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Obtaining a matrix of complex values from associations giving the real and imaginary parts of each element?

Eigenvalues of matrix not giving imaginary partsPlot values of an $mtimes n$ matrix on the complex plane with color varying along $m$Real and Imaginary matrixDefining a non-standard algebraic numberFind the parameter values for my matrix for it to have imaginary eigenvaluesEfficiently select the smallest magnitude element from each column of a matrixGenerate random matrix where the entries in each column are drawn from a different rangeSample matrix indices in proportion to the matrix element valuesKeyed eigensystem for nested AssociationConverting a list of associations into a single association

5

$begingroup$

I have a list of associations keyed by real and imaginary numbers, like so:

matrix = {

   {<|"r" -> 0.368252, "i" -> 0.0199587|>, 

    <|"r" -> -0.461644, "i" -> 0.109868|>, 

    <|"r" -> -0.216081, "i" -> 0.562557|>, 

    <|"r" -> -0.479881, "i" -> -0.212978|>}, 



   {<|"r" -> 0.105028, "i" -> 0.632264|>, 

    <|"r" -> 0.116589, "i" -> -0.490063|>, 

    <|"r" -> 0.463378, "i" -> 0.231656|>,

    <|"r" -> -0.148665, "i" -> 0.212065|>},



   {<|"r" -> 0.463253, "i" -> 0.201161|>,

    <|"r" -> 0.460547, "i" -> 0.397829|>,

    <|"r" -> 0.222257, "i" -> 0.0129121|>,

    <|"r" -> 0.168641, "i" -> -0.544568|>},



   {<|"r" -> 0.255221, "i" -> -0.364687|>,

    <|"r" -> 0.191895, "i" -> -0.337437|>,

    <|"r" -> -0.12278, "i" -> 0.551195|>,

    <|"r" -> 0.560485, "i" -> 0.134702|>}

}

Given this, I can write

testmatrix = Join[Values[matrix], 2]`

to get a matrix, but it is a matrix of tuples. How can I get the complex number defined in each <|r -> Re[z], i -> Im[z]|> rather than the tuples?

matrix expression-manipulation associations

share|improve this question

edited 2 hours ago

MarcoB

36.6k556112

asked 10 hours ago

MKFMKF

1588

$endgroup$

add a comment | 

5

$begingroup$

I have a list of associations keyed by real and imaginary numbers, like so:

matrix = {

   {<|"r" -> 0.368252, "i" -> 0.0199587|>, 

    <|"r" -> -0.461644, "i" -> 0.109868|>, 

    <|"r" -> -0.216081, "i" -> 0.562557|>, 

    <|"r" -> -0.479881, "i" -> -0.212978|>}, 



   {<|"r" -> 0.105028, "i" -> 0.632264|>, 

    <|"r" -> 0.116589, "i" -> -0.490063|>, 

    <|"r" -> 0.463378, "i" -> 0.231656|>,

    <|"r" -> -0.148665, "i" -> 0.212065|>},



   {<|"r" -> 0.463253, "i" -> 0.201161|>,

    <|"r" -> 0.460547, "i" -> 0.397829|>,

    <|"r" -> 0.222257, "i" -> 0.0129121|>,

    <|"r" -> 0.168641, "i" -> -0.544568|>},



   {<|"r" -> 0.255221, "i" -> -0.364687|>,

    <|"r" -> 0.191895, "i" -> -0.337437|>,

    <|"r" -> -0.12278, "i" -> 0.551195|>,

    <|"r" -> 0.560485, "i" -> 0.134702|>}

}

Given this, I can write

testmatrix = Join[Values[matrix], 2]`

to get a matrix, but it is a matrix of tuples. How can I get the complex number defined in each <|r -> Re[z], i -> Im[z]|> rather than the tuples?

matrix expression-manipulation associations

share|improve this question

edited 2 hours ago

MarcoB

36.6k556112

asked 10 hours ago

MKFMKF

1588

$endgroup$

add a comment | 

$begingroup$

I have a list of associations keyed by real and imaginary numbers, like so:

