hecon_3(3)

📦

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🌸 `hecon_3(3)` — {he,sy}con_3: condition number estimate 🌸

okay bestie, buckle up 💖 this is hecon_3(3) from the Library Functions Manual, and it's literally the glow-up your linear algebra era has been waiting for. Six routines, all doing the same iconic job in different flavors: they estimate the reciprocal of the condition number. Periodt.

✨ SYNOPSIS ✨

Six subroutines, all serving the same vibe with different dtypes. Obsessed. 🫶

Functions
    subroutine checon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)
        CHECON_3
    subroutine csycon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)
        CSYCON_3
    subroutine dsycon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work,
        iwork, info)
        DSYCON_3
    subroutine ssycon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work,
        iwork, info)
        SSYCON_3
    subroutine zhecon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)
        ZHECON_3
    subroutine zsycon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)
        ZSYCON_3

Spot the pattern? The complex ones (checon_3, csycon_3, zhecon_3, zsycon_3) don't need iwork. The real ones (dsycon_3, ssycon_3) do. That's the whole tea. 🍵

💅 Detailed Description 💅

Not me about to dump six function docs on you — but respectfully, that's exactly what's happening. Each one gets its own subsection below, Function Documentation style, with the full signature, the Purpose block, every single parameter, the Authors, the Contributors, and where the source lives. No skipping. No cap. 🔥

👑 Function Documentation 👑

💜 `checon_3` — CHECON_3 💜

The full signature, character for character:

subroutine checon_3 (character uplo, integer n, complex, dimension( lda, * )
    a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv,
    real anorm, real rcond, complex, dimension( * ) work, integer info)

⭐ Purpose

So CHECON_3 estimates the reciprocal of the condition number — in the 1-norm — of a complex Hermitian matrix A, using the factorization computed by CHETRF_RK or CHETRF_BK:

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

where, in the most chill way possible:

U (or L) is a unit upper (or lower) triangular matrix
U**H (or L**H) is the conjugate of U (or L)
P is a permutation matrix
P**T is the transpose of P
D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks

An estimate is obtained for norm(inv(A)), and then the reciprocal of the condition number is computed as:

RCOND = 1 / (ANORM * norm(inv(A))).

This routine uses the BLAS3 solver CHETRS_3. Slay. ✨

🎀 Parameters

UPLO — UPLO is CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix:
- = 'U': Upper triangular, form is A = P*U*D*(U**H)*(P**T);
- = 'L': Lower triangular, form is A = P*L*D*(L**H)*(P**T).
N — N is INTEGER. The order of the matrix A. N >= 0.
A — A is COMPLEX array, dimension (LDA,N). Holds the diagonal of the block diagonal matrix D and the factors U or L as computed by CHETRF_RK and CHETRF_BK:
1. ONLY the diagonal elements of the Hermitian block diagonal matrix D go on the diagonal of A, i.e. D(k,k) = A(k,k); — and the superdiagonal (or subdiagonal) elements of D should be provided on entry in array E.
2. If UPLO = 'U': factor U lives in the superdiagonal part of A. If UPLO = 'L': factor L lives in the subdiagonal 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). On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian 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.

NOTE: for a 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both the UPLO = 'U' and UPLO = 'L' cases. 🙈

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

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 164 of file checon_3.f.

🩷 `csycon_3` — CSYCON_3 🩷

The full signature, verbatim:

subroutine csycon_3 (character uplo, integer n, complex, dimension( lda, * )
    a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv,
    real anorm, real rcond, complex, dimension( * ) work, integer info)

⭐ Purpose

CSYCON_3 estimates the reciprocal of the condition number — again, in the 1-norm — of a complex symmetric matrix A, using the factorization computed by CSYTRF_RK or CSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where:

U (or L) is a unit upper (or lower) triangular matrix
U**T (or L**T) is the transpose of U (or L)
P is a permutation matrix
P**T is the transpose of P
D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as:

RCOND = 1 / (ANORM * norm(inv(A))).

This routine uses the BLAS3 solver CSYTRS_3. Main character energy, honestly. 💅

🎀 Parameters

UPLO — UPLO is CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix:
- = 'U': Upper triangular, form is A = P*U*D*(U**T)*(P**T);
- = 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T).
N — N is INTEGER. The order of the matrix A. N >= 0.
A — A is COMPLEX array, dimension (LDA,N). Holds the diagonal of the block diagonal matrix D and the factors U or L as computed by CSYTRF_RK and CSYTRF_BK:
1. ONLY the diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); — the superdiagonal (or subdiagonal) elements of D should be provided on entry in array E.
2. If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal 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). 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.

