Mixing
What's the best syntax for defining a matrix/tensor via its indices?
$begingroup$
This is a question about math notation. The context is, I'm trying to correctly define a problem of scheduling the flow through a set of devices, $D = {d_1, d_2, ... d_n}$, over a finite discrete future planning horizon $T$ = $(1,2,3dots,60)$. The schedule of all devices over the planning horizon can be described by a real valued matrix, $Q$, with $|D|$ rows and $|T|$ columns. To define $Q$ I could state just that. But given a definition of $D$ and $T$ which form the "index sets", or just "indices" of matrix, to define $Q$ could/should I just say "Let $Q = D times T rightarrow mathbb{R}$", or something else that is more succinct and direct than "Let $Q$ be a matrix with $|D|$ rows and $|T|$ columns"?
matrices notation tensors
asked Jan 28 '18 at 7:11
spinkusspinkus
1257
$endgroup$
add a comment |
$begingroup$
This is a question about math notation. The context is, I'm trying to correctly define a problem of scheduling the flow through a set of devices, $D = {d_1, d_2, ... d_n}$, over a finite discrete future planning horizon $T$ = $(1,2,3dots,60)$. The schedule of all devices over the planning horizon can be described by a real valued matrix, $Q$, with $|D|$ rows and $|T|$ columns. To define $Q$ I could state just that. But given a definition of $D$ and $T$ which form the "index sets", or just "indices" of matrix, to define $Q$ could/should I just say "Let $Q = D times T rightarrow mathbb{R}$", or something else that is more succinct and direct than "Let $Q$ be a matrix with $|D|$ rows and $|T|$ columns"?
matrices notation tensors
asked Jan 28 '18 at 7:11
spinkusspinkus
1257
$endgroup$
$begingroup$
This depends a bit on the intended audience. Sometimes having a super technical definition isn't as useful as a more clear but less precise one. Perhaps the shortest commonly used notation would be $Qinmathbb{R}^{|D|times|T|}$ (or $Qinmathbb{R}^{mtimes n}$ if you defined $m$ to be the size of $T$).
$endgroup$
– tch
Jan 16 at 4:06
add a comment |
$begingroup$
This is a question about math notation. The context is, I'm trying to correctly define a problem of scheduling the flow through a set of devices, $D = {d_1, d_2, ... d_n}$, over a finite discrete future planning horizon $T$ = $(1,2,3dots,60)$. The schedule of all devices over the planning horizon can be described by a real valued matrix, $Q$, with $|D|$ rows and $|T|$ columns. To define $Q$ I could state just that. But given a definition of $D$ and $T$ which form the "index sets", or just "indices" of matrix, to define $Q$ could/should I just say "Let $Q = D times T rightarrow mathbb{R}$", or something else that is more succinct and direct than "Let $Q$ be a matrix with $|D|$ rows and $|T|$ columns"?
matrices notation tensors
asked Jan 28 '18 at 7:11
spinkusspinkus
1257
$endgroup$
This is a question about math notation. The context is, I'm trying to correctly define a problem of scheduling the flow through a set of devices, $D = {d_1, d_2, ... d_n}$, over a finite discrete future planning horizon $T$ = $(1,2,3dots,60)$. The schedule of all devices over the planning horizon can be described by a real valued matrix, $Q$, with $|D|$ rows and $|T|$ columns. To define $Q$ I could state just that. But given a definition of $D$ and $T$ which form the "index sets", or just "indices" of matrix, to define $Q$ could/should I just say "Let $Q = D times T rightarrow mathbb{R}$", or something else that is more succinct and direct than "Let $Q$ be a matrix with $|D|$ rows and $|T|$ columns"?
matrices notation tensors
matrices notation tensors
asked Jan 28 '18 at 7:11
spinkusspinkus
1257
asked Jan 28 '18 at 7:11
spinkusspinkus
1257
edited Jan 16 at 3:45
spinkus
asked Jan 28 '18 at 7:11
spinkusspinkus
1257
asked Jan 28 '18 at 7:11
spinkusspinkus
1257
asked Jan 28 '18 at 7:11
spinkusspinkus
1257
1257
$begingroup$
This depends a bit on the intended audience. Sometimes having a super technical definition isn't as useful as a more clear but less precise one. Perhaps the shortest commonly used notation would be $Qinmathbb{R}^{|D|times|T|}$ (or $Qinmathbb{R}^{mtimes n}$ if you defined $m$ to be the size of $T$).
$endgroup$
– tch
Jan 16 at 4:06
add a comment |
$begingroup$
This depends a bit on the intended audience. Sometimes having a super technical definition isn't as useful as a more clear but less precise one. Perhaps the shortest commonly used notation would be $Qinmathbb{R}^{|D|times|T|}$ (or $Qinmathbb{R}^{mtimes n}$ if you defined $m$ to be the size of $T$).
$endgroup$
– tch
Jan 16 at 4:06
$begingroup$
This depends a bit on the intended audience. Sometimes having a super technical definition isn't as useful as a more clear but less precise one. Perhaps the shortest commonly used notation would be $Qinmathbb{R}^{|D|times|T|}$ (or $Qinmathbb{R}^{mtimes n}$ if you defined $m$ to be the size of $T$).
$endgroup$
– tch
Jan 16 at 4:06
$begingroup$
This depends a bit on the intended audience. Sometimes having a super technical definition isn't as useful as a more clear but less precise one. Perhaps the shortest commonly used notation would be $Qinmathbb{R}^{|D|times|T|}$ (or $Qinmathbb{R}^{mtimes n}$ if you defined $m$ to be the size of $T$).