matrix = {

   {<|"r" -> 0.368252, "i" -> 0.0199587|>, 

    <|"r" -> -0.461644, "i" -> 0.109868|>, 

    <|"r" -> -0.216081, "i" -> 0.562557|>, 

    <|"r" -> -0.479881, "i" -> -0.212978|>}, 



   {<|"r" -> 0.105028, "i" -> 0.632264|>, 

    <|"r" -> 0.116589, "i" -> -0.490063|>, 

    <|"r" -> 0.463378, "i" -> 0.231656|>,

    <|"r" -> -0.148665, "i" -> 0.212065|>},



   {<|"r" -> 0.463253, "i" -> 0.201161|>,

    <|"r" -> 0.460547, "i" -> 0.397829|>,

    <|"r" -> 0.222257, "i" -> 0.0129121|>,

    <|"r" -> 0.168641, "i" -> -0.544568|>},



   {<|"r" -> 0.255221, "i" -> -0.364687|>,

    <|"r" -> 0.191895, "i" -> -0.337437|>,

    <|"r" -> -0.12278, "i" -> 0.551195|>,

    <|"r" -> 0.560485, "i" -> 0.134702|>}

}

Given this, I can write

testmatrix = Join[Values[matrix], 2]`

to get a matrix, but it is a matrix of tuples. How can I get the complex number defined in each <|r -> Re[z], i -> Im[z]|> rather than the tuples?

matrix expression-manipulation associations

share|improve this question

edited 2 hours ago

MarcoB

36.6k556112

asked 10 hours ago

MKFMKF

1588

$endgroup$

matrix = {

   {<|"r" -> 0.368252, "i" -> 0.0199587|>, 

    <|"r" -> -0.461644, "i" -> 0.109868|>, 

    <|"r" -> -0.216081, "i" -> 0.562557|>, 

    <|"r" -> -0.479881, "i" -> -0.212978|>}, 



   {<|"r" -> 0.105028, "i" -> 0.632264|>, 

    <|"r" -> 0.116589, "i" -> -0.490063|>, 

    <|"r" -> 0.463378, "i" -> 0.231656|>,

    <|"r" -> -0.148665, "i" -> 0.212065|>},



   {<|"r" -> 0.463253, "i" -> 0.201161|>,

    <|"r" -> 0.460547, "i" -> 0.397829|>,

    <|"r" -> 0.222257, "i" -> 0.0129121|>,

    <|"r" -> 0.168641, "i" -> -0.544568|>},



   {<|"r" -> 0.255221, "i" -> -0.364687|>,

    <|"r" -> 0.191895, "i" -> -0.337437|>,

    <|"r" -> -0.12278, "i" -> 0.551195|>,

    <|"r" -> 0.560485, "i" -> 0.134702|>}

}

testmatrix = Join[Values[matrix], 2]`

share|improve this question

edited 2 hours ago

MarcoB

36.6k556112

asked 10 hours ago

MKFMKF

1588

share|improve this question

edited 2 hours ago

MarcoB

36.6k556112

asked 10 hours ago

MKFMKF

1588

edited 2 hours ago

MarcoB

36.6k556112

edited 2 hours ago

MarcoB

36.6k556112

asked 10 hours ago

MKFMKF

1588

asked 10 hours ago

MKFMKF

1588

2 Answers
2

active

oldest

votes

6

$begingroup$

Apply[Complex, matrix, {2}]

{{0.368252 +0.0199587 I,-0.461644+0.109868 I,-0.216081+0.562557 I,-0.479881-0.212978 I},

{0.105028 +0.632264 I,0.116589 -0.490063 I,0.463378 +0.231656 I,-0.148665+0.212065 I},

{0.463253 +0.201161 I,0.460547 +0.397829 I,0.222257 +0.0129121 I,0.168641 -0.544568 I},

{0.255221 -0.364687 I,0.191895 -0.337437 I,-0.12278+0.551195 I,0.560485 +0.134702 I}}

share|improve this answer

answered 5 hours ago

kglrkglr

186k10203422

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Huh, that's a great one! A word of warning though: This method produces unpacked arrays.
  $endgroup$
  – Henrik Schumacher
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The Apply[Complex] method will also fail if the entries are not integers or inexact real numbers, e.g. Complex @@ {Pi, Sqrt[2]}.
  $endgroup$
  – J. M. is computer-less♦
  2 hours ago
  

  
  
  
  

add a comment | 

5

$begingroup$

matrix[[All, All, "r"]] + I matrix[[All, All, "i"]]

or

Join[Values[matrix], 2].{1, I}

share|improve this answer

edited 3 hours ago

answered 10 hours ago

Henrik SchumacherHenrik Schumacher

55.3k576154

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Even better: Values[matrix].{1, I}, which preserves the matrix structure.
  $endgroup$
  – J. M. is computer-less♦
  2 hours ago
  

  
  
  
  

add a comment | 

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6

$begingroup$

Apply[Complex, matrix, {2}]

