Converting from “matrix” data into “coordinate” dataListVectorPlot3DOrganise data in tableHow to...
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Converting from “matrix” data into “coordinate” data
ListVectorPlot3DOrganise data in tableHow to multiply specific columns in a matrix of data?How do I partition a matrix?Reshaping list of 2D points by first coordinateBin a large matrixTurning table into association for Classifysubtraction of Y valuesInserting columns into a large table of data and converting it into a {x,y,z} listConvert Negative Integers into Signed Binary?
$begingroup$
Say I have data which looks like data1 - this is "matrix" like data (is there a better descriptor?). The data looks like a matrix, and at each point in the matrix, it has a value. I can plot these in ListContourPlot and the like. e.g.
datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];
(* matrix like data *)
data1 = N[ Table[PDF[datafunction, {x, y}] /. {x -> xinsert, y -> yinsert}, {xinsert, -4, 4, 1}, {yinsert, -2, 2, 1}]];
ListContourPlot[data1]
However, I can also create the same effect by making "coordinate" like data, where the data is a list of coordinates.
(* coordinate like data *)
data2 = RandomVariate[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], 1000];
ListPlot[data2]
How would I convert data1 into data2? How do I convert matrix-like into coordinate-like?
I need to do some PCA analysis, I require the data to be in the form of individual points.
list-manipulation data-structures
asked 9 hours ago
TomiTomi
974514
$endgroup$
add a comment |
$begingroup$
Say I have data which looks like data1 - this is "matrix" like data (is there a better descriptor?). The data looks like a matrix, and at each point in the matrix, it has a value. I can plot these in ListContourPlot and the like. e.g.
datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];
(* matrix like data *)
data1 = N[ Table[PDF[datafunction, {x, y}] /. {x -> xinsert, y -> yinsert}, {xinsert, -4, 4, 1}, {yinsert, -2, 2, 1}]];
ListContourPlot[data1]
However, I can also create the same effect by making "coordinate" like data, where the data is a list of coordinates.
(* coordinate like data *)
data2 = RandomVariate[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], 1000];
ListPlot[data2]
How would I convert data1 into data2? How do I convert matrix-like into coordinate-like?
I need to do some PCA analysis, I require the data to be in the form of individual points.
list-manipulation data-structures
asked 9 hours ago
TomiTomi
974514
$endgroup$
1
$begingroup$
How do you think one could infer the individual counts from a total count? Once we have totaled data and thrown away the parts there is no way to reconstruct them. The mapping between sums and their constituents is not bijective.
$endgroup$
– Sjoerd C. de Vries
8 hours ago
add a comment |
$begingroup$
Say I have data which looks like data1 - this is "matrix" like data (is there a better descriptor?). The data looks like a matrix, and at each point in the matrix, it has a value. I can plot these in ListContourPlot and the like. e.g.
datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];
(* matrix like data *)
data1 = N[ Table[PDF[datafunction, {x, y}] /. {x -> xinsert, y -> yinsert}, {xinsert, -4, 4, 1}, {yinsert, -2, 2, 1}]];
ListContourPlot[data1]
However, I can also create the same effect by making "coordinate" like data, where the data is a list of coordinates.
(* coordinate like data *)
data2 = RandomVariate[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], 1000];
ListPlot[data2]
How would I convert data1 into data2? How do I convert matrix-like into coordinate-like?
I need to do some PCA analysis, I require the data to be in the form of individual points.
list-manipulation data-structures
asked 9 hours ago
TomiTomi
974514
$endgroup$
Say I have data which looks like data1 - this is "matrix" like data (is there a better descriptor?). The data looks like a matrix, and at each point in the matrix, it has a value. I can plot these in ListContourPlot and the like. e.g.
datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];
(* matrix like data *)
data1 = N[ Table[PDF[datafunction, {x, y}] /. {x -> xinsert, y -> yinsert}, {xinsert, -4, 4, 1}, {yinsert, -2, 2, 1}]];
ListContourPlot[data1]
However, I can also create the same effect by making "coordinate" like data, where the data is a list of coordinates.
(* coordinate like data *)
data2 = RandomVariate[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], 1000];
ListPlot[data2]
How would I convert data1 into data2? How do I convert matrix-like into coordinate-like?
I need to do some PCA analysis, I require the data to be in the form of individual points.
list-manipulation data-structures
list-manipulation data-structures
asked 9 hours ago
TomiTomi
974514
asked 9 hours ago
TomiTomi
974514
edited 7 hours ago
Tomi
asked 9 hours ago
TomiTomi
974514
asked 9 hours ago
TomiTomi
974514
asked 9 hours ago
TomiTomi
974514
974514
1
$begingroup$
How do you think one could infer the individual counts from a total count? Once we have totaled data and thrown away the parts there is no way to reconstruct them. The mapping between sums and their constituents is not bijective.
