Fast element-wise division of matrix, generated from vector with `Outer`, and another matrix
up vote
4
down vote
favorite
m = {a, b, c};
n = {{e, r, t}, {y, u, i}, {g, h, j}};
k = Outer[Divide, m, m];
k/n
gives
{{1/e, a/(b r), a/(c t)}, {b/(a y), 1/u, b/(c i)}, {c/(a g), c/(b h),
1/j}}
I want to do this with very large matrices filled with numbers of arbitrary precision. Is there a faster way?
EDIT
The sizes I am looking at for my practical applications start at 20000 and 20000^2 for the vector and matrix, respectively (of course the examples don't have to be with that many).
I am also interested in any method that might parallelise well.
list-manipulation matrix performance-tuning array
asked 8 hours ago
ThunderBiggi
376112
add a comment |
up vote
4
down vote
favorite
m = {a, b, c};
n = {{e, r, t}, {y, u, i}, {g, h, j}};
k = Outer[Divide, m, m];
k/n
gives
{{1/e, a/(b r), a/(c t)}, {b/(a y), 1/u, b/(c i)}, {c/(a g), c/(b h),
1/j}}
I want to do this with very large matrices filled with numbers of arbitrary precision. Is there a faster way?
EDIT
The sizes I am looking at for my practical applications start at 20000 and 20000^2 for the vector and matrix, respectively (of course the examples don't have to be with that many).
I am also interested in any method that might parallelise well.
list-manipulation matrix performance-tuning array
asked 8 hours ago
ThunderBiggi
376112
What is the length ofmin practical use?
– Αλέξανδρος Ζεγγ
5 hours ago
You can trym/(n ConstantArray[m, Length[m]])and see how fast it is.
– C. E.
2 hours ago
@ΑλέξανδροςΖεγγ I editted my question to include some information on that.
– ThunderBiggi
1 hour ago
add a comment |
up vote
4
down vote
favorite
up vote
4
down vote
favorite
m = {a, b, c};
n = {{e, r, t}, {y, u, i}, {g, h, j}};
k = Outer[Divide, m, m];
k/n
gives
{{1/e, a/(b r), a/(c t)}, {b/(a y), 1/u, b/(c i)}, {c/(a g), c/(b h),
1/j}}
I want to do this with very large matrices filled with numbers of arbitrary precision. Is there a faster way?
EDIT
The sizes I am looking at for my practical applications start at 20000 and 20000^2 for the vector and matrix, respectively (of course the examples don't have to be with that many).
I am also interested in any method that might parallelise well.
list-manipulation matrix performance-tuning array
asked 8 hours ago
ThunderBiggi
376112
m = {a, b, c};
n = {{e, r, t}, {y, u, i}, {g, h, j}};
k = Outer[Divide, m, m];
k/n
gives
{{1/e, a/(b r), a/(c t)}, {b/(a y), 1/u, b/(c i)}, {c/(a g), c/(b h),
1/j}}
I want to do this with very large matrices filled with numbers of arbitrary precision. Is there a faster way?
EDIT
The sizes I am looking at for my practical applications start at 20000 and 20000^2 for the vector and matrix, respectively (of course the examples don't have to be with that many).
I am also interested in any method that might parallelise well.
list-manipulation matrix performance-tuning array
list-manipulation matrix performance-tuning array
asked 8 hours ago
ThunderBiggi
376112
asked 8 hours ago
ThunderBiggi
376112
edited 1 hour ago
asked 8 hours ago
ThunderBiggi
376112
asked 8 hours ago
ThunderBiggi
376112
asked 8 hours ago
ThunderBiggi
376112
376112
What is the length ofmin practical use?
– Αλέξανδρος Ζεγγ
5 hours ago
You can trym/(n ConstantArray[m, Length[m]])and see how fast it is.
– C. E.
2 hours ago
@ΑλέξανδροςΖεγγ I editted my question to include some information on that.
– ThunderBiggi
1 hour ago
add a comment |
What is the length ofmin practical use?
– Αλέξανδρος Ζεγγ
5 hours ago
You can trym/(n ConstantArray[m, Length[m]])and see how fast it is.
– C. E.
2 hours ago
@ΑλέξανδροςΖεγγ I editted my question to include some information on that.
