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












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











$endgroup$

















    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?






    matrix expression-manipulation associations







    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?






      matrix expression-manipulation associations







      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




      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

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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









          $endgroup$













          • $begingroup$
            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

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          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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          body.skin-minerva .mw-parser-output table.infobox caption{text-align:center} 日野市 日野市 日文轉寫  • 日文 日野市  • 平假名 ひのし  • 罗马字 Hino-shi 金剛寺（關東三十六不動尊靈場第9號）的不動堂 市旗 徽章 日野市在東京都的位置 日野市 日野市在日本的位置 坐标： 35°40′17″N 139°23′42″E  /  35.6714°N 139.395°E  / 35.6714; 139.395 国家   日本 地方 關東地方 都道府縣 東京都 接鄰行政區 府中市、國立市、立川市、昭島市、八王子市、多摩市 政府  • 市長 大坪冬彦 面积  •  总计 27.53 平方公里（10.63 平方英里） 人口 （2014年12月1日）  • 總計 183,323  • 密度 6,660/平方公里（17,200/平方英里） 象徵  • 市樹 樫  • 市花 菊花  • 市鳥 普通翠鳥 时区 日本標準時間 （UTC+9） 地方公共團體編號 13212-8 邮政编码 〒 191-8686 市役所地址 日野市神明一丁目12番1號 電話號碼 +81-42-585-1111 法人編號 1000020132128 網站 http://www.city.hino.lg.jp/ 人口：日野市官方網頁 日野市 （日语： 日野市 ／ ひのし   Hino shi   * / ? ）為一位于東京都（不含島嶼部分）中央地帶的城市。從東京站乘坐中央線特別快速列車45分鐘即可到該市。面積27.53km²。1963年（昭和38年）11月3日，該市開始實行市制，為全日本第559個市。汽車企業日野自動車的總部位於這裡。 往東京都特別區部的通勤率為20.9%，往八王子市的通勤率為12.0%（平成22年國勢調査）。 目录 1 概要 ...
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          Tu-95轟炸機

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          body.skin-minerva .mw-parser-output table.infobox caption{text-align:center} 图-95 Ту–95 北约代号：熊（Bear） 一架在安格斯空军基地的图-95MS 概觀 類型 战略轰炸机 代號 北约代号： Bear （熊） 乘員 7名 駕駛員2名，機尾炮手1名，其他人員4名 首飛 1952年11月12日 服役 1956年 設計 圖波列夫設計局 產量 超过500架 現況 现役 主要用戶   蘇聯   俄羅斯 衍生機型 图-114、图-119、Tu-95 技术数据 長度 49.50米（162呎5吋） 翼展 51.10米（167呎8吋） 高度 12.12米（39呎9吋） 翼面積 310平方米（3,330平方呎） 空重 90,000公斤（198,000磅） 最大起飛重量 188,000公斤（414,500磅） 發動機 4具库兹涅佐夫NK-12MV型渦輪螺旋槳發動機 功率 4×11,000千瓦（14,800馬力） 性能數據 最大速度 925公里／時（500節，575哩／時） 爬升率 10米／秒（2,000呎／分） 最大升限 12,000米（39,000呎） 最大航程 15,000公里（8,100海浬，9,400哩） 翼負荷 606公斤／平方米（124磅／平方呎） 推重比 235 W／公斤（0.143馬力／磅） 武器装备 機炮 1具/2具AM-23型23公釐雷達控制機砲（機尾） 飛彈 空对地导弹： Kh-20、Kh-22 Kh-26、Kh-55 炸彈 60枚FAB-250炸彈，或 30枚FAB-500炸彈。 其他 载弹量（包括飞弹）：最多15,000公斤（33,000磅） Tu-95熊式MR型機 图-95 （俄语： Ту–95 ， 英语： Tu-95 ），北約代號： Bear （ 熊 ），是蘇聯圖波列夫設計局所研製，是全世界唯一服役的大型四渦輪螺旋槳發動機...
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