DLASQ2(3)

💅 DLASQ2 — Library