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

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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?










share|improve this question











$endgroup$

















    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?










    share|improve this question











    $endgroup$















      5












      5








      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?










      share|improve this question











      $endgroup$




      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















      share|improve this question













      share|improve this question




      share|improve this question








      edited 3 hours ago









      MarcoB

      36.6k556112




      36.6k556112










      asked 11 hours ago









      MKFMKF

      1588




      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









          $endgroup$













          • $begingroup$
            Huh, that's a great one! A word of warning though: This method produces unpacked arrays.
            $endgroup$
            – Henrik Schumacher
            4 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
            3 hours ago



















          5












          $begingroup$

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


          or



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





          share|improve this answer











          $endgroup$













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











          Your Answer





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          2 Answers
          2






          active

          oldest

          votes








          2 Answers
          2






          active

          oldest

          votes









          active

          oldest

          votes






          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









          $endgroup$













          • $begingroup$
            Huh, that's a great one! A word of warning though: This method produces unpacked arrays.
            $endgroup$
            – Henrik Schumacher
            4 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
            3 hours ago
















          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









          $endgroup$













          • $begingroup$
            Huh, that's a great one! A word of warning though: This method produces unpacked arrays.
            $endgroup$
            – Henrik Schumacher
            4 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
            3 hours ago














          6












          6








          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









          $endgroup$



          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












          share|improve this answer



          share|improve this answer










          answered 6 hours ago









          kglrkglr

          186k10203422




          186k10203422












          • $begingroup$
            Huh, that's a great one! A word of warning though: This method produces unpacked arrays.
            $endgroup$
            – Henrik Schumacher
            4 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
            3 hours ago


















          • $begingroup$
            Huh, that's a great one! A word of warning though: This method produces unpacked arrays.
            $endgroup$
            – Henrik Schumacher
            4 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
            3 hours ago
















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




          $begingroup$
          Huh, that's a great one! A word of warning though: This method produces unpacked arrays.
          $endgroup$
          – Henrik Schumacher
          4 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
          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
          3 hours ago











          5












          $begingroup$

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


          or



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





          share|improve this answer











          $endgroup$













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
















          5












          $begingroup$

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


          or



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





          share|improve this answer











          $endgroup$













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














          5












          5








          5





          $begingroup$

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


          or



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





          share|improve this answer











          $endgroup$



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


          or



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






          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited 4 hours ago

























          answered 11 hours ago









          Henrik SchumacherHenrik Schumacher

          55.3k576154




          55.3k576154












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


















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
















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




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


















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