gecon(3)

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version 3.12.1 · 9 versions
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🎀 gecon(3) — gecon: condition number estimate 🎀

💖 NAME 💖

gecon — bestie, the official name line is literally gecon - gecon: condition number estimate. It's giving condition-number-estimate main character energy, and this whole page is the gecon family being iconic about it. 🫶

🌸 SYNOPSIS 🌸

🦋 Functions 🦋

  • subroutine cgecon (norm, n, a, lda, anorm, rcond, work, rwork, info) — label: CGECON
  • subroutine dgecon (norm, n, a, lda, anorm, rcond, work, iwork, info) — label: DGECON
  • subroutine sgecon (norm, n, a, lda, anorm, rcond, work, iwork, info) — label: SGECON
  • subroutine zgecon (norm, n, a, lda, anorm, rcond, work, rwork, info) — label: ZGECON

✨ Detailed Description ✨

Okay so the source has this heading and literally no extra prose attached to it. No cap, that's the whole section. The real tea starts in Function Documentation. 💅

📚 Function Documentation 📚

💜 subroutine cgecon — CGECON

subroutine cgecon (character norm, integer n, complex, dimension( lda, * )
       a, integer lda, real anorm, real rcond, complex, dimension( * ) work,
       real, dimension( * ) rwork, integer info)

Label: CGECON

🎀 Purpose 🎀

Bestie, CGECON estimates the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by CGETRF. It gets an estimate for norm(inv(A)), and then the reciprocal of the condition number is computed as:

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

🧚 Parameters 🧚

  • NORM — NORM is CHARACTER*1. Tells you whether you want the 1-norm condition number or the infinity-norm condition number: = '1' or 'O': 1-norm; = 'I': Infinity-norm.
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • A — A is COMPLEX array, dimension (LDA,N). The factors L and U from the factorization A = P*L*U as computed by CGETRF.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • ANORM — ANORM is REAL. If NORM = '1' or 'O', this is the 1-norm of the original matrix A. If NORM = 'I', this is the infinity-norm of the original matrix A.
  • RCOND — RCOND is REAL. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
  • WORK — WORK is COMPLEX array, dimension (2*N).
  • RWORK — RWORK is REAL array, dimension (2*N).
  • INFO — INFO is INTEGER.
    • = 0: successful exit.
    • < 0: if INFO = -i, the i-th argument had an illegal value. NaNs are illegal values for ANORM, and they propagate to the output parameter RCOND. Infinity is illegal for ANORM, and it propagates to the output parameter RCOND as 0.
    • = 1: if RCOND = NaN, or RCOND = Inf, or the computed norm of the inverse of A is 0. In the latter, RCOND = 0 is returned.

👑 Author 👑

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

📍 Definition at line 📍

Definition at line 130 of file cgecon.f.

💙 subroutine dgecon — DGECON

subroutine dgecon (character norm, integer n, double precision, dimension(
       lda, * ) a, integer lda, double precision anorm, double precision rcond,
       double precision, dimension( * ) work, integer, dimension( * ) iwork,
       integer info)

Label: DGECON

🎀 Purpose 🎀

DGECON estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGETRF. It gets an estimate for norm(inv(A)), and then the reciprocal of the condition number is computed as:

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

🧚 Parameters 🧚

  • NORM — NORM is CHARACTER*1. Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm.
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • A — A is DOUBLE PRECISION array, dimension (LDA,N). The factors L and U from the factorization A = P*L*U as computed by DGETRF.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • ANORM — ANORM is DOUBLE PRECISION. If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-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/(norm(A) * norm(inv(A))).
  • WORK — WORK is DOUBLE PRECISION array, dimension (4*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. NaNs are illegal values for ANORM, and they propagate to the output parameter RCOND. Infinity is illegal for ANORM, and it propagates to the output parameter RCOND as 0.
    • = 1: if RCOND = NaN, or RCOND = Inf, or the computed norm of the inverse of A is 0. In the latter, RCOND = 0 is returned.

👑 Author 👑

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

📍 Definition at line 📍

Definition at line 130 of file dgecon.f.

💚 subroutine sgecon — SGECON

subroutine sgecon (character norm, integer n, real, dimension( lda, * ) a,
       integer lda, real anorm, real rcond, real, dimension( * ) work, integer,
       dimension( * ) iwork, integer info)

Label: SGECON

🎀 Purpose 🎀

SGECON estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGETRF. It gets an estimate for norm(inv(A)), and then the reciprocal of the condition number is computed as:

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

🧚 Parameters 🧚

  • NORM — NORM is CHARACTER*1. Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm.
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • A — A is REAL array, dimension (LDA,N). The factors L and U from the factorization A = P*L*U as computed by SGETRF.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • ANORM — ANORM is REAL. If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A.
  • RCOND — RCOND is REAL. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
  • WORK — WORK is REAL array, dimension (4*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. NaNs are illegal values for ANORM, and they propagate to the output parameter RCOND. Infinity is illegal for ANORM, and it propagates to the output parameter RCOND as 0.
    • = 1: if RCOND = NaN, or RCOND = Inf, or the computed norm of the inverse of A is 0. In the latter, RCOND = 0 is returned.

👑 Author 👑

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

📍 Definition at line 📍

Definition at line 130 of file sgecon.f.

💛 subroutine zgecon — ZGECON

subroutine zgecon (character norm, integer n, complex*16, dimension( lda, *
       ) a, integer lda, double precision anorm, double precision rcond,
       complex*16, dimension( * ) work, double precision, dimension( * ) rwork,
       integer info)

Label: ZGECON

🎀 Purpose 🎀

ZGECON estimates the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF. It gets an estimate for norm(inv(A)), and then the reciprocal of the condition number is computed as:

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

🧚 Parameters 🧚

  • NORM — NORM is CHARACTER*1. Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm.
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • A — A is COMPLEX*16 array, dimension (LDA,N). The factors L and U from the factorization A = P*L*U as computed by ZGETRF.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • ANORM — ANORM is DOUBLE PRECISION. If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-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/(norm(A) * norm(inv(A))).
  • WORK — WORK is COMPLEX*16 array, dimension (2*N).
  • RWORK
  • RWORK — DOUBLE PRECISION</p> array, dimension (2*N). that's it, that's the whole vibe 💖

INFO — INTEGER, and bestie she is telling you things:

  • = 0: successful exit. slay, we ate, no notes ✨
  • < 0: if INFO = -i, the i-th argument had an illegal value. also — NaNs are illegal values for ANORM, and they propagate to the output parameter RCOND. and Infinity is illegal for ANORM too, and it propagates to the output parameter RCOND as 0. 🫠
  • = 1: if RCOND = NaN, or RCOND = Inf, or the computed norm of the inverse of A is 0. in that last case, RCOND = 0 is returned. 🙈

👑 Author 👑

like, the actual people:

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

Definition at line 130 of file zgecon.f.

🌸 Author 🌸

so this whole thing was Generated automatically by Doxygen for LAPACK from the source code. not a human, a robot, and honestly it did great 💅

okay that's the whole page, you made it, I'm so proud of you 🎀 this is from LAPACK, Version 3.12.0, and it's the gecon(3) page — go forth and compute those condition numbers responsibly, ily, bye 🦋💜

📦 where this page comes from