Matlab and Mathematica equivalent commands
Remarks:
I prepare matrices m1, m2,
magic3, magic9 in Matlab and save them in
files
>> m1=rand(3)
m1 =
0.1386 0.8407 0.2435
0.1493 0.2543 0.9293
0.2575 0.8143 0.3500
>> m2=rand(3)
m2 =
0.1966 0.4733 0.5853
0.2511 0.3517 0.5497
0.6160 0.8308 0.9172
>> save 'm1.dat' m1 -ascii
>> save 'm2.dat' m2 -ascii
>> magic3=magic(3)
magic3 =
8 1 6
3 5 7
4 9 2
>> save 'magic3.dat' magic3 -ascii
>> magic9 = magic(9)
magic9 =
47 58 69 80 1 12 23 34 45
57 68 79 9 11 22 33 44 46
67 78 8 10 21 32 43 54 56
77 7 18 20 31 42 53 55 66
6 17 19 30 41 52 63 65 76
16 27 29 40 51 62 64 75 5
26 28 39 50 61 72 74 4 15
36 38 49 60 71 73 3 14 25
37 48 59 70 81 2 13 24 35
>> save 'magic9.dat' magic9 -ascii
then import them in Mathematica:
In[67]:= SetDirectory["~/Desktop"];
In[143]:= m1=Import["m1.dat","Data"];
m2=Import["m2.dat","Data"];
magic3=Import["magic3.dat","Data"];
magic9=Import["magic9.dat","Data"];
The following comparison uses the variables defined above:
| Matlab | Mathematica | remarks |
|---|---|---|
| "In Matlab, everything is a matrix." | "In Mathematica, everything is an expression." | |
[] |
{} |
empty list |
[1 2 3] |
{1, 2, 3} |
|
[1; 2; 3] |
{{1}, {2}, {3}} |
|
[1 2; 3 4] |
{{1, 2}, {3, 4}} |
|
% this is a comment |
(* this is a comment *) |
|
command1; command2; |
command1; command2; |
In both Mathematica and Matlab, ; indicates the
end of a command and suppresses its output. |
command1, command2 |
command1; command2 |
Matlab commands can be chained by ,; Mathematica
commands can't be chained by ,. |
'Hello world!' |
"Hello world!" |
Matlab uses single quote for string. Mathematica uses double. |
% this is a comment |
(* this is a comment *) |
|
command1; command2; |
command1; command2; |
In both Mathematica and Matlab, ; indicates the
end of a command and suppresses its output. |
command1, command2 |
command1; command2 |
Matlab commands can be chained by ,; Mathematica
commands can't be chained by ,. |
'Hello world!' |
"Hello world!" |
Matlab uses single quote for string. Mathematica uses double. |
5:2:25 or [5:2:25] |
Range[5, 25, 2] |
|
x(2:4) |
x[[2;;4]] |
|
x(2, 3) |
x[[2, 3]] |
|
x(:, 2) |
x[[All, 2]] |
|
x(2, :) |
x[[2, All]] |
|
x([1 3], :) |
x[[{1, 3}, All]] |
|
x(1:3, :) |
x[[1;;3, All]] |
|
x([1 3], [2 3]) |
x[[{1, 3}, {2, 3}]] |
|
x(:, 2) = [1; 2; 3] |
x = Join[x[[{1}]], Transpose[{1, 2, 3}], x[[All, 3;;]],
2] |
Mathematica needs x = explicitly to get
x updated |
x(:) |
Flatten[Transpose[x]] |
Concatenate columns to one column. |
y=x', y(:)' |
Flatten[x] |
Concatenate rows to one row. |
m=[1, 2; 3, 4; 1, 1]; size(m) |
m={{1, 2}, {3, 4}, {1, 1}}; Dimensions[m] |
matrix dimension |
[x [3; 5; 2]] |
Join[x, Transpose[{3, 5, 2}], 2] |
Append a column to a matrix, assuming there are 3 rows. |
[x' [1; 6]' |
Append[x, {1, 6}] |
Append a row to a matrix, assuming there are 2 columns |
[x y] |
Join[x, y, 2] |
Horizontally concatenate two matrices, assuming size(x,
1) equals size(y, 1) and Dimensions[x,
1] equals Dimensions[y, 1] |
m1*m2 |
m1.m2 |
Matrix multiplication, assuming m1 is n ×
m matrix and m2 is m × p
matrix. |
m1 .* m2 |
MapThread[Times, {m1, m2}] |
Elementwise matrix multiplication, assuming m1 and
m2 are n × m arrays. |
m .^ 2 |
Map[#^2&, m, {2}] |
Elementwise exponentiation. Notice by virtue of Listability
attribute of Power, Map[#^2&, m]
which is equivalent to Map[#^2&, m, 1] also
works. |
exp(m) |
Exp[m] or E^m |
Elementwise exponentiation. |
log(m) |
Log[m] |
Elementwise logrithm. |
abs(m) |
Abs[m] |
Elementwise absolute value. |
-m |
-m |
Elementwise negation. |
ones(3, 4) |
Table[1, {3}, {4}] |
Matrix of ones. |
m + 1 |
m + 1 |
Elementwise addition. m is a matrix. |
m' |
