hecon_rook(3)

📦

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💖 hecon_rook(3) 💖

okay so bestie, you found a Library Functions Manual page, and it's a long one — this is hecon_rook, and it's basically the condition-number-estimate queen of the LAPACK rook family 👑. She comes in two parts and we're on part one, so buckle up 🎀

✨ NAME ✨

hecon_rook — {he,sy}con_rook: condition number estimate

🌸 SYNOPSIS 🌸

🦋 Functions 🦋

subroutine checon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info) — CHECON_ROOK estimates the reciprocal of the condition number for HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)
subroutine csycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info) — CSYCON_ROOK
subroutine dsycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info) — DSYCON_ROOK
subroutine ssycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info) — SSYCON_ROOK
subroutine zhecon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info) — ZHECON_ROOK estimates the reciprocal of the condition number for HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)
subroutine zsycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info) — ZSYCON_ROOK

🫶 Detailed Description 🫶

so the original page has this heading and then just… nothing under it. truly gave us nothing and left 💀. iconic minimalism honestly. moving on!

⭐ Function Documentation ⭐

💅 `subroutine checon_rook` 💅

subroutine checon_rook (character uplo, integer n, complex, dimension( lda,
* ) a, integer lda, integer, dimension( * ) ipiv, real anorm, real
rcond, complex, dimension( * ) work, integer info)

CHECON_ROOK estimates the reciprocal of the condition number for HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)

🌈 Purpose 🌈

okay so here's the vibe: CHECON_ROOK estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF_ROOK.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

like… she's out here approximating the inverse's norm so you don't have to, and that's on periodt 💅

🎀 Parameters 🎀

UPLO

UPLO is CHARACTER*1 — it specifies whether the details of the factorization are stored as an upper or lower triangular matrix.

= 'U': Upper triangular, form is A = U*D*U**H;
= 'L': Lower triangular, form is A = L*D*L**H.

N

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

A

A is COMPLEX array, dimension (LDA,N) — the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHETRF_ROOK.

LDA

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

IPIV

IPIV is INTEGER array, dimension (N) — details of the interchanges and the block structure of D as determined by CHETRF_ROOK.

ANORM

ANORM is REAL — the 1-norm of the original matrix A.

RCOND

RCOND is REAL — the reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is COMPLEX array, dimension (2*N).

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 🧚

December 2016, Igor Kozachenko, Computer Science Division, University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

Definition at line 137 of file checon_rook.f.

🍓 `subroutine csycon_rook` 🍓

subroutine csycon_rook (character uplo, integer n, complex, dimension( lda,
* ) a, integer lda, integer, dimension( * ) ipiv, real anorm, real
rcond, complex, dimension( * ) work, integer info)

CSYCON_ROOK

🌈 Purpose 🌈

CSYCON_ROOK estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF_ROOK.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

note the **T bestie — this one's symmetric, not Hermitian, so it's transpose and not conjugate-transpose. the way that little H vs T changes everything 😭

🎀 Parameters 🎀

UPLO

UPLO is CHARACTER*1 — it specifies whether the details of the factorization are stored as an upper or lower triangular matrix.

= 'U': Upper triangular, form is A = U*D*U**T;
= 'L': Lower triangular, form is A = L*D*L**T.

N

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

A

A is COMPLEX array, dimension (LDA,N) — the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF_ROOK.

LDA

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

IPIV

IPIV is INTEGER array, dimension (N) — details of the interchanges and the block structure of D as determined by CSYTRF_ROOK.

ANORM

ANORM is REAL — the 1-norm of the original matrix A.

RCOND

WORK

WORK is COMPLEX array, dimension (2*N).

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 🧚

April 2012, Igor Kozachenko, Computer Science Division, University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

Definition at line 137 of file csycon_rook.f.

🦋 `subroutine dsycon_rook` 🦋

subroutine dsycon_rook (character uplo, integer n, double precision,
dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double
precision anorm, double precision rcond, double precision, dimension( *
) work, integer, dimension( * ) iwork, integer info)

DSYCON_ROOK

🌈 Purpose 🌈

DSYCON_ROOK estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF_ROOK.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

double precision version, and yes she brought her own IWORK along for the ride — extra baggage but make it useful 🎀

🎀 Parameters 🎀

UPLO

UPLO is CHARACTER*1 — it specifies whether the details of the factorization are stored as an upper or lower triangular matrix.

= 'U': Upper triangular, form is A = U*D*U**T;
= 'L': Lower triangular, form is A = L*D*L**T.

N

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

A

A is DOUBLE PRECISION array, dimension (LDA,N) — the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSYTRF_ROOK.

LDA

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

IPIV

IPIV is INTEGER array, dimension (N) — details of the interchanges and the block structure of D as determined by DSYTRF_ROOK.

ANORM

ANORM is DOUBLE PRECISION — the 1-norm of the original matrix A.

RCOND

RCOND is DOUBLE PRECISION — the reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is DOUBLE PRECISION array, dimension (2*N).

IWORK

IWORK is INTEGER array, dimension (N).

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 🧚

April 2012, Igor Kozachenko, Computer Science Division, University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

Definition at line 142 of file dsycon_rook.f.

