SRC/dtfttp.f(3)

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version 3.12.1 · 7 versions
, in arch rolling

✨ SRC/dtfttp.f ✨

okay so bestie, this is a whole entire LAPACK manpage and honestly? it's giving "math girlie explains her homework" vibes 💅. We're looking at dtfttp.f from the LAPACK Library Functions Manual, and no cap, it's actually kinda iconic once you get past the Fortran.

🎀 SYNOPSIS 🎀

Functions/Subroutines

  • subroutine dtfttp (transr, uplo, n, arf, ap, info) — DTFTTP copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP).

🦋 Function/Subroutine Documentation 🦋

subroutine dtfttp (character transr, character uplo, integer n, double precision, dimension( 0: * ) arf, double precision, dimension( 0: * ) ap, integer info)

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

💖 Purpose:

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

like, that's the whole point of her existence, periodt ✨

🌸 Parameters

  • TRANSR — TRANSR is CHARACTER*1 and it's literally telling you which format ARF is in:
!>          = 'N':  ARF is in Normal format;
!>          = 'T':  ARF is in Transpose format;
  • UPLO — also CHARACTER*1, and it's the vibe check for which triangle we're dealing with:
!>          = 'U':  A is upper triangular;
!>          = 'L':  A is lower triangular.
  • N — N is INTEGER, no cap. This is the order of the matrix A. And lowkey important: N >= 0. we respect the bounds in this house 🫶
  • ARF — ARF is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ). On entry, this holds the upper or lower triangular matrix A stored in RFP format. For a further discussion, see Notes below. (we will be getting into it, don't worry)
  • AP — AP is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ). On exit, this is the upper or lower triangular matrix A, packed columnwise in a linear array. And here's the exact tea on how the j-th column of A gets stored:
!>          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.

(copy these formulas exactly, bestie, they're not vibes—they're facts)

  • INFO — INFO is INTEGER and it's the emotional state report:
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value

so if INFO is negative, like, something went wrong with that argument. rude 💀

👑 Author

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

(these are the legends who made it happen, we stan)

🌈 Further Details:

okay this is the part where she gets detailed, and we absolutely are not skipping it because every single diagram matters.
!>
!>  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
!>

like... the way these matrices are arranged? highkey satisfying if you're into that. and if you're not? lowkey fair, but she said what she said 💅

Definition at line 186 of file dtfttp.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

LAPACK • Version 3.12.0 • SRC/dtfttp.f(3)

okay that's the whole thing bestie, you ate that, go forth and pack those triangular matrices 🫶✨💖

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