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

okay so this page is from the Library Functions Manual, and it’s literally the glow-up for /home/abui..._gbrcond.f(3) — yes bestie, the SLA_GBRCOND page. buckle up 💅

💖 NAME 💖

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

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🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

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

SLA_GBRCOND estimates the Skeel condition number for a general banded matrix. no cap, that’s the whole vibe ✨

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🦋 Function/Subroutine Documentation 🦋

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. it’s giving main-character numerical linear algebra energy fr fr 👑

✨ 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. iconic behavior, honestly 💅

🎀 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 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 — LDAB is INTEGER. the leading dimension of the array AB. LDAB >= KL+KU+1.
• AFB — AFB is 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 — 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 SGBTRF; 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 REAL 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 REAL 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 166 of file sla_gbrcond.f.

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👑 Author 👑

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that’s the whole page, bestie — signed off by LAPACK Version 3.12.0, page /home/abui..._gbrcond.f(3) 🫶✨