$endgroup$
– tch
Jan 16 at 4:06
add a comment |
1 Answer
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$begingroup$
Is there any advantage to representing your flows as a matrix ? Will you be adding sets of flow values from different scenarios, for example ?
If not, you might as well just define a function $f:D times T rightarrow mathbb{R}$ where $f(d_i, t)$ is the flow through device $d_i$ at time $t$. And you might want to think about whether your domain is really the whole of $mathbb{R}$. For example, can flow values be negative ?
answered Jan 16 at 12:20
gandalf61gandalf61
8,771725
$endgroup$
$begingroup$
Hmm interesting idea. I do need to define the matrix though as I need to define constraints on the joint flows. Adding is another potential use case. Yes the flows can be negative some flows in are related to flows out. I now know the class of problem is usually called a "network flow problem" popular in traffic routing for instance, except that it is less common to include the time domain, as above.
$endgroup$
– spinkus
Jan 16 at 21:46
add a comment |
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1 Answer
1
active
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1 Answer
1
active
oldest
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votes
$begingroup$
Is there any advantage to representing your flows as a matrix ? Will you be adding sets of flow values from different scenarios, for example ?
If not, you might as well just define a function $f:D times T rightarrow mathbb{R}$ where $f(d_i, t)$ is the flow through device $d_i$ at time $t$. And you might want to think about whether your domain is really the whole of $mathbb{R}$. For example, can flow values be negative ?
answered Jan 16 at 12:20
gandalf61gandalf61
8,771725
$endgroup$
$begingroup$
Hmm interesting idea. I do need to define the matrix though as I need to define constraints on the joint flows. Adding is another potential use case. Yes the flows can be negative some flows in are related to flows out. I now know the class of problem is usually called a "network flow problem" popular in traffic routing for instance, except that it is less common to include the time domain, as above.
$endgroup$
– spinkus
Jan 16 at 21:46
add a comment |
$begingroup$
Is there any advantage to representing your flows as a matrix ? Will you be adding sets of flow values from different scenarios, for example ?
If not, you might as well just define a function $f:D times T rightarrow mathbb{R}$ where $f(d_i, t)$ is the flow through device $d_i$ at time $t$. And you might want to think about whether your domain is really the whole of $mathbb{R}$. For example, can flow values be negative ?
answered Jan 16 at 12:20
gandalf61gandalf61
8,771725
$endgroup$
$begingroup$
Hmm interesting idea. I do need to define the matrix though as I need to define constraints on the joint flows. Adding is another potential use case. Yes the flows can be negative some flows in are related to flows out. I now know the class of problem is usually called a "network flow problem" popular in traffic routing for instance, except that it is less common to include the time domain, as above.
$endgroup$
– spinkus
Jan 16 at 21:46
add a comment |
$begingroup$
Is there any advantage to representing your flows as a matrix ? Will you be adding sets of flow values from different scenarios, for example ?
If not, you might as well just define a function $f:D times T rightarrow mathbb{R}$ where $f(d_i, t)$ is the flow through device $d_i$ at time $t$. And you might want to think about whether your domain is really the whole of $mathbb{R}$. For example, can flow values be negative ?
answered Jan 16 at 12:20
gandalf61gandalf61
8,771725
$endgroup$
Is there any advantage to representing your flows as a matrix ? Will you be adding sets of flow values from different scenarios, for example ?
If not, you might as well just define a function $f:D times T rightarrow mathbb{R}$ where $f(d_i, t)$ is the flow through device $d_i$ at time $t$. And you might want to think about whether your domain is really the whole of $mathbb{R}$. For example, can flow values be negative ?
answered Jan 16 at 12:20
gandalf61gandalf61
8,771725
answered Jan 16 at 12:20
gandalf61gandalf61
8,771725
answered Jan 16 at 12:20
gandalf61gandalf61
8,771725
answered Jan 16 at 12:20
gandalf61gandalf61
8,771725
8,771725
$begingroup$
Hmm interesting idea. I do need to define the matrix though as I need to define constraints on the joint flows. Adding is another potential use case. Yes the flows can be negative some flows in are related to flows out. I now know the class of problem is usually called a "network flow problem" popular in traffic routing for instance, except that it is less common to include the time domain, as above.
$endgroup$
– spinkus
Jan 16 at 21:46
add a comment |
$begingroup$
Hmm interesting idea. I do need to define the matrix though as I need to define constraints on the joint flows. Adding is another potential use case. Yes the flows can be negative some flows in are related to flows out. I now know the class of problem is usually called a "network flow problem" popular in traffic routing for instance, except that it is less common to include the time domain, as above.
$endgroup$
– spinkus
Jan 16 at 21:46
$begingroup$
Hmm interesting idea. I do need to define the matrix though as I need to define constraints on the joint flows. Adding is another potential use case. Yes the flows can be negative some flows in are related to flows out. I now know the class of problem is usually called a "network flow problem" popular in traffic routing for instance, except that it is less common to include the time domain, as above.
$endgroup$
– spinkus
Jan 16 at 21:46
$begingroup$
Hmm interesting idea. I do need to define the matrix though as I need to define constraints on the joint flows. Adding is another potential use case. Yes the flows can be negative some flows in are related to flows out. I now know the class of problem is usually called a "network flow problem" popular in traffic routing for instance, except that it is less common to include the time domain, as above.
$endgroup$
– spinkus
Jan 16 at 21:46
add a comment |
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$begingroup$
This depends a bit on the intended audience. Sometimes having a super technical definition isn't as useful as a more clear but less precise one. Perhaps the shortest commonly used notation would be $Qinmathbb{R}^{|D|times|T|}$ (or $Qinmathbb{R}^{mtimes n}$ if you defined $m$ to be the size of $T$).
$endgroup$
– tch
Jan 16 at 4:06