%% PhS gh
%% Produit de matrices
%% échelle et étendue de l'image
60 setxunit
0 12 setxrange
-1 12 setyrange
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% définitions des couleurs
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/coul0 {noir} def
/coul1 {noir} def
/coul2 {bleu} def
/coul3 {rouge} def
/coul4 {vert} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% On définit les coefficients intéressants comme noeuds
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
coul1
0.2 setdboxit
(ai1) cnode
$a_{i1}$
1 3 [2.5 dup] cctexlabel
(ai2) cnode
$a_{i2}$
2 3 [2.5 dup] cctexlabel
(aip) cnode
$a_{ip}$
5 3 [2.5 dup] cctexlabel
(b1j) cnode
$b_{1j}$
9 10 [2.5 dup] cctexlabel
(b2j) cnode
$b_{2j}$
9 9 [2.5 dup] cctexlabel
(bpj) cnode
$b_{pj}$
9 6 [2.5 dup] cctexlabel
coul2
(ai1) (b1j) (<->) ncarc
(ai2) (b2j) (<->) ncarc
(aip) (bpj) (<->) ncarc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% On place les autres coefficients
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
.5 setlinewidth
pointilles
coul0
$a_{11}$
1 5 [2.5 dup] cctexlabel
$a_{12}$
2 5 [2.5 dup] cctexlabel
[2.5 5 4.5 5] (-) ligne
$a_{1p}$
5 5 [2.5 dup] cctexlabel
coul0
$a_{n1}$
1 1 [2.5 dup] cctexlabel
$a_{n2}$
2 1 [2.5 dup] cctexlabel
[2.5 1 4.5 1] (-) ligne
$a_{np}$
5 1 [2.5 dup] cctexlabel
coul0
$b_{11}$
7 10 [2.5 dup] cctexlabel
$b_{21}$
7 9 [2.5 dup] cctexlabel
[7 8.5 7 6.5] (-) ligne
$b_{p1}$
7 6 [2.5 dup] cctexlabel
coul0
$b_{1q}$
11 10 [2.5 dup] cctexlabel
$b_{2q}$
11 9 [2.5 dup] cctexlabel
[11 8.5 11 6.5] (-) ligne
$b_{pq}$
11 6 [2.5 dup] cctexlabel
[1 1.5 1 2.5] (-) ligne
[2 1.5 2 2.5] (-) ligne
[5 1.5 5 2.5] (-) ligne
[1 3.5 1 4.5] (-) ligne
[2 3.5 2 4.5] (-) ligne
[5 3.5 5 4.5] (-) ligne
[9.5 10 10.5 10] (-) ligne
[9.5 9 10.5 9] (-) ligne
[9.5 6 10.5 6] (-) ligne
[7.5 10 8.5 10] (-) ligne
[7.5 9 8.5 9] (-) ligne
[7.5 6 8.5 6] (-) ligne
coul3
$c_{ij}$
9 3 [2.5 dup] cctexlabel
coul1
pointilles
[2.5 3 4.5 3] (-) ligne
[9 6.5 9 8.5] (-) ligne
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% tracés autour de c22
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
coul2
.5 setlinewidth
continu
[.5 3.5 5.5 3.5] (-) ligne
[.5 2.5 5.5 2.5] (-) ligne
[8.5 5.5 8.5 10.5] (-) ligne
[9.5 5.5 9.5 10.5] (-) ligne
pointilles
[5.5 3.5 8.5 3.5] (-) ligne
[5.5 2.5 8.5 2.5] (-) ligne
[8.5 3.5 8.5 5.5] (-) ligne
[9.5 3.5 9.5 5.5] (-) ligne
2.5 setlinewidth
continu
[8.5 3.5 9.5 3.5] (-) ligne
[8.5 2.5 9.5 2.5] (-) ligne
[8.5 2.5 8.5 3.5] (-) ligne
[9.5 2.5 9.5 3.5] (-) ligne
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% tracés des parenthèses
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
coul1
1 setlinewidth
105 255 [.8 3 0.5 2.5 0] Ellipse
-75 75 [5.2 3 0.5 2.5 0] Ellipse
105 255 [6.8 8 0.5 2.5 0] Ellipse
-75 75 [11.2 8 0.5 2.5 0] Ellipse
coul3
105 255 [6.8 3 0.5 2.5 0] Ellipse
-75 75 [11.2 3 0.5 2.5 0] Ellipse
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Noms des matrices
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
18 setfontsize
coul1
$A$
3 0 [2.5 dup] cctexlabel
coul3
setTimes
(n lignes) 3 -.2 dltext
% (,) 3 -.2 dctext
coul2
setTimes
(p colonnes) 3 -.2 drtext
coul1
$B$
9 11.2 [2.5 dup] cctexlabel
coul2
setTimes
(p lignes) 9 11 dltext
% (,) ) 9 11 dctext
coul3
setTimes
(q colonnes) 9 11 drtext
coul1
$C=A\times B$
9 0 [2.5 dup] cctexlabel
coul3
setTimes
(n lignes) 9 -.2 dltext
% (,) 9 -.2 dctext
coul3
setTimes
(q colonnes) 9 -.2 drtext
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Formule du produit matriciel
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
coul1
$c_{ij}=\displaystyle\sum_{k=1}^p a_{ik}b_{kj}$
3 8 [2.5 dup] cctexlabel