ZTFTTR(3)

💅 ZTFTTR(3) — Library Functions Manual 💅

okay bestie, welcome to the ztfttr.f(3) page in the Library Functions Manual. This is the LAPACK source-file page for ZTFTTR, and the path is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ztfttr.f. Let's get into it. 🫶

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ztfttr.f — that's the file this page is about, bestie. 💖

🦋 SYNOPSIS 🦋

Functions/Subroutines

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).

💖 Function/Subroutine Documentation 💖

`subroutine ZTFTTR (...)`

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).

🎀 Purpose 🎀

okay so the whole point: ZTFTTR copies a triangular matrix A from rectangular full packed format (TF) to standard full format (TR). That's the mission. 💅

🍓 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 — N is INTEGER; it's the order of the matrix A. N >= 0.
ARF — ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ), and on entry it's the upper or lower triangular matrix A stored in RFP format. For a further discussion see Notes below.
A — A is COMPLEX*16 array, dimension ( LDA, N ). On exit, this is 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; it's 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, this is the part where it gets a lil visual. 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 ztfttr.f.

🌸 Author 🌸

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