SRC/spbcon.f(3)

💖 NAME 💖

okay so SRC/spbcon.f is the file, and it's living its best life in the Library Functions Manual — very demure, very Fortran 💅

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✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

       subroutine spbcon (uplo, n, kd, ab, ldab, anorm, rcond, work, iwork,
           info)
           SPBCON

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💅 Function/Subroutine Documentation 💅

       subroutine spbcon (character uplo, integer n, integer kd, real, dimension(
           ldab, * ) ab, integer ldab, real anorm, real rcond, real, dimension( * )
           work, integer, dimension( * ) iwork, integer info)
       SPBCON

🌸 Purpose 🌸

SPBCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF.

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 — CHARACTER*1. = 'U': Upper triangular factor stored in AB; = 'L': Lower triangular factor stored in AB.
• N — INTEGER. The order of the matrix A. N >= 0.
• KD — INTEGER. The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
• AB — REAL array, dimension (LDAB,N). The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T 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 — INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• ANORM — REAL. The 1-norm (or infinity-norm) of the symmetric band matrix A.
• RCOND — 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 — REAL array, dimension (3*N).
• IWORK — INTEGER array, dimension (N).
• INFO — 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 130 of file spbcon.f.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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that's the whole page, bestie 🫶 the footer says LAPACK Version 3.12.0 and source SRC/spbcon.f(3); there's no date printed on it, so no invented date here, periodt ✨💖