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3

$begingroup$

Consider some function f[x,y]. I want to create a table in the form

table = x1,y1,f[x1,y1],x1,y2,f[x1,y2],...,x2,y1,f[x2,y1],x2,y2,f[x2,y2],...,

where $x_i,x_i+1$ and $y_i,y_i+1$ are separated by some distances $Delta x$, $Delta y$, and i ranges from 1 to some N.

The only way I know is to manually create a table

table=Join[Table[x1,y,f[x1,y],y,y1,yN,Deltay],Table[x2,y,f[x2,y],y,y1,yN,Deltay],...] 

However, this is not a smart way, especially for large N. Could you please provide some smarter way to build the table?

table

share|improve this question

asked Mar 22 at 14:23

John TaylorJohn Taylor

792211

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Have a look at Menu/Help/WolframDocumentation/Table. That's what will help you.
  $endgroup$
  – Alexei Boulbitch
  Mar 22 at 14:32
  

  
  
  
  

add a comment | 

3

$begingroup$

Consider some function f[x,y]. I want to create a table in the form

table = x1,y1,f[x1,y1],x1,y2,f[x1,y2],...,x2,y1,f[x2,y1],x2,y2,f[x2,y2],...,

where $x_i,x_i+1$ and $y_i,y_i+1$ are separated by some distances $Delta x$, $Delta y$, and i ranges from 1 to some N.

The only way I know is to manually create a table

table=Join[Table[x1,y,f[x1,y],y,y1,yN,Deltay],Table[x2,y,f[x2,y],y,y1,yN,Deltay],...] 

However, this is not a smart way, especially for large N. Could you please provide some smarter way to build the table?

table

share|improve this question

asked Mar 22 at 14:23

John TaylorJohn Taylor

792211

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Have a look at Menu/Help/WolframDocumentation/Table. That's what will help you.
  $endgroup$
  – Alexei Boulbitch
  Mar 22 at 14:32
  

  
  
  
  

add a comment | 

$begingroup$

Consider some function f[x,y]. I want to create a table in the form

table = x1,y1,f[x1,y1],x1,y2,f[x1,y2],...,x2,y1,f[x2,y1],x2,y2,f[x2,y2],...,

where $x_i,x_i+1$ and $y_i,y_i+1$ are separated by some distances $Delta x$, $Delta y$, and i ranges from 1 to some N.

The only way I know is to manually create a table

table=Join[Table[x1,y,f[x1,y],y,y1,yN,Deltay],Table[x2,y,f[x2,y],y,y1,yN,Deltay],...] 

However, this is not a smart way, especially for large N. Could you please provide some smarter way to build the table?

table

share|improve this question

asked Mar 22 at 14:23

John TaylorJohn Taylor

792211

$endgroup$

table = x1,y1,f[x1,y1],x1,y2,f[x1,y2],...,x2,y1,f[x2,y1],x2,y2,f[x2,y2],...,

table=Join[Table[x1,y,f[x1,y],y,y1,yN,Deltay],Table[x2,y,f[x2,y],y,y1,yN,Deltay],...] 

share|improve this question

asked Mar 22 at 14:23

John TaylorJohn Taylor

792211

share|improve this question

asked Mar 22 at 14:23

John TaylorJohn Taylor

792211

asked Mar 22 at 14:23

John TaylorJohn Taylor

792211

asked Mar 22 at 14:23

John TaylorJohn Taylor

792211

2 Answers
2

active

oldest

votes

6

$begingroup$

x1 = 1; xN = 9; Δx = 3;
y1 = 0; yN = 5; Δy = 1;

table = Join @@ Table[i, j, f[i, j], i, x1, xN, Δx, j, y1, yN, Δy] 

1, 0, f[1, 0], 1, 1, f[1, 1], 1, 2, f[1, 2], 1, 3,
f[1, 3], 1, 4, f[1, 4], 1, 5, f[1, 5],

4, 0, f[4, 0], 4, 1,
f[4, 1], 4, 2, f[4, 2], 4, 3, f[4, 3], 4, 4, f[4, 4], 4, 5,
f[4, 5],

7, 0, f[7, 0], 7, 1, f[7, 1], 7, 2, f[7, 2], 7, 3,
f[7, 3], 7, 4, f[7, 4], 7, 5, f[7, 5]

Also

table2 = ##, f @ ## & @@@ Tuples[Range[x1, xN, Δx], Range[y1, yN, Δy]]
table2 == table

True

share|improve this answer

edited Mar 22 at 14:36

answered Mar 22 at 14:30

kglrkglr

190k10209427

$endgroup$

add a comment | 

2

$begingroup$

This would be a nice answer (using the Outer product to create the 2D array):

x1 = 1; xN = 9; dx = 3;
y1 = 0; yN = 5; dy = 1; 
Partition[Flatten[
 Outer[Through[List, f[#1, #2]] &, Range[x1, xN, dx], Range[y1, yN, dy]]], 3]

except that Outer returns too many levels -- hence the Flatten and Partition are needed to remove the extra brackets. Answer is the same as kglr's.

share|improve this answer

answered Mar 22 at 16:06

bill sbill s

55.1k377159

$endgroup$

add a comment | 

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6

$begingroup$

x1 = 1; xN = 9; Δx = 3;
y1 = 0; yN = 5; Δy = 1;

table = Join @@ Table[i, j, f[i, j], i, x1, xN, Δx, j, y1, yN, Δy] 

1, 0, f[1, 0], 1, 1, f[1, 1], 1, 2, f[1, 2], 1, 3,
f[1, 3], 1, 4, f[1, 4], 1, 5, f[1, 5],

4, 0, f[4, 0], 4, 1,
f[4, 1], 4, 2, f[4, 2], 4, 3, f[4, 3], 4, 4, f[4, 4], 4, 5,
f[4, 5],

