1% ------------------------------------------------------ 2% Package: matrix_utls 3% Title: Matrix utilities package consists of: 4% 1. Kronecker (Tensor) product, 5% 2. Hadamard (Element-Wise) product, 6% 3. Creating (MxN) matrix of empty cells, 7% 4. Creating (MxN) matrix of a unique (int/float/letters) value, 8% 5. Creating (MxN) matrix of random (int/float) values, 9% 6. Creating (MxM) Identity matrix, 10% 7. Scalar-by-Vector multiplication, 11% 8. Scalar-by-Matrix multiplication, 12% 9. Vector-by-Vector multiplication, 13% 10. Vector-by-Matrix multiplication, 14% 11. Matrix-by-Vector multiplication, and 15% 12. Matrix-by-Matrix multiplication. 16% Version: 1.1 17% Authors: Ali Al-Bayaty <albayaty@pdx.edu> 18% Marek Perkowski <h8mp@pdx.edu> 19% Electrical & Computer Engineering Dept. 20% Portland State University 21% Date: 02/25/2020 22% ------------------------------------------------------ 23 24 25:- module(matrix_utls, 26 [ kronecker/3, 27 hadamard/3, 28 create_empty_matrix/3, 29 create_val_matrix/4, 30 create_rand_matrix/5, 31 create_I_matrix/2, 32 s_v_multiply/3, 33 s_m_multiply/3, 34 v_v_multiply/3, 35 v_m_multiply/3, 36 m_v_multiply/3, 37 m_m_multiply/3 38 ]). 39 40 41% Saving and restoring the temporary results (facts) to/from the KB: 42:- dynamic outRes/1, subOutRes/1, addRes/1.
Where,
A is the input (multiplicand) matrix of size [GxH],
B is the input (multiplier) matrix of size [JxK], and
O is the output matrix of size [(GxJ)x(HxK)].
53kronecker(A, B, O):- 54 assert(outRes([])), 55 assert(subOutRes([])), 56 maplist(get_A_Rows(B), A), 57 retract(subOutRes(_)), 58 retract(outRes(O)). 59 60% Getting the rows of A: 61get_A_Rows(B, A_Row):- 62 maplist(get_B_Rows(A_Row), B). 63 64% Getting the cells from 1 row of A: 65get_A_Cells(B_Row, A_Cell):- 66 maplist(get_B_Cells(A_Cell), B_Row). 67 68% Getting the rows of B: 69get_B_Rows(A_Row, B_Row):- 70 maplist(get_A_Cells(B_Row), A_Row), 71 retract(outRes(Out)), 72 retract(subOutRes(SubOut)), 73 append(Out, [SubOut], FinalOut), 74 assert(subOutRes([])), 75 assert(outRes(FinalOut)). 76 77% Getting the cells from 1 row of B: 78get_B_Cells(A_Cell, B_Cell):- 79 % Element-wise cells multiplications: 80 R is A_Cell * B_Cell, 81 retract(subOutRes(SubOut)), 82 append(SubOut, [R], FinalSubOut), 83 assert(subOutRes(FinalSubOut)).
Where, A is the input (multiplicand) matrix of size [GxH], B is the input (multiplier) matrix of size [GxH], and O is the output matrix of size [GxH].
