/home/abui...RC/slag2.f(3)

okay bestie, welcome to /home/abui...RC/slag2.f(3) — a page straight outta the Library Functions Manual, and it’s giving “LAPACK math girlie explains eigenvalues with scaling” energy. 💅✨

🌸 NAME 🌸

The name here is the whole file path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slag2.f

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine SLAG2 (a, lda, b, ldb, safmin, scale1, scale2, wr1, wr2, wi)

SLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow. literally the whole point, and she ate. 🔥

💖 Function/Subroutine Documentation 💖

subroutine SLAG2

subroutine SLAG2 (real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real safmin, real scale1, real scale2, real wr1, real wr2, real wi)

SLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow. bestie, this is the main character subroutine. 👑

🧚 Purpose 🧚

SLAG2 computes the eigenvalues of a 2 x 2 generalized eigenvalue problem

A - w B

with scaling as necessary to avoid over-/underflow. 🫶

The scaling factor results in a modified eigenvalue equation:

s A - w B

where s is a non-negative scaling factor chosen so that w, w B, and s A do not overflow and, if possible, do not underflow, either. that’s the vibe check: no overflow, no underflow, just math. 💀✨

🌈 Parameters 🌈

• A — A is REAL array, dimension (LDA, 2). On entry, the 2 x 2 matrix A. It is assumed that its 1-norm is less than 1/SAFMIN. Entries less than sqrt(SAFMIN)*norm(A) are subject to being treated as zero. okay so those tiny entries might get ignored, that’s just how it is. 🙈
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= 2. periodt.
• B — B is REAL array, dimension (LDB, 2). On entry, the 2 x 2 upper triangular matrix B. It is assumed that the one-norm of B is less than 1/SAFMIN. The diagonals should be at least sqrt(SAFMIN) times the largest element of B (in absolute value); if a diagonal is smaller than that, then +/- sqrt(SAFMIN) will be used instead of that diagonal. she will substitute on you, respectfully. 💅
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= 2. no notes.
• SAFMIN — SAFMIN is REAL. The smallest positive number s.t. 1/SAFMIN does not overflow. (This should always be SLAMCH('S') -- it is an argument in order to avoid having to call SLAMCH frequently.) efficiency icon behavior. ⚡
• SCALE1 — SCALE1 is REAL. A scaling factor used to avoid over-/underflow in the eigenvalue equation which defines the first eigenvalue. If the eigenvalues are complex, then the eigenvalues are ( WR1 +/- WI i ) / SCALE1 (which may lie outside the exponent range of the machine), SCALE1=SCALE2, and SCALE1 will always be positive. If the eigenvalues are real, then the first (real) eigenvalue is WR1 / SCALE1 , but this may overflow or underflow, and in fact, SCALE1 may be zero or less than the underflow threshold if the exact eigenvalue is sufficiently large. yes she can get spicy with the exponent range. 😭
• SCALE2 — SCALE2 is REAL. A scaling factor used to avoid over-/underflow in the eigenvalue equation which defines the second eigenvalue. If the eigenvalues are complex, then SCALE2=SCALE1. If the eigenvalues are real, then the second (real) eigenvalue is WR2 / SCALE2 , but this may overflow or underflow, and in fact, SCALE2 may be zero or less than the underflow threshold if the exact eigenvalue is sufficiently large. same energy, second eigenvalue edition. 💜
• WR1 — WR1 is REAL. If the eigenvalue is real, then WR1 is SCALE1 times the eigenvalue closest to the (2,2) element of A B**(-1). If the eigenvalue is complex, then WR1=WR2 is SCALE1 times the real part of the eigenvalues. iconic little real-part moment. 🌸
• WR2 — WR2 is REAL. If the eigenvalue is real, then WR2 is SCALE2 times the other eigenvalue. If the eigenvalue is complex, then WR1=WR2 is SCALE1 times the real part of the eigenvalues. she’s matching WR1’s freak. 🎀
• WI — WI is REAL. If the eigenvalue is real, then WI is zero. If the eigenvalue is complex, then WI is SCALE1 times the imaginary part of the eigenvalues. WI will always be non-negative. always non-negative, we love a consistent queen. 👑

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 154 of file slag2.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code. automation ate, honestly. 🦋

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okay that’s the whole page, bestie! cute little footer sign-off: LAPACK Version 3.12.0 and the page path /home/abui...RC/slag2.f(3) — mwah, math icon behavior 💋✨