DPBEQU(3)

💖 DPBEQU(3) — Library Functions Manual 💖

okay so bestie, welcome to DPBEQU(3) from the Library Functions Manual — this is the LAPACK routine page for DPBEQU, and we are gonna get into the scaling tea ☕✨

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🌸 NAME 🌸

the file for this routine lives here, no cap:

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

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✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

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

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🎀 Function/Subroutine Documentation 🎀

the full signature is giving very much “I know my types” energy:

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

🌸 Purpose 🌸

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. periodt 💅

🎀 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; if INFO = 0, the page literally says 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.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole vibe check 🫶 this footer moment is brought to you by LAPACK, Version 3.12.0, with the path /home/abui...RC/dpbequ.f(3) — byeee, ily, go scale responsibly 💅✨