%% PhS gh %% Produit de matrices %% échelle et étendue de l'image 60 setxunit 0 10 setxrange -1 10 setyrange %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% définitions des couleurs %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% /coul0 {0 0 0 0.5 setcmykcolor} def /coul1 {noir} def /coul2 {120 255 div 70 255 div 9 255 div setrgbcolor} def /coul3 {rouge} def /coul4 {bleu} def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% On définit les coefficients intéressants comme noeuds %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% coul1 0.2 setdboxit (a21) cnode $a_{21}$ 1 3 [2.5 dup] cctexlabel (a22) cnode $a_{22}$ 2 3 [2.5 dup] cctexlabel (a2p) cnode $a_{2p}$ 4 3 [2.5 dup] cctexlabel (b12) cnode $b_{12}$ 7 8 [2.5 dup] cctexlabel (b22) cnode $b_{22}$ 7 7 [2.5 dup] cctexlabel (bp2) cnode $b_{p2}$ 7 5 [2.5 dup] cctexlabel coul2 (a21) (b12) (<->) ncarc (a22) (b22) (<->) ncarc (a2p) (bp2) (<->) ncarc %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% On place les autres coefficients %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% .5 setlinewidth pointilles coul0 $a_{11}$ 1 4 [2.5 dup] cctexlabel $a_{12}$ 2 4 [2.5 dup] cctexlabel [2.5 4 3.5 4] (-) ligne $a_{1p}$ 4 4 [2.5 dup] cctexlabel coul0 $a_{n1}$ 1 1 [2.5 dup] cctexlabel $a_{n2}$ 2 1 [2.5 dup] cctexlabel [2.5 1 3.5 1] (-) ligne $a_{np}$ 4 1 [2.5 dup] cctexlabel coul0 $b_{11}$ 6 8 [2.5 dup] cctexlabel $b_{21}$ 6 7 [2.5 dup] cctexlabel [6 6.5 6 5.5] (-) ligne $b_{p1}$ 6 5 [2.5 dup] cctexlabel coul0 $b_{1q}$ 9 8 [2.5 dup] cctexlabel $b_{2q}$ 9 7 [2.5 dup] cctexlabel [9 6.5 9 5.5] (-) ligne $b_{pq}$ 9 5 [2.5 dup] cctexlabel [1 1.5 1 2.5] (-) ligne [2 1.5 2 2.5] (-) ligne [4 1.5 4 2.5] (-) ligne [7.5 8 8.5 8] (-) ligne [7.5 7 8.5 7] (-) ligne [7.5 5 8.5 5] (-) ligne coul3 $c_{22}$ 7 3 [2.5 dup] cctexlabel coul1 pointilles [2.5 3 3.5 3] (-) ligne [7 6.5 7 5.5] (-) ligne %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% tracés autour de c22 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% coul2 .5 setlinewidth continu [.5 3.5 4.5 3.5] (-) ligne [.5 2.5 4.5 2.5] (-) ligne [6.5 4.5 6.5 8.5] (-) ligne [7.5 4.5 7.5 8.5] (-) ligne pointilles [4.5 3.5 6.5 3.5] (-) ligne [4.5 2.5 6.5 2.5] (-) ligne [6.5 3.5 6.5 4.5] (-) ligne [7.5 3.5 7.5 4.5] (-) ligne 2.5 setlinewidth continu [7.5 3.5 6.5 3.5] (-) ligne [7.5 2.5 6.5 2.5] (-) ligne [6.5 2.5 6.5 3.5] (-) ligne [7.5 2.5 7.5 3.5] (-) ligne %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% tracés des parenthèses %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% coul1 1 setlinewidth 105 255 [.8 2.5 0.5 2 0] Ellipse -75 75 [4.2 2.5 0.5 2 0] Ellipse 105 255 [5.8 6.5 0.5 2 0] Ellipse -75 75 [9.2 6.5 0.5 2 0] Ellipse coul3 105 255 [5.8 2.5 0.5 2 0] Ellipse -75 75 [9.2 2.5 0.5 2 0] Ellipse %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Noms des matrices %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 18 setfontsize coul1 $A$ 2.5 0 [2.5 dup] cctexlabel coul3 setTimes (n lignes) 2.5 -.2 dltext % (,) 2.5 -.2 dctext coul2 setTimes (p colonnes) 2.5 -.2 drtext coul1 $B$ 7.5 9.2 [2.5 dup] cctexlabel coul2 setTimes (p lignes) 7.5 9 dltext % (,) ) 7.5 9 dctext coul3 setTimes (q colonnes) 7.5 9 drtext coul1 $C=A\times B$ 7.5 0 [2.5 dup] cctexlabel coul3 setTimes (n lignes) 7.5 -.2 dltext % (,) 7.5 -.2 dctext coul3 setTimes (q colonnes) 7.5 -.2 drtext %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Formule du produit matriciel %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% coul1 $c_{ij}=\displaystyle\sum_{k=1}^p a_{ik}b_{kj}$ 2.5 7.5 [2.5 dup] cctexlabel