7, 0, f[7, 0], 7, 1, f[7, 1], 7, 2, f[7, 2], 7, 3,
f[7, 3], 7, 4, f[7, 4], 7, 5, f[7, 5]

Also

table2 = ##, f @ ## & @@@ Tuples[Range[x1, xN, Δx], Range[y1, yN, Δy]]
table2 == table

True

share|improve this answer

edited Mar 22 at 14:36

answered Mar 22 at 14:30

kglrkglr

190k10209427

$endgroup$

add a comment | 

6

$begingroup$

x1 = 1; xN = 9; Δx = 3;
y1 = 0; yN = 5; Δy = 1;

table = Join @@ Table[i, j, f[i, j], i, x1, xN, Δx, j, y1, yN, Δy] 

1, 0, f[1, 0], 1, 1, f[1, 1], 1, 2, f[1, 2], 1, 3,
f[1, 3], 1, 4, f[1, 4], 1, 5, f[1, 5],

4, 0, f[4, 0], 4, 1,
f[4, 1], 4, 2, f[4, 2], 4, 3, f[4, 3], 4, 4, f[4, 4], 4, 5,
f[4, 5],

7, 0, f[7, 0], 7, 1, f[7, 1], 7, 2, f[7, 2], 7, 3,
f[7, 3], 7, 4, f[7, 4], 7, 5, f[7, 5]

Also

table2 = ##, f @ ## & @@@ Tuples[Range[x1, xN, Δx], Range[y1, yN, Δy]]
table2 == table

True

share|improve this answer

edited Mar 22 at 14:36

answered Mar 22 at 14:30

kglrkglr

190k10209427

$endgroup$

add a comment | 

$begingroup$

x1 = 1; xN = 9; Δx = 3;
y1 = 0; yN = 5; Δy = 1;

table = Join @@ Table[i, j, f[i, j], i, x1, xN, Δx, j, y1, yN, Δy] 

1, 0, f[1, 0], 1, 1, f[1, 1], 1, 2, f[1, 2], 1, 3,
f[1, 3], 1, 4, f[1, 4], 1, 5, f[1, 5],

4, 0, f[4, 0], 4, 1,
f[4, 1], 4, 2, f[4, 2], 4, 3, f[4, 3], 4, 4, f[4, 4], 4, 5,
f[4, 5],

7, 0, f[7, 0], 7, 1, f[7, 1], 7, 2, f[7, 2], 7, 3,
f[7, 3], 7, 4, f[7, 4], 7, 5, f[7, 5]

Also

table2 = ##, f @ ## & @@@ Tuples[Range[x1, xN, Δx], Range[y1, yN, Δy]]
table2 == table

True

share|improve this answer

edited Mar 22 at 14:36

answered Mar 22 at 14:30

kglrkglr

190k10209427

$endgroup$

x1 = 1; xN = 9; Δx = 3;
y1 = 0; yN = 5; Δy = 1;

table = Join @@ Table[i, j, f[i, j], i, x1, xN, Δx, j, y1, yN, Δy] 

table2 = ##, f @ ## & @@@ Tuples[Range[x1, xN, Δx], Range[y1, yN, Δy]]
table2 == table

share|improve this answer

edited Mar 22 at 14:36

answered Mar 22 at 14:30

kglrkglr

190k10209427

answered Mar 22 at 14:30

kglrkglr

190k10209427

answered Mar 22 at 14:30

kglrkglr

190k10209427

2

$begingroup$

This would be a nice answer (using the Outer product to create the 2D array):

x1 = 1; xN = 9; dx = 3;
y1 = 0; yN = 5; dy = 1; 
Partition[Flatten[
 Outer[Through[List, f[#1, #2]] &, Range[x1, xN, dx], Range[y1, yN, dy]]], 3]

except that Outer returns too many levels -- hence the Flatten and Partition are needed to remove the extra brackets. Answer is the same as kglr's.

share|improve this answer

answered Mar 22 at 16:06

bill sbill s

55.1k377159

$endgroup$

add a comment | 

2

$begingroup$

This would be a nice answer (using the Outer product to create the 2D array):

x1 = 1; xN = 9; dx = 3;
y1 = 0; yN = 5; dy = 1; 
Partition[Flatten[
 Outer[Through[List, f[#1, #2]] &, Range[x1, xN, dx], Range[y1, yN, dy]]], 3]

except that Outer returns too many levels -- hence the Flatten and Partition are needed to remove the extra brackets. Answer is the same as kglr's.

share|improve this answer

answered Mar 22 at 16:06

bill sbill s

55.1k377159

$endgroup$

add a comment | 

$begingroup$

This would be a nice answer (using the Outer product to create the 2D array):

x1 = 1; xN = 9; dx = 3;
y1 = 0; yN = 5; dy = 1; 
Partition[Flatten[
 Outer[Through[List, f[#1, #2]] &, Range[x1, xN, dx], Range[y1, yN, dy]]], 3]

except that Outer returns too many levels -- hence the Flatten and Partition are needed to remove the extra brackets. Answer is the same as kglr's.

share|improve this answer

answered Mar 22 at 16:06

bill sbill s

55.1k377159

$endgroup$

x1 = 1; xN = 9; dx = 3;
y1 = 0; yN = 5; dy = 1; 
Partition[Flatten[
 Outer[Through[List, f[#1, #2]] &, Range[x1, xN, dx], Range[y1, yN, dy]]], 3]

share|improve this answer

answered Mar 22 at 16:06

bill sbill s

55.1k377159

answered Mar 22 at 16:06

bill sbill s

55.1k377159

answered Mar 22 at 16:06

bill sbill s

55.1k377159