– ThunderBiggi
1 hour ago
What is the length of
m in practical use?– Αλέξανδρος Ζεγγ
5 hours ago
What is the length of
m in practical use?– Αλέξανδρος Ζεγγ
5 hours ago
You can try
m/(n ConstantArray[m, Length[m]]) and see how fast it is.– C. E.
2 hours ago
You can try
m/(n ConstantArray[m, Length[m]]) and see how fast it is.– C. E.
2 hours ago
@ΑλέξανδροςΖεγγ I editted my question to include some information on that.
– ThunderBiggi
1 hour ago
@ΑλέξανδροςΖεγγ I editted my question to include some information on that.
– ThunderBiggi
1 hour ago
add a comment |
2 Answers
2
active
oldest
votes
up vote
3
down vote
Pretty printing your result gives...
{{1/e, a/(b r), a/(c t)}, {b/(a y), 1/u, b/(c i)}, {c/(a g), c/(b h),1/j}}//MatrixForm
$left(
begin{array}{ccc}
frac{1}{e} & frac{a}{b r} & frac{a}{c t} \
frac{b}{a y} & frac{1}{u} & frac{b}{c i} \
frac{c}{a g} & frac{c}{b h} & frac{1}{j} \
end{array}
right)$
Try this, it avoids constructing the huge Outer[ ] matrix
Map[#/m &, MapThread[#1 #2 &, {m, 1/n}]] // MatrixForm
$left(
begin{array}{ccc}
frac{1}{e} & frac{a}{b r} & frac{a}{c t} \
frac{b}{a y} & frac{1}{u} & frac{b}{c i} \
frac{c}{a g} & frac{c}{b h} & frac{1}{j} \
end{array}
right)$
answered 7 hours ago
MikeY
1,762410
add a comment |
up vote
3
down vote
m = RandomReal[{-1, 1}, {2000}];
n = RandomReal[{-1, 1}, {2000, 2000}];
a = Outer[Divide, m, m]/n; // RepeatedTiming // First
b = Map[#/m &, MapThread[#1 #2 &, {m, 1/n}]]; //
RepeatedTiming // First
c = m /(ConstantArray[m, Length[m]] n); // RepeatedTiming // First
d = KroneckerProduct[m, 1./m]/n; // RepeatedTiming // First
a == b == c == d
0.958
0.128
0.0281
0.0236
True
Edit
A parallelized version
cf = Compile[{{x, _Real}, {y, _Real, 1}, {z, _Real, 1}},
x/(y z),
CompilationTarget -> "C",
RuntimeAttributes -> {Listable},
Parallelization -> True,
RuntimeOptions -> "Speed"
];
e = cf[m, n, m]; // RepeatedTiming // First
a == e
0.0096
True
Timing has been measured on a Quad Core CPU which shows that this does not scale too well. Btw., the timing with CompilationTarget -> "C" is only 4% slower, so there is always no point to compile it into a library.
answered 1 hour ago
Henrik Schumacher
47.3k466134
I was just typing a comparison of the answers so far, but you were first. I wouldn't've expected thatKroneckerProductwould be that quick. Any ideas on any way that might parallelise well? I will edit my question to include that as well.
– ThunderBiggi
1 hour ago
See my edit for a parallelized version.
– Henrik Schumacher
1 hour ago
I am using arbitrary precision numbers, so I guess 'Compile' is not really an option.
– ThunderBiggi
28 mins ago
Also, interestingly, but on my machine, with Mathematica 11.3,ais faster thanbthough still slower than the other two.
– ThunderBiggi
23 mins ago
Yeah, I was also surprised thatawas so slow on my machine. I don't know what to think about it...
– Henrik Schumacher
15 mins ago
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
Pretty printing your result gives...
{{1/e, a/(b r), a/(c t)}, {b/(a y), 1/u, b/(c i)}, {c/(a g), c/(b h),1/j}}//MatrixForm
$left(
begin{array}{ccc}
frac{1}{e} & frac{a}{b r} & frac{a}{c t} \
frac{b}{a y} & frac{1}{u} & frac{b}{c i} \
frac{c}{a g} & frac{c}{b h} & frac{1}{j} \
end{array}
right)$
Try this, it avoids constructing the huge Outer[ ] matrix
Map[#/m &, MapThread[#1 #2 &, {m, 1/n}]] // MatrixForm
$left(
begin{array}{ccc}
frac{1}{e} & frac{a}{b r} & frac{a}{c t} \
frac{b}{a y} & frac{1}{u} & frac{b}{c i} \
frac{c}{a g} & frac{c}{b h} & frac{1}{j} \
end{array}
right)$
answered 7 hours ago
MikeY
1,762410
add a comment |
up vote
3
down vote
Pretty printing your result gives...
