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

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🌸 NAME 🌸

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

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

double precision function DLA_GBRCOND (trans, n, kl, ku, ab, ldab, afb,
    ldafb, ipiv, cmode, c, info, work, iwork)

DLA_GBRCOND estimates the Skeel condition number for a general banded matrix. Slay.

💖 Function/Subroutine Documentation 💖

🫶 Signature

double precision function DLA_GBRCOND (character trans, integer n, integer
    kl, integer ku, double precision, dimension( ldab, * ) ab, integer ldab,
    double precision, dimension( ldafb, * ) afb, integer ldafb, integer,
    dimension( * ) ipiv, integer cmode, double precision, dimension( * ) c,
    integer info, double precision, dimension( * ) work, integer, dimension(
    * ) iwork)

DLA_GBRCOND estimates the Skeel condition number for a general banded matrix. Periodt. 💜

🎯 Purpose

Okay so here is the tea: DLA_GBRCOND Estimates the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE as follows:

• CMODE = 1 → op2(C) = C
• CMODE = 0 → op2(C) = I
• CMODE = -1 → op2(C) = inv(C)

The Skeel condition number cond(A) = norminf( |inv(A)||A| ) is computed by computing scaling factors R such that diag(R)*A*op2(C) is row equilibrated and computing the standard infinity-norm condition number.

💅 Parameters

• TRANS — 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 — 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDAFB,N). Details of the LU factorization of the band matrix A, as computed by DGBTRF. 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 DGBTRF; row i of the matrix was interchanged with row IPIV(i).
• CMODE — CMODE is INTEGER. Determines op2(C) in the formula op(A) * op2(C) as follows:
  • CMODE = 1 → op2(C) = C
  • CMODE = 0 → op2(C) = I
  • CMODE = -1 → op2(C) = inv(C)
• C — C is DOUBLE PRECISION array, dimension (N). The vector C in the formula op(A) * op2(C).
• INFO — INFO is INTEGER.
  • = 0: Successful exit.
  • i > 0: The ith argument is invalid.
• WORK — WORK is DOUBLE PRECISION array, dimension (5*N). Workspace.
• IWORK — IWORK is INTEGER array, dimension (N). Workspace.

🖋️ Author

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

Definition at line 167 of file dla_gbrcond.f.

🖋️ Author

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