Operation acting on arbitrary number of matrices, element-wise
$begingroup$
I have a certain number of $N times M$ matrices:
$$ M_1 = begin{pmatrix} a_{11} & a_{12} & ... & a_{1M} \
a_{21} & & & \
vdots & & ddots & \
a_{N1} & & & a_{NM}
end{pmatrix}
$$
$$ M_2 = begin{pmatrix} b_{11} & b_{12} & ... & b_{1M} \
b_{21} & & & \
vdots & & ddots & \
b_{N1} & & & b_{NM}
end{pmatrix}
$$
and I want to create a new matrix, applying a certain operation $f$ element by element, obtaining something like
$$ M = begin{pmatrix} f(a_{11},b_{11},...) & f(a_{12},b_{12},...) & ... & f(a_{1M},b_{1M},...) \
f(a_{21},b_{21},...) & & & \
vdots & & ddots & \
f(a_{N1},b_{N1},...) & & & f(a_{NM},b_{NM},...)
end{pmatrix}
$$
where the $f$ takes as many arguments as the number of matrices.
As of now I am implementing this using a Table,
With[{dims = Dimensions[dataA]}, Table[f[dataA[[x, y]], dataB[[x, y]], dataC[[x, y]]], {x, 1, dims[[1]]}, {y, 1, dims[[2]]}]]]
I was wondering if there's some more idiomatic Mathematica way of doing this.
matrix
asked Jan 22 at 16:14
zakkzakk
463514
$endgroup$
add a comment |
$begingroup$
I have a certain number of $N times M$ matrices:
$$ M_1 = begin{pmatrix} a_{11} & a_{12} & ... & a_{1M} \
a_{21} & & & \
vdots & & ddots & \
a_{N1} & & & a_{NM}
end{pmatrix}
$$
$$ M_2 = begin{pmatrix} b_{11} & b_{12} & ... & b_{1M} \
b_{21} & & & \
vdots & & ddots & \
b_{N1} & & & b_{NM}
end{pmatrix}
$$
and I want to create a new matrix, applying a certain operation $f$ element by element, obtaining something like
$$ M = begin{pmatrix} f(a_{11},b_{11},...) & f(a_{12},b_{12},...) & ... & f(a_{1M},b_{1M},...) \
f(a_{21},b_{21},...) & & & \
vdots & & ddots & \
f(a_{N1},b_{N1},...) & & & f(a_{NM},b_{NM},...)
end{pmatrix}
$$
where the $f$ takes as many arguments as the number of matrices.
As of now I am implementing this using a Table,
With[{dims = Dimensions[dataA]}, Table[f[dataA[[x, y]], dataB[[x, y]], dataC[[x, y]]], {x, 1, dims[[1]]}, {y, 1, dims[[2]]}]]]
I was wondering if there's some more idiomatic Mathematica way of doing this.
matrix
asked Jan 22 at 16:14
zakkzakk
463514
$endgroup$
add a comment |
$begingroup$
I have a certain number of $N times M$ matrices:
$$ M_1 = begin{pmatrix} a_{11} & a_{12} & ... & a_{1M} \
a_{21} & & & \
vdots & & ddots & \
a_{N1} & & & a_{NM}
end{pmatrix}
$$
$$ M_2 = begin{pmatrix} b_{11} & b_{12} & ... & b_{1M} \
b_{21} & & & \
vdots & & ddots & \
b_{N1} & & & b_{NM}
end{pmatrix}
$$
and I want to create a new matrix, applying a certain operation $f$ element by element, obtaining something like
$$ M = begin{pmatrix} f(a_{11},b_{11},...) & f(a_{12},b_{12},...) & ... & f(a_{1M},b_{1M},...) \
f(a_{21},b_{21},...) & & & \
vdots & & ddots & \
f(a_{N1},b_{N1},...) & & & f(a_{NM},b_{NM},...)
end{pmatrix}
$$
where the $f$ takes as many arguments as the number of matrices.
As of now I am implementing this using a Table,
With[{dims = Dimensions[dataA]}, Table[f[dataA[[x, y]], dataB[[x, y]], dataC[[x, y]]], {x, 1, dims[[1]]}, {y, 1, dims[[2]]}]]]
I was wondering if there's some more idiomatic Mathematica way of doing this.
matrix
asked Jan 22 at 16:14
zakkzakk
463514
$endgroup$
I have a certain number of $N times M$ matrices:
$$ M_1 = begin{pmatrix} a_{11} & a_{12} & ... & a_{1M} \
a_{21} & & & \
vdots & & ddots & \
a_{N1} & & & a_{NM}
end{pmatrix}
$$
$$ M_2 = begin{pmatrix} b_{11} & b_{12} & ... & b_{1M} \
b_{21} & & & \
vdots & & ddots & \
b_{N1} & & & b_{NM}
end{pmatrix}
$$
and I want to create a new matrix, applying a certain operation $f$ element by element, obtaining something like
$$ M = begin{pmatrix} f(a_{11},b_{11},...) & f(a_{12},b_{12},...) & ... & f(a_{1M},b_{1M},...) \
f(a_{21},b_{21},...) & & & \
vdots & & ddots & \
f(a_{N1},b_{N1},...) & & & f(a_{NM},b_{NM},...)
end{pmatrix}
$$
where the $f$ takes as many arguments as the number of matrices.
