SRC/ctfttp.f(3)

💅 SRC/ctfttp.f(3) 💅

okay bestie, welcome to the Library Functions Manual page for SRC/ctfttp.f(3). This is the ctfttp subroutine, and she is literally here to copy a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP). No cap. 💖

✨ NAME ✨

SRC/ctfttp.f

That's the name, bestie. Periodt. 💅

🦋 SYNOPSIS 🦋

Functions/Subroutines

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

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

👑 Function/Subroutine Documentation 👑

💫 subroutine ctfttp 💫

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

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

🎀 Purpose 🎀

The purpose is exactly this: CTFTTP 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 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 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, here comes the packed-format lore. Stay with me, bestie — this is the part where the diagrams really eat. 💀✨

First, standard packed format when N is even. Example: 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, standard packed format when N is odd. Example: 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 ctfttp.f.

🌟 Author 🌟

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okay bestie, that's the whole page! This iconic little manpage is from LAPACK Version 3.12.0 and lives at SRC/ctfttp.f(3). Go convert those triangular matrices and slay. 💅🎀✨