ZTPTTF(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 ZTPTTF(3) 💖

okay so welcome to ZTPTTF(3), from the Library Functions Manual — the header path up top is /home/abui...RC/ztpttf.f(3), and we are about to get into some packed-triangle business, bestie 🫶.

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ztpttf.f

🌸 SYNOPSIS 🌸

✨ Functions/Subroutines ✨

subroutine ZTPTTF (transr, uplo, n, ap, arf, info)

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

💅 Function/Subroutine Documentation 💅

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

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

🎀 Purpose 🎀

The Purpose block is literally giving: ZTPTTF copies a triangular matrix A from standard packed format (TP) to rectangular full packed format (TF). Slay 💅.

🦋 Parameters 🦋

💖 TRANSR 💖

  • TRANSR is CHARACTER*1
  • = 'N': ARF in Normal format is wanted;
  • = 'C': ARF in Conjugate-transpose format is wanted.

💖 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.

💖 AP 💖

  • AP is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
  • On entry, 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.

💖 ARF 💖

  • ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
  • On exit, the upper or lower triangular matrix A stored in RFP format. For a further discussion see Notes below.

💖 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 we’re looking at Standard Packed Format when N is even. The example is N = 6, no cap.

    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 up: Standard Packed Format when N is odd, with N = 5 for the example 🌸.

     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 206 of file ztpttf.f 🧚

Definition at line 206 of file ztpttf.f.

👑 Author 👑

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