CTFTTP(3)

💖 CTFTTP 💖 — a.k.a. the file at /home/abui...RC/ctfttp.f(3)

okay so bestie, this whole page lives in the Library Functions Manual, and it's literally all about one lil subroutine in ctfttp.f. no cap, that's it. let's get into it 🫶

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🌸 NAME 🌸

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

yes that's the whole name section. it's giving "my full government name" energy 💀 iykyk.

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✨ 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). that's the whole vibe, honestly — glow-up your triangle from one packing to a different packing 🔥

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🎀 Function/Subroutine Documentation 🎀

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). (yes, same sentence, bestie, the docs said it twice so we're saying it twice 💅)

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💜 Purpose

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

so basically: matrix A walks in wearing TF, walks out wearing TP. a whole wardrobe change. iconic 👑

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🦋 Parameters

🌈 TRANSR

!>          TRANSR is CHARACTER*1
!>          = 'N':  ARF is in Normal format;
!>          = 'C':  ARF is in Conjugate-transpose format;
!>

it's a CHARACTER*1, so one whole character, and it picks the format of ARF:

• '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.
!>

also CHARACTER*1. pick a side:

• 'U' — A is upper triangular ⬆️
• 'L' — A is lower triangular ⬇️

🧚 N

!>          N is INTEGER
!>          The order of the matrix A. N >= 0.
!>

N is INTEGER, it's the order of the matrix A, and it must satisfy N >= 0. no negative orders, that's not the move 🙈

🎀 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.
!>

ARF is a COMPLEX array with dimension ( N*(N+1)/2 ). On entry, it holds the upper or lower triangular matrix A stored in RFP format. for a further discussion, see Notes below 👀 (it's the Further Details section, bestie, keep scrolling)

💅 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.
!>

AP is a COMPLEX array with dimension ( N*(N+1)/2 ) too. On exit, it's the upper or lower triangular matrix A, packed columnwise in a linear array 😤 the indexing is the main character here:

• 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

write those down, they will 100% show up on the exam 🫠

⭐ INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

INFO is INTEGER and it's the vibe check on your whole call:

• = 0 — successful exit, we ate, no notes 💅
• < 0 — if INFO = -i, the i-th argument had an illegal value 😭 something you passed was not it

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👑 Author

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

four whole institutions co-signed this. the group project actually got finished, which is honestly aspirational 🫶

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🔥 Further Details:

okay bestie this is the part with the diagrams and they're genuinely kind of gorgeous, so I'm pasting the whole thing exactly — do not skip it, it's lowkey the best part 💖

!>
!>  We first consider Standard Packed Format when N is even.
!>  We give 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
!>
!>
!>  We next  consider Standard Packed Format when N is odd.
!>  We give an example where 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
!>

the -- marks are the conjugate indicators, btw. tiny little hats. adorable. 🎩

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🫶 Definition at line 207 of file ctfttp.f 🌈

line 207, bestie. go look, it's right there ✨

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. (so nobody hand-wrote this, a robot did, and honestly? slay 🤖💅)

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and that's the whole page!! no cap, you now know everything CTFTTP has ever wanted to tell you. go forth and pack your triangles correctly 🦋

LAPACK, Version 3.12.0 — and the file itself is /home/abui...RC/ctfttp.f(3). mwah, bye bestie 💖🎀✨