CSYCONVF(3)

💅 CSYCONVF(3) — bestie edition

okay so this page lives at /home/abui.../csyconvf.f(3) in the Library Functions Manual, and honestly? it's a glow-up page. it's the kind of routine that doesn't do math so much as redress the math — swapping factorization formats like outfits. slay.

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✨ NAME ✨

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

that's the file, that's the whole name section, we move 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine CSYCONVF (uplo, way, n, a, lda, e, ipiv, info)

CSYCONVF — yes that's the whole description the synopsis gives us, she's mysterious like that 🎀

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🦋 Function/Subroutine Documentation 🦋

subroutine CSYCONVF (character uplo, character way, integer n, complex,
    dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer,
    dimension( * ) ipiv, integer info)

CSYCONVF — again, icon behavior. now let's get into it 👑

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💖 Purpose 💖

okay so bestie, listen:

if parameter WAY = 'C':

CSYCONVF converts the factorization output format used in CSYTRF — the one you hand in through parameter A — into the factorization output format used in CSYTRF_RK (or CSYTRF_BK), and that converted version gets stored on exit in parameters A and E. it also converts, in place, the details of the interchanges stored in IPIV from the format used in CSYTRF into the format used in CSYTRF_RK (or CSYTRF_BK). 💫

if parameter WAY = 'R':

CSYCONVF performs the conversion in the reverse direction — i.e. it converts the factorization output format used in CSYTRF_RK (or CSYTRF_BK), handed in through parameters A and E, into the factorization output format used in CSYTRF, which is stored on exit in parameter A. it also converts, in place, the details of the interchanges stored in IPIV from the CSYTRF_RK (or CSYTRF_BK) format into the CSYTRF format. 🔁

and the fun part: CSYCONVF can also convert in the Hermitian matrix case, i.e. between the formats used in CHETRF and CHETRF_RK (or CHETRF_BK). it's giving versatility, no cap 🦋

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💜 Parameters 💜

UPLO

UPLO is CHARACTER*1 specifies whether the details of the factorization are stored as an upper or lower triangular matrix A. - = 'U': Upper triangular - = 'L': Lower triangular

WAY

WAY is CHARACTER*1 - = 'C': Convert - = 'R': Revert

N

N is INTEGER the order of the matrix A. N >= 0.

A

A is COMPLEX array, dimension (LDA,N)

1) If WAY ='C':

on entry, contains factorization details in the format used in CSYTRF: - a) all elements of the symmetric block diagonal matrix D on the diagonal of A and on superdiagonal (or subdiagonal) of A, and - b) If UPLO = 'U': multipliers used to obtain factor U in the superdiagonal part of A. If UPLO = 'L': multipliers used to obtain factor L in the superdiagonal part of A. on exit, contains factorization details in the format used in CSYTRF_RK or CSYTRF_BK: - a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D are stored on exit in array E), and - b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A.

2) If WAY = 'R':

on entry, contains factorization details in the format used in CSYTRF_RK or CSYTRF_BK: - a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D are stored on exit in array E), and - b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A. on exit, contains factorization details in the format used in CSYTRF: - a) all elements of the symmetric block diagonal matrix D on the diagonal of A and on superdiagonal (or subdiagonal) of A, and - b) If UPLO = 'U': multipliers used to obtain factor U in the superdiagonal part of A. If UPLO = 'L': multipliers used to obtain factor L in the superdiagonal part of A.

LDA

LDA is INTEGER the leading dimension of the array A. LDA >= max(1,N).

E

E is COMPLEX array, dimension (N)

1) If WAY ='C':

on entry, just a workspace. on exit, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where: - If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0; - If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.

2) If WAY = 'R':

on entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where: - If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) not referenced; - If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) not referenced. on exit, is not changed 🫶

IPIV

IPIV is INTEGER array, dimension (N)

1) If WAY ='C':

on entry, details of the interchanges and the block structure of D in the format used in CSYTRF. on exit, details of the interchanges and the block structure of D in the format used in CSYTRF_RK (or CSYTRF_BK).

1) If WAY ='R':

on entry, details of the interchanges and the block structure of D in the format used in CSYTRF_RK (or CSYTRF_BK). on exit, details of the interchanges and the block structure of D in the format used in CSYTRF.

(yes, the original really does label both of those "1)" — we do not fix, we do not edit, we preserve the lore 🙈)

INFO

INFO is INTEGER - = 0: successful exit 🎉 - < 0: if INFO = -i, the i-th argument had an illegal value 💀

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👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

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🌈 Contributors: 🌈

November 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley

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🧚 Definition at line 208 of file csyconvf.f. 🧚

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⭐ Author ⭐

generated automatically by Doxygen for LAPACK from the source code. not a human, just a very efficient little bot doing its thing ✨

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that's the whole page bestie, every single parameter, every UPLO, every WAY, every E(1) and E(N), every block-diagonal D, preserved with love 💖

she's LAPACK, Version 3.12.0, and the file is /home/abui.../csyconvf.f(3) — go convert some formats, you absolute main character 🫶💅🎀