or through an <tt>R</tt>-inspired access notation (that uses the ciao
style extension to `[]`). Examples include:
+ Access the second row, third column of matrix <tt>X</tt>. Indices start from
`0`,
~~~~
_E_ <== _X_[2,3]
~~~~
+ Access all the second row, the output is a list ofe elements.
~~~~
_L_ <== _X_[2,_]
~~~~
+ Access all the second, thrd and fourth rows, the output is a list of elements.
~~~~
_L_ <== _X_[2..4,_]
~~~~
+ Access all the fifth, sixth and eight rows, the output is a list of elements.
~~~~
_L_ <== _X_[2..4+3,_]
~~~~
The matrix library also supports a B-Prolog/ECliPSe inspired `foreach`iterator to iterate over
elements of a matrix:
+ Copy a vector, element by element.
~~~~
foreach(I in 0..N1, X[I] <== Y[I])
~~~~
+ The lower-triangular matrix _Z_ is the difference between the
lower-triangular and upper-triangular parts of _X_.
~~~~
foreach([I in 0..N1, J in I..N1], Z[I,J] <== X[I,J] - X[I,J])
~~~~
+ Add all elements of a matrix by using _Sum_ as an accumulator.
~~~~
foreach([I in 0..N1, J in 0..N1], plus(X[I,J]), 0, Sum)
~~~~
Notice that the library does not support all known matrix operations. Please
contact the YAP maintainers if you require extra functionality.
+ _X_ <== array[ _Dim1_,..., _Dimn_] of _Objects_
The of/2 operator can be used to create a new array of
_Objects_. The objects supported are:
+ `Unbound Variable`
create an array of free variables
+ `ints `
create an array of integers
+ `floats `
create an array of floating-point numbers
+ `_I_: _J_`
create an array with integers from _I_ to _J_
+ `[..]`
create an array from the values in a list
The dimensions can be given as an integer, and the matrix will be
indexed `C`-style from `0..( _Max_-1)`, or can be given
as an interval ` _Base_.. _Limit_`. In the latter case,
matrices of integers and of floating-point numbers should have the same
_Base_ on every dimension.
*/
/*
A matrix is an object with integer or floating point numbers. A matrix
may have a number of dimensions. These routines implement a number of
routine manipulation procedures.
'$matrix'(Type,D1,D2,...,Dn,data(......))
Type = int, float
Operations:
typedef enum {
MAT_SUM=0,
MAT_SUB=1,
MAT_TIMES=2,
MAT_DIV=3,
MAT_IDIV=4,
MAT_ZDIV=5
} op_type;
*/
/** @pred ?_LHS_ <== ?_RHS_ is semidet
General matrix assignment operation. It evaluates the right-hand side
according to the
left-hand side and to the matrix:
+ if _LHS_ is part of an integer or floating-point matrix,
perform non-backtrackable assignment.
+ other unify left-hand side and right-hand size.
The right-hand side supports the following operators:
+ `[]/2`
written as _M_[ _Offset_]: obtain an element or list of elements
of matrix _M_ at offset _Offset_.
+ `matrix/1`
create a vector from a list
+ `matrix/2`
create a matrix from a list. Options are:
+ dim=
a list of dimensions
+ type=
integers, floating-point or terms
+ base=
a list of base offsets per dimension (all must be the same for arrays of
integers and floating-points
+ `matrix/3`
create matrix giving two options
+ `dim/1`
list with matrix dimensions
+ `nrow/1`
number of rows in bi-dimensional matrix
+ `ncol/1`
number of columns in bi-dimensional matrix
+ `length/1`
size of a matrix
+ `size/1`
size of a matrix
+ `max/1`
maximum element of a numeric matrix
+ `maxarg/1`
argument of maximum element of a numeric matrix
+ `min/1`
minimum element of a numeric matrix
+ `minarg/1`
argument of minimum element of a numeric matrix
+ `list/1`
represent matrix as a list
+ `lists/2`
represent matrix as list of embedded lists
+ `../2`
_I_.. _J_ generates a list with all integers from _I_ to
_J_, included.
+ `+/2`
add two numbers, add two matrices element-by-element, or add a number to
all elements of a matrix or list.
+ `-/2 `
subtract two numbers, subtract two matrices or lists element-by-element, or subtract a number from
all elements of a matrix or list
+ `* /2`
multiply two numbers, multiply two matrices or lists
element-by-element, or multiply a number from all elements of a
matrix or list
+ `log/1`
natural logarithm of a number, matrix or list
+ `exp/1 `
natural exponentiation of a number, matrix or list
*/
/** @pred matrix_add(+ _Matrix_,+ _Position_,+ _Operand_)
Add _Operand_ to the element of _Matrix_ at position
_Position_.
*/
/** @pred matrix_agg_cols(+ _Matrix_,+Operator,+ _Aggregate_)
If _Matrix_ is a n-dimensional matrix, unify _Aggregate_ with
the one dimensional matrix where each element is obtained by adding all
Matrix elements with same first index. Currently, only addition is supported.
*/
/** @pred matrix_agg_lines(+ _Matrix_,+Operator,+ _Aggregate_)
If _Matrix_ is a n-dimensional matrix, unify _Aggregate_ with
the n-1 dimensional matrix where each element is obtained by adding all
_Matrix_ elements with same last n-1 index. Currently, only addition is supported.
*/
/** @pred matrix_arg_to_offset(+ _Matrix_,+ _Position_,- _Offset_)
Given matrix _Matrix_ return what is the numerical _Offset_ of
the element at _Position_.
