SRC/ztfttp.f(3)

💖 SRC/ztfttp.f 💖 — Library Functions Manual

okay bestie, welcome to the cutest little page for SRC/ztfttp.f in the Library Functions Manual. This one is a Fortran subroutine moment, and it is literally giving “move a triangular matrix from rectangular full packed format to standard packed format.” no cap, that’s the whole plot 💅

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✨ NAME ✨

SRC/ztfttp.f

🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine ztfttp (transr, uplo, n, arf, ap, info) — ZTFTTP copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP). 🫶

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🦋 Function/Subroutine Documentation 🦋

🎀 subroutine ztfttp (character transr, character uplo, integer n, complex*16, dimension( 0: * ) arf, complex*16, dimension( 0: * ) ap, integer info)

ZTFTTP copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP). 💖

🧚 Purpose:

ZTFTTP copies a triangular matrix A from rectangular full packed format (TF) to standard packed format (TP). ✨

🧸 Parameters

• TRANSR — TRANSR is CHARACTER*1
  • = 'N': ARF is in Normal format;
  • = 'C': ARF is in Conjugate-transpose format;
• UPLO — UPLO is CHARACTER*1
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• N — N is INTEGER. The order of the matrix A. N >= 0.
• ARF — ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ),. On entry, the upper or lower triangular matrix A stored in RFP format. For a further discussion see Notes below.
• AP — AP is COMPLEX*16 array, dimension ( N*(N+1)/2 ),. On exit, the upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
  • if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
  • if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
• INFO — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

👑 Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🔥 Further Details:

okay so first up, let’s talk Standard Packed Format when N is even. We’re giving an example where N = 6 🍓

      AP is Upper             AP is Lower

   00 01 02 03 04 05       00
      11 12 13 14 15       10 11
         22 23 24 25       20 21 22
            33 34 35       30 31 32 33
               44 45       40 41 42 43 44
                  55       50 51 52 53 54 55

Let TRANSR = 'N'. RFP holds AP as follows:

• For UPLO = 'U', the upper trapezoid A(0:5,0:2) consists of the last three columns of AP upper. The lower triangle A(4:6,0:2) consists of conjugate-transpose of the first three columns of AP upper.
• For UPLO = 'L', the lower trapezoid A(1:6,0:2) consists of the first three columns of AP lower. The upper triangle A(0:2,0:2) consists of conjugate-transpose of the last three columns of AP lower.

To denote conjugate we place -- above the element. This covers the case N even and TRANSR = 'N'. 💀

         RFP A                   RFP A

                                -- -- --
        03 04 05                33 43 53
                                   -- --
        13 14 15                00 44 54
                                      --
        23 24 25                10 11 55

        33 34 35                20 21 22
        --
        00 44 45                30 31 32
        -- --
        01 11 55                40 41 42
        -- -- --
        02 12 22                50 51 52

Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-transpose of RFP A above. One therefore gets: 🦋

           RFP A                   RFP A

     -- -- -- --                -- -- -- -- -- --
     03 13 23 33 00 01 02    33 00 10 20 30 40 50
     -- -- -- -- --                -- -- -- -- --
     04 14 24 34 44 11 12    43 44 11 21 31 41 51
     -- -- -- -- -- --                -- -- -- --
     05 15 25 35 45 55 22    53 54 55 22 32 42 52

Next we consider Standard Packed Format when N is odd. Example time: N = 5 🎀

     AP is Upper                 AP is Lower

   00 01 02 03 04              00
      11 12 13 14              10 11
         22 23 24              20 21 22
            33 34              30 31 32 33
               44              40 41 42 43 44

Let TRANSR = 'N'. RFP holds AP as follows:

• For UPLO = 'U', the upper trapezoid A(0:4,0:2) consists of the last three columns of AP upper. The lower triangle A(3:4,0:1) consists of conjugate-transpose of the first two columns of AP upper.
• For UPLO = 'L', the lower trapezoid A(0:4,0:2) consists of the first three columns of AP lower. The upper triangle A(0:1,1:2) consists of conjugate-transpose of the last two columns of AP lower.

To denote conjugate we place -- above the element. This covers the case N odd and TRANSR = 'N'. 🌈

         RFP A                   RFP A

                                   -- --
        02 03 04                00 33 43
                                      --
        12 13 14                10 11 44

        22 23 24                20 21 22
        --
        00 33 34                30 31 32
        -- --
        01 11 44                40 41 42

Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-transpose of RFP A above. One therefore gets: 👑

           RFP A                   RFP A

     -- -- --                   -- -- -- -- -- --
     02 12 22 00 01             00 10 20 30 40 50
     -- -- -- --                   -- -- -- -- --
     03 13 23 33 11             33 11 21 31 41 51
     -- -- -- -- --                   -- -- -- --
     04 14 24 34 44             43 44 22 32 42 52

Definition at line 207 of file ztfttp.f. 💅

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🌈 Author 🌈

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