SRC/zla_gbrcond_x.f(3)

💅 NAME

SRC/zla_gbrcond_x.f — okay bestie, this page is from the Library Functions Manual, and it’s all about one very specific Fortran function. No cap. ✨

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🌸 SYNOPSIS

Functions/Subroutines 🎀

double precision function zla_gbrcond_x (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, x, info, work, rwork)

ZLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices. It’s giving “banded matrix girlie” and we respect it. 💅

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🛠️ Function/Subroutine Documentation

Here’s the full signature, exactly as the page spells it:

double precision function zla_gbrcond_x (character trans, integer n, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, complex*16, dimension( * ) x, integer info, complex*16, dimension( * ) work, double precision, dimension( * ) rwork)

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

💡 Purpose

ZLA_GBRCOND_X Computes the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX*16 vector. (Yes, capital C in “Computes” and capital X — we’re keeping the page’s exact energy. 😌)

🎀 Parameters

• TRANS — is CHARACTER*1. 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 — is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
• KL — is INTEGER. The number of subdiagonals within the band of A. KL >= 0.
• KU — is INTEGER. The number of superdiagonals within the band of A. KU >= 0.
• AB — is COMPLEX*16 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 — is INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1.
• AFB — is COMPLEX*16 array, dimension (LDAFB,N). Details of the LU factorization of the band matrix A, as computed by ZGBTRF. 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 — is INTEGER. The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
• IPIV — is INTEGER array, dimension (N). The pivot indices from the factorization A = P*L*U as computed by ZGBTRF; row i of the matrix was interchanged with row IPIV(i).
• X — is COMPLEX*16 array, dimension (N). The vector X in the formula op(A) * diag(X).
• INFO — is INTEGER.

= 0:  Successful exit.
i > 0:  The ith argument is invalid.

• WORK — is COMPLEX*16 array, dimension (2*N). Workspace.
• RWORK — is DOUBLE PRECISION array, dimension (N). Workspace.

👑 Author

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

📍 Definition at line 152 of file zla_gbrcond_x.f.

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🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that’s the whole page! This one is from LAPACK Version 3.12.0, source SRC/zla_gbrcond_x.f(3), and the footer doesn’t give a date, so I’m not making one up — periodt. 💅✨