$endgroup$
– Sjoerd C. de Vries
8 hours ago
add a comment |
1
$begingroup$
How do you think one could infer the individual counts from a total count? Once we have totaled data and thrown away the parts there is no way to reconstruct them. The mapping between sums and their constituents is not bijective.
$endgroup$
– Sjoerd C. de Vries
8 hours ago
1
1
$begingroup$
How do you think one could infer the individual counts from a total count? Once we have totaled data and thrown away the parts there is no way to reconstruct them. The mapping between sums and their constituents is not bijective.
$endgroup$
– Sjoerd C. de Vries
8 hours ago
$begingroup$
How do you think one could infer the individual counts from a total count? Once we have totaled data and thrown away the parts there is no way to reconstruct them. The mapping between sums and their constituents is not bijective.
$endgroup$
– Sjoerd C. de Vries
8 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
The reshaping can be done in several ways. Below is given one using SparseArray.
First generating the data (simpler than in the question):
datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];
data1 = N[Table[PDF[datafunction][{x, y}], {x, -4, 4, 1}, {y, -2, 2, 1}]];
MatrixForm[data1]
Make index-to-value associations corresponding to the ranges used to make data1:
aX = AssociationThread[Range[Length[#]], #] &@Range[-4, 4, 1];
aY = AssociationThread[Range[Length[#]], #] &@Range[-2, 2, 1];
Convert to a sparse array, take the corresponding rules, and map the {x,y} indexes to the actual x's and y's.
arules = Most[ArrayRules[SparseArray[data1]]];
data2 = Map[{aX[#[[1, 1]]], aY[#[[1, 2]]], #[[2]]} &, arules]
Plot (note the axes ticks):
ListContourPlot[data2]
answered 7 hours ago
Anton AntonovAnton Antonov
24k167114
$endgroup$
add a comment |
$begingroup$
An alternative approach based on Rescaleing the "NonzeroPositions" of SparseArray[data1]:
xrange = {-4, 4};
yrange = {-2, 2};
sa = SparseArray[data1];
nzp = sa["NonzeroPositions"];
nzv = sa["NonzeroValues"];
data2b = Join[Transpose[Rescale[#, MinMax@#, #2] & @@@
Thread[ {Transpose@nzp, {xrange, yrange}}]], List /@ nzv, 2];
data2b == data2 (* from Anton's answer *)
True
answered 12 mins ago
kglrkglr
188k10203421
$endgroup$
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
$begingroup$
The reshaping can be done in several ways. Below is given one using SparseArray.
First generating the data (simpler than in the question):
datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];
data1 = N[Table[PDF[datafunction][{x, y}], {x, -4, 4, 1}, {y, -2, 2, 1}]];
MatrixForm[data1]
Make index-to-value associations corresponding to the ranges used to make data1:
aX = AssociationThread[Range[Length[#]], #] &@Range[-4, 4, 1];
aY = AssociationThread[Range[Length[#]], #] &@Range[-2, 2, 1];
Convert to a sparse array, take the corresponding rules, and map the {x,y} indexes to the actual x's and y's.
arules = Most[ArrayRules[SparseArray[data1]]];
data2 = Map[{aX[#[[1, 1]]], aY[#[[1, 2]]], #[[2]]} &, arules]
Plot (note the axes ticks):
ListContourPlot[data2]
answered 7 hours ago
Anton AntonovAnton Antonov
24k167114
$endgroup$
add a comment |
$begingroup$
The reshaping can be done in several ways. Below is given one using SparseArray.
First generating the data (simpler than in the question):
datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];
data1 = N[Table[PDF[datafunction][{x, y}], {x, -4, 4, 1}, {y, -2, 2, 1}]];
MatrixForm[data1]
Make index-to-value associations corresponding to the ranges used to make data1:
aX = AssociationThread[Range[Length[#]], #] &@Range[-4, 4, 1];
aY = AssociationThread[Range[Length[#]], #] &@Range[-2, 2, 1];
Convert to a sparse array, take the corresponding rules, and map the {x,y} indexes to the actual x's and y's.
arules = Most[ArrayRules[SparseArray[data1]]];
data2 = Map[{aX[#[[1, 1]]], aY[#[[1, 2]]], #[[2]]} &, arules]
Plot (note the axes ticks):
ListContourPlot[data2]
answered 7 hours ago
Anton AntonovAnton Antonov
24k167114
$endgroup$
add a comment |
$begingroup$
The reshaping can be done in several ways. Below is given one using SparseArray.