*/
/** @pred matrix_column(+ _Matrix_,+ _Column_,- _NewMatrix_)
Select from _Matrix_ the column matching _Column_ as new matrix _NewMatrix_. _Column_ must have one less dimension than the original matrix.
*/
/** @pred matrix_dec(+ _Matrix_,+ _Position_)
Decrement the element of _Matrix_ at position _Position_.
*/
/** @pred matrix_dec(+ _Matrix_,+ _Position_,- _Element_)
Decrement the element of _Matrix_ at position _Position_ and
unify with _Element_.
*/
/** @pred matrix_dims(+ _Matrix_,- _Dims_)
Unify _Dims_ with a list of dimensions for _Matrix_.
*/
/** @pred matrix_expand(+ _Matrix_,+ _NewDimensions_,- _New_)
Expand _Matrix_ to occupy new dimensions. The elements in
_NewDimensions_ are either 0, for an existing dimension, or a
positive integer with the size of the new dimension.
*/
/** @pred matrix_get(+ _Matrix_,+ _Position_,- _Elem_)
Unify _Elem_ with the element of _Matrix_ at position
_Position_.
*/
/** @pred matrix_get(+ _Matrix_[+ _Position_],- _Elem_)
Unify _Elem_ with the element _Matrix_[ _Position_].
*/
/** @pred matrix_inc(+ _Matrix_,+ _Position_)
Increment the element of _Matrix_ at position _Position_.
*/
/** @pred matrix_inc(+ _Matrix_,+ _Position_,- _Element_)
Increment the element of _Matrix_ at position _Position_ and
unify with _Element_.
*/
/** @pred matrix_max(+ _Matrix_,+ _Max_)
Unify _Max_ with the maximum in matrix _Matrix_.
*/
/** @pred matrix_maxarg(+ _Matrix_,+ _Maxarg_)
Unify _Max_ with the position of the maximum in matrix _Matrix_.
*/
/** @pred matrix_min(+ _Matrix_,+ _Min_)
Unify _Min_ with the minimum in matrix _Matrix_.
*/
/** @pred matrix_minarg(+ _Matrix_,+ _Minarg_)
Unify _Min_ with the position of the minimum in matrix _Matrix_.
*/
/** @pred matrix_ndims(+ _Matrix_,- _Dims_)
Unify _NDims_ with the number of dimensions for _Matrix_.
*/
/** @pred matrix_new(+ _Type_,+ _Dims_,+ _List_,- _Matrix_)
Create a new matrix _Matrix_ of type _Type_, which may be one of
`ints` or `floats`, with dimensions _Dims_, and
initialized from list _List_.
*/
/** @pred matrix_new(+ _Type_,+ _Dims_,- _Matrix_)
Create a new matrix _Matrix_ of type _Type_, which may be one of
`ints` or `floats`, and with a list of dimensions _Dims_.
The matrix will be initialized to zeros.
~~~~~
?- matrix_new(ints,[2,3],Matrix).
Matrix = {..}
~~~~~
Notice that currently YAP will always write a matrix of numbers as `{..}`.
*/
/** @pred matrix_new_set(? _Dims_,+ _OldMatrix_,+ _Value_,- _NewMatrix_)
Create a new matrix _NewMatrix_ of type _Type_, with dimensions
_Dims_. The elements of _NewMatrix_ are set to _Value_.
*/
/** @pred matrix_offset_to_arg(+ _Matrix_,- _Offset_,+ _Position_)
Given a position _Position _ for matrix _Matrix_ return the
corresponding numerical _Offset_ from the beginning of the matrix.
*/
/** @pred matrix_op(+ _Matrix1_,+ _Matrix2_,+ _Op_,- _Result_)
_Result_ is the result of applying _Op_ to matrix _Matrix1_
and _Matrix2_. Currently, only addition (`+`) is supported.
*/
/** @pred matrix_op_to_all(+ _Matrix1_,+ _Op_,+ _Operand_,- _Result_)
_Result_ is the result of applying _Op_ to all elements of
_Matrix1_, with _Operand_ as the second argument. Currently,
only addition (`+`), multiplication (`\*`), and division
(`/`) are supported.
*/
/** @pred matrix_op_to_cols(+ _Matrix1_,+ _Cols_,+ _Op_,- _Result_)
_Result_ is the result of applying _Op_ to all elements of
_Matrix1_, with the corresponding element in _Cols_ as the
second argument. Currently, only addition (`+`) is
supported. Notice that _Cols_ will have n-1 dimensions.
*/
/** @pred matrix_op_to_lines(+ _Matrix1_,+ _Lines_,+ _Op_,- _Result_)
_Result_ is the result of applying _Op_ to all elements of
_Matrix1_, with the corresponding element in _Lines_ as the
second argument. Currently, only division (`/`) is supported.
*/
/** @pred matrix_select(+ _Matrix_,+ _Dimension_,+ _Index_,- _New_)
Select from _Matrix_ the elements who have _Index_ at
_Dimension_.
*/
/** @pred matrix_set(+ _Matrix_,+ _Position_,+ _Elem_)
Set the element of _Matrix_ at position
_Position_ to _Elem_.
*/
/** @pred matrix_set(+ _Matrix_[+ _Position_],+ _Elem_)
Set the element of _Matrix_[ _Position_] to _Elem_.
*/
/** @pred matrix_set_all(+ _Matrix_,+ _Elem_)
Set all element of _Matrix_ to _Elem_.
*/
/** @pred matrix_shuffle(+ _Matrix_,+ _NewOrder_,- _Shuffle_)
Shuffle the dimensions of matrix _Matrix_ according to
_NewOrder_. The list _NewOrder_ must have all the dimensions of
_Matrix_, starting from 0.
