la_gercond(3)

📦

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, in arch rolling

🌸 NAME 🌸

okay bestie, this is la_gercond(3) from the Library Functions Manual, and this is part 1. 💖

la_gercond — la_gercond: Skeel condition number estimate. That’s the whole point of this icon. ✨

✨ SYNOPSIS ✨

Functions

Here’s the whole cast, bestie — signatures first, then the one-line vibe for each 🫶

real function cla_gercond_c (trans, n, a, lda, af, ldaf, ipiv, c,
           capply, info, work, rwork)
real function cla_gercond_x (trans, n, a, lda, af, ldaf, ipiv, x, info,
           work, rwork)
double precision function dla_gercond (trans, n, a, lda, af, ldaf, ipiv,
           cmode, c, info, work, iwork)
real function sla_gercond (trans, n, a, lda, af, ldaf, ipiv, cmode, c,
           info, work, iwork)
double precision function zla_gercond_c (trans, n, a, lda, af, ldaf,
           ipiv, c, capply, info, work, rwork)
double precision function zla_gercond_x (trans, n, a, lda, af, ldaf,
           ipiv, x, info, work, rwork)

cla_gercond_c — CLA_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices. 💅
cla_gercond_x — CLA_GERCOND_X computes the infinity norm condition number of op(A)*diag(x) for general matrices. 🌸
dla_gercond — DLA_GERCOND estimates the Skeel condition number for a general matrix. 🔥
sla_gercond — SLA_GERCOND estimates the Skeel condition number for a general matrix. ⭐
zla_gercond_c — ZLA_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices. 🦋
zla_gercond_x — ZLA_GERCOND_X computes the infinity norm condition number of op(A)*diag(x) for general matrices. 🎀

💖 Detailed Description 💖

okay so this page is basically the la_gercond family reunion: real and double precision, complex and real, with the _c and _x variants showing up too. The detailed docs below are where the actual function-by-function lore lives. no cap. 👑

🧚 Function Documentation 🧚

💅 `cla_gercond_c`

   real function cla_gercond_c (character trans, integer n, complex, dimension(
       lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf,
       integer, dimension( * ) ipiv, real, dimension( * ) c, logical capply,
       integer info, complex, dimension( * ) work, real, dimension( * ) rwork)

CLA_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices. literally that. ✨

Purpose

CLA_GERCOND_C computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a REAL vector. 💖

Parameters

TRANS — TRANS is CHARACTER*1. Specifies the form of the system of equations:
- 'N': A * X = B (No transpose)
- 'T': A**T * X = B (Transpose)
- 'C': A**H * X = B (Conjugate Transpose = Transpose)
N — N is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0. 🌸
A — A is COMPLEX array, dimension (LDA,N). On entry, the N-by-N matrix A. 💅
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
AF — AF is COMPLEX array, dimension (LDAF,N). The factors L and U from the factorization A = P*L*U as computed by CGETRF. 🔥
LDAF — LDAF is INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).
IPIV — IPIV is INTEGER array, dimension (N). The pivot indices from the factorization A = P*L*U as computed by CGETRF; row i of the matrix was interchanged with row IPIV(i). 🫶
C — C is REAL array, dimension (N). The vector C in the formula op(A) * inv(diag(C)). 🍓
CAPPLY — CAPPLY is LOGICAL. If .TRUE. then access the vector C in the formula above. ⭐
INFO — INFO is INTEGER.
- = 0: Successful exit.
- i > 0: The ith argument is invalid. 💀
WORK — WORK is COMPLEX array, dimension (2*N). Workspace. 🧚
RWORK — RWORK is REAL array, dimension (N). Workspace. 💜

Author

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

Definition at line 140 of file cla_gercond_c.f.

🌈 `cla_gercond_x`

   real function cla_gercond_x (character trans, integer n, complex, dimension(
       lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf,
       integer, dimension( * ) ipiv, complex, dimension( * ) x, integer info,
       complex, dimension( * ) work, real, dimension( * ) rwork)

CLA_GERCOND_X computes the infinity norm condition number of op(A)*diag(x) for general matrices. iconic. 💅

Purpose

CLA_GERCOND_X computes the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX vector. ✨