As of now I am implementing this using a Table,
With[{dims = Dimensions[dataA]}, Table[f[dataA[[x, y]], dataB[[x, y]], dataC[[x, y]]], {x, 1, dims[[1]]}, {y, 1, dims[[2]]}]]]
I was wondering if there's some more idiomatic Mathematica way of doing this.
matrix
matrix
asked Jan 22 at 16:14
zakkzakk
463514
asked Jan 22 at 16:14
zakkzakk
463514
asked Jan 22 at 16:14
zakkzakk
463514
asked Jan 22 at 16:14
zakkzakk
463514
asked Jan 22 at 16:14
zakkzakk
463514
463514
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
MapThread is designed to do exactly this. Example:
A = {{a11, a12}, {a21, a22}};
B = {{b11, b12}, {b21, b22}};
MapThread[f, {A, B}, 2]
Gives
{{f[a11, b11], f[a12, b12]}, {f[a21, b21], f[a22, b22]}}
The 2 is because you want to apply to elements of lists of lists. The arguments to "f" are 2 levels deep.
answered Jan 22 at 16:23
or1426or1426
1562
$endgroup$
$begingroup$
Exactly what I was looking for! Thanks!
$endgroup$
– zakk
Jan 22 at 17:10
add a comment |
$begingroup$
m1 = Array[a, {3, 3}];
m2 = Array[b, {3, 3}];
SetAttributes[foo, Listable]
foo[m1, m2] // MatrixForm // TeXForm
$left(
begin{array}{ccc}
text{foo}(a(1,1),b(1,1)) & text{foo}(a(1,2),b(1,2)) & text{foo}(a(1,3),b(1,3)) \
text{foo}(a(2,1),b(2,1)) & text{foo}(a(2,2),b(2,2)) & text{foo}(a(2,3),b(2,3)) \
text{foo}(a(3,1),b(3,1)) & text{foo}(a(3,2),b(3,2)) & text{foo}(a(3,3),b(3,3)) \
end{array}
right)$
answered Jan 22 at 16:25
kglrkglr
183k10202417
$endgroup$
$begingroup$
Thank you very much!
$endgroup$
– zakk
Jan 22 at 17:11
add a comment |
Your Answer
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
MapThread is designed to do exactly this. Example:
A = {{a11, a12}, {a21, a22}};
B = {{b11, b12}, {b21, b22}};
MapThread[f, {A, B}, 2]
Gives
{{f[a11, b11], f[a12, b12]}, {f[a21, b21], f[a22, b22]}}
The 2 is because you want to apply to elements of lists of lists. The arguments to "f" are 2 levels deep.
answered Jan 22 at 16:23
or1426or1426
1562
$endgroup$
$begingroup$
Exactly what I was looking for! Thanks!
$endgroup$
– zakk
Jan 22 at 17:10
add a comment |
$begingroup$
MapThread is designed to do exactly this. Example:
A = {{a11, a12}, {a21, a22}};
B = {{b11, b12}, {b21, b22}};
MapThread[f, {A, B}, 2]
Gives
{{f[a11, b11], f[a12, b12]}, {f[a21, b21], f[a22, b22]}}
The 2 is because you want to apply to elements of lists of lists. The arguments to "f" are 2 levels deep.
answered Jan 22 at 16:23
or1426or1426
1562
$endgroup$
$begingroup$
Exactly what I was looking for! Thanks!
$endgroup$
– zakk
Jan 22 at 17:10
add a comment |
$begingroup$
MapThread is designed to do exactly this. Example:
A = {{a11, a12}, {a21, a22}};
B = {{b11, b12}, {b21, b22}};
MapThread[f, {A, B}, 2]
Gives
{{f[a11, b11], f[a12, b12]}, {f[a21, b21], f[a22, b22]}}
The 2 is because you want to apply to elements of lists of lists. The arguments to "f" are 2 levels deep.
answered Jan 22 at 16:23
or1426or1426
1562
$endgroup$
MapThread is designed to do exactly this. Example:
A = {{a11, a12}, {a21, a22}};
B = {{b11, b12}, {b21, b22}};
MapThread[f, {A, B}, 2]
Gives
{{f[a11, b11], f[a12, b12]}, {f[a21, b21], f[a22, b22]}}
The 2 is because you want to apply to elements of lists of lists. The arguments to "f" are 2 levels deep.
answered Jan 22 at 16:23
or1426or1426
1562
answered Jan 22 at 16:23
or1426or1426
1562
answered Jan 22 at 16:23
or1426or1426
1562
answered Jan 22 at 16:23
or1426or1426
1562
1562
$begingroup$
Exactly what I was looking for! Thanks!