*/
/** @pred matrix_size(+ _Matrix_,- _NElems_)
Unify _NElems_ with the number of elements for _Matrix_.
*/
/** @pred matrix_sum(+ _Matrix_,+ _Sum_)
Unify _Sum_ with the sum of all elements in matrix _Matrix_.
*/
/** @pred matrix_to_list(+ _Matrix_,- _Elems_)
Unify _Elems_ with the list including all the elements in _Matrix_.
*/
/** @pred matrix_transpose(+ _Matrix_,- _Transpose_)
Transpose matrix _Matrix_ to _Transpose_. Equivalent to:
~~~~~
matrix_transpose(Matrix,Transpose) :-
matrix_shuffle(Matrix,[1,0],Transpose).
~~~~~
*/
/** @pred matrix_type(+ _Matrix_,- _Type_)
Unify _NElems_ with the type of the elements in _Matrix_.
*/
:- load_foreign_files([matrix], [], init_matrix).
:- multifile rhs_opaque/1, array_extension/2.
:- meta_predicate foreach(+,0), foreach(+,2, +, -).
:- use_module(library(maplist)).
:- use_module(library(mapargs)).
:- use_module(library(lists)).
( X <== '[]'(Dims0, array) of V ) :-
var(V), !,
foldl( norm_dim, Dims0, Dims, Bases, 1, Size ),
length( L, Size ),
X <== matrix( L, [dim=Dims,base=Bases] ).
( X <== '[]'(Dims0, array) of ints ) :- !,
foldl( norm_dim, Dims0, Dims, Bases, 1, _Size ),
matrix_new( ints , Dims, X ),
matrix_base(X, Bases).
( X <== '[]'(Dims0, array) of floats ) :- !,
foldl( norm_dim, Dims0, Dims, Bases, 1, _Size ),
matrix_new( floats , Dims, X ),
matrix_base(X, Bases).
( X <== '[]'(Dims0, array) of (I:J) ) :- !,
foldl( norm_dim, Dims0, Dims, Bases, 1, Size ),
matrix_seq(I, J, Dims, X),
matrixn_size(X, Size),
matrix_base(X, Bases).
( X <== '[]'(Dims0, array) of L ) :-
length( L, Size ), !,
foldl( norm_dim, Dims0, Dims, Bases, 1, Size ),
X <== matrix( L, [dim=Dims,base=Bases] ).
( X <== '[]'(Dims0, array) of Pattern ) :- !,
array_extension(Pattern, Goal),
foldl( norm_dim, Dims0, Dims, Bases, 1, Size ),
call(Goal, Pattern, Dims, Size, L),
X <== matrix( L, [dim=Dims,base=Bases] ).
( LHS <== RHS ) :-
rhs(RHS, R),
set_lhs( LHS, R).
norm_dim( I..J, D, I, P0, P) :- !,
D is J+1-I,
P is P0*D.
norm_dim( I, I, 0, P0, P ) :-
P is P0*I.
rhs(RHS, RHS) :- var(RHS), !.
% base case
rhs(A, A) :- atom(A), !.
rhs(RHS, RHS) :- number(RHS), !.
rhs(RHS, RHS) :- opaque(RHS), !.
rhs(RHS, RHS) :- RHS = '$matrix'(_, _, _, _, _), !.
rhs(matrix(List), RHS) :- !,
rhs( List, A1),
new_matrix(A1, [], RHS).
rhs(matrix(List, Opt1), RHS) :- !,
rhs( List, A1),
new_matrix(A1, Opt1, RHS).
rhs(matrix(List, Opt1, Opt2), RHS) :- !,
rhs( List, A1),
new_matrix(A1, [Opt1, Opt2], RHS).
rhs(dim(RHS), Dims) :- !,
rhs(RHS, X1),
matrix_dims( X1, Dims ).
rhs(dims(RHS), Dims) :- !,
rhs(RHS, X1),
matrix_dims( X1, Dims ).
rhs(nrow(RHS), NRow) :- !,
rhs(RHS, X1),
matrix_dims( X1, [NRow,_] ).
rhs(ncol(RHS), NCol) :- !,
rhs(RHS, X1),
matrix_dims( X1, [_,NCol] ).
rhs(length(RHS), Size) :- !,
rhs(RHS, X1),
matrix_size( X1, Size ).
rhs(size(RHS), Size) :- !,
rhs(RHS, X1),
matrix_size( X1, Size ).
rhs(max(RHS), Size) :- !,
rhs(RHS, X1),
matrix_max( X1, Size ).
rhs(min(RHS), Size) :- !,
rhs(RHS, X1),
matrix_min( X1, Size ).
rhs(maxarg(RHS), Size) :- !,
rhs(RHS, X1),
matrix_maxarg( X1, Size ).
rhs(minarg(RHS), Size) :- !,
rhs(RHS, X1),
matrix_minarg( X1, Size ).
rhs(list(RHS), List) :- !,
rhs(RHS, X1),
matrix_to_list( X1, List ).
rhs(lists(RHS), List) :- !,
rhs(RHS, X1),
matrix_to_lists( X1, List ).
rhs('[]'(Args, RHS), Val) :-
!,
rhs(RHS, X1),
matrix_dims( X1, Dims, Bases),
maplist( index(Range), Args, Dims, Bases, NArgs),
(
var(Range)
->
matrix_get( X1, NArgs, Val )
;
matrix_get_range( X1, NArgs, Val )
).
rhs('..'(I, J), [I1|Is]) :- !,
rhs(I, I1),
rhs(J, J1),
once( foldl(inc, Is, I1, J1) ).
