A
1
, A
2
, ... )
komanda ishlatiladi. Bu holda A1, A2, ..., matritsalar ko’rsatilgan o’lchov bo’yicha
birlashtiriladi:
cat (2, A, V) = [A, V] cat (1, A,
V) = [A; V]
Matlabda matritsalarni burish uchun fliplr (A), flipud (A) komandalaridan
foydalaniladi. fliplr (A) komandasi A matritsani chapdan o’ngga ustunlarini
almashtirish yo’nalishida buradi. flipud (A) esa A matritsani pastdan yuqoriga
qatorlarini almashtirish yo’nalishida buradi. Masalan, A quyidagicha bo’lsin:
A= [ 2 3 7 1 9 0]
U holda fliplr (A) q [9 0; 7 1; 2 3] , flipud (A) q [3 2 ; 1 7; 0 9] kabi
bo’ladi. Byerilgan matritsani soat stryelkasiga qarshi 900 ga buruvchi rot 90 (A)
komandasidir.
Misol: B=[1 3 5 7 1 9 2 3 4];
rot 90(B)=[5 1 4 ; 3 9 3 ; 1 7 2];
Undan tashqari matlabda maxsus ko’rinishdagi matritsalarni hosil qilish imkoniyati
bor. Ana shunday matritsalarni hosil qiluvchi komandalarni kyeltirib o’tamiz:
-
size (A) – A matritsaning o’lchovi;
-
length (A) –A vyektor uzunligi (elyemyentlar soni);
-
ndims (A) – A matritsa o’lchovlari soni;
-
isempty (A) – A matritsa bo’sh bo’lsa 1, aks holda 0 qiymatni byeradi;
-
isegual (A, V) – A=V bo’lsa 1 ni byeradi, aks xolda “0” ni byeradi;
inumeric (A) – A matritsa sonli tipda bo’lsa 1 ni byeradi, aks holda “0” ni
byeradi; Namunalar:
1 – misol: Berilgan A va B matritsalarni bir biriga ko’paytirish:
147
>> A=[-1 0 1; 0 -1 0; 1 -1 1]
A =
-1
0 1
0
-1 0
1
-1 1
>> B=[1 1 0; 2 -1 0; 3 0 1]
B =
-1
1 0
2 -1 0
3 0 1
>> A*B ans =
2 -1 1
-2 1 0
2 2 1
Endi shu amalni algoritmi haqida ya’ni o’z qo’limiz yordamida bajaramiz:
>> for i=1:3; for j=1:3; C(i,j)=0; for k=1:3; C(i,j)=C(i,j)+A(i,k)*B(k,j); end; end; end;
C C =
2
-1 1
-2 1 0
2 2 1
2-Misol: A va B matritsalarni bir-biriga qo’shish
>> A=[-1 0 1; 0 -1 0; 1 -1 1];
>> B=[1 1 0; 2 -1 0; 3 0 1];
>> A+B ans =
0 1 1
2
-2 0
4
-1 2
Endi shu matritsalarni qo’shish amalini algoritmini o’zimiz bajarib ko’ramiz:
>> for i=1:3; for j=1:3; C(i,j)=A(i,j)+B(i,j);end; end; C
C =
0 1 1
2
-2 0
4
-1 2
3 – misol: Matlabda matritsalarni chapdan o’ngga burishda fliplr komandasidan
foydalanish:
>> A=[-1 0 1; 0 -1 0; 1 -1 1]
A =
-1 0 1
0
-1 0
1
1
-1
>> fliplr(A) ans
=
2
0
-1
0
-1 0
148
1 -1 1
Endi shu komandani qo’lda bajarib chiqamiz:
>> for i=1:3; for j=1:3; C(i,j)=A(3-i+1,j);end; end; C
C =
1
-1 1
0
-1 0
1
0 1
4 - misol: Matlabda matritsalarni yuqoridan
pastga burishda flipud
komandasidan foydalanish:
>> A=[-1 0 1; 0 -1 0; 1 -1 1]
A =
-1 0 1
0 -1 0
1 -1 1
>> flipud(A)
ans =
1 -1 1
0 -1 0
- 1 0 1
Endi shu amalni algoritmi bilan tanishib chiqamiz:
>> for i=1:3; for j=1:3; C(j,i)=A(j,3-i+1); end; end; C
C =
1 0
-1
0
-1 0
1
-1 1