NOTE: for a 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both the UPLO = 'U' and UPLO = 'L' cases. 🙈

IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D, as determined by CSYTRF_RK or CSYTRF_BK.
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

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 164 of file csycon_3.f.

💙 `dsycon_3` — DSYCON_3 💙

The full signature, exactly as written (yes, it wraps, that's the source's business not mine):

subroutine dsycon_3 (character uplo, integer n, double precision, dimension(
    lda, * ) a, integer lda, double precision, dimension( * ) e, integer,
    dimension( * ) ipiv, double precision anorm, double precision rcond,
    double precision, dimension( * ) work, integer, dimension( * ) iwork,
    integer info)

⭐ Purpose

DSYCON_3 estimates the reciprocal of the condition number — 1-norm girlie — of a real symmetric matrix A, using the factorization computed by DSYTRF_RK or DSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where:

U (or L) is a unit upper (or lower) triangular matrix
U**T (or L**T) is the transpose of U (or L)
P is a permutation matrix
P**T is the transpose of P
D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as:

RCOND = 1 / (ANORM * norm(inv(A))).

This routine uses the BLAS3 solver DSYTRS_3. 🫶

🎀 Parameters

UPLO —

okay bestie that's where the page cuts off mid-parameter-list 💀 the UPLO rundown for dsycon_3 (and everything after it — the rest of dsycon_3, plus ssycon_3, zhecon_3, and zsycon_3) is coming in part 2. don't go anywhere, the lore continues 🧚‍♀️🌸

UPLO — CHARACTER*1. Tells you whether the factorization details are stored as an upper or lower triangular matrix, bestie: = 'U': upper triangular, form is A = P*U*D*(U**T)*(P**T); = 'L': lower triangular, form is A = P*L*D*(L**T)*(P**T). 💅
N — INTEGER. The order of the matrix A. N >= 0. Simple as that, no cap. ✨
A — DOUBLE PRECISION array, dimension (LDA,N). This is lowkey the main character: it holds the diagonal of the block diagonal matrix D and the factors U or L as computed by DSYTRF_RK and 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 should be provided on entry 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. 🫶
LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N). Respect the leading dimension, fr fr. 💖
E — DOUBLE PRECISION array, dimension (N). 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. 🌸

NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases. Not me checking E(k) when it literally says “not referenced” 💀

IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by DSYTRF_RK or DSYTRF_BK. Iconic pivot behavior. 👑
ANORM — DOUBLE PRECISION. The 1-norm of the original matrix A. That’s the vibe check for the original matrix. 🔥
RCOND — 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. It’s giving “how invertible are we really” energy. 🦋
WORK — DOUBLE PRECISION array, dimension (2*N). Workspace, bestie. Let it cook. 🍓
IWORK — INTEGER array, dimension (N). Integer workspace. Slay. ✨
INFO — INTEGER. Status tea: = 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 169 of file dsycon_3.f.

🌸 subroutine `ssycon_3` 🌸

subroutine ssycon_3 (character uplo, integer n, real, dimension( lda, * ) a,
    integer lda, real, dimension( * ) e, integer, dimension( * ) ipiv, real
    anorm, real rcond, real, dimension( * ) work, integer, dimension( * )
    iwork, integer info)

`SSYCON_3`

🎯 Purpose

SSYCON_3 estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization computed by DSYTRF_RK or DSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). This routine uses BLAS3 solver SSYTRS_3. Obsessed with a BLAS3 solver moment, honestly. 🔥

🧮 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 = P*U*D*(U**T)*(P**T); = 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T). 💅
N — INTEGER. The order of the matrix A. N >= 0. ✨
A — REAL array, dimension (LDA,N). Diagonal of the block diagonal matrix D and factors U or L as computed by SSYTRF_RK and 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 should be provided on entry 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. 🫶
LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N). 💖
E — REAL array, dimension (N). 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. 🌸

NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases. The way this note keeps showing up 😭

IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by SSYTRF_RK or SSYTRF_BK. 👑
ANORM — REAL. The 1-norm of the original matrix A. 🔥
RCOND — 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 — REAL array, dimension (2*N). Workspace, periodt. 🍓
IWORK — INTEGER array, dimension (N). Integer workspace. ✨
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 169 of file ssycon_3.f.