rhs([H|T], [NH|NT]) :- !,
rhs(H, NH),
rhs(T, NT).
rhs(log(RHS), Logs ) :- !,
rhs(RHS, X1),
matrix_to_logs( X1, Logs ).
rhs(exp(RHS), Logs ) :- !,
rhs(RHS, X1),
matrix_to_exps( X1, Logs ).
rhs(S, NS) :-
rhs_opaque( S ), !,
S = NS.
rhs(E1+E2, V) :- !,
rhs(E1, R1),
rhs(E2, R2),
mplus(R1, R2, V).
rhs(E1-E2, V) :- !,
rhs(E1, R1),
rhs(E2, R2),
msub(R1, R2, V).
rhs(S, NS) :-
S =.. [N|As],
maplist(rhs, As, Bs),
NS =.. [N|Bs].
set_lhs(V, R) :- var(V), !, V = R.
set_lhs(V, R) :- number(V), !, V = R.
set_lhs('[]'(Args, M), Val) :-
matrix_dims( M, Dims, Bases),
maplist( index(Range), Args, Dims, Bases, NArgs),
(
var(Range)
->
matrix_set( M, NArgs, Val )
;
matrix_set_range( M, NArgs, Val )
).
%
% ranges of arguments
%
index(Range, V, M, Base, Indx) :- var(V), !,
Max is (M-1)+Base,
index(Range, Base..Max, M, Base, Indx).
index(Range, '*', M, Base, Indx) :- !,
Max is (M-1)+Base,
index(Range, Base..Max, M, Base, Indx).
index(Range, Exp, M, _Base, Indx) :- !,
index(Exp, M, Indx0),
( integer(Indx0) -> Indx = Indx0 ;
Indx0 = [Indx] -> true ;
Indx0 = Indx, Range = range ).
index(I, _M, I ) :- integer(I), !.
index(I..J, _M, [I|O] ) :- !,
I1 is I, J1 is J,
once( foldl(inc, O, I1, J1) ).
index(I:J, _M, [I|O] ) :- !,
I1 is I, J1 is J,
once( foldl(inc, O, I1, J1) ).
index(I+J, M, O ) :- !,
index(I, M, I1),
index(J, M, J1),
add_index(I1, J1, O).
index(I-J, M, O ) :- !,
index(I, M, I1),
index(J, M, J1),
sub_index(I1, J1, O).
index(I*J, M, O ) :- !,
index(I, M, I1),
index(J, M, J1),
O is I1*J1.
index(I div J, M, O ) :- !,
index(I, M, I1),
index(J, M, J1),
O is I1 div J1.
index(I rem J, M, O ) :- !,
index(I, M, I1),
index(J, M, J1),
O is I1 rem J1.
index(I, M, NI ) :-
maplist(indx(M), I, NI).
indx(M, I, NI) :- index(I, M, NI).
add_index(I1, J1, O) :-
integer(I1),
integer(J1), !,
O is I1+J1.
add_index(I1, J1, O) :-
integer(I1), !,
maplist(plus(I1), J1, O).
add_index(I1, J1, O) :-
integer(J1), !,
maplist(plus(J1), I1, O).
add_index(I1, J1, O) :-
ord_union(I1, J1, O).
sub_index(I1, J1, O) :-
integer(I1),
integer(J1), !,
O is I1-J1.
sub_index(I1, J1, O) :-
integer(I1), !,
maplist(rminus(I1), J1, O).
sub_index(I1, J1, O) :-
integer(J1), !,
maplist(minus(J1), I1, O).
sub_index(I1, J1, O) :-
ord_subtract(I1, J1, O).
minus(X, Y, Z) :- Z is X-Y.
rminus(X, Y, Z) :- Z is Y-X.
times(X, Y, Z) :- Z is Y*X.
div(X, Y, Z) :- Z is X/Y.
rdiv(X, Y, Z) :- Z is Y/X.
zdiv(X, Y, Z) :- (X == 0 -> Z = 0 ; X == 0.0 -> Z = 0.0 ; Z is X / Y ).
mplus(I1, I2, V) :-
number(I1) ->
( number(I2) -> V is I1+I2 ;
matrix(I2) -> matrix_op_to_all(I1, +, I2, V) ;
is_list(I2) -> maplist(plus(I1), I2, V) ;
V = I1+I2 ) ;
matrix(I1) ->
( number(I2) -> matrix_op_to_all(I1, +, I2, V) ;
matrix(I2) -> matrix_op(I1, I2, +, V) ;
V = I1+I2 ) ;
is_list(I1) ->
( number(I2) -> maplist(plus(I2), I1, V) ;
is_list(I2) -> maplist(plus, I1, I2, V) ;
V = I1+I2 ) ;
V = I1 +I2.
msub(I1, I2, V) :-
number(I1) ->
( number(I2) -> V is I1-I2 ;
matrix(I2) -> matrix_op_to_all(I1, -, NI2, V) ;
is_list(I2) -> maplist(minus(I1), I2, V) ;
V = I1-I2 ) ;
matrix(I1) ->
( number(I2) -> NI2 is -I2, matrix_op_to_all(I1, +, NI2, V) ;
matrix(I2) -> matrix_op(I1, I2, -, V) ;
V = I1-I2 ) ;
is_list(I1) ->
( number(I2) -> NI2 is -I2, maplist(plus(NI2), I1, V) ;
is_list(I2) -> maplist(minus, I1, I2, V) ;
V = I1-I2 ) ;
V = I1-I2.
mtimes(I1, I2, V) :-
number(I1) ->
( number(I2) -> V is I1*I2 ;
matrix(I2) -> matrix_op_to_all(I1, *, I2, V) ;
is_list(I2) -> maplist(times(I1), I2, V) ;
V = I1*I2 ) ;
matrix(I1) ->
( number(I2) -> matrix_op_to_all(I1, *, I2, V) ;
matrix(I2) -> matrix_op(I1, I2, *, V) ;
V = I1*I2 ) ;
is_list(I1) ->
( number(I2) -> maplist(times(I2), I1, V) ;
is_list(I2) -> maplist(times, I1, I2, V) ;
V = I1*I2 ) ;
V = I1 *I2.
