DTRTTF(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 DTRTTF(3) — the LAPACK manual page, but make it make sense

okay so real talk: this is a page out of the LAPACK library manual, bestie. The whole thing technically lives at a path so long it needs its own zip code, and yes we're keeping it in the NAME section because that's just how these pages roll. Buckle up 🎀

✨ NAME ✨

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

like, that's the whole name. it's giving "my file path is my personality." no cap. 🫶

🌸 SYNOPSIS 🌸

Functions/Subroutines

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

DTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF). that's the whole vibe. TR ➡️ TF. glow-up complete. ✨

🦋 Function/Subroutine Documentation 🦋

subroutine DTRTTF (character transr, character uplo, integer n, double
    precision, dimension( 0: lda-1, 0: * ) a, integer lda, double precision,
    dimension( 0: * ) arf, integer info)

DTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF). yes, it's a repackaging situation. the matrix is the same girl, she's just wearing a different outfit now 💅

💖 Purpose 💖

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

🎀 Parameters 🎀

  • TRANSR — TRANSR is CHARACTER*1. the format check, iykyk:
    • = 'N': ARF in Normal form is wanted;
    • = 'T': ARF in Transpose form is wanted.
  • UPLO — UPLO is CHARACTER*1, aka which triangle are we even talking about:
    • = 'U': Upper triangle of A is stored;
    • = 'L': Lower triangle of A is stored.
  • N — N is INTEGER. the order of the matrix A. N >= 0. zero is literally valid, no drama. 🔥
  • A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, the triangular matrix A. here's the tea:
    • 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.

so like, half of it is main character and the other half is literally not even invited 🫶

  • LDA — LDA is INTEGER. the leading dimension of the matrix A. LDA >= max(1,N). respect the minimum, bestie. 🙈
  • ARF — ARF is DOUBLE PRECISION array, dimension (NT). NT=N*(N+1)/2. On exit, the triangular matrix A in RFP format. this is the glow-up destination ✨
  • INFO — INFO is INTEGER:
    • = 0: successful exit — slay, we ate 💅
    • < 0: if INFO = -i, the i-th argument had an illegal value — bestie, check your inputs 😭

👑 Author 👑

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

the whole squad really showed up for this one 🫶

🌈 Further Details: 🌈

heads up, the rest of this is straight up ASCII art of triangular matrices. it's iconic, it's giving graph paper realness, and honestly it's the best part. read it slow. 💜
!>
!>  We first consider Rectangular Full Packed (RFP) 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
!>  the 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
!>  the transpose of the last three columns of AP lower.
!>  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 = 'T'. RFP A in both UPLO cases is just the
!>  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 then consider Rectangular Full Packed (RFP) 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
!>  the 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
!>  the transpose of the last two columns of AP lower.
!>  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 = 'T'. RFP A in both UPLO cases is just the
!>  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 193 of file dtrttf.f. — yes, line 193, we counted, we're obsessed 🤓

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. (a bot wrote this section and honestly? it ate. 🤖💅)

okay and that's the whole page, bestie 🫶 one last thing for the sign-off: this is LAPACK, Version 3.12.0, and the whole thing is documented out of that dtrttf.f(3) file path up top that we are absolutely not retyping. go repack some triangles. periodt. 💖✨🎀

📦 where this page comes from