STRTTF(3)

📦 version 3.12.0, in opensuse-leap 16.0

🦋 strttf.f(3) — Library Functions Manual 🦋

Okay bestie, welcome to the strttf.f(3) glow-up. It’s LAPACK, it’s a subroutine page, and it’s giving “triangular matrix goes from full format to rectangular full packed format.” Stay with me. 💅

💖 NAME 💖

strttf.f — this page is for the file at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/strttf.f. That’s the whole name section, and yes it’s just a path being its main-character self. 🫶

✨ SYNOPSIS ✨

Functions/Subroutines

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

STRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF). That’s the whole pitch. Slay. 🔥

📚 Function/Subroutine Documentation 📚

subroutine STRTTF

Full signature, exactly as it appears, because we do not mess with types:

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

STRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF). Yes bestie, it’s a converter. It takes the triangle you already have and packs it into RFP format. ✨

🎯 Purpose

Okay so the purpose is literally: STRTTF copies a triangular matrix A from standard full format (TR) to rectangular full packed format (TF) . That’s it. That’s the job. No cap. 💖

🌸 Parameters 🌸

  • TRANSR — CHARACTER*1. = 'N': ARF in Normal form is wanted; = 'T': ARF in Transpose form is wanted. So you’re picking whether the packed ARF output is Normal or Transpose form. Choose your fighter. 🎀
  • UPLO — CHARACTER*1. = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. Pick which triangle is the main character. 💅
  • N — INTEGER. The order of the matrix A. N >= 0. That’s the rule, bestie. 🦋
  • A — REAL array, dimension (LDA,N). On entry, 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. Basically only the chosen triangle is read; the other side is not referenced. 🙈
  • LDA — INTEGER. The leading dimension of the matrix A. LDA >= max(1,N). Respect the leading dimension, bestie. 🫶
  • ARF — REAL array, dimension (NT). NT=N*(N+1)/2. On exit, the triangular matrix A in RFP format. That’s the packed output, and it’s giving rectangular full packed realness. 🌈
  • INFO — INTEGER. = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value. So if INFO is negative, check the argument at that position. 🚨

👑 Author

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

🧚 Further Details 🧚

This is the part where RFP format gets explained with diagrams. It’s long, it’s iconic, and the matrix layouts are kept exactly as-is. The !> markers are part of the original comment block, so I left them exactly. 💀

First up: Rectangular Full Packed (RFP) Format when N is even. 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

Then we consider Rectangular Full Packed (RFP) Format when N is odd. 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 strttf.f. 📌

💜 Author

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