SRC/ztrttf.f(3)

🦋 SRC/ztrttf.f 🦋

okay so this is a Library Functions Manual page, and the main character is ztrttf. It’s giving “copy a triangular matrix from standard full format (TR) to rectangular full packed format (TF)” energy, and we’re keeping every flag, value, and detail. no cap 💅

🌸 NAME 🌸

SRC/ztrttf.f

💅 SYNOPSIS 💅

✨ Functions/Subroutines ✨

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

🎀 Function/Subroutine Documentation 🎀

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

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

💖 Purpose 💖

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

🧚 Parameters 🧚

TRANSR

TRANSR is CHARACTER*1

• = 'N': ARF in Normal mode is wanted;
• = 'C': ARF in Conjugate Transpose mode 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.

A

A is COMPLEX*16 array, dimension ( LDA, N )

On entry, 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 matrix A. LDA >= max(1,N).

ARF

ARF is COMPLEX*16 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 🌈

okay bestie, here’s the exact packed-format lore. First we consider Standard Packed Format when N is even. Example where N = 6:

!>
!>  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
!>

And next we consider Standard Packed Format when N is odd. Example where N = 5:

!>
!>  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 ztrttf.f.

💻 Author 💻

Generated automatically by Doxygen for LAPACK from the source code.

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💖 That’s the whole page, bestie: LAPACK, Version 3.12.0, source page SRC/ztrttf.f(3). Stay packed and slay! 💖