%
% three types of matrix: integers, floats and general terms.
%
matrix_new(terms,Dims, '$matrix'(Dims, NDims, Size, Offsets, Matrix) ) :-
length(Dims,NDims),
foldl(size, Dims, 1, Size),
maplist(zero, Dims, Offsets),
functor( Matrix, c, Size).
matrix_new(ints,Dims,Matrix) :-
length(Dims,NDims),
new_ints_matrix_set(NDims, Dims, 0, Matrix).
matrix_new(floats,Dims,Matrix) :-
length(Dims,NDims),
new_floats_matrix_set(NDims, Dims, 0.0, Matrix).
matrix_new(terms, Dims, Data, '$matrix'(Dims, NDims, Size, Offsets, Matrix) ) :-
length(Dims,NDims),
foldl(size, Dims, 1, Size),
maplist(zero, Dims, Offsets),
functor( Matrix, c, Size),
Matrix =.. [c|Data].
matrix_new(ints,Dims,Data,Matrix) :-
length(Dims,NDims),
new_ints_matrix(NDims, Dims, Data, Matrix).
matrix_new(floats,Dims,Data,Matrix) :-
length(Dims,NDims),
new_floats_matrix(NDims, Dims, Data, Matrix).
matrix_dims( Mat, Dims) :-
( opaque(Mat) -> matrixn_dims( Mat, Dims ) ;
Mat = '$matrix'( Dims, _, _, _, _) ).
matrix_dims( Mat, Dims, Bases) :-
( opaque(Mat) -> matrixn_dims( Mat, Dims, Bases ) ;
Mat = '$matrix'( Dims, _, _, Bases, _) ).
matrix_ndims( Mat, NDims) :-
( opaque(Mat) -> matrixn_ndims( Mat, NDims ) ;
Mat = '$matrix'( _, NDims, _, _, _) ).
matrix_size( Mat, Size) :-
( opaque(Mat) -> matrixn_size( Mat, Size ) ;
Mat = '$matrix'( _, _, Size, _, _) ).
matrix_to_list( Mat, ToList) :-
( opaque(Mat) -> matrixn_to_list( Mat, ToList ) ;
Mat = '$matrix'( _, _, _, _, M), M=.. [_|ToList] ).
matrix_to_lists( Mat, ToList) :-
matrix_dims( Mat, [D|Dims] ),
D1 is D-1,
foreach( I in 0..D1, matrix_slicer( Dims, Mat, [I|L]-L), ToList, [] ).
matrix_slicer( [_], M, Pos-[_], [O|L0], L0) :- !,
O <== '[]'(Pos,M).
matrix_slicer( [D|Dims], M, Pos-[I|L], [O|L0], L0) :-
D1 is D-1,
foreach( I in 0..D1 , L^matrix_slicer( Dims, M, Pos-L), O, [] ).
matrix_get( Mat, Pos, El) :-
( opaque(Mat) -> matrixn_get( Mat, Pos, El ) ;
m_get(Mat, Pos, El) ).
matrix_get_range( Mat, Pos, Els) :-
slice(Pos, Keys),
maplist( matrix_get(Mat), Keys, Els).
slice([], [[]]).
slice([[H|T]|Extra], Els) :- !,
slice(Extra, Els0),
foldl(add_index_prefix( Els0 ), [H|T], Els, [] ).
slice([H|Extra], Els) :- !,
slice(Extra, Els0),
add_index_prefix( Els0 , H, Els, [] ).
add_index_prefix( [] , _H ) --> [].
add_index_prefix( [L|Els0] , H ) --> [[H|L]],
add_index_prefix( Els0 , H ).
matrix_set_range( Mat, Pos, Els) :-
slice(Pos, Keys),
maplist( matrix_set(Mat), Keys, Els).
matrix_set( Mat, Pos, El) :-
( opaque(Mat) -> matrixn_set( Mat, Pos, El ) ;
m_set(Mat, Pos, El) ).
matrix_new_set(ints,Dims,Elem,Matrix) :-
length(Dims,NDims),
new_ints_matrix_set(NDims, Dims, Elem, Matrix).
matrix_new_set(floats,Dims,Elem,Matrix) :-
length(Dims,NDims),
new_floats_matrix_set(NDims, Dims, Elem, Matrix).
matrix_type(Matrix,Type) :-
( matrix_type_as_number(Matrix, 0) -> Type = ints ;
opaque( Matrix ) -> Type = floats ;
Type = terms ).
matrix_base(Matrix, Bases) :-
( opaque( Matrix ) -> maplist('='(Base), Bases), matrixn_set_base( Matrix, Base ) ;
nb_setarg(4, Matrix, Bases ) ).
matrix_arg_to_offset(M, Index, Offset) :-
( opaque(M) -> matrixn_arg_to_offset( M, Index, Offset ) ;
M = '$matrix'(Dims, _, Size, Bases, _) -> foldl2(indx, Index, Dims, Bases, Size, _, 0, Offset) ).