{{1/e, a/(b r), a/(c t)}, {b/(a y), 1/u, b/(c i)}, {c/(a g), c/(b h),1/j}}//MatrixForm
$left(
begin{array}{ccc}
frac{1}{e} & frac{a}{b r} & frac{a}{c t} \
frac{b}{a y} & frac{1}{u} & frac{b}{c i} \
frac{c}{a g} & frac{c}{b h} & frac{1}{j} \
end{array}
right)$
Try this, it avoids constructing the huge Outer[ ] matrix
Map[#/m &, MapThread[#1 #2 &, {m, 1/n}]] // MatrixForm
$left(
begin{array}{ccc}
frac{1}{e} & frac{a}{b r} & frac{a}{c t} \
frac{b}{a y} & frac{1}{u} & frac{b}{c i} \
frac{c}{a g} & frac{c}{b h} & frac{1}{j} \
end{array}
right)$
answered 7 hours ago
MikeY
1,762410
add a comment |
up vote
3
down vote
up vote
3
down vote
Pretty printing your result gives...
{{1/e, a/(b r), a/(c t)}, {b/(a y), 1/u, b/(c i)}, {c/(a g), c/(b h),1/j}}//MatrixForm
$left(
begin{array}{ccc}
frac{1}{e} & frac{a}{b r} & frac{a}{c t} \
frac{b}{a y} & frac{1}{u} & frac{b}{c i} \
frac{c}{a g} & frac{c}{b h} & frac{1}{j} \
end{array}
right)$
Try this, it avoids constructing the huge Outer[ ] matrix
Map[#/m &, MapThread[#1 #2 &, {m, 1/n}]] // MatrixForm
$left(
begin{array}{ccc}
frac{1}{e} & frac{a}{b r} & frac{a}{c t} \
frac{b}{a y} & frac{1}{u} & frac{b}{c i} \
frac{c}{a g} & frac{c}{b h} & frac{1}{j} \
end{array}
right)$
answered 7 hours ago
MikeY
1,762410
Pretty printing your result gives...
{{1/e, a/(b r), a/(c t)}, {b/(a y), 1/u, b/(c i)}, {c/(a g), c/(b h),1/j}}//MatrixForm
$left(
begin{array}{ccc}
frac{1}{e} & frac{a}{b r} & frac{a}{c t} \
frac{b}{a y} & frac{1}{u} & frac{b}{c i} \
frac{c}{a g} & frac{c}{b h} & frac{1}{j} \
end{array}
right)$
Try this, it avoids constructing the huge Outer[ ] matrix
Map[#/m &, MapThread[#1 #2 &, {m, 1/n}]] // MatrixForm
$left(
begin{array}{ccc}
frac{1}{e} & frac{a}{b r} & frac{a}{c t} \
frac{b}{a y} & frac{1}{u} & frac{b}{c i} \
frac{c}{a g} & frac{c}{b h} & frac{1}{j} \
end{array}
right)$
answered 7 hours ago
MikeY
1,762410
answered 7 hours ago
MikeY
1,762410
answered 7 hours ago
MikeY
1,762410
answered 7 hours ago
MikeY
1,762410
1,762410
add a comment |
add a comment |
up vote
3
down vote
m = RandomReal[{-1, 1}, {2000}];
n = RandomReal[{-1, 1}, {2000, 2000}];
a = Outer[Divide, m, m]/n; // RepeatedTiming // First
b = Map[#/m &, MapThread[#1 #2 &, {m, 1/n}]]; //
RepeatedTiming // First
c = m /(ConstantArray[m, Length[m]] n); // RepeatedTiming // First
d = KroneckerProduct[m, 1./m]/n; // RepeatedTiming // First
a == b == c == d
0.958
0.128
0.0281
0.0236
True
Edit
A parallelized version
cf = Compile[{{x, _Real}, {y, _Real, 1}, {z, _Real, 1}},
x/(y z),
CompilationTarget -> "C",
RuntimeAttributes -> {Listable},
Parallelization -> True,
RuntimeOptions -> "Speed"
];
e = cf[m, n, m]; // RepeatedTiming // First
a == e
0.0096
True
Timing has been measured on a Quad Core CPU which shows that this does not scale too well. Btw., the timing with CompilationTarget -> "C" is only 4% slower, so there is always no point to compile it into a library.
answered 1 hour ago
Henrik Schumacher
47.3k466134
I was just typing a comparison of the answers so far, but you were first. I wouldn't've expected thatKroneckerProductwould be that quick. Any ideas on any way that might parallelise well? I will edit my question to include that as well.
