SRC/dpbequ.f(3)

🌸 NAME 🌸

SRC/dpbequ.f — okay bestie, this page is from the Library Functions Manual, and it's here to explain DPBEQU like we're in the group chat. 💖

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

That's the whole synopsis, no cap. 💅

💖 Function/Subroutine Documentation 💖

   subroutine dpbequ (character uplo, integer n, integer kd, double precision,
       dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )
       s, double precision scond, double precision amax, integer info)
       DPBEQU

This is the full signature, bestie — every type and dimension exactly as the page says. 🫶

🎀 Purpose 🎀

Okay so here's the tea: DPBEQU 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. Slay. ✨

🌈 Parameters 🌈

• UPLO — CHARACTER*1. = 'U': Upper triangular of A is stored; = 'L': Lower triangular of A is stored. 💅
• N — INTEGER. The order of the matrix A. N >= 0.
• KD — INTEGER. The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
• AB — DOUBLE PRECISION 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 — INTEGER. The leading dimension of the array A. LDAB >= KD+1.
• S — DOUBLE PRECISION array, dimension (N). If INFO = 0, S contains the scale factors for A.
• SCOND — DOUBLE PRECISION. The page literally says: 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 — DOUBLE PRECISION. Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.
• INFO — 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 dpbequ.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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Okay that's the whole page, bestie — mwah! 💋 This was SRC/dpbequ.f(3) from LAPACK Version 3.12.0. Go equilibrate something and hydrate. 🫶✨