matrix_offset_to_arg(M, Offset, Index) :-
( opaque(M) -> matrixn_offset_to_arg( M, Offset, Index ) ;
M = '$matrix'(Dims, _, Size, Bases, _) -> foldl2(offset, Index, Dims, Bases, Size, _, Offset, _) ).
matrix_max(M, Max) :-
( opaque(M) -> matrixn_max( M, Max ) ;
M = '$matrix'(_, _, _, _, C) ->
arg(1,C,V0), foldargs(max, M, V0, Max) ;
M = [V0|L], foldl(max, L, V0, Max) ).
max(New, Old, Max) :- ( New >= Old -> New = Max ; Old = Max ).
matrix_maxarg(M, MaxArg) :-
( opaque(M) -> matrixn_maxarg( M, MaxArg );
M = '$matrix'(_, _, _, _, C) ->
arg(1,C,V0), foldargs(maxarg, M, V0-0-0, _-Offset-_), matrix_offset_to_arg(M, Offset, MaxArg) ;
M = [V0|L], foldl(maxarg, L, V0-0-1, _Max-Off-_ ), MaxArg = [Off] ).
maxarg(New, Old-OPos-I0, Max-MPos-I) :- I is I0+1, ( New > Old -> New = Max, MPos = I0 ; Old = Max, MPos = OPos ).
matrix_min(M, Min) :-
( opaque(M) -> matrixn_min( M, Min ) ;
M = '$matrix'(_, _, _, _, C) ->
arg(1,C,V0), foldargs(min, M, V0, Max) ;
M = [V0|L], foldl(min, L, V0, Max) ).
min(New, Old, Max) :- ( New =< Old -> New = Max ; Old = Max ).
matrix_minarg(M, MinArg) :-
( opaque(M) -> matrixn_minarg( M, MinArg );
M = '$matrix'(_, _, _, _, C) ->
arg(1,C,V0), foldargs(minarg, M, V0-0-0, _-Offset-_), matrix_offset_to_arg(M, Offset, MinArg) ;
M = [V0|L], foldl(minarg, L, V0-0-1, _Min-Off-_ ), MinArg = [Off] ).
minarg(New, Old-OPos-I0, Min-MPos-I) :- I is I0+1, ( New < Old -> New = Min, MPos = I0 ; Old = Min, MPos = OPos ).
matrix_to_logs(M, LogM) :-
( opaque(M) -> matrixn_to_logs( M, LogM ) ;
M = '$matrix'(A, B, D, E, C) ->
LogM = '$matrix'(A, B, D, E, LogC),
mapargs(log, C, LogC) ;
M = [V0|L] -> maplist(log, [V0|L], LogM ) ;
LogM is log(M) ).
log(X, Y) :- Y is log(X).
matrix_to_exps(M, ExpM) :-
( opaque(M) -> matrixn_to_exps( M, ExpM ) ;
M = '$matrix'(A, B, D, E, C) ->
ExpM = '$matrix'(A, B, D, E, ExpC),
mapargs(exp, C, ExpC) ;
M = [V0|L] -> maplist(exp, [V0|L], ExpM ) ;
ExpM is exp(M) ).
exp(X, Y) :- Y is exp(X).
matrix_agg_lines(M1,+,NM) :-
do_matrix_agg_lines(M1,0,NM).
/* other operations: *, logprod */
matrix_agg_cols(M1,+,NM) :-
do_matrix_agg_cols(M1,0,NM).
/* other operations: *, logprod */
matrix_op(M1,M2,+,NM) :-
( opaque(M1), opaque(M2) ->
do_matrix_op(M1,M2,0,NM) ;
matrix_m(M1, '$matrix'(A,B,D,E,C1)),
matrix_m(M2, '$matrix'(A,B,D,E,C2)),
mapargs(plus, C1, C2, C),
NM = '$matrix'(A,B,D,E,C) ).
matrix_op(M1,M2,-,NM) :-
( opaque(M1), opaque(M2) ->
do_matrix_op(M1,M2,1,NM) ;
matrix_m(M1, '$matrix'(A,B,D,E,C1)),
matrix_m(M2, '$matrix'(A,B,D,E,C2)),
mapargs(minus, C1, C2, C),
NM = '$matrix'(A,B,D,E,C) ).
matrix_op(M1,M2,*,NM) :-
( opaque(M1), opaque(M2) ->
do_matrix_op(M1,M2,2,NM) ;
matrix_m(M1, '$matrix'(A,B,D,E,C1)),
matrix_m(M2, '$matrix'(A,B,D,E,C2)),
mapargs(times, C1, C2, C),
NM = '$matrix'(A,B,D,E,C) ).
matrix_op(M1,M2,/,NM) :-
( opaque(M1), opaque(M2) ->
do_matrix_op(M1,M2,3,NM) ;
matrix_m(M1, '$matrix'(A,B,D,E,C1)),
matrix_m(M2, '$matrix'(A,B,D,E,C2)),
mapargs(div, C1, C2, C),
NM = '$matrix'(A,B,D,E,C) ).
matrix_op(M1,M2,zdiv,NM) :-
( opaque(M1), opaque(M2) ->
do_matrix_op(M1,M2,5,NM) ;
matrix_m(M1, '$matrix'(A,B,D,E,C1)),
matrix_m(M2, '$matrix'(A,B,D,E,C2)),
mapargs(zdiv, C1, C2, C),
NM = '$matrix'(A,B,D,E,C) ).
matrix_op_to_all(M1,+,Num,NM) :-
( opaque(M1) ->
do_matrix_op_to_all(M1,0,Num,NM)
;
M1 = '$matrix'(A,B,D,E,C),
mapargs(plus(Num), C, NC),
NM = '$matrix'(A,B,D,E,NC)
).
matrix_op_to_all(M1,-,Num,NM) :-
( opaque(M1) ->
do_matrix_op_to_all(M1,1,Num,NM)
;
M1 = '$matrix'(A,B,D,E,C),
mapargs(minus(Num), C, NC),
NM = '$matrix'(A,B,D,E,NC)
).
matrix_op_to_all(M1,*,Num,NM) :-
( opaque(M1) ->
do_matrix_op_to_all(M1,2,Num,NM)
;
M1 = '$matrix'(A,B,D,E,C),
mapargs(times(Num), C, NC),
NM = '$matrix'(A,B,D,E,NC)
).
matrix_op_to_all(M1,/,Num,NM) :-
% can only use floats.
