syconvf_rook(3)

📦

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🎀 syconvf_rook(3) — Library Functions Manual 🎀

🌸 NAME 🌸

syconvf_rook — syconvf_rook: convert to/from hetrf_rook to hetrf_rk format 💖

💅 SYNOPSIS 💅

✨ Functions ✨

subroutine csyconvf_rook (uplo, way, n, a, lda, e, ipiv, info)
subroutine dsyconvf_rook (uplo, way, n, a, lda, e, ipiv, info)
subroutine ssyconvf_rook (uplo, way, n, a, lda, e, ipiv, info)
subroutine zsyconvf_rook (uplo, way, n, a, lda, e, ipiv, info)

CSYCONVF_ROOK
DSYCONVF_ROOK
SSYCONVF_ROOK
ZSYCONVF_ROOK

🦋 Detailed Description 🦋

okay bestie, this is where the actual function lore lives 👑 no cap, every routine below is serving its own little conversion moment ✨

🌟 Function Documentation 🌟

🌈 `csyconvf_rook` / `CSYCONVF_ROOK` 🌈

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

💖 Purpose 💖

okay so if WAY = 'C', CSYCONVF_ROOK converts the factorization output format used in CSYTRF_ROOK — the one provided on entry in parameter A — into the factorization output format used in CSYTRF_RK (or CSYTRF_BK) that gets stored on exit in parameters A and E. The IPIV format for CSYTRF_ROOK and CSYTRF_RK (or CSYTRF_BK) is the same and is not converted. periodt 💅

If WAY = 'R', CSYCONVF_ROOK does the conversion in reverse direction, i.e. it converts the factorization output format used in CSYTRF_RK (or CSYTRF_BK) provided on entry in parameters A and E into the factorization output format used in CSYTRF_ROOK that gets stored on exit in parameter A. The IPIV format for CSYTRF_ROOK and CSYTRF_RK (or CSYTRF_BK) is the same and is not converted. iconic ✨

CSYCONVF_ROOK can also convert in the Hermitian matrix case, i.e. between formats used in CHETRF_ROOK and CHETRF_RK (or CHETRF_BK). 🦋

🌸 Parameters 🌸

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 — is CHARACTER*1.
- = 'C': Convert
- = 'R': Revert
N — is INTEGER. The order of matrix A. N >= 0.
A — is COMPLEX array, dimension (LDA,N).
- 1) If WAY ='C':
  - On entry, contains factorization details in format used in CSYTRF_ROOK:
    - 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 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 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 format used in CSYTRF_ROOK:
    - 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 — is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
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 — is INTEGER array, dimension (N). On entry, details of the interchanges and the block structure of D as determined:
1. by CSYTRF_ROOK, if WAY ='C';
2. by CSYTRF_RK (or CSYTRF_BK), if WAY ='R'. The IPIV format is the same for all these routines. On exit, is not changed.
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.

💜 Contributors 💜

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

Definition at line 199 of file csyconvf_rook.f.

🌈 `dsyconvf_rook` / `DSYCONVF_ROOK` 🌈

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

💖 Purpose 💖

If parameter WAY = 'C', DSYCONVF_ROOK converts the factorization output format used in DSYTRF_ROOK 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. The IPIV format for DSYTRF_ROOK and DSYTRF_RK (or DSYTRF_BK) is the same and is not converted. 💫

If parameter WAY = 'R', DSYCONVF_ROOK 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_ROOK that is stored on exit in parameter A. The IPIV format for DSYTRF_ROOK and DSYTRF_RK (or DSYTRF_BK) is the same and is not converted. 🦋

🌸 Parameters 🌸

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 — is CHARACTER*1.
- = 'C': Convert
- = 'R': Revert
N — is INTEGER. The order of matrix A. N >= 0.
A —

🎀 `A`

A is a DOUBLE PRECISION array, dimension (LDA,N). it's literally the main character of this whole operation, and what lives inside it depends on which way you're going 👑

1) If WAY ='C':

On entry, it's holding factorization details in the format used in DSYTRF_ROOK:

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, it's holding factorization details in the 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, it's holding factorization details in the 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, it's holding factorization details in the format used in DSYTRF_ROOK:

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.

like, it goes back to being the full glam package. we love a reversible transformation 💅

🦋 `LDA`

LDA is INTEGER. it's the leading dimension of the array A. and the vibe check is: LDA >= max(1,N). no exceptions bestie, fr fr.

🌸 `E`

E is a DOUBLE PRECISION array, dimension (N). she's the off-diagonal bestie, the one carrying all the 2-by-2 block tea 🍓

1) If WAY ='C':

On entry, just a workspace. that's it. she's hanging out, not doing much.

On exit, she 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, she 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. she did her job, she's not moving, iconic behaviour 💀

🫶 `IPIV`

IPIV is an INTEGER array, dimension (N). on entry, it's got the details of the interchanges and the block structure of D as determined:

by DSYTRF_ROOK, if WAY ='C';
by DSYTRF_RK (or DSYTRF_BK), if WAY ='R'.

The IPIV format is the same for all these routines — so no conversion needed, it just vibes through unchanged 😌

On exit, is not changed. periodt.

✨ `INFO`

INFO is INTEGER. the receipts, basically:

= 0: successful exit 🎉
< 0: if INFO = -i, the i-th argument had an illegal value 🙈 (so like, go check argument number i, she's the problem)

👑 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 196 of file dsyconvf_rook.f.

