SRC/sla_gbrcond.f(3)

🎀 SRC/sla_gbrcond.f 🎀

okay bestie, welcome to the Library Functions Manual page for this absolute Fortran icon. It's giving SLA_GBRCOND energy: estimating the Skeel condition number for a general banded matrix. No cap, let's get into it. 💅

✨ NAME ✨

SRC/sla_gbrcond.f

✨ SYNOPSIS ✨

Under Functions/Subroutines we have this main-character function:

real function sla_gbrcond (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv,
           cmode, c, info, work, iwork)

And the summary is literally: SLA_GBRCOND estimates the Skeel condition number for a general banded matrix. 🫶

🌸 Function/Subroutine Documentation 🌸

Here's the full signature, bestie — every argument accounted for:

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

SLA_GBRCOND estimates the Skeel condition number for a general banded matrix. That's the whole vibe. ✨

💖 Purpose 💖

SLA_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 — 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 — INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
• KL — INTEGER. The number of subdiagonals within the band of A. KL >= 0.
• KU — INTEGER. The number of superdiagonals within the band of A. KU >= 0.
• AB — REAL 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 — INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1.
• AFB — REAL array, dimension (LDAFB,N). Details of the LU factorization of the band matrix A, as computed by SGBTRF. 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 — INTEGER. The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
• IPIV — INTEGER array, dimension (N). The pivot indices from the factorization A = P*L*U as computed by SGBTRF; row i of the matrix was interchanged with row IPIV(i).
• CMODE — 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 — REAL array, dimension (N). The vector C in the formula op(A) * op2(C).
• INFO — INTEGER.
  • = 0: Successful exit.
  • i > 0: The ith argument is invalid.
• WORK — REAL array, dimension (5*N). Workspace.
• IWORK — INTEGER array, dimension (N). Workspace.

👑 Author 👑

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

Definition at line 166 of file sla_gbrcond.f.

💅 Author 💅

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie — absolutely ate. This cutie is from LAPACK Version 3.12.0, source SRC/sla_gbrcond.f(3). periodt. 💖✨