Transpose[m] |
Matrix transpose. |
pinv(m) |
Inverse[m] |
Matrix inverse. |
sum(m) |
Total[Transpose[matrix], {2}] |
Columnwise sum. |
sum(m,1) |
Total[Transpose[matrix], {2}] |
Columnwise sum. |
sum(m,2) |
List/@Total[matrix, {2}] |
Row-wise sum. |
prod(m) |
Apply[Times, m] or Times@@m |
Columnwise product. Times[{1, 3}, {2, 4}] has
threading behavior. |
floor(m) |
Floor[m] |
Elementwise flooring. |
ceil(m) |
Ceiling[m] |
Elementwise ceiling. |
max(m) |
Max /@ Transpose[m] |
Columnwise maximum. |
max(m1, m2) |
Table[Max[m1[[i, j]], m2[[i, j]]], {i, Length[m1]}, {j,
Length[Transpose[m1]]}] |
Elementwise maximum. |
max(magic3, [], 1) |
Max /@ Transpose[magic3] |
Columnwise maximum. |
max(magic3, [], 2) |
{Max[#]} & /@ magic3 |
Row-wise maximum. |
max(max(magic3)) or
max(magic3(:)) |
Max[magic3] |
Maximum matrix element. |
[maxval idx] = max(m) |
maxval = Max /@ Transpose[m]; idx =
MapThread[Position[##][[1,1]]&, {Transpose[m], Max /@
Transpose[m]}] |
|
m < 2 |
Map[#<2&, m, {2}] |
Elementwise test. Notice {2} isn't neglegible as
Less isn't Listable (Attributes[Less]
doesn't contain Listable). |
magic(3) |
A Mathematica program for constructing odd-order magic squares. | |
flipud(magic3) |
? | Flip matrix up/down direction. |
fliplr(magic3) |
? | Flip matrix left/right direction. |
magic3 = magic(3), find(m<5) |
Select[Flatten[Transpose[magic3]],
#<5&] |
Find positions of elements less than 3. |
[r,c] = find(magic3<5) |
{r, c} = {#[[All, 1, 1]], #[[All, 1, 2]]}
&[Position[magic3, #] & /@ Cases[magic3, _?(# > 5
&), {2}]] |
Why the ordering of results are different? |
eye(3) |
IdentityMatrix[3] |
Identity matrix. |
rand() |
RandomReal[] |
or rand |
rand(3) |
Table[RandomReal[], {3}, {3}] |
Create matrix with random reals. |
x = rand(2, 3) |
x = RandomReal[{0, 1}, {2, 3}] |
|
disp(m) or disp('hello') |
Print[m] or
Print["Hello"] |
|
who |
Names["*"] |
|
whos |
? | |
clear |
Clear[] |
|
clear('x') |
Clear[x] |
|
load('file.dat') |
Import["file.dat","Data"] |
file.dat contains tabulated numbers |
save file.mat x |
DumpSave["file.mx", x] |
|
save file.txt x --ascii |
Export["file.txt", "Data"] |
|
save file.mat x |
DumpSave["file.mx", x] |
|
matlab -nodesktop |
math (Linux), MathematicaKernel (Mac
OS X, Windows), or MathematicaScript -script |
Non-GUI session. |
MathematicaScript -script |
Scripting. | |
magic(3) |
A Mathematica program for constructing odd-order magic squares. | |
flipud(magic3) |
? | Flip matrix up/down direction. |
fliplr(magic3) |
? | Flip matrix left/right direction. |
magic3 = magic(3), find(m<5) |
Select[Flatten[Transpose[magic3]],
#<5&] |
Find positions of elements less than 3. |
[r,c] = find(magic3<5) |
{r, c} = {#[[All, 1, 1]], #[[All, 1, 2]]}
&[Position[magic3, #] & /@ Cases[magic3, _?(# > 5
&), {2}]] |
Why the ordering of results are different? |
eye(3) |
IdentityMatrix[3] |
Identity matrix. |
rand() |
RandomReal[] |
or rand |
rand(3) |
Table[RandomReal[], {3}, {3}] |
Create matrix with random reals. |
x = rand(2, 3) |
x = RandomReal[{0, 1}, {2, 3}] |
|
disp(m) |
Print[m] |
m is a matrix/expression. |
fprintf('hello world!\n') |
Print["Hello world!"]` | |
find(m > 1) |
Positions[m, _?(#>1&)] |
find indices of elements of matrix m that is
larger than 1 |
pack |
Share[] |
Consolidate memory. |
who |
Names["*"] |
|
whos |
? | |
clear |
Clear[] |
|
clear('x') |
Clear[x] |
|
load('file.dat') |
Import["file.dat","Data"] |
file.dat contains tabulated numbers |
save file.mat x |
DumpSave["file.mx", x] |
|
save file.txt x --ascii |
Export["file.txt", "Data"] |
|
save file.mat x |
DumpSave["file.mx", x] |
|
matlab -nodesktop |
math (Linux) MathematicaKernel (Mac
OS X, Windows), or MathematicaScript -script |
Non-GUI session. |