94hadamard(A, B, O):- 95 % Checking the dimensional equality: 96 checkRows(A ,B, Num_Rows), 97 checkCols(A, B, Num_Cols), 98 assert(outRes([])), 99 assert(subOutRes([])), 100 forall(between(1, Num_Rows, Row_Index), 101 doRows(A, B, Row_Index, Num_Cols)), 102 retract(subOutRes(_)), 103 retract(outRes(O)). 104 105% Checking the rows equality: 106checkRows(A, B, Num_A_Rows):- 107 length(A, Num_A_Rows), 108 length(B, Num_B_Rows), 109 ( Num_A_Rows =\= Num_B_Rows 110 -> writeln('\nError: Matrices do not have equal dimensionality (rows) ...\n'), 111 abort 112 ; ! ). 113 114% Checking the cols equality: 115checkCols(A, B, Num_A_Cols):- 116 nth1(1, A, A_Row), 117 nth1(1, B, B_Row), 118 length(A_Row, Num_A_Cols), 119 length(B_Row, Num_B_Cols), 120 ( Num_A_Cols =\= Num_B_Cols 121 -> writeln('\nError: Matrices do not have equal dimensionality (columns) ...\n'), 122 abort 123 ; !). 124 125doRows(A, B, Row_Index, Num_Cols):- 126 nth1(Row_Index, A, A_Row), 127 nth1(Row_Index, B, B_Row), 128 forall(between(1, Num_Cols, Col_Index), 129 doCols(A_Row, B_Row, Col_Index)), 130 retract(outRes(Out)), 131 retract(subOutRes(SubOut)), 132 append(Out, [SubOut], FinalOut), 133 assert(subOutRes([])), 134 assert(outRes(FinalOut)). 135 136doCols(A_Row, B_Row, Col_Index):- 137 nth1(Col_Index, A_Row, A_Cell), 138 nth1(Col_Index, B_Row, B_Cell), 139 R is A_Cell * B_Cell, 140 retract(subOutRes(SubOut)), 141 append(SubOut, [R], FinalSubOut), 142 assert(subOutRes(FinalSubOut)).
Where, Rows is the number of rows, Cols is the number of columns, and Mat is the resultant matrix of size [Rows x Cols].
153create_empty_matrix(Rows, Cols, Mat):-
154 length(Mat, Rows),
155 % Creating temporary Lists based on the number of rows:
156 maplist(create_list(Cols), Mat).
Where, Rows is the number of rows, Cols is the number of columns, and Mat is the resultant matrix of size [Rows x Cols].
167create_val_matrix(Rows, Cols, Mat, Value):-
168 create_empty_matrix(Rows, Cols, Mat),
169 setValue(Value, 1, Mat).
Where, Rows is the number of rows, Cols is the number of columns, and Mat is the resultant matrix of size [Rows x Cols].
180create_rand_matrix(Rows, Cols, Mat, Min_Value, Max_Value):- 181 create_empty_matrix(Rows, Cols, Mat), 182 setValue([Min_Value, Max_Value], 2, Mat). 183 184% Creating the columns of Mat: 185create_list(Cols, Sub_Mat):- 186 length(Sub_Mat, Cols). 187 188% Setting values for each cell of Mat: 189setValue(Value, Type, Mat):- 190 maplist(setRows(Value, Type), Mat). 191setRows(Value, Type, Mat_Rows):- 192 maplist(setCells(Value, Type), Mat_Rows). 193setCells(Value, 1, Mat_Cell):- Mat_Cell = Value, !. 194setCells(Value, 2, Mat_Cell):- 195 nth1(1, Value, Min_Value), 196 nth1(2, Value, Max_Value), 197 random(Min_Value, Max_Value, Mat_Cell), !.
Where, Dim is the number of rows and columns, and Mat is the resultant identity matrix of size [Dim x Dim].
207create_I_matrix(Dim, Mat):- 208 Dim_1 is Dim - 1, 209 create_val_matrix(1, Dim_1, Zeros, 0), 210 nth1(1, Zeros, Zero), 211 length(Mat, Dim), 212 numlist(1, Dim, Index), 213 maplist(insert_Ones(Zero), Index, Mat). 214 215insert_Ones(Zero, Index, Sub_Mat):- 216 nth1(Index, Sub_Mat, 1, Zero).
Where, S is the input (multiplicand) scalar (i.e. number), V is the input (multiplier) vector of size [1xH] or [Gx1], and O is the resultant vector of size [1xH] or [Gx1].
227s_v_multiply(S, V, O):-
228 s_m_multiply(S, V, O).
Where, S is the input (multiplicand) scalar (i.e. number), M is the input (multiplier) matrix of size [GxH], and O is the resultant matrix of size [GxH].
