CTPTTF(3)

🎀 CTPTTF(3) — Library Functions Manual 🎀

Okay bestie, welcome to CTPTTF(3), straight outta the Library Functions Manual. This page came from /home/abui...RC/ctpttf.f(3), and it is fully giving “tiny subroutine, huge triangular-matrix energy” 💅✨

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ctpttf.f — that’s the source file this whole page is obsessed with, no cap.

🦋 SYNOPSIS 🦋

💫 Functions/Subroutines 💫

• subroutine CTPTTF (transr, uplo, n, ap, arf, info) — CTPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF). Literally its whole main-character arc. Slay. 🔥

🧚 Function/Subroutine Documentation 🧚

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

CTPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF). That’s the vibe check and it passed 💖

💖 Purpose 💖

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

That’s it. That’s the purpose. Iconic behavior, honestly 👑

✨ 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 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 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 up: we consider Standard Packed Format when N is even. Example time, and the example is N = 6. Here’s the packed-format moment:

    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 like this, bestie:

• 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 where N = 5, because we love range:

   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 ctpttf.f.

💀 Author 💀

Generated automatically by Doxygen for LAPACK from the source code.

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