$endgroup$
– zakk
Jan 22 at 17:10
add a comment |
$begingroup$
Exactly what I was looking for! Thanks!
$endgroup$
– zakk
Jan 22 at 17:10
$begingroup$
Exactly what I was looking for! Thanks!
$endgroup$
– zakk
Jan 22 at 17:10
$begingroup$
Exactly what I was looking for! Thanks!
$endgroup$
– zakk
Jan 22 at 17:10
add a comment |
$begingroup$
m1 = Array[a, {3, 3}];
m2 = Array[b, {3, 3}];
SetAttributes[foo, Listable]
foo[m1, m2] // MatrixForm // TeXForm
$left(
begin{array}{ccc}
text{foo}(a(1,1),b(1,1)) & text{foo}(a(1,2),b(1,2)) & text{foo}(a(1,3),b(1,3)) \
text{foo}(a(2,1),b(2,1)) & text{foo}(a(2,2),b(2,2)) & text{foo}(a(2,3),b(2,3)) \
text{foo}(a(3,1),b(3,1)) & text{foo}(a(3,2),b(3,2)) & text{foo}(a(3,3),b(3,3)) \
end{array}
right)$
answered Jan 22 at 16:25
kglrkglr
183k10202417
$endgroup$
$begingroup$
Thank you very much!
$endgroup$
– zakk
Jan 22 at 17:11
add a comment |
$begingroup$
m1 = Array[a, {3, 3}];
m2 = Array[b, {3, 3}];
SetAttributes[foo, Listable]
foo[m1, m2] // MatrixForm // TeXForm
$left(
begin{array}{ccc}
text{foo}(a(1,1),b(1,1)) & text{foo}(a(1,2),b(1,2)) & text{foo}(a(1,3),b(1,3)) \
text{foo}(a(2,1),b(2,1)) & text{foo}(a(2,2),b(2,2)) & text{foo}(a(2,3),b(2,3)) \
text{foo}(a(3,1),b(3,1)) & text{foo}(a(3,2),b(3,2)) & text{foo}(a(3,3),b(3,3)) \
end{array}
right)$
answered Jan 22 at 16:25
kglrkglr
183k10202417
$endgroup$
$begingroup$
Thank you very much!
$endgroup$
– zakk
Jan 22 at 17:11
add a comment |
$begingroup$
m1 = Array[a, {3, 3}];
m2 = Array[b, {3, 3}];
SetAttributes[foo, Listable]
foo[m1, m2] // MatrixForm // TeXForm
$left(
begin{array}{ccc}
text{foo}(a(1,1),b(1,1)) & text{foo}(a(1,2),b(1,2)) & text{foo}(a(1,3),b(1,3)) \
text{foo}(a(2,1),b(2,1)) & text{foo}(a(2,2),b(2,2)) & text{foo}(a(2,3),b(2,3)) \
text{foo}(a(3,1),b(3,1)) & text{foo}(a(3,2),b(3,2)) & text{foo}(a(3,3),b(3,3)) \
end{array}
right)$
answered Jan 22 at 16:25
kglrkglr
183k10202417
$endgroup$
m1 = Array[a, {3, 3}];
m2 = Array[b, {3, 3}];
SetAttributes[foo, Listable]
foo[m1, m2] // MatrixForm // TeXForm
$left(
begin{array}{ccc}
text{foo}(a(1,1),b(1,1)) & text{foo}(a(1,2),b(1,2)) & text{foo}(a(1,3),b(1,3)) \
text{foo}(a(2,1),b(2,1)) & text{foo}(a(2,2),b(2,2)) & text{foo}(a(2,3),b(2,3)) \
text{foo}(a(3,1),b(3,1)) & text{foo}(a(3,2),b(3,2)) & text{foo}(a(3,3),b(3,3)) \
end{array}
right)$
answered Jan 22 at 16:25
kglrkglr
183k10202417
answered Jan 22 at 16:25
kglrkglr
183k10202417
answered Jan 22 at 16:25
kglrkglr
183k10202417
answered Jan 22 at 16:25
kglrkglr
183k10202417
183k10202417
$begingroup$
Thank you very much!
$endgroup$
– zakk
Jan 22 at 17:11
add a comment |
$begingroup$
Thank you very much!
$endgroup$
– zakk
Jan 22 at 17:11
$begingroup$
Thank you very much!
$endgroup$
– zakk
Jan 22 at 17:11
$begingroup$
Thank you very much!
$endgroup$
– zakk
Jan 22 at 17:11
add a comment |
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