SRC/dpbcon.f(3)

💅 SRC/dpbcon.f

okay so this page is SRC/dpbcon.f(3), straight out of the Library Functions Manual, and it's all about the DPBCON subroutine. it's giving real symmetric positive definite band matrix condition-number energy, and honestly? obsessed. 💖✨

✨ NAME ✨

SRC/dpbcon.f

🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine dpbcon (uplo, n, kd, ab, ldab, anorm, rcond, work, iwork, info)
• DPBCON

🎀 Function/Subroutine Documentation 🎀

full signature, bestie — copy it exactly:

subroutine dpbcon (character uplo, integer n, integer kd, double precision,
    dimension( ldab, * ) ab, integer ldab, double precision anorm, double
    precision rcond, double precision, dimension( * ) work, integer,
    dimension( * ) iwork, integer info)
DPBCON

🫶 Purpose

DPBCON 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 DPBTRF.

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 — 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 subdiagonals if UPLO = 'L'. KD >= 0.
• AB — is DOUBLE PRECISION 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 — is INTEGER; the leading dimension of the array AB. LDAB >= KD+1.
• ANORM — is DOUBLE PRECISION; the 1-norm (or infinity-norm) of the symmetric 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 DOUBLE PRECISION array, dimension (3*N).
• IWORK — is INTEGER array, dimension (N).
• 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 130 of file dpbcon.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 that's the whole page, bestie. this one is LAPACK Version 3.12.0, SRC/dpbcon.f(3) — slay. 🫶✨