CTFTRI(3)

💅 ctftri.f(3) — Library Functions Manual 🎀

okay so bestie, this page lives in the Library Functions Manual, it's the doc for ctftri.f(3), and honestly? it's giving "linear algebra but make it fashion" ✨ buckle up 🦋

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ctftri.f

like, that's literally the whole name, that's the path, no notes 💀

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine CTFTRI (transr, uplo, diag, n, a, info)
    CTFTRI

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👑 Function/Subroutine Documentation 👑

subroutine CTFTRI (character transr, character uplo, character diag, integer n,
    complex, dimension( 0: * ) a, integer info)
    CTFTRI

🎀 Purpose 🎀

!>

!> CTFTRI computes the inverse of a triangular matrix A stored in RFP

!> format.

!>

!> This is a Level 3 BLAS version of the algorithm.

!>

so yeah — it flips your triangular matrix inside out and hands you the inverse, and it's the Level 3 BLAS glow-up of the algorithm 💖 no cap.

🦋 Parameters 🦋

• TRANSR — is CHARACTER*1
  • = 'N': The Normal TRANSR of RFP A is stored;
  • = 'C': The Conjugate-transpose TRANSR of RFP A is stored.
• UPLO — is CHARACTER*1
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• DIAG — is CHARACTER*1
  • = 'N': A is non-unit triangular;
  • = 'U': A is unit triangular.
• N — is INTEGER
  • The order of the matrix A. N >= 0.
• A — is COMPLEX array, dimension ( N*(N+1)/2 );
  • On entry, the triangular matrix A in RFP format. RFP format is described by TRANSR, UPLO, and N as follows: If TRANSR = 'N' then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A as defined when TRANSR = 'N'. The contents of RFP A are defined by UPLO as follows: If UPLO = 'U' the RFP A contains the nt elements of upper packed A; If UPLO = 'L' the RFP A contains the nt elements of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is even and N is odd. See the Note below for more details.
  • On exit, the (triangular) inverse of the original matrix, in the same storage format.
• INFO — is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse can not be computed. 😭 (bestie that one's a real "we can't fix this" moment)

💜 Author 💜

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🌈 Further Details: 🌈

!>

!> 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

!>

the little -- marks up there are the conjugate markers, bestie — they sit above the element, not inside it, do not come for me 💅

🌟 Definition at line 220 of file ctftri.f. 🌟

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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ngl if INFO > 0 you got a zero on the diagonal and the whole thing is singular — no inverse for you, the matrix said "not today" 💀

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and that's the whole page, bestie 🎀 this was LAPACK, Version 3.12.0, and the file is /home/abui...RC/ctftri.f(3) — mwah, periodt ✨💖