First generating the data (simpler than in the question):
datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];
data1 = N[Table[PDF[datafunction][{x, y}], {x, -4, 4, 1}, {y, -2, 2, 1}]];
MatrixForm[data1]
Make index-to-value associations corresponding to the ranges used to make data1:
aX = AssociationThread[Range[Length[#]], #] &@Range[-4, 4, 1];
aY = AssociationThread[Range[Length[#]], #] &@Range[-2, 2, 1];
Convert to a sparse array, take the corresponding rules, and map the {x,y} indexes to the actual x's and y's.
arules = Most[ArrayRules[SparseArray[data1]]];
data2 = Map[{aX[#[[1, 1]]], aY[#[[1, 2]]], #[[2]]} &, arules]
Plot (note the axes ticks):
ListContourPlot[data2]
answered 7 hours ago
Anton AntonovAnton Antonov
24k167114
$endgroup$
The reshaping can be done in several ways. Below is given one using SparseArray.
First generating the data (simpler than in the question):
datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];
data1 = N[Table[PDF[datafunction][{x, y}], {x, -4, 4, 1}, {y, -2, 2, 1}]];
MatrixForm[data1]
Make index-to-value associations corresponding to the ranges used to make data1:
aX = AssociationThread[Range[Length[#]], #] &@Range[-4, 4, 1];
aY = AssociationThread[Range[Length[#]], #] &@Range[-2, 2, 1];
Convert to a sparse array, take the corresponding rules, and map the {x,y} indexes to the actual x's and y's.
arules = Most[ArrayRules[SparseArray[data1]]];
data2 = Map[{aX[#[[1, 1]]], aY[#[[1, 2]]], #[[2]]} &, arules]
Plot (note the axes ticks):
ListContourPlot[data2]
answered 7 hours ago
Anton AntonovAnton Antonov
24k167114
answered 7 hours ago
Anton AntonovAnton Antonov
24k167114
answered 7 hours ago
Anton AntonovAnton Antonov
24k167114
answered 7 hours ago
Anton AntonovAnton Antonov
24k167114
24k167114
add a comment |
add a comment |
$begingroup$
An alternative approach based on Rescaleing the "NonzeroPositions" of SparseArray[data1]:
xrange = {-4, 4};
yrange = {-2, 2};
sa = SparseArray[data1];
nzp = sa["NonzeroPositions"];
nzv = sa["NonzeroValues"];
data2b = Join[Transpose[Rescale[#, MinMax@#, #2] & @@@
Thread[ {Transpose@nzp, {xrange, yrange}}]], List /@ nzv, 2];
data2b == data2 (* from Anton's answer *)
True
answered 12 mins ago
kglrkglr
188k10203421
$endgroup$
add a comment |
$begingroup$
An alternative approach based on Rescaleing the "NonzeroPositions" of SparseArray[data1]:
xrange = {-4, 4};
yrange = {-2, 2};
sa = SparseArray[data1];
nzp = sa["NonzeroPositions"];
nzv = sa["NonzeroValues"];
data2b = Join[Transpose[Rescale[#, MinMax@#, #2] & @@@
Thread[ {Transpose@nzp, {xrange, yrange}}]], List /@ nzv, 2];
data2b == data2 (* from Anton's answer *)
True
answered 12 mins ago
kglrkglr
188k10203421
$endgroup$
add a comment |
$begingroup$
An alternative approach based on Rescaleing the "NonzeroPositions" of SparseArray[data1]:
xrange = {-4, 4};
yrange = {-2, 2};
sa = SparseArray[data1];
nzp = sa["NonzeroPositions"];
nzv = sa["NonzeroValues"];
data2b = Join[Transpose[Rescale[#, MinMax@#, #2] & @@@
Thread[ {Transpose@nzp, {xrange, yrange}}]], List /@ nzv, 2];
data2b == data2 (* from Anton's answer *)
True
answered 12 mins ago
kglrkglr
188k10203421
$endgroup$
An alternative approach based on Rescaleing the "NonzeroPositions" of SparseArray[data1]:
xrange = {-4, 4};
yrange = {-2, 2};
sa = SparseArray[data1];
nzp = sa["NonzeroPositions"];
nzv = sa["NonzeroValues"];
data2b = Join[Transpose[Rescale[#, MinMax@#, #2] & @@@
Thread[ {Transpose@nzp, {xrange, yrange}}]], List /@ nzv, 2];
data2b == data2 (* from Anton's answer *)
True
answered 12 mins ago
kglrkglr
188k10203421
answered 12 mins ago
kglrkglr
188k10203421
answered 12 mins ago
kglrkglr
188k10203421
answered 12 mins ago
kglrkglr
188k10203421
188k10203421
add a comment |
add a comment |
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$begingroup$
How do you think one could infer the individual counts from a total count? Once we have totaled data and thrown away the parts there is no way to reconstruct them. The mapping between sums and their constituents is not bijective.
$endgroup$
– Sjoerd C. de Vries
8 hours ago