SPBEQU(3)

✨ SPBEQU(3) ✨

Okay so bestie, welcome to SPBEQU(3) from the Library Functions Manual — this page is also chilling at /home/abui...RC/spbequ.f(3). It’s giving “tiny Fortran routine with main character energy,” and we’re gonna get into every single detail. 🫶

🦋 NAME 🦋

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/spbequ.f — that’s the file this whole page is about, no cap.

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

subroutine SPBEQU (uplo, n, kd, ab, ldab, s, scond, amax, info)
    SPBEQU

SPBEQU

💖 Function/Subroutine Documentation 💖

subroutine SPBEQU (character uplo, integer n, integer kd, real, dimension(
    ldab, * ) ab, integer ldab, real, dimension( * ) s, real scond, real
    amax, integer info)

SPBEQU

🎯 Purpose 🎯

Not me getting emotional over a band-matrix equilibration routine 😭 — but okay, here’s the tea: SPBEQU computes row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings. Iconic behavior, honestly. ✨

🧸 Parameters 🧸

• UPLO is CHARACTER*1
  • = 'U': Upper triangular of A is stored;
  • = 'L': Lower triangular of A is stored.
• 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 REAL array, dimension (LDAB,N) The upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

• LDAB is INTEGER The leading dimension of the array A. LDAB >= KD+1.
• S is REAL array, dimension (N) If INFO = 0, S contains the scale factors for A.
• SCOND is REAL If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S.
• AMAX is REAL Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.
• INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • > 0: if INFO = i, the i-th diagonal element is nonpositive.

👑 Author 👑

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

Definition at line 128 of file spbequ.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off time 💅: this footer gives LAPACK Version 3.12.0 and the source path /home/abui...RC/spbequ.f(3) — no date shown, so we’re not inventing one, bestie. Bye and stay iconic 🎀✨