🦋 subroutine `zhecon_3` 🦋

subroutine zhecon_3 (character uplo, integer n, complex*16, dimension( lda,
    * ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( *
    ) ipiv, double precision anorm, double precision rcond, complex*16,
    dimension( * ) work, integer info)

`ZHECON_3`

🎯 Purpose

ZHECON_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian matrix A using the factorization computed by ZHETRF_RK or ZHETRF_BK:

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**H (or L**H) is the conjugate of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). This routine uses BLAS3 solver ZHETRS_3. Hermitian main character energy, literally. 👑

🧮 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 = P*U*D*(U**H)*(P**T); = 'L': Lower triangular, form is A = P*L*D*(L**H)*(P**T). 💅
N — INTEGER. The order of the matrix A. N >= 0. ✨
A — COMPLEX*16 array, dimension (LDA,N). Diagonal of the block diagonal matrix D and factors U or L as computed by ZHETRF_RK and ZHETRF_BK:
- a) ONLY diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry 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. 🫶
LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N). 💖
E — COMPLEX*16 array, dimension (N). On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian 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. 🌸

NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases. This note is literally everywhere and I respect it 💀

IPIV
IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by ZHETRF_RK or ZHETRF_BK. 🫶
ANORM — DOUBLE PRECISION. The 1-norm of the original matrix A. 💅
RCOND — 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 — 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 164 of file zhecon_3.f.

`zsycon_3` 💖

   subroutine zsycon_3 (character uplo, integer n, complex*16, dimension( lda,
       * ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( *
       ) ipiv, double precision anorm, double precision rcond, complex*16,
       dimension( * ) work, integer info)

ZSYCON_3

Purpose:

Okay bestie, here’s the whole vibe: ZSYCON_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization computed by ZSYTRF_RK or ZSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). This routine uses BLAS3 solver ZSYTRS_3. 👑

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 = P*U*D*(U**T)*(P**T);
- = 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T).
N — INTEGER. The order of the matrix A. N >= 0. 🌸
A — COMPLEX*16 array, dimension (LDA,N). Diagonal of the block diagonal matrix D and factors U or L as computed by ZSYTRF_RK and 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 should be provided on entry 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.
LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N). 💜
E — COMPLEX*16 array, dimension (N). 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.

NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases. 😭

IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by ZSYTRF_RK or ZSYTRF_BK. 🫶
ANORM — DOUBLE PRECISION. The 1-norm of the original matrix A. 💅
RCOND — 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 — 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 164 of file zsycon_3.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Footer sign-off, bestie: LAPACK Version 3.12.0 on the hecon_3(3) page — no extra date line in this last footer chunk, so that’s the whole cute little bow on top. Bye bestie! 💖✨💅

📦 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_3(3)

🌸 hecon_3(3) — {he,sy}con_3: condition number estimate 🌸

✨ SYNOPSIS ✨

💅 Detailed Description 💅

👑 Function Documentation 👑

💜 checon_3 — CHECON_3 💜

⭐ Purpose

🎀 Parameters

🌈 Author

🦋 Contributors

🩷 csycon_3 — CSYCON_3 🩷

⭐ Purpose

🎀 Parameters

🌈 Author

🦋 Contributors

💙 dsycon_3 — DSYCON_3 💙

⭐ Purpose

🎀 Parameters

👑 Author

🌸 subroutine ssycon_3 🌸

SSYCON_3

🎯 Purpose

🧮 Parameters

👑 Author

🦋 subroutine zhecon_3 🦋

ZHECON_3

🎯 Purpose

🧮 Parameters

Author

Contributors:

zsycon_3 💖

Purpose:

Parameters

Author

Contributors:

Author

🌸 `hecon_3(3)` — {he,sy}con_3: condition number estimate 🌸

💜 `checon_3` — CHECON_3 💜

🩷 `csycon_3` — CSYCON_3 🩷

💙 `dsycon_3` — DSYCON_3 💙

🌸 subroutine `ssycon_3` 🌸

`SSYCON_3`

🦋 subroutine `zhecon_3` 🦋

`ZHECON_3`

`zsycon_3` 💖