Parameters

TRANS — TRANS is CHARACTER*1. Specifies the form of the system of equations:
- 'N': A * X = B (No transpose)
- 'T': A**T * X = B (Transpose)
- 'C': A**H * X = B (Conjugate Transpose = Transpose)
N — N is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0. 🌸
A — A is COMPLEX array, dimension (LDA,N). On entry, the N-by-N matrix A. 💖
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
AF — AF is COMPLEX array, dimension (LDAF,N). The factors L and U from the factorization A = P*L*U as computed by CGETRF. 🔥
LDAF — LDAF is INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).
IPIV — IPIV is INTEGER array, dimension (N). The pivot indices from the factorization A = P*L*U as computed by CGETRF; row i of the matrix was interchanged with row IPIV(i). 🫶
X — X is COMPLEX array, dimension (N). The vector X in the formula op(A) * diag(X). 🍓
INFO — INFO is INTEGER.
- = 0: Successful exit.
- i > 0: The ith argument is invalid. 💀
WORK — WORK is COMPLEX array, dimension (2*N). Workspace. 🧚
RWORK — RWORK is REAL array, dimension (N). Workspace. 💜

Author

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

Definition at line 133 of file cla_gercond_x.f.

👑 `dla_gercond`

   double precision function dla_gercond (character trans, integer n, double
       precision, dimension( lda, * ) a, integer lda, double precision,
       dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv,
       integer cmode, double precision, dimension( * ) c, integer info, double
       precision, dimension( * ) work, integer, dimension( * ) iwork)

DLA_GERCOND estimates the Skeel condition number for a general matrix. main character energy fr fr. 💅

Purpose

DLA_GERCOND estimates the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE as follows:

CMODE =  1    op2(C) = C
CMODE =  0    op2(C) = I
CMODE = -1    op2(C) = inv(C)

The Skeel condition number cond(A) = norminf( |inv(A)||A| ) is computed by computing scaling factors R such that diag(R)*A*op2(C) is row equilibrated and computing the standard infinity-norm condition number. 🔥

Parameters

TRANS — TRANS is CHARACTER*1. Specifies the form of the system of equations:
- 'N': A * X = B (No transpose)
- 'T': A**T * X = B (Transpose)
- 'C': A**H * X = B (Conjugate Transpose = Transpose)
N — N is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0. 🌸
A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, the N-by-N matrix A. 💖
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
AF — AF is DOUBLE PRECISION array, dimension (LDAF,N). The factors L and U from the factorization A = P*L*U as computed by DGETRF. 🔥
LDAF — LDAF is INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).
IPIV — IPIV is INTEGER array, dimension (N). The pivot indices from the factorization A = P*L*U as computed by DGETRF; row i of the matrix was interchanged with row IPIV(i). 🫶
CMODE — CMODE is INTEGER. Determines op2(C) in the formula op(A) * op2(C) as follows:
- CMODE = 1: op2(C) = C
- CMODE = 0: op2(C) = I
- CMODE = -1: op2(C) = inv(C) 🌈
C — C is DOUBLE PRECISION array, dimension (N). The vector C in the formula op(A) * op2(C). 🍓
INFO — INFO is INTEGER.
- = 0: Successful exit.
- i > 0: The ith argument is invalid. 💀
WORK — WORK is DOUBLE PRECISION array, dimension (3*N). Workspace. 🧚
IWORK — IWORK is INTEGER array, dimension (N). Workspace. 💜

Author

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

Definition at line 149 of file dla_gercond.f.

⭐ `sla_gercond`

   real function sla_gercond (character trans, integer n, real, dimension( lda,
       * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf,
       integer, dimension( * ) ipiv, integer cmode, real, dimension( * ) c,
       integer info, real, dimension( * ) work, integer, dimension( * ) iwork)

SLA_GERCOND estimates the Skeel condition number for a general matrix. slay. ✨

Purpose

SLA_GERCOND estimates the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE as follows:

CMODE =  1    op2(C) = C
CMODE =  0    op2(C) = I
CMODE = -1    op2(C) = inv(C)

Parameters

TRANS

okay so we’re still in the parameter list, and TRANS is first up 💅

TRANS — is CHARACTER*1. Specifies the form of the system of equations:
- = 'N': A * X = B (No transpose)
- = 'T': A**T * X = B (Transpose)
- = 'C': A**H * X = B (Conjugate Transpose = Transpose)
N — is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
A — is REAL array, dimension (LDA,N). On entry, the N-by-N matrix A.
LDA — is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
AF — is REAL array, dimension (LDAF,N). The factors L and U from the factorization A = P*L*U as computed by SGETRF.
LDAF — is INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).
IPIV — is INTEGER array, dimension (N). The pivot indices from the factorization A = P*L*U as computed by SGETRF; row i of the matrix was interchanged with row IPIV(i).
CMODE — is INTEGER. Determines op2(C) in the formula op(A) * op2(C) as follows:
- CMODE = 1 → op2(C) = C
- CMODE = 0 → op2(C) = I
- CMODE = -1 → op2(C) = inv(C)
C — is REAL array, dimension (N). The vector C in the formula op(A) * op2(C).
INFO — is INTEGER
- = 0: Successful exit.
- i > 0: The ith argument is invalid.
WORK — is REAL array, dimension (3*N). Workspace.
IWORK — is INTEGER array, dimension (N). Workspace.2 👀

Author 👑

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

Definition at line 148 of file sla_gercond.f.