FNum is float(Num),
( opaque(M1) ->
do_matrix_op_to_all(M1,3,FNum,NM)
;
M1 = '$matrix'(A,B,D,E,C),
mapargs(div(Num), C, NC),
NM = '$matrix'(A,B,D,E,NC)
).
/* other operations: *, logprod */
matrix_op_to_lines(M1,M2,/,NM) :-
do_matrix_op_to_lines(M1,M2,3,NM).
/* other operations: *, logprod */
matrix_op_to_cols(M1,M2,+,NM) :-
do_matrix_op_to_cols(M1,M2,0,NM).
/* other operations: *, logprod */
matrix_transpose(M1,M2) :-
matrix_shuffle(M1,[1,0],M2).
size(N0, N1, N2) :-
N2 is N0*N1.
% use 1 to get access to matrix
m_get('$matrix'(Dims, _, Sz, Bases, M), Indx, V) :-
foldl2(indx, Indx, Dims, Bases, Sz, _, 1, Offset),
arg(Offset, M, V).
m_set('$matrix'(Dims, _, Sz, Bases, M), Indx, V) :-
foldl2(indx, Indx, Dims, Bases, Sz, _, 1, Offset),
arg(Offset, M, V).
indx( I, Dim, Base, BlkSz, NBlkSz, I0, IF) :-
NBlkSz is BlkSz div Dim ,
IF is (I-Base)*NBlkSz + I0.
offset( I, Dim, BlkSz, NBlkSz, Base, I0, IF) :-
NBlkSz is BlkSz div Dim,
I is I0 div NBlkSz + Base,
IF is I0 rem NBlkSz.
inc(I1, I, I1) :-
I1 is I+1.
new_matrix(M0, Opts0, M) :-
opaque(M), !,
matrix_to_list(M0, L),
new_matrix(L, Opts0, M).
new_matrix('$matrix'(_,_,_,_,C), Opts0, M) :- !,
C =..[_|L],
new_matrix(L, Opts0, M).
new_matrix(C, Opts0, M) :-
functor(C, c, _), !,
C =..[_|L],
new_matrix(L, Opts0, M).
new_matrix(List, Opts0, M) :-
foldl2(el_list(MDims), List, Flat, [], 0, Dim), !,
fix_opts(Opts0, Opts),
foldl2(process_new_opt, Opts, Type, TypeF, [Dim|MDims], Dims, Base),
( var(TypeF) -> guess_type( Flat, Type ) ; true ),
matrix_new( Type, Dims, Flat, M),
( nonvar(Base) -> matrix_base(M, Base); true ).
new_matrix([H|List], Opts0, M) :-
length( [H|List], Size),
fix_opts(Opts0, Opts),
foldl2(process_new_opt(Base), Opts, Type, TypeF, [Size], Dims),
( var(TypeF) -> guess_type( [H|List], Type ) ; true ),
matrix_new( Type, Dims, [H|List], M),
( nonvar(Base) -> matrix_base(M, Base); true ).
fix_opts(V, _) :-
var(V), !,
throw(error(instantiation_error, V)).
fix_opts(A=B, [A=B]).
fix_opts(A, A) :-
is_list(A), !.
fix_opts(V, _) :-
var(V), !,
throw(error(domain_error(options=V), new_matrix)).
guess_type( List, Type ) :-
maplist( integer, List), !,
Type = ints.
guess_type( List, Type ) :-
maplist( number, List), !,
Type = floats.
guess_type( _List, terms ).
process_new_opt(_Base, dim=Dim, Type, Type, _, Dim) :- !.
process_new_opt(_Base, type=Type, _, Type, Dim, Dim) :- !.
process_new_opt( Base, base=Base, Type, Type, Dim, Dim) :- !.
process_new_opt(_Base, Opt, Type, Type, Dim, Dim) :-
throw(error(domain_error(opt=Opt), new_matrix)).
el_list(_, V, _Els, _NEls, _I0, _I1) :-
var(V), !,
fail.
el_list([N|Extra], El, Els, NEls, I0, I1) :-
foldl2(el_list(Extra), El, Els, NEls, 0, N), !,
I1 is I0+1.
el_list([N], El, Els, NEls, I0, I1) :-
El = [_|_],
length(El, N),
append(El, NEls, Els),
I1 is I0+1.
foreach( Domain, Goal) :-
strip_module(Goal, M, Locals^NG), !,
term_variables(Domain+Locals, LocalVarsL),
LocalVars =.. [vs|LocalVarsL],
iterate( Domain, [], LocalVars, M:NG, [], [] ),
terms:reset_variables( LocalVars ).
foreach( Domain, Goal ) :-
strip_module(Goal, M, NG),
term_variables(Domain, LocalVarsL),
LocalVars =.. [vs|LocalVarsL],
iterate( Domain, [], LocalVars, M:NG, [], [] ),
terms:reset_variables( LocalVars ).
