DSYCONVF(3)

💅 DSYCONVF(3) 💅

Okay bestie, welcome to the Library Functions Manual corner of LAPACK. This page is giving “one subroutine, one job, and a whole lot of array lore” and I’m honestly obsessed. 🦋

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✨ NAME ✨

The name line is literally this path, no edits, no cap:

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

That’s the whole NAME section. She’s lowkey just a file path, and that’s iconic. 💅

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💅 SYNOPSIS 💅

🎀 Functions/Subroutines 🎀

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

And yes, the star of the show is DSYCONVF. Main character energy fr fr. ✨

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🎀 Function/Subroutine Documentation 🎀

Here’s the full signature, kept exactly as it appears, because we do not mess with code signatures in this group chat:

   subroutine DSYCONVF (character uplo, character way, integer n, double
       precision, dimension( lda, * ) a, integer lda, double precision,
       dimension( * ) e, integer, dimension( * ) ipiv, integer info)
       DSYCONVF

🫶 Purpose 🫶

So here’s the vibe check, bestie. This subroutine is a format converter for factorization details. Very “glow-up but for arrays.” 💖

If parameter WAY = 'C':

• DSYCONVF converts the factorization output format used in DSYTRF provided on entry in parameter A into the factorization output format used in DSYTRF_RK (or DSYTRF_BK) that is stored on exit in parameters A and E.
• It also converts in place details of the interchanges stored in IPIV from the format used in DSYTRF into the format used in DSYTRF_RK (or DSYTRF_BK).

If parameter WAY = 'R':

• DSYCONVF performs the conversion in reverse direction, i.e. converts the factorization output format used in DSYTRF_RK (or DSYTRF_BK) provided on entry in parameters A and E into the factorization output format used in DSYTRF that is stored on exit in parameter A.
• It also converts in place details of the interchanges stored in IPIV from the format used in DSYTRF_RK (or DSYTRF_BK) into the format used in DSYTRF.

No cap, that’s the whole plot: convert one way with 'C', revert the other way with 'R'. 🦋

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🌸 Parameters 🌸

💖 UPLO 💖

UPLO is CHARACTER*1.

It 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 a DOUBLE PRECISION array, dimension (LDA,N).

1. If WAY ='C':
   • On entry, contains factorization details in format used in DSYTRF:
     • 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 format used in DSYTRF_RK or DSYTRF_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 format used in DSYTRF_RK or DSYTRF_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 format used in DSYTRF:
     • 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 a DOUBLE PRECISION 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 an 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 DSYTRF. On exit, details of the interchanges and the block structure of D in the format used in DSYTRF_RK ( or DSYTRF_BK).
• 1) If WAY ='R': On entry, details of the interchanges and the block structure of D in the format used in DSYTRF_RK ( or DSYTRF_BK). On exit, details of the interchanges and the block structure of D in the format used in DSYTRF.

Yes, the source labels both as 1) — we’re preserving the typo because that’s the assignment, bestie. 🙈

💖 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.

🧚 Contributors: 🧚

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

Definition at line 205 of file dsyconvf.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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Okay that’s the page, bestie! Footer tea: LAPACK, Version 3.12.0, and the file path /home/abui.../dsyconvf.f(3). Date? Not listed in this footer, so I’m not inventing one — periodt. 💖✨