CPBEQU(3)

💅 CPBEQU(3) — Library Functions Manual ✨

okay bestie, this page lives at /home/abui...RC/cpbequ.f(3), and it’s here to explain the CPBEQU subroutine. No cap. 💖

🌸 NAME 🌸

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

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🫶 SYNOPSIS 🫶

Functions/Subroutines 🦋

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

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🦋 Function/Subroutine Documentation 🦋

Here’s the full signature, bestie — copied exactly so nobody comes for us:

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

🎀 Purpose 🎀

CPBEQU computes row and column scalings intended to equilibrate a Hermitian 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 linear algebra moment ✨

🌸 Parameters 🌸

UPLO 💅

• UPLO is CHARACTER*1.
  • = 'U': Upper triangular of A is stored;
  • = 'L': Lower triangular of A is stored.

N ⭐

• N is INTEGER.
• The order of the matrix A. N >= 0.

KD 🦋

• 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 💖

• AB is COMPLEX array, dimension (LDAB,N).
• The upper or lower triangle of the Hermitian 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 🌈

• LDAB is INTEGER.
• The leading dimension of the array A. LDAB >= KD+1.

S 🍓

• S is REAL array, dimension (N).
• If INFO = 0, S contains the scale factors for A.

SCOND 🧚

• SCOND is REAL.
• If INFO = 0, the docs say 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 💜

• 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 🔥

• 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 129 of file cpbequ.f 📌

This lil subroutine is defined at line 129 of file cpbequ.f. periodt.

🎀 Author (generated automatically) 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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Footer tea, bestie: LAPACK Version 3.12.0 and /home/abui...RC/cpbequ.f(3) — date? Not in the footer, so we’re not inventing one. 💅💖