SLASQ2(3)

💖 SLASQ2 💖

okay so bestie, welcome to the Library Functions Manual page for slasq2.f(3) — aka SLASQ2, aka the high-relative-accuracy eigenvalue moment. It's giving LAPACK-core, qd-array main character energy, and we're gonna read the whole thing together 🫶

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🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slasq2.f

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine SLASQ2 (n, z, info)

SLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr 💅

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🦋 Function/Subroutine Documentation 🦋

subroutine SLASQ2 (integer n, real, dimension( * ) z, integer info)

SLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr. No cap, that's the whole serve ✨

💅 Purpose 💅

okay so the purpose is literally: SLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd array Z to high relative accuracy — and those eigenvalues are computed to high relative accuracy in the absence of denormalization, underflow and overflow. It's that serious, bestie 💅

To see the relation of Z to the tridiagonal matrix, let L be a unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and let U be an upper bidiagonal matrix with 1's above and diagonal Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the symmetric tridiagonal to which it is similar 🎀

Note: SLASQ2 defines a logical variable, IEEE, which is true on machines which follow ieee-754 floating-point standard in their handling of infinities and NaNs, and false otherwise. This variable is passed to SLASQ3.

🫶 Parameters 🫶

• N — N is INTEGER. It's the number of rows and columns in the matrix. N >= 0.
• Z — Z is REAL array, dimension ( 4*N ). On entry Z holds the qd array. On exit, entries 1 to N hold the eigenvalues in decreasing order, Z( 2*N+1 ) holds the trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 ) holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of shifts that failed.
• INFO — INFO is INTEGER.
  • = 0: successful exit
  • < 0: if the i-th argument is a scalar and had an illegal value, then INFO = -i; if the i-th argument is an array and the j-entry had an illegal value, then INFO = -(i*100+j)
  • > 0: the algorithm failed
    • = 1: a split was marked by a positive value in E
    • = 2: current block of Z not diagonalized after 100*N iterations (in inner while loop). On exit Z holds a qd array with the same eigenvalues as the given Z.
    • = 3: termination criterion of outer while loop not met (program created more than N unreduced blocks)

👑 Author 👑

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

🌈 Further Details 🌈

• Local Variables: I0:N0 defines a current unreduced segment of Z.
• The shifts are accumulated in SIGMA.
• Iteration count is in ITER.
• Ping-pong is controlled by PP (alternates between 0 and 1).

Definition at line 111 of file slasq2.f.

📚 Author 📚

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page 💖 stay accurate, stay high-relative, and remember the qd array is literally the moment. This footer is giving LAPACK Version 3.12.0 and page path /home/abui...RC/slasq2.f(3) — no date listed, so no invented date, periodt ✨