SRC/cpoequ.f(3)

🌸 NAME

okay so bestie, this is the Library Functions Manual page for SRC/cpoequ.f — yes, the NAME section is literally that path, and honestly? iconic minimalism. 💅

✨ SYNOPSIS

🫶 Functions/Subroutines

       subroutine cpoequ (n, a, lda, s, scond, amax, info)
           CPOEQU

that's the whole synopsis, no cap. 🎀

💖 Function/Subroutine Documentation

   subroutine cpoequ (integer n, complex, dimension( lda, * ) a, integer lda,
       real, dimension( * ) s, real scond, real amax, integer info)
       CPOEQU

okay so this is the glow-up signature, and yes, CPOEQU is the main character. 👑

🌟 Purpose

CPOEQU computes row and column scalings intended to equilibrate a Hermitian positive definite 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. literally the math is mathing 💅

🧚 Parameters

• N — N is INTEGER; the order of the matrix A. N >= 0. she's the size, periodt. 👑
• A — A is COMPLEX array, dimension (LDA,N); the N-by-N Hermitian positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced. so don't stress about the off-diagonals here, iykyk. 🦋
• LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,N). very demure, very dimension-coded. 🎀
• 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. not me double-checking that caveat — we respect it. 💅
• 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. periodt. 💀

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 112 of file cpoequ.f.

💅 Author

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 cute little sign-off: LAPACK, Version 3.12.0, and SRC/cpoequ.f(3) — source/version/page-tag realness, bestie. bye! 🫶🌈