SRC/slasd5.f(3)

💖 SRC/slasd5.f(3) 💖

okay so this is a page from the Library Functions Manual, and it is fully devoted to one tiny Fortran subroutine: slasd5. It is giving “small but mathematically booked and busy” energy, and I am obsessed. ✨

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🎀 NAME 🎀

SRC/slasd5.f

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

• subroutine slasd5 (i, d, z, delta, rho, dsigma, work) — SLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc.

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🦋 Function/Subroutine Documentation 🦋

subroutine slasd5 (integer i, real, dimension( 2 ) d, real, dimension( 2 )
    z, real, dimension( 2 ) delta, real rho, real dsigma, real, dimension( 2
    ) work)

SLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc.

🔥 Purpose 🔥

okay so here is the main character moment, bestie: this subroutine computes the square root of the I-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix:

diag( D ) * diag( D ) +  RHO * Z * transpose(Z) .

The diagonal entries in the array D are assumed to satisfy:

0 <= D(i) < D(j)  for  i < j .

We also assume RHO > 0 and that the Euclidean norm of the vector Z is one.

💅 Parameters 💅

• I — I is INTEGER. The index of the eigenvalue to be computed. I = 1 or I = 2.
• D — D is REAL array, dimension (2). The original eigenvalues. We assume 0 <= D(1) < D(2).
• Z — Z is REAL array, dimension (2). The components of the updating vector.
• DELTA — DELTA is REAL array, dimension (2). Contains (D(j) - sigma_I) in its j-th component. The vector DELTA contains the information necessary to construct the eigenvectors.
• RHO — RHO is REAL. The scalar in the symmetric updating formula.
• DSIGMA — DSIGMA is REAL. The computed sigma_I, the I-th updated eigenvalue.
• WORK — WORK is REAL array, dimension (2). WORK contains (D(j) + sigma_I) in its j-th component.

🌟 Author 🌟

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

👑 Contributors 👑

• Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

Definition at line 115 of file slasd5.f.

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🪄 Author 🪄

Generated automatically by Doxygen for LAPACK from the source code.

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and that is the whole page, bestie. LAPACK Version 3.12.0, source SRC/slasd5.f(3) — mwah 💋. The footer does not print a date, so I am not gonna make one up 🙈.