{{0.368252 +0.0199587 I,-0.461644+0.109868 I,-0.216081+0.562557 I,-0.479881-0.212978 I},

{0.105028 +0.632264 I,0.116589 -0.490063 I,0.463378 +0.231656 I,-0.148665+0.212065 I},

{0.463253 +0.201161 I,0.460547 +0.397829 I,0.222257 +0.0129121 I,0.168641 -0.544568 I},

{0.255221 -0.364687 I,0.191895 -0.337437 I,-0.12278+0.551195 I,0.560485 +0.134702 I}}

share|improve this answer

answered 5 hours ago

kglrkglr

186k10203422

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Huh, that's a great one! A word of warning though: This method produces unpacked arrays.
  $endgroup$
  – Henrik Schumacher
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The Apply[Complex] method will also fail if the entries are not integers or inexact real numbers, e.g. Complex @@ {Pi, Sqrt[2]}.
  $endgroup$
  – J. M. is computer-less♦
  2 hours ago
  

  
  
  
  

add a comment | 

6

$begingroup$

Apply[Complex, matrix, {2}]

{{0.368252 +0.0199587 I,-0.461644+0.109868 I,-0.216081+0.562557 I,-0.479881-0.212978 I},

{0.105028 +0.632264 I,0.116589 -0.490063 I,0.463378 +0.231656 I,-0.148665+0.212065 I},

{0.463253 +0.201161 I,0.460547 +0.397829 I,0.222257 +0.0129121 I,0.168641 -0.544568 I},

{0.255221 -0.364687 I,0.191895 -0.337437 I,-0.12278+0.551195 I,0.560485 +0.134702 I}}

share|improve this answer

answered 5 hours ago

kglrkglr

186k10203422

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Huh, that's a great one! A word of warning though: This method produces unpacked arrays.
  $endgroup$
  – Henrik Schumacher
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The Apply[Complex] method will also fail if the entries are not integers or inexact real numbers, e.g. Complex @@ {Pi, Sqrt[2]}.
  $endgroup$
  – J. M. is computer-less♦
  2 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

Apply[Complex, matrix, {2}]

{{0.368252 +0.0199587 I,-0.461644+0.109868 I,-0.216081+0.562557 I,-0.479881-0.212978 I},

{0.105028 +0.632264 I,0.116589 -0.490063 I,0.463378 +0.231656 I,-0.148665+0.212065 I},

{0.463253 +0.201161 I,0.460547 +0.397829 I,0.222257 +0.0129121 I,0.168641 -0.544568 I},

{0.255221 -0.364687 I,0.191895 -0.337437 I,-0.12278+0.551195 I,0.560485 +0.134702 I}}

share|improve this answer

answered 5 hours ago

kglrkglr

186k10203422

$endgroup$

Apply[Complex, matrix, {2}]

share|improve this answer

answered 5 hours ago

kglrkglr

186k10203422

answered 5 hours ago

kglrkglr

186k10203422

answered 5 hours ago

kglrkglr

186k10203422

5

$begingroup$

matrix[[All, All, "r"]] + I matrix[[All, All, "i"]]

or

Join[Values[matrix], 2].{1, I}

share|improve this answer

edited 3 hours ago

answered 10 hours ago

Henrik SchumacherHenrik Schumacher

55.3k576154

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Even better: Values[matrix].{1, I}, which preserves the matrix structure.
  $endgroup$
  – J. M. is computer-less♦
  2 hours ago
  

  
  
  
  

add a comment | 

5

$begingroup$

matrix[[All, All, "r"]] + I matrix[[All, All, "i"]]

or

Join[Values[matrix], 2].{1, I}

share|improve this answer

edited 3 hours ago

answered 10 hours ago

Henrik SchumacherHenrik Schumacher

55.3k576154

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Even better: Values[matrix].{1, I}, which preserves the matrix structure.
  $endgroup$
  – J. M. is computer-less♦
  2 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

matrix[[All, All, "r"]] + I matrix[[All, All, "i"]]

or

Join[Values[matrix], 2].{1, I}

share|improve this answer

edited 3 hours ago

answered 10 hours ago

Henrik SchumacherHenrik Schumacher

55.3k576154

$endgroup$

matrix[[All, All, "r"]] + I matrix[[All, All, "i"]]

Join[Values[matrix], 2].{1, I}

share|improve this answer

edited 3 hours ago

answered 10 hours ago

Henrik SchumacherHenrik Schumacher

55.3k576154

answered 10 hours ago

Henrik SchumacherHenrik Schumacher

55.3k576154

answered 10 hours ago

Henrik SchumacherHenrik Schumacher

55.3k576154