tfttr(3)

📦

version 3.12.1 · 9 versions

3.12.1 · arch rolling (latest)
3.12.0 · opensuse-leap 16.0
3.12.1 · ubuntu stonking
3.12.1 · ubuntu questing
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3.12.0 · ubuntu noble
3.12.0 · centos-stream 10, fedora 43, fedora 44
3.12.1 · ubuntu resolute
3.12.1 · debian trixie

🎀 tfttr(3) 🎀

okay so this is the manual page for tfttr — library functions manual, very demure, very linear-algebra. It's actually a whole family of routines and bestie, they all do basically the same thing for different data types. Grab a snack, this one is long 🍓

✨ NAME ✨

tfttr — triangular matrix, RFP (tf) to full (tr)

like, that is genuinely the entire name line. no notes. it slaps the triangular matrix out of RFP (that's "tf") and into full format (that's "tr"). the letters are the function, iykyk 💅

🌸 SYNOPSIS 🌸

💖 Functions 💖

Four whole subroutines, one per flavour of number. Same argument list, different types. Iconic consistency, honestly 👑

subroutine ctfttr (transr, uplo, n, arf, a, lda, info) — CTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR).
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).
subroutine stfttr (transr, uplo, n, arf, a, lda, info) — STFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR).
subroutine ztfttr (transr, uplo, n, arf, a, lda, info) — ZTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR).

🦋 DETAILED DESCRIPTION 🦋

okay so the detailed description is lowkey just vibes — the page jumps straight into the function documentation without a big speech first. The real tea is all down there 👇

💅 FUNCTION DOCUMENTATION 💅

🍓 subroutine ctfttr 🍓

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

CTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR). bestie it's a glow-up for your matrix — same data, way better outfit ✨

🌈 Purpose:

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

like. that's the whole plot. no plot twists. 🫶

💜 Parameters

TRANSR

TRANSR is CHARACTER*1

= 'N': ARF is in Normal format;
= 'C': ARF is in Conjugate-transpose format;

UPLO

UPLO is CHARACTER*1

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

N is INTEGER

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

ARF

ARF is COMPLEX 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.

A is COMPLEX 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 this next part is the whole "here's the actual picture" moment and honestly it's kind of gorgeous. Stick with me 🧚

We first consider Standard Packed 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 conjugate-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 conjugate-transpose of the last three columns of AP lower.

To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate-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 next consider Standard Packed 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 conjugate-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 conjugate-transpose of the last two columns of AP lower.

To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate-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 215 of file ctfttr.f.

🌟 subroutine dtfttr 🌟

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). same energy as ctfttr, just double precision this time 💖

🌈 Purpose:

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

💜 Parameters

TRANSR

TRANSR is CHARACTER*1

= 'N': ARF is in Normal format;
= 'T': ARF is in Transpose format.

⚠️ heads up bestie — this one is 'T' for Transpose, not 'C' like the complex version. don't mix them up, fr fr 🙈

UPLO

UPLO is CHARACTER*1

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

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 (if UPLO = 'U') or lower (if UPLO = 'L') matrix A in RFP format. See the below for more details.

A is DOUBLE PRECISION array, dimension (LDA,N)

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:

(…and this is where part 1 of the page runs out — the details are still coming, bestie, hold that thought 🎀)

okay so continuing the dtfttr visual tea, because RFP format is literally doing the most and we need the receipts:

           !>
           !>  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
           !>

Definition at line 195 of file dtfttr.f.

`stfttr` 💖 the REAL single-precision bestie

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

stfttr copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR). no cap, that's the whole job and she does it.

Purpose 🎀

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

Parameters ✨

TRANSR — CHARACTER*1. = 'N': ARF is in Normal format; = 'T': ARF is in Transpose format.
UPLO — CHARACTER*1. = 'U': A is upper triangular; = 'L': A is lower triangular.
N — INTEGER. The order of the matrices ARF and A. N >= 0.
ARF — REAL array, dimension (N*(N+1)/2). On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') matrix A in RFP format. See the details below for more info, bestie.
A — REAL 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
INFO — 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 RFP format again, but make it stfttr edition — same energy, same diagrams:

           !>
           !>  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
           !>

Definition at line 195 of file stfttr.f.

`ztfttr` 💜 the COMPLEX*16 edition, she's fancy

subroutine ztfttr (character transr, character uplo, integer n, complex*16,
    dimension( 0: * ) arf, complex*16, dimension( 0: lda-1, 0: * ) a,
    integer lda, integer info)

ztfttr copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR). same assignment, but make it complex, periodt.

Purpose 🔥

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

Parameters 🌈

TRANSR — CHARACTER*1. = 'N': ARF is in Normal format; = 'C': ARF is in Conjugate-transpose format.
UPLO — CHARACTER*1. = 'U': A is upper triangular; = 'L': A is lower triangular.
N — INTEGER. The order of the matrix A. N >= 0.
ARF — COMPLEX*16 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.
A —
A — COMPLEX*16 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 bestie, first we consider Standard Packed 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 conjugate-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 conjugate-transpose of the last three columns of AP lower. To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate-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 next consider Standard Packed 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 conjugate-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 conjugate-transpose of the last two columns of AP lower. To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate-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 215 of file ztfttr.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

Footer sign-off: LAPACK Version 3.12.0, tfttr(3). The footer doesn't print a separate date, so we're not inventing one — periodt. 💖✨👑

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

tfttr(3)

🎀 tfttr(3) 🎀

✨ NAME ✨

🌸 SYNOPSIS 🌸

💖 Functions 💖

🦋 DETAILED DESCRIPTION 🦋

💅 FUNCTION DOCUMENTATION 💅

🍓 subroutine ctfttr 🍓

🌈 Purpose:

💜 Parameters

👑 Author

🔥 Further Details:

🌟 subroutine dtfttr 🌟

🌈 Purpose:

💜 Parameters

👑 Author

🔥 Further Details:

stfttr 💖 the REAL single-precision bestie

Purpose 🎀

Parameters ✨

Author 🌸

Further Details 🦋

ztfttr 💜 the COMPLEX*16 edition, she's fancy

Purpose 🔥

Parameters 🌈

✨ Author ✨

🌈 Further Details: 🌈

🧚 Author 🧚

`stfttr` 💖 the REAL single-precision bestie

`ztfttr` 💜 the COMPLEX*16 edition, she's fancy