ZPBCON(3)

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zpbcon.f

okay so bestie, this is the zpbcon.f(3) page — ZPBCON(3) from the Library Functions Manual — and it's all about that condition-number estimate life. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine ZPBCON (uplo, n, kd, ab, ldab, anorm, rcond, work, rwork,
           info)

ZPBCON

🫶 Function/Subroutine Documentation 🫶

Here's the full signature, bestie — copy it exactly:

subroutine ZPBCON (character uplo, integer n, integer kd, complex*16,
       dimension( ldab, * ) ab, integer ldab, double precision anorm, double
       precision rcond, complex*16, dimension( * ) work, double precision,
       dimension( * ) rwork, integer info)

ZPBCON

🎀 Purpose 🎀

ZPBCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPBTRF.

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 is CHARACTER*1.
  • = 'U': upper triangular factor stored in AB;
  • = 'L': lower triangular factor stored in AB.
• N — N is INTEGER. The order of the matrix A. N >= 0.
• KD — KD is INTEGER. The number of superdiagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
• AB — AB is COMPLEX*16 array, dimension (LDAB,N). The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows:
  • if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
  • if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• ANORM — ANORM is DOUBLE PRECISION. The 1-norm (or infinity-norm) of the Hermitian band 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 131 of file zpbcon.f.

💌 Author 💌

Generated automatically by Doxygen for LAPACK from the source code.

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Signing off with the footer info, bestie: LAPACK Version 3.12.0, and the footer path is /home/abui...RC/zpbcon.f(3). That's the source/version tea, periodt. 💖✨