CPBCON(3)

🎀 NAME

okay bestie, welcome to the CPBCON(3) page from the LAPACK Library Functions Manual ✨ the source file is literally this:

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

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✨ SYNOPSIS ✨

Functions/Subroutines

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

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💖 Function/Subroutine Documentation 💖

the full signature is giving:

   subroutine CPBCON (character uplo, integer n, integer kd, complex,
       dimension( ldab, * ) ab, integer ldab, real anorm, real rcond, complex,
       dimension( * ) work, real, dimension( * ) rwork, integer info)

CPBCON — that's the routine, periodt. 🫶

🔥 Purpose:

CPBCON 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 CPBTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). No cap, that's the whole point. 💅

🌸 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 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 REAL
  • The 1-norm (or infinity-norm) of the Hermitian band 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 131 of file cpbcon.f.

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🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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later bestie! 💖 this was LAPACK Version 3.12.0, and the page path is /home/abui...RC/cpbcon.f(3) 🎀✨