239s_m_multiply(S, M, O):- 240 assert(outRes([])), 241 assert(subOutRes([])), 242 length(M, M_Rows), 243 forall(between(1, M_Rows, Row_Index), do_Rows(S, M, Row_Index)), 244 retract(subOutRes(_)), 245 retract(outRes(O)). 246 247do_Rows(S, M, Row_Index):- 248 nth1(Row_Index, M, M_Row), 249 length(M_Row, M_Cols), 250 forall(between(1, M_Cols, Col_Index), do_Cols(S, M_Row, Col_Index)), 251 retract(outRes(Out)), 252 retract(subOutRes(SubOut)), 253 append(Out, [SubOut], FinalOut), 254 assert(subOutRes([])), 255 assert(outRes(FinalOut)). 256 257do_Cols(S, M_Row, Col_Index):- 258 nth1(Col_Index, M_Row, M_Cell), 259 R is S * M_Cell, 260 retract(subOutRes(SubOut)), 261 append(SubOut, [R], FinalSubOut), 262 assert(subOutRes(FinalSubOut)).
Where, V1 is the input (multiplicand) vector of size [1xJ] or [Kx1], V2 is the input (multiplier) vector of size [Jx1] or [1xK], and O is the resultant scalar of size [1x1] or matrix of size [KxK].
273v_v_multiply(V1, V2, O):-
274 m_m_multiply(V1, V2, O).
Where, V is the input (multiplicand) vector of size [1xJ], M is the input (multiplier) matrix of size [JxK], and O is the resultant vector of size [1xK].
285v_m_multiply(V, M, O):-
286 m_m_multiply(V, M, O).
Where, M is the input (multiplicand) matrix of size [JxK], V is the input (multiplier) vector of size [Kx1], and O is the resultant vector of size [Jx1].
297m_v_multiply(M, V, O):-
298 m_m_multiply(M, V, O).
Where, M1 is the input (multiplicand) matrix of size [GxH], M2 is the input (multiplier) matrix of size [HxJ], and O is the resultant matrix of size [GxJ].
309m_m_multiply(M1, M2, O):- 310 length(M1, Num_M1_Rows), 311 length(M2, Num_M2_Rows), 312 nth1(1, M1, M1_Row), 313 length(M1_Row, Num_M1_Cols), 314 nth1(1, M2, M2_Row), 315 length(M2_Row, Num_M2_Cols), 316 checkDim(Num_M1_Cols, Num_M2_Rows), 317 assert(outRes([])), 318 assert(subOutRes([])), 319 assert(addRes(0.0)), 320 forall(between(1, Num_M1_Rows, M1_Row_Index), 321 do_M1_Rows(M1, M2, M1_Row_Index, Num_M1_Cols, Num_M2_Cols)), 322 retract(addRes(_)), 323 retract(subOutRes(_)), 324 retract(outRes(O)). 325 326% Checking the equal dimensionality requirement: 327checkDim(Num_M1_Cols, Num_M2_Rows):- 328 ( Num_M1_Cols =\= Num_M2_Rows 329 -> writeln('\nError: Matrices do not have equal dimensionality requirement:'), 330 write('M1 cols = '), write(Num_M1_Cols), nl, 331 write('M2 rows = '), write(Num_M2_Rows), nl, 332 writeln('Hint: Both matrices should have equal dimensions (rows and cols).\n'), 333 abort 334 ; ! ). 335 336do_M1_Rows(M1, M2, M1_Row_Index, Num_M1_Cols, Num_M2_Cols):- 337 forall(between(1, Num_M2_Cols, M2_Col_Index), 338 do_M2_Col(M1, M2, M1_Row_Index,Num_M1_Cols, M2_Col_Index)), 339 retract(outRes(Out)), 340 retract(subOutRes(SubOut)), 341 append(Out, [SubOut], FinalOut), 342 assert(subOutRes([])), 343 assert(outRes(FinalOut)). 