SRC/zpbcon.f(3)

🎀 SRC/zpbcon.f(3) 🎀

okay so this page is from the Library Functions Manual, and it’s giving “I estimate reciprocal condition numbers for complex Hermitian positive definite band matrices” energy. The name on the cover is SRC/zpbcon.f — periodt.

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💅 NAME 💅

SRC/zpbcon.f — that’s the name, bestie. This is the manual page for the ZPBCON subroutine, and it is lowkey all about condition-number estimates. 🦋

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✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

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

ZPBCON — yes, that’s the main character. 👑

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👑 Function/Subroutine Documentation 👑

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 — say it with your chest. 💅

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🌸 Purpose 🌸

bestie, 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)))

That’s the whole glow-up. ✨

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🦋 Parameters 🦋

• UPLO — is CHARACTER*1.
  • = 'U': Upper triangular factor stored in AB;
  • = 'L': Lower triangular factor stored in AB.
• N — is INTEGER. The order of the matrix A. N >= 0.
• 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 — 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 — is INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• ANORM — is DOUBLE PRECISION. The 1-norm (or infinity-norm) of the Hermitian band matrix A.
• 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 — is COMPLEX*16 array, dimension (2*N).
• RWORK — is DOUBLE PRECISION array, dimension (N).
• INFO — is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

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🫶 Author 🫶

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

Definition at line 131 of file zpbcon.f. 📌

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🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code. no cap, the robots handled the paperwork. 🤖✨

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💖 xoxo, your LAPACK bestie — source/version/date vibes from the footer: LAPACK, Version 3.12.0, page SRC/zpbcon.f(3). The footer doesn’t list a date, so I’m not inventing one, bestie 💀🫶