5 – misol: Berilgan matritsani soat strelkasiga qarshi 90
0
ga burish uchun
ishlatiladigan rot90(A) komandasi:
>> A=[-1 0 1; 0 -1 0; 1 -1 1]
A =
-1 0 1
0 -1 0
1 -1 1
>> rot90(A)
ans =
1 0 1
0
-1
-1
-1 0 1
Endi shu amalning bajarilish tartibi ya’ni algoritmi haqida:
149
>> for i=1:3; for j=1:3; C(i,j)=A(j,3-i+1); end; end; C
C =
1 0 1
0
-1
-1
1
0 1
Undan tashqari matlabda maxsus ko’rinishdagi
matritsalarni hosil qilish
imkoniyati bor. Ana shunday matritsalarni hosil qiluvchi komandalarni kyeltirib
o’tamiz:
>> A=[-1 0 1; 0 -1 0; 1 -1 1]
A =
-1 0 1
0
-1 0
1
-1 1
>> size(A)
ans =
3 3
>> length(A)
ans = 3
>> ndims(A)
ans =
2
>> isempty(A)
ans =
0
6 - misol: diag(A) komandasi berilgan matritsaning diagonalida tugan
elementlarni ekranga chiqaradi:
>> A=[-1 0 1; 0 -1 0; 1 -1 1]
A =
-1 0 1
0
-1 0
1
-1 1
>> diag(A)
ans =
-1
-1 1
Shu amalni o’zimiz bajarib chqamiz:
>> for i=1:3; D(i)=A(i,i);end; D
D =
-1
-1 1
150
7 – misol: eye(n) komandasi birlik matritsa hosil qilish:
>> eye(5)
ans =
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1
0
0
0 0 0 1
Endi shu matritsani m-faylga funksiyasini yaratamiz:
Ushbu m-faylga birlik matritsa hosil qiladigan
protsedura yasadik va uning
nomini diagonal.m deb nomladik. Endi bu m-fayl yordamida diagonal(n)
komandasi hosil bo’ldi. Endi ushbu komanda yordamida ham eye(n)
komandasining bajargan ishini bajarsa bo’ladi: >> diagonal(5) ans =
1
0
0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0
0
0 1
8-misol: Berilgan matritsaning diagonaildan yuqori qismini elementlarini 0 bilan
almashtirish:
>> A=[-1 2 4 0 3; -2 1 0 3 4; -2 -1 0 -2 1; -2 3 -1 -1 1; 1 1 1 -1 -1]
A =
151
-1 2 4 0 3
-2 1 0 3 4
-2
-1 0
-2 1
-2 3
-1
-1 1
1 1 1
-1
-1
>> tril(A)
ans =
-1
0 0 0 0
-2
1 0 0 0
-2
-1 0 0 0
-2 3
-1
-1 0
1 1 1
-1
-1
Endi shu komandani o’zimiz m-faylga yozib yangi yuqori degan komanda hosil
qilamiz :
>> B=yuqori(A)
x =
5
B =
-1
0 0 0 0
-2
1 0 0 0
-2
-1 0 0 0
152
-2 3
-1
-1 0
1 1
1
-1
-1
9 – misol :triu komandasi esa matritsaning diagonalidan pastki qismini
nollarga aylantiradi:
>> A=[-1 2 4 0 3; -2 1 0 3 4; -2 -1 0 -2 1; -2 3 -1 -1 1; 1 1 1 -1 -1]
A =
-1
2 4 0
-2
1 0 3
2 -1 0
147
2 -1 1
147
1 -1 1
148
>>
flipud(
A) ans
= 148
-1 2 4 0 3 151
0 0 0
-1 1
0 0 0 0
-1
Ushbu triu protsedurasini algoritmini o’zimiz tuzib m-faylga yozib chiqamiz va
quyidagi natijalarga erishamiz:
>>
B=pastki(A)
x =
5
153
B =
-1
2 4 0 3
0 1 0 3 4
0 0 0
-2 1
0 0 0
-1 1
0 0 0 0
-1
10 – misol :
RESHAPE – matrisa o’lchamini o’zgartish :
>> A=[-1 0 2 0; 0 1 2 -1; -1 -2 -3 2]
A =
-1 0 2 0
0 1 2
-1
-1
-2
-3 2
>> reshape(A,2,6)
ans =
-1
-1 1 2
-3
-1
0
0
-2 2 0 2
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