`zla_gercond_c` 🦋

double precision function zla_gercond_c (character trans, integer n,
     complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
     ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, double
     precision, dimension( * ) c, logical capply, integer info, complex*16,
     dimension( * ) work, double precision, dimension( * ) rwork)

ZLA_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices. no cap, that’s the whole vibe ✨

Purpose 🌸

ZLA_GERCOND_C computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.

Parameters 💖

TRANS — is CHARACTER*1. Specifies the form of the system of equations:
- = 'N': A * X = B (No transpose)
- = 'T': A**T * X = B (Transpose)
- = 'C': A**H * X = B (Conjugate Transpose = Transpose)
N — is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
A — is COMPLEX*16 array, dimension (LDA,N). On entry, the N-by-N matrix A
LDA — is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
AF — is COMPLEX*16 array, dimension (LDAF,N). The factors L and U from the factorization A = P*L*U as computed by ZGETRF.
LDAF — is INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).
IPIV — is INTEGER array, dimension (N). The pivot indices from the factorization A = P*L*U as computed by ZGETRF; row i of the matrix was interchanged with row IPIV(i).
C — is DOUBLE PRECISION array, dimension (N). The vector C in the formula op(A) * inv(diag(C)).
CAPPLY — is LOGICAL. If .TRUE. then access the vector C in the formula above.
INFO — is INTEGER
- = 0: Successful exit.
- i > 0: The ith argument is invalid.
WORK — is COMPLEX*16 array, dimension (2*N). Workspace.
RWORK — is DOUBLE PRECISION array, dimension (N). Workspace.

Author 👑

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

Definition at line 140 of file zla_gercond_c.f.

`zla_gercond_x` 🎀

double precision function zla_gercond_x (character trans, integer n,
     complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
     ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, complex*16,
     dimension( * ) x, integer info, complex*16, dimension( * ) work, double
     precision, dimension( * ) rwork)

ZLA_GERCOND_X computes the infinity norm condition number of op(A)*diag(x) for general matrices. literally the same energy but with X doing main character work 💅

Purpose 🌈

ZLA_GERCOND_X computes the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX*16 vector.

Parameters 💜

TRANS — is CHARACTER*1. Specifies the form of the system of equations:
- = 'N': A * X = B (No transpose)
- = 'T': A**T * X = B (Transpose)
- = 'C': A**H * X = B (Conjugate Transpose = Transpose)
N — is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
A — is COMPLEX*16 array, dimension (LDA,N). On entry, the N-by-N matrix A.
LDA — is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
AF — is COMPLEX*16 array, dimension (LDAF,N). The factors L and U from the factorization A = P*L*U as computed by ZGETRF.
LDAF — is INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).
IPIV — is INTEGER array, dimension (N). The pivot indices from the factorization A = P*L*U as computed by ZGETRF; row i of the matrix was interchanged with row IPIV(i).
X — is COMPLEX*16 array, dimension (N). The vector X in the formula op(A) * diag(X).
INFO — is INTEGER
- = 0: Successful exit.
- i > 0: The ith argument is invalid.
WORK — is COMPLEX*16 array, dimension (2*N). Workspace.
RWORK — is DOUBLE PRECISION array, dimension (N). Workspace.

Author 👑

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

Definition at line 133 of file zla_gercond_x.f.

Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

✨ okay bestie, that’s the whole lore — source/version stamp: LAPACK 3.12.0, page la_gercond(3), signing off with immaculate numerical-analysis energy 💖

📦 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

la_gercond(3)

🌸 NAME 🌸

✨ SYNOPSIS ✨

Functions

💖 Detailed Description 💖

🧚 Function Documentation 🧚

💅 cla_gercond_c

Purpose

Parameters

Author

🌈 cla_gercond_x

Purpose

Parameters

Author

👑 dla_gercond

Purpose

Parameters

Author

⭐ sla_gercond

Purpose

Parameters

Author 👑

zla_gercond_c 🦋

Purpose 🌸

Parameters 💖

Author 👑

zla_gercond_x 🎀

Purpose 🌈

Parameters 💜

Author 👑

Author 🫶

💅 `cla_gercond_c`

🌈 `cla_gercond_x`

👑 `dla_gercond`

⭐ `sla_gercond`

`zla_gercond_c` 🦋

`zla_gercond_x` 🎀