SRC/zpbequ.f(3)

🎀 NAME 🎀

SRC/zpbequ.f — bestie, this is the zpbequ page from the Library Functions Manual, and we are gonna get into it. 💅

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine zpbequ (uplo, n, kd, ab, ldab, s, scond, amax, info) — ZPBEQU

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💖 Function/Subroutine Documentation 💖

subroutine zpbequ (character uplo, integer n, integer kd, complex*16,
       dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )
       s, double precision scond, double precision amax, integer info)

ZPBEQU — that's the main character, periodt. 👑

🎯 Purpose 🎯

Okay so ZPBEQU 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. The math is mathing. ✨

🌸 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 — COMPLEX*16 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 — 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, 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 129 of file zpbequ.f

Yep, that's where it lives in the source, bestie. 🫶

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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Mwah 💋 — this page is from LAPACK Version 3.12.0, SRC/zpbequ.f(3). Bye bestie, go equilibrate something iconic! 💖✨