DTFTTP(3)

💖 DTFTTP(3) — like, the LAPACK manual page, but make it make sense 💖

okay bestie, so this is <pink>DTFTTP</pink>, and before we even get into it — real talk — this page lives at /home/abui...RC/dtfttp.f(3) and it's part of the Library Functions Manual, which is giving "the grown-ups' documentation" energy but honestly it's just a Fortran file that does one job and does it flawlessly. 🎀

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✨ NAME ✨

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

like... that's the whole name. it's a whole path. iconic of it, honestly. the main character of this page is that one .f file, no cap. 🦋

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✨ 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). that's it. that's the whole vibe. TF in, TP out, slay. 💅

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✨ Function/Subroutine Documentation ✨

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

so, DTFTTP copies a triangular matrix A from rectangular full packed format (TF) to standard packed format (TP). literally what the synopsis said, but now it's official. 🔥

🎯 Purpose:

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

yes queen, say it again for the people in the back. 😭

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🌸 Parameters 🌸

• TRANSR — this one's a CHARACTER*1, bestie. it tells you which format ARF is chillin' in:
  • = 'N': ARF is in Normal format;
  • = 'T': ARF is in Transpose format;

iykyk, one letter, huge consequences. 🫶

• UPLO — also a CHARACTER*1, and it's the "which half of the triangle are we even talking about" flag:
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• N — N is INTEGER, and it's The order of the matrix A. N >= 0. that's the whole rule, don't push it. 🚨
• ARF — ARF is DOUBLE PRECISION 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 (<- and yes, the notes are right there below, keep scrolling, they're a whole journey).
• AP — AP is DOUBLE PRECISION 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.

that's the index math, memorize it or weep at it, your call 💀

• INFO — INFO is INTEGER, the little status report at the end:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value 🙈

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👑 Author 👑

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

the whole squad, tbh. 🫡

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🧚 Further Details:

!>
!>  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

okay breathe, we're halfway. 💜

!>
!>  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

and that's the whole even-and-odd saga. you ate that. 🌈

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📍 Definition

Definition at line 186 of file dtfttp.f. go look, it's right there. ⭐

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✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code. (not a human, just a very diligent little robot 🎀)

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LAPACK — Version 3.12.0 — and the footer of this whole thing was /home/abui...RC/dtfttp.f(3), so like... now you know exactly which file to point at when someone asks. mwah, go forth and pack some triangles, bestie 💋💖🧚‍♀️