CTFTTR(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 NAME 💖

okay bestie, welcome to the ctfttr.f(3) page from the Library Functions Manual — the file path is /home/abui...RC/ctfttr.f(3), and it's giving LAPACK subroutine energy. We're about to make rectangular full packed format make sense, no cap. ✨

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine CTFTTR (transr, uplo, n, arf, a, lda, info)

CTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR). That's the whole assignment. 💅

🦋 Function/Subroutine Documentation 🦋

subroutine CTFTTR (character transr, character uplo, integer n, complex, dimension( 0: * ) arf, complex, dimension( 0: lda-1, 0: * ) a, integer lda, integer info)

CTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR). slay. 🫶

🌸 Purpose 🌸

okay so the actual purpose, straight up: CTFTTR copies a triangular matrix A from rectangular full packed format (TF) to standard full format (TR). That's it. That's the plot. 🔥

🎀 Parameters 🎀

  • TRANSR — TRANSR is CHARACTER*1. = 'N': ARF is in Normal format; = 'C': ARF is in Conjugate-transpose format. Pick your vibe. 🌈
  • UPLO — UPLO is CHARACTER*1. = 'U': A is upper triangular; = 'L': A is lower triangular. Both are valid, bestie. 💅
  • N — N is INTEGER. It's the order of the matrix A. Constraint: N >= 0. No negative chaos allowed. 😭
  • ARF — ARF is COMPLEX array, dimension ( N*(N+1)/2 ). On entry, it's the upper or lower triangular matrix A stored in RFP format. For a further discussion see Notes below. (Yes, it says Notes — iykyk.) 🦋
  • A — A is COMPLEX array, dimension ( LDA, N ). On exit, this is the triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. Respect the triangle, periodt. 🔺
  • LDA — LDA is INTEGER. It's the leading dimension of the array A. Constraint: LDA >= max(1,N). No cap. 🎀
  • INFO — INFO is INTEGER. = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value. So negative INFO means something was not it. 💀

👑 Author 👑

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

The legends. 🌟

🔥 Further Details 🔥

okay this is where it gets visual, bestie. We first consider Standard Packed Format when N is even. We give an example where N = 6. The AP upper and AP lower layouts are:

      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'. Here's the visual:

         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

We next consider Standard Packed Format when N is odd. We give an example where N = 5. The AP upper and AP lower layouts are:

     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'. Here's the visual:

         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

and for the record, this definition lives at line 215 of file ctfttr.f. 🫶

🌈 Author 🌈

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okay that's the whole page, bestie! This was LAPACK Version 3.12.0, and the file is /home/abui...RC/ctfttr.f(3). You ate that. 💅✨

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