💜 `subroutine ssycon_rook` 💜

subroutine ssycon_rook (character uplo, integer n, real, dimension( lda, * )
a, integer lda, integer, dimension( * ) ipiv, real anorm, real rcond,
real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

SSYCON_ROOK

🌈 Purpose 🌈

SSYCON_ROOK estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF_ROOK.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

🎀 Parameters 🎀

UPLO —
UPLO — CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': upper triangular, form is A = U*D*U**T; = 'L': lower triangular, form is A = L*D*L**T. 💅
N — INTEGER. The order of matrix A. N >= 0. ✨
A — REAL array, dimension (LDA,N). Holds the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by SSYTRF_ROOK. 🫶
LDA — INTEGER. The leading dimension of array A. LDA >= max(1,N). 🌸
IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by SSYTRF_ROOK. 🎀
ANORM — REAL. The 1-norm of the original matrix A. ⭐
RCOND — REAL. The reciprocal of the condition number of matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine. 🔥
WORK — REAL array, dimension (2*N). 💖
IWORK — INTEGER array, dimension (N). 🦋
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

December 2016, Igor Kozachenko, Computer Science Division, University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

📍 Definition at line 142 of file ssycon_rook.f.

🦋 subroutine `zhecon_rook`

   subroutine zhecon_rook (character uplo, integer n, complex*16, dimension(
       lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision
       anorm, double precision rcond, complex*16, dimension( * ) work, integer
       info)

ZHECON_ROOK estimates the reciprocal of the condition number for THE matrices using a factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges). 😭✨

✨ Purpose

ZHECON_ROOK estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF_ROOK. 🧚

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). 💜

💅 Parameters

UPLO — CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**H; = 'L': Lower triangular, form is A = L*D*L**H. 🌈
N — INTEGER. The order of matrix A. N >= 0. ⭐
A — COMPLEX*16 array, dimension (LDA,N). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHETRF_ROOK. 💖
LDA — INTEGER. The leading dimension of array A. LDA >= max(1,N). 🌸
IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CHETRF_ROOK. 🎀
ANORM — DOUBLE PRECISION. The 1-norm of the original matrix A. 🔥
RCOND — DOUBLE PRECISION. The reciprocal of the condition number of matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine. 👑
WORK — COMPLEX*16 array, dimension (2*N). 🦋
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

June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

📍 Definition at line 137 of file zhecon_rook.f.

🦋 subroutine `zsycon_rook`

   subroutine zsycon_rook (character uplo, integer n, complex*16, dimension(
       lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision
       anorm, double precision rcond, complex*16, dimension( * ) work, integer
       info)

ZSYCON_ROOK 🫶

✨ Purpose

ZSYCON_ROOK estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF_ROOK. 🌟

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). 💜

💅 Parameters

UPLO — CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T; = 'L': Lower triangular, form is A = L*D*L**T. 🌈
N — INTEGER. The order of matrix A. N >= 0. ⭐
A — COMPLEX*16 array, dimension (LDA,N). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZSYTRF_ROOK. 💖
LDA — INTEGER. The leading dimension of array A. LDA >= max(1,N). 🌸
IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by ZSYTRF_ROOK. 🎀
ANORM — DOUBLE PRECISION. The 1-norm of the original matrix A. 🔥
RCOND — DOUBLE PRECISION. The reciprocal of the condition number of matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine. 👑
WORK — COMPLEX*16 array, dimension (2*N). 🦋
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

December 2016, Igor Kozachenko, Computer Science Division, University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

📍 Definition at line 137 of file zsycon_rook.f.

👑 Author

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Signing off from LAPACK Version 3.12.0, page hecon_rook(3) — the footer didn’t give us a date, so no date tea today, just source-code sparkle 🧚✨💖

📦 where this page comes from

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💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

hecon_rook(3)

💖 hecon_rook(3) 💖

✨ NAME ✨

🌸 SYNOPSIS 🌸

🦋 Functions 🦋

🫶 Detailed Description 🫶

⭐ Function Documentation ⭐

💅 subroutine checon_rook 💅

🌈 Purpose 🌈

🎀 Parameters 🎀

👑 Author 👑

🧚 Contributors 🧚

🍓 subroutine csycon_rook 🍓

🌈 Purpose 🌈

🎀 Parameters 🎀

👑 Author 👑

🧚 Contributors 🧚

🦋 subroutine dsycon_rook 🦋

🌈 Purpose 🌈

🎀 Parameters 🎀

👑 Author 👑

🧚 Contributors 🧚

💜 subroutine ssycon_rook 💜

🌈 Purpose 🌈

🎀 Parameters 🎀

👑 Author

🫶 Contributors

🦋 subroutine zhecon_rook

✨ Purpose

💅 Parameters

👑 Author

🫶 Contributors

🦋 subroutine zsycon_rook

✨ Purpose

💅 Parameters

👑 Author

🫶 Contributors

👑 Author

💅 `subroutine checon_rook` 💅

🍓 `subroutine csycon_rook` 🍓

🦋 `subroutine dsycon_rook` 🦋

💜 `subroutine ssycon_rook` 💜

🦋 subroutine `zhecon_rook`

🦋 subroutine `zsycon_rook`