/home/abui...brcond_x.f(3)

💖 bestie, you're looking at the manual page for /home/abui...brcond_x.f(3) — page name, yes — and it belongs to the Library Functions Manual. This is the LAPACK banded-matrix condition-number lore. ✨

💖 NAME 💖

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

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

       real function CLA_GBRCOND_X (trans, n, kl, ku, ab, ldab, afb, ldafb,
           ipiv, x, info, work, rwork)

CLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.

🌸 Function/Subroutine Documentation 🌸

real function CLA_GBRCOND_X (...)

   real function CLA_GBRCOND_X (character trans, integer n, integer kl, integer
       ku, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension(
       ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, complex,
       dimension( * ) x, integer info, complex, dimension( * ) work, real,
       dimension( * ) rwork)

CLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.

🎯 Purpose 🎯

Okay so CLA_GBRCOND_X computes the infinity norm condition number of op(A) * diag(X) — and X is a COMPLEX vector. That's the whole serve. 💅

🧚 Parameters 🧚

• TRANS — TRANS is CHARACTER*1; it specifies the form of the system of equations:
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate Transpose = Transpose)
• N — N is INTEGER; the number of linear equations, i.e., the order of the matrix A. N >= 0.
• KL — KL is INTEGER; the number of subdiagonals within the band of A. KL >= 0.
• KU — KU is INTEGER; the number of superdiagonals within the band of A. KU >= 0.
• AB — AB is COMPLEX array, dimension (LDAB,N). On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl).
• LDAB — LDAB is INTEGER; the leading dimension of the array AB. LDAB >= KL+KU+1.
• AFB — AFB is COMPLEX array, dimension (LDAFB,N). Details of the LU factorization of the band matrix A, as computed by CGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
• LDAFB — LDAFB is INTEGER; the leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
• IPIV — IPIV is INTEGER array, dimension (N). The pivot indices from the factorization A = P*L*U as computed by CGBTRF; row i of the matrix was interchanged with row IPIV(i).
• X — X is COMPLEX array, dimension (N). The vector X in the formula op(A) * diag(X).
• INFO — INFO is INTEGER
  • = 0: Successful exit.
  • i > 0: The ith argument is invalid.
• WORK — WORK is COMPLEX array, dimension (2*N). Workspace.
• RWORK — RWORK is REAL array, dimension (N). Workspace.

👑 Author 👑

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

Definition at line 151 of file cla_gbrcond_x.f.

💅 Author 💅

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, that's the whole page. Footer check: LAPACK, Version 3.12.0, page path /home/abui...brcond_x.f(3) — and no date is listed, so I'm not inventing one. Doxygen generated it automatically from the source code. Go slay your general-banded-matrix condition-number era. 🫶💖