– ThunderBiggi
1 hour ago
See my edit for a parallelized version.
– Henrik Schumacher
1 hour ago
I am using arbitrary precision numbers, so I guess 'Compile' is not really an option.
– ThunderBiggi
28 mins ago
Also, interestingly, but on my machine, with Mathematica 11.3,ais faster thanbthough still slower than the other two.
– ThunderBiggi
23 mins ago
Yeah, I was also surprised thatawas so slow on my machine. I don't know what to think about it...
– Henrik Schumacher
15 mins ago
add a comment |
up vote
3
down vote
m = RandomReal[{-1, 1}, {2000}];
n = RandomReal[{-1, 1}, {2000, 2000}];
a = Outer[Divide, m, m]/n; // RepeatedTiming // First
b = Map[#/m &, MapThread[#1 #2 &, {m, 1/n}]]; //
RepeatedTiming // First
c = m /(ConstantArray[m, Length[m]] n); // RepeatedTiming // First
d = KroneckerProduct[m, 1./m]/n; // RepeatedTiming // First
a == b == c == d
0.958
0.128
0.0281
0.0236
True
Edit
A parallelized version
cf = Compile[{{x, _Real}, {y, _Real, 1}, {z, _Real, 1}},
x/(y z),
CompilationTarget -> "C",
RuntimeAttributes -> {Listable},
Parallelization -> True,
RuntimeOptions -> "Speed"
];
e = cf[m, n, m]; // RepeatedTiming // First
a == e
0.0096
True
Timing has been measured on a Quad Core CPU which shows that this does not scale too well. Btw., the timing with CompilationTarget -> "C" is only 4% slower, so there is always no point to compile it into a library.
answered 1 hour ago
Henrik Schumacher
47.3k466134
I was just typing a comparison of the answers so far, but you were first. I wouldn't've expected thatKroneckerProductwould be that quick. Any ideas on any way that might parallelise well? I will edit my question to include that as well.
– ThunderBiggi
1 hour ago
See my edit for a parallelized version.
– Henrik Schumacher
1 hour ago
I am using arbitrary precision numbers, so I guess 'Compile' is not really an option.
– ThunderBiggi
28 mins ago
Also, interestingly, but on my machine, with Mathematica 11.3,ais faster thanbthough still slower than the other two.
– ThunderBiggi
23 mins ago
Yeah, I was also surprised thatawas so slow on my machine. I don't know what to think about it...
– Henrik Schumacher
15 mins ago
add a comment |
up vote
3
down vote
up vote
3
down vote
m = RandomReal[{-1, 1}, {2000}];
n = RandomReal[{-1, 1}, {2000, 2000}];
a = Outer[Divide, m, m]/n; // RepeatedTiming // First
b = Map[#/m &, MapThread[#1 #2 &, {m, 1/n}]]; //
RepeatedTiming // First
c = m /(ConstantArray[m, Length[m]] n); // RepeatedTiming // First
d = KroneckerProduct[m, 1./m]/n; // RepeatedTiming // First
a == b == c == d
0.958
0.128
0.0281
0.0236
True
Edit
A parallelized version
cf = Compile[{{x, _Real}, {y, _Real, 1}, {z, _Real, 1}},
x/(y z),
CompilationTarget -> "C",
RuntimeAttributes -> {Listable},
Parallelization -> True,
RuntimeOptions -> "Speed"
];
e = cf[m, n, m]; // RepeatedTiming // First
a == e
0.0096
True
Timing has been measured on a Quad Core CPU which shows that this does not scale too well. Btw., the timing with CompilationTarget -> "C" is only 4% slower, so there is always no point to compile it into a library.