foreach( Domain, Goal, Inp, Out) :-
strip_module(Goal, M, Locals^NG), !,
term_variables(Domain+Locals, LocalVarsL),
LocalVars =.. [vs|LocalVarsL],
iterate( Domain, [], LocalVars, M:NG, [], [], Inp, Out).
foreach( Domain, Goal, Inp, Out ) :-
strip_module(Goal, M, NG),
term_variables(Domain, LocalVarsL),
LocalVars =.. [vs|LocalVarsL],
iterate( Domain, [], LocalVars, M:NG, [], [], Inp, Out ).
iterate( [], [], LocalVars, Goal, Vs, Bs ) :-
terms:freshen_variables(LocalVars),
Vs = Bs,
MG <== Goal,
once( MG ),
terms:reset_variables(LocalVars).
iterate( [], [H|Cont], LocalVars, Goal, Vs, Bs ) :-
iterate(H, Cont, LocalVars, Goal, Vs, Bs ).
iterate( [H|L], [], LocalVars, Goal, Vs, Bs ) :- !,
iterate(H, L, LocalVars, Goal, Vs, Bs ).
iterate( [H|L], Cont, LocalVars, Goal, Vs, Bs ) :- !,
append(L, Cont, LCont),
iterate(H, LCont, LocalVars, Goal, Vs, Bs ).
iterate( [] ins _A .. _B, [H|L], LocalVars, Goal, Vs, Bs ) :- !,
iterate(H, L, LocalVars, Goal, Vs, Bs ).
iterate( [] ins _A .. _B, [], LocalVars, Goal, Vs, Bs ) :- !,
iterate([], [], LocalVars, Goal, Vs, Bs ).
iterate( [V|Ps] ins A..B, Cont, LocalVars, Goal, Vs, Bs ) :-
eval(A, Vs, Bs, NA),
eval(B, Vs, Bs, NB),
( NA > NB -> true ;
A1 is NA+1,
iterate( Ps ins NA..NB, Cont, LocalVars, Goal, [V|Vs], [NA|Bs] ),
iterate( [V|Ps] ins A1..NB, Cont, LocalVars, Goal, Vs, Bs )
).
iterate( V in A..B, Cont, LocalVars, Goal, Vs, Bs) :-
var(V),
eval(A, Vs, Bs, NA),
eval(B, Vs, Bs, NB),
( NA > NB -> true ;
A1 is NA+1,
(Cont = [H|L] ->
iterate( H, L, LocalVars, Goal, [V|Vs], [NA|Bs] )
;
iterate( [], [], LocalVars, Goal, [V|Vs], [NA|Bs] )
),
iterate( V in A1..NB, Cont, LocalVars, Goal, Vs, Bs )
).
iterate( [], [], LocalVars, Goal, Vs, Bs, Inp, Out ) :-
terms:freshen_variables(LocalVars),
Vs = Bs,
MG <== Goal,
once( call(MG, Inp, Out) ),
terms:reset_variables(LocalVars).
iterate( [], [H|Cont], LocalVars, Goal, Vs, Bs, Inp, Out ) :-
iterate(H, Cont, LocalVars, Goal, Vs, Bs, Inp, Out ).
iterate( [H|L], [], LocalVars, Goal, Vs, Bs, Inp, Out ) :- !,
iterate(H, L, LocalVars, Goal, Vs, Bs, Inp, Out ).
iterate( [H|L], Cont, LocalVars, Goal, Vs, Bs, Inp, Out ) :- !,
append(L, Cont, LCont),
iterate(H, LCont, LocalVars, Goal, Vs, Bs, Inp, Out ).
iterate( [] ins _A .. _B, [], LocalVars, Goal, Vs, Bs, Inp, Out ) :- !,
iterate([], [], LocalVars, Goal, Vs, Bs, Inp, Out ).
iterate( [] ins _A .. _B, [H|L], LocalVars, Goal, Vs, Bs, Inp, Out ) :- !,
iterate(H, L, LocalVars, Goal, Vs, Bs, Inp, Out ).
iterate( [V|Ps] ins A..B, Cont, LocalVars, Goal, Vs, Bs, Inp, Out ) :-
eval(A, Vs, Bs, NA),
eval(B, Vs, Bs, NB),
( NA > NB -> Inp = Out ;
A1 is NA+1,
iterate( Ps ins A..B, Cont, LocalVars, Goal, [V|Vs], [NA|Bs], Inp, Mid ),
iterate( [V|Ps] ins A1..NB, Cont, LocalVars, Goal, Vs, Bs, Mid, Out )
).
iterate( V in A..B, Cont, LocalVars, Goal, Vs, Bs, Inp, Out) :-
var(V),
eval(A, Vs, Bs, NA),
eval(B, Vs, Bs, NB),
( NA > NB -> Inp = Out ;
A1 is NA+1,
(Cont = [H|L] ->
iterate( H, L, LocalVars, Goal, [V|Vs], [NA|Bs], Inp, Mid )
;
iterate( [], [], LocalVars, Goal, [V|Vs], [NA|Bs], Inp, Mid )
),
iterate( V in A1..NB, Cont, LocalVars, Goal, Vs, Bs, Mid, Out )
).
eval(I, _Vs, _Bs, I) :- integer(I), !.
eval(I, Vs, Bs, NI) :-
copy_term(I+Vs, IA+Bs),
NI <== IA.
matrix_seq(A, B, Dims, M) :-
ints(A, B, L),
matrix_new(ints, Dims, L, M).
ints(A,B,O) :-
( A > B -> O = [] ; O = [A|L], A1 is A+1, ints(A1,B,L) ).
zero(_, 0).
/** @} */