SRC/dtpttf.f(3)

Hey bestie! 💖 You're reading SRC/dtpttf.f(3) from the Library Functions Manual — yes, the manual name is folded in, we're doing it cute today. This page is all about DTPTTF, and honestly? iconic. No cap, this subroutine is the main character energy of packed-format conversions. ✨

NAME 🏷️

SRC/dtpttf.f — that's the name, bestie. The star of this page is the DTPTTF subroutine. No cap. 💅

SYNOPSIS ✨

Functions/Subroutines 💫

Here's the exact signature, character for character:

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

And the one-line vibe check: DTPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF). Slay. 👑

Function/Subroutine Documentation 🧚

Okay so this is the full documentation for dtpttf, and we're going to go through literally every parameter, every matrix example, every credit — no skipping, periodt. 🫶

Purpose: 🎯

The purpose is right here, bestie: DTPTTF copies a triangular matrix A from standard packed format (TP) to rectangular full packed format (TF). That's the whole glow-up. The way that TP becomes TF? Obsessed. ✨

Parameters 📋

Vibe check every single one, no skipping. 💖

TRANSR 💅

TRANSR is CHARACTER*1:

• = 'N': ARF in Normal format is wanted;
• = 'T': ARF in Conjugate-transpose format is wanted.

UPLO 🦋

UPLO is CHARACTER*1:

• = 'U': A is upper triangular;
• = 'L': A is lower triangular.

N 🔢

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

AP 🍓

AP is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ). On entry, 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.

ARF 🌸

ARF is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ). On exit, the upper or lower triangular matrix A stored in RFP format. For a further discussion see Notes below.

INFO 💀

INFO is INTEGER:

• = 0: successful exit
• < 0: if INFO = -i, the i-th argument had an illegal value

Author 👑

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

Further Details: 🔍

Here's where it gets lowkey a lot of matrices, but it ate, fr fr. This is the RFP format tour, iykyk. The matrices are exact, so don't touch the numbers. 💖

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

Next: Rectangular Full Packed (RFP) Format when N is odd. Example 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 185 of file dtpttf.f. 🧾

dtpttf.f at line 185. That's where the definition lives. Don't ask me why line 185, it just is. 💅

Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

---

Okay bestie, that's the whole SRC/dtpttf.f(3) page! 💖 Footer check: LAPACK Version 3.12.0, source SRC/dtpttf.f(3) — and the footer doesn't list a date, so I'm not making one up, periodt. 🫶✨