💜 `ssyconvf_rook` — the single-precision twin, same energy 💜

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

SSYCONVF_ROOK 🦋 — literally the same gig as her double-precision sister, just in REAL. copy that, paste the vibe, change the type. we stan a consistent family 👑

🎯 Purpose:

If parameter WAY = 'C':

SSYCONVF_ROOK converts the factorization output format used in SSYTRF_ROOK provided on entry in parameter A into the factorization output format used in SSYTRF_RK (or SSYTRF_BK) that is stored on exit in parameters A and E. IPIV format for SSYTRF_ROOK and SSYTRF_RK (or SSYTRF_BK) is the same and is not converted.

If parameter WAY = 'R':

SSYCONVF_ROOK performs the conversion in reverse direction, i.e. converts the factorization output format used in SSYTRF_RK (or SSYTRF_BK) provided on entry in parameters A and E into the factorization output format used in SSYTRF_ROOK that is stored on exit in parameter A. IPIV format for SSYTRF_ROOK and SSYTRF_RK (or SSYTRF_BK) is the same and is not converted.

so yeah — A and E get makeovers, IPIV shows up in the same outfit both times. iykyk 🫶

🌸 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

pick your fighter 💅

🌟 `WAY`

WAY is CHARACTER*1:

= 'C': Convert
= 'R': Revert

one letter, two whole destinies ✨

🌟 `N`

N is INTEGER. the order of the matrix A. and N >= 0. keep it non-negative bestie, that's the whole rule 🎀

🌟 `A`

A is REAL array, dimension (LDA,N).

1) If WAY ='C':

On entry, contains factorization details in format used in SSYTRF_ROOK:

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 SSYTRF_RK or SSYTRF_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 SSYTRF_RK or SSYTRF_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 SSYTRF_ROOK:

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. and yeah, LDA >= max(1,N) — same rule, same energy, no cap 🔥

🌟 `E`

E is REAL 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. she's a stable queen 🧚

🌟 `IPIV`

IPIV is INTEGER array, dimension (N). on entry, details of the interchanges and the block structure of D as determined:

by SSYTRF_ROOK, if WAY ='C';
by SSYTRF_RK (or SSYTRF_BK), if WAY ='R'.

The IPIV format is the same for all these routines.

On exit, is not changed. again. she's not being converted, bestie, don't even ask 💀

🌟 `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.

🌈 Contributors:

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

Definition at line 196 of file ssyconvf_rook.f.

💅 Parameters 💅

okay bestie, parameter time — every single argument gets its moment, no skips, no cap 💖

UPLO — 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 — CHARACTER*1.
- = 'C': Convert
- = 'R': Revert
N — INTEGER. The order of the matrix A. N >= 0.
A — COMPLEX*16 array, dimension (LDA,N).

1) If WAY ='C':

On entry, contains factorization details in format used in ZSYTRF_ROOK:
- 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 ZSYTRF_RK or ZSYTRF_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 ZSYTRF_RK or ZSYTRF_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 ZSYTRF_ROOK:
- 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
E — COMPLEX*16 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 — INTEGER array, dimension (N). On entry, details of the interchanges and the block structure of D as determined:
1. by ZSYTRF_ROOK, if WAY ='C';
2. by ZSYTRF_RK (or ZSYTRF_BK), if WAY ='R'.

The IPIV format is the same for all these routines.

On exit, is not changed.

INFO — 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.

🫶 Contributors 🫶

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

📌 Definition at line 📌

Definition at line 199 of file zsyconvf_rook.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

💖 that’s the whole page, bestie! LAPACK Version 3.12.0, syconvf_rook(3) — slay and goodbye! 💖

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

syconvf_rook(3)

🎀 syconvf_rook(3) — Library Functions Manual 🎀

🌸 NAME 🌸

💅 SYNOPSIS 💅

✨ Functions ✨

🦋 Detailed Description 🦋

🌟 Function Documentation 🌟

🌈 csyconvf_rook / CSYCONVF_ROOK 🌈

💖 Purpose 💖

🌸 Parameters 🌸

✨ Author ✨

💜 Contributors 💜

🌈 dsyconvf_rook / DSYCONVF_ROOK 🌈

💖 Purpose 💖

🌸 Parameters 🌸

🎀 A

🦋 LDA

🌸 E

🫶 IPIV

✨ INFO

👑 Author

🌈 Contributors:

💜 ssyconvf_rook — the single-precision twin, same energy 💜

🎯 Purpose:

🌸 Parameters

🌟 UPLO

🌟 WAY

🌟 N

🌟 A

🌟 LDA

🌟 E

🌟 IPIV

🌟 INFO

👑 Author

🌈 Contributors:

💅 Parameters 💅

👑 Author 👑

🫶 Contributors 🫶

📌 Definition at line 📌

🤖 Author 🤖

🌈 `csyconvf_rook` / `CSYCONVF_ROOK` 🌈

🌈 `dsyconvf_rook` / `DSYCONVF_ROOK` 🌈

🎀 `A`

🦋 `LDA`

🌸 `E`

🫶 `IPIV`

✨ `INFO`

💜 `ssyconvf_rook` — the single-precision twin, same energy 💜

🌟 `UPLO`

🌟 `WAY`

🌟 `N`

🌟 `A`

🌟 `LDA`

🌟 `E`

🌟 `IPIV`

🌟 `INFO`