SRC/dtfttr.f(3)

🌸 NAME 🌸

This is SRC/dtfttr.f(3) — bestie, it's the manual page for the dtfttr routine, and it's here to explain how to copy a triangular matrix from rectangular full packed format into standard full format. ✨

🎀 SYNOPSIS 🎀

Functions/Subroutines

• subroutine dtfttr (transr, uplo, n, arf, a, lda, info) — DTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR). Slay.

✨ Function/Subroutine Documentation ✨

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

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

💖 Purpose 💖

Okay so the whole mission is literally this: DTFTTR copies a triangular matrix A from rectangular full packed format (TF) to standard full format (TR). That's the vibe. 🫶

🔥 Parameters 🔥

• TRANSR — TRANSR is CHARACTER*1
  • = 'N': ARF is in Normal format;
  • = 'T': ARF is in Transpose format.
• UPLO — UPLO is CHARACTER*1
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• N — N is INTEGER. The order of the matrices ARF and A. N >= 0.
• ARF — ARF is DOUBLE PRECISION array, dimension (N*(N+1)/2). On entry, the upper matrix A if UPLO = 'U', or the lower matrix A if UPLO = 'L', in RFP format. Peep the details below for the full breakdown. 👀
• A — A is DOUBLE PRECISION array, dimension (LDA,N). On exit, 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.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• 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 🧚

Okay so first up: Rectangular Full Packed (RFP) Format when N is even. Example: N = 6, bestie.

      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 like this:

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'. In both UPLO cases, RFP A is literally just the transpose of RFP A above. So you get:

          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 like this:

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'. Again, in both UPLO cases, RFP A 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 195 of file dtfttr.f.

👑 Author 👑

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That's the whole page, bestie! Signing off from SRC/dtfttr.f(3) with LAPACK Version 3.12.0 — mwah 💋✨