SRC/cpbequ.f(3)

🌸 NAME 🌸

SRC/cpbequ.f — okay bestie, this is the SRC/cpbequ.f(3) page from the Library Functions Manual, and it's all about the CPBEQU subroutine. 💅

✨ SYNOPSIS ✨

💖 Functions/Subroutines 💖

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

🦋 Function/Subroutine Documentation 🦋

Here's the full signature, no cap:

   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. 🫶

💜 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). It holds 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, 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.

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 This page was rendered from LAPACK Version 3.12.0 and source SRC/cpbequ.f(3). The footer doesn't print a separate date on this one, bestie, so I'm not inventing one — periodt. 🫶