344 345do_M2_Col(M1, M2, M1_Row_Index,Num_M1_Cols, M2_Col_Index):- 346 nth1(M1_Row_Index, M1, M1_Row), 347 forall(between(1, Num_M1_Cols, M1_Col_Index), 348 doMultiply(M1_Row, M2, M1_Col_Index, M2_Col_Index)), 349 retract(subOutRes(SubOut)), 350 retract(addRes(SubAdd)), 351 append(SubOut, [SubAdd], FinalSubOut), 352 assert(addRes(0.0)), 353 assert(subOutRes(FinalSubOut)). 354 355doMultiply(M1_Row, M2, M1_Col_Index, M2_Col_Index):- 356 nth1(M1_Col_Index, M1_Row, M1_Cell), 357 nth1(M1_Col_Index, M2, M2_Row), 358 nth1(M2_Col_Index, M2_Row, M2_Cell), 359 R is M1_Cell * M2_Cell, 360 retract(addRes(SubAdd)), 361 Out is SubAdd + R, 362 assert(addRes(Out)). 363 364 365% ------------------------------------------------------ 366% %%%%%%%%%%%%%%%%%%% EXAMPLES %%%%%%%%%%%%%%%%%%%%%%%%% 367% ------------------------------------------------------ 368% ?- kronecker([[1,2],[2,-1]], [[1,2],[3,4]], M). 369% M = [[1, 2, 2, 4], 370% [3, 4, 6, 8], 371% [2, 4, -1, -2], 372% [6, 8, -3, -4]]. 373% 374% ?- hadamard([[1,2],[2,-1]], [[1,2],[3,4]], M). 375% M = [[1, 4], 376% [6, -4]]. 377% 378% ?- create_empty_matrix(2, 3, M). 379% M = [[_928, _934, _940], 380% [_946, _952, _958]]. 381% 382% ?- create_val_matrix(2, 3, M, 1). 383% M = [[1, 1, 1], 384% [1, 1, 1]]. 385% 386% ?- create_val_matrix(2, 3, M, Aa). 387% M = [[Aa, Aa, Aa], 388% [Aa, Aa, Aa]]. 389% 390% ?- create_rand_matrix(2, 3, M, -2.0, 2.0). 391% M = [[-0.331722127869, 1.2472310874774, -0.3789740703109], 392% [0.04395141605513, 0.5567944218039, -0.27190713107775]]. 393% 394% ?- create_I_matrix(3, M). 395% M = [[1, 0, 0], 396% [0, 1, 0], 397% [0, 0, 1]]. 398% 399% ?- s_v_multiply(5, [[1, 2, 3]], M). 400% M = [[5, 10, 15]]. 401% 402% ?- s_v_multiply(5, [[1], [2], [3]], M). 403% M = [[5], 404% [10], 405% [15]]. 406% 407% ?- s_m_multiply(5, [[1,2,3], [4,5,6]], M). 408% M = [[5, 10, 15], 409% [20, 25, 30]]. 410% 411% ?- v_v_multiply([[1, 2, 3]], [[1], [2], [3]], M). 412% M = [[14.0]]. 413% 414% ?- v_v_multiply([[1], [2], [3]], [[1, 2, 3]], M). 415% M = [[1.0, 2.0, 3.0], 416% [2.0, 4.0, 6.0], 417% [3.0, 6.0, 9.0]]. 418% 419% ?- v_m_multiply([[1, 2, 3]], [[1,2], [3,4], [5,6]], M). 420% M = [[22.0, 28.0]]. 421% 422% ?- m_v_multiply([[1,2], [3,4], [5,6]], [[1], [2]], M). 423% M = [[5.0], 424% [11.0], 425% [17.0]]. 426% 427% ?- m_m_multiply([[1,2,3],[4,5,6],[7,8,9]], 428% [[1,0,0],[0,1,0],[0,0,1]], M). 429% M = [[1.0, 2.0, 3.0], 430% [4.0, 5.0, 6.0], 431% [7.0, 8.0, 9.0]]. 432% 433% ------------------------------------------------------