pocon(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

💅 pocon(3) — the LAPACK condition-number page

okay so bestie, this is pocon — pocon: condition number estimate — and it lives in the Library Functions Manual. it's a whole little family of four LAPACK routines that estimate how hecked-up (technically: how ill-conditioned) your matrix is. let's get into it ✨

🌸 SYNOPSIS 🌸

✨ Functions

  • subroutine cpocon (uplo, n, a, lda, anorm, rcond, work, rwork, info) — CPOCON
  • subroutine dpocon (uplo, n, a, lda, anorm, rcond, work, iwork, info) — DPOCON
  • subroutine spocon (uplo, n, a, lda, anorm, rcond, work, iwork, info) — SPOCON
  • subroutine zpocon (uplo, n, a, lda, anorm, rcond, work, rwork, info) — ZPOCON

🦋 Detailed Description

ok so the detailed detailed stuff is all down in Function Documentation below 👇 that's where the real tea is.

🎀 Function Documentation 🎀

💖 subroutine cpocon (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real anorm, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CPOCON

🌟 Purpose:

!>
!> CPOCON estimates the reciprocal of the condition number (in the
!> 1-norm) of a complex Hermitian positive definite matrix using the
!> Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF.
!>
!> 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, translate: it takes your Cholesky factor from CPOTRF and gives you back a reciprocal condition number. reciprocal = "bigger number means better-behaved matrix", so don't panic when small numbers show up 💀

🧚 Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

N

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

A

!>          A is COMPLEX array, dimension (LDA,N)
!>          The triangular factor U or L from the Cholesky factorization
!>          A = U**H*U or A = L*L**H, as computed by CPOTRF.
!>

LDA

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

ANORM

!>          ANORM is REAL
!>          The 1-norm (or infinity-norm) of the Hermitian 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)
!>

RWORK

!>          RWORK is REAL 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.

Definition at line 119 of file cpocon.f.

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

DPOCON

🌟 Purpose:

!>
!> DPOCON estimates the reciprocal of the condition number (in the
!> 1-norm) of a real symmetric positive definite matrix using the
!> Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF.
!>
!> 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, real symmetric, DPOTRF factor. same energy, different float type. slay 💅

🧚 Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

N

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

A

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          The triangular factor U or L from the Cholesky factorization
!>          A = U**T*U or A = L*L**T, as computed by DPOTRF.
!>

LDA

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

ANORM

!>          ANORM is DOUBLE PRECISION
!>          The 1-norm (or infinity-norm) of the symmetric 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 (3*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.

Definition at line 119 of file dpocon.f.

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

SPOCON

🌟 Purpose:

!>
!> SPOCON estimates the reciprocal of the condition number (in the
!> 1-norm) of a real symmetric positive definite matrix using the
!> Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF.
!>
!> An estimate is obtained for norm(inv(A)), and the reciprocal of the
!> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
!>

single precision twin of DPOCON, but it's SPOTRF doing the factorization. iconic 🌈

🧚 Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

N

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

A

!>          A is REAL array, dimension (LDA,N)
!>          The triangular factor U or L from the Cholesky factorization
!>          A = U**T*U or A = L*L**T, as computed by SPOTRF.
!>

LDA

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

ANORM

!>          ANORM is REAL
!>          The 1-norm (or infinity-norm) of the symmetric 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 REAL array, dimension (3*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.

Definition at line 119 of file spocon.f.

💛 subroutine zpocon (character uplo, 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)

ZPOCON

🌟 Purpose:

!>
!> ZPOCON estimates the reciprocal of the condition number (in the
!> 1-norm) of a complex Hermitian positive definite matrix using the
!> Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.
!>
!> An estimate is obtained for norm(inv(A)), and the reciprocal of the
!> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
!>

the double-precision complex one, ZPOTRF factor, Hermitian, conjugate-transpose everywhere. main character energy tbh 🫶

🧚 Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

N

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

A

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The triangular factor U or L from the Cholesky factorization
!>          A = U**H*U or A = L*L**H, as computed by ZPOTRF.
!>

LDA

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

ANORM

!>          ANORM is DOUBLE PRECISION
!>          The 1-norm (or infinity-norm) of the Hermitian 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 COMPLEX*16 array, dimension (2*N)
!>

RWORK

!>          RWORK is DOUBLE PRECISION 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.

Definition at line 119 of file zpocon.f.

💀 Author

Generated automatically by Doxygen for LAPACK from the source code.

⚠️ bestie note: these are estimates of the reciprocal condition number, and RCOND is the reciprocal — so a tiny RCOND means your matrix is sus and your solutions are gonna be noisy. that's not me being dramatic, that's literally what "reciprocal of the condition number" means 😭

that's the whole page!! auto-generated by Doxygen for LAPACK from the source code, LAPACK Version 3.12.0, dated with pocon(3) in the footer — mwah 💋 go be well-conditioned, ily 🎀✨

📦 where this page comes from