answered 1 hour ago
Henrik Schumacher
47.3k466134
m = RandomReal[{-1, 1}, {2000}];
n = RandomReal[{-1, 1}, {2000, 2000}];
a = Outer[Divide, m, m]/n; // RepeatedTiming // First
b = Map[#/m &, MapThread[#1 #2 &, {m, 1/n}]]; //
RepeatedTiming // First
c = m /(ConstantArray[m, Length[m]] n); // RepeatedTiming // First
d = KroneckerProduct[m, 1./m]/n; // RepeatedTiming // First
a == b == c == d
0.958
0.128
0.0281
0.0236
True
Edit
A parallelized version
cf = Compile[{{x, _Real}, {y, _Real, 1}, {z, _Real, 1}},
x/(y z),
CompilationTarget -> "C",
RuntimeAttributes -> {Listable},
Parallelization -> True,
RuntimeOptions -> "Speed"
];
e = cf[m, n, m]; // RepeatedTiming // First
a == e
0.0096
True
Timing has been measured on a Quad Core CPU which shows that this does not scale too well. Btw., the timing with CompilationTarget -> "C" is only 4% slower, so there is always no point to compile it into a library.
answered 1 hour ago
Henrik Schumacher
47.3k466134
edited 1 hour ago
answered 1 hour ago
Henrik Schumacher
47.3k466134
answered 1 hour ago
Henrik Schumacher
47.3k466134
answered 1 hour ago
Henrik Schumacher
47.3k466134
47.3k466134
I was just typing a comparison of the answers so far, but you were first. I wouldn't've expected thatKroneckerProductwould be that quick. Any ideas on any way that might parallelise well? I will edit my question to include that as well.
– ThunderBiggi
1 hour ago
See my edit for a parallelized version.
– Henrik Schumacher
1 hour ago
I am using arbitrary precision numbers, so I guess 'Compile' is not really an option.
– ThunderBiggi
28 mins ago
Also, interestingly, but on my machine, with Mathematica 11.3,ais faster thanbthough still slower than the other two.
– ThunderBiggi
23 mins ago
Yeah, I was also surprised thatawas so slow on my machine. I don't know what to think about it...
– Henrik Schumacher
15 mins ago
add a comment |
I was just typing a comparison of the answers so far, but you were first. I wouldn't've expected thatKroneckerProductwould be that quick. Any ideas on any way that might parallelise well? I will edit my question to include that as well.
– ThunderBiggi
1 hour ago
See my edit for a parallelized version.
– Henrik Schumacher
1 hour ago
I am using arbitrary precision numbers, so I guess 'Compile' is not really an option.
– ThunderBiggi
28 mins ago
Also, interestingly, but on my machine, with Mathematica 11.3,ais faster thanbthough still slower than the other two.
– ThunderBiggi
23 mins ago
Yeah, I was also surprised thatawas so slow on my machine. I don't know what to think about it...
– Henrik Schumacher
15 mins ago
I was just typing a comparison of the answers so far, but you were first. I wouldn't've expected that
KroneckerProduct would be that quick. Any ideas on any way that might parallelise well? I will edit my question to include that as well.– ThunderBiggi
1 hour ago
I was just typing a comparison of the answers so far, but you were first. I wouldn't've expected that
KroneckerProduct would be that quick. Any ideas on any way that might parallelise well? I will edit my question to include that as well.– ThunderBiggi
1 hour ago
See my edit for a parallelized version.
– Henrik Schumacher
1 hour ago
See my edit for a parallelized version.
– Henrik Schumacher
1 hour ago
I am using arbitrary precision numbers, so I guess 'Compile' is not really an option.
– ThunderBiggi
28 mins ago
I am using arbitrary precision numbers, so I guess 'Compile' is not really an option.
– ThunderBiggi
28 mins ago
Also, interestingly, but on my machine, with Mathematica 11.3,
a is faster than b though still slower than the other two.– ThunderBiggi
23 mins ago
Also, interestingly, but on my machine, with Mathematica 11.3,
a is faster than b though still slower than the other two.– ThunderBiggi
23 mins ago
Yeah, I was also surprised that
a was so slow on my machine. I don't know what to think about it...– Henrik Schumacher
15 mins ago
Yeah, I was also surprised that
a was so slow on my machine. I don't know what to think about it...– Henrik Schumacher
15 mins ago
add a comment |
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What is the length of
min practical use?– Αλέξανδρος Ζεγγ
5 hours ago
You can try
m/(n ConstantArray[m, Length[m]])and see how fast it is.– C. E.
2 hours ago
@ΑλέξανδροςΖεγγ I editted my question to include some information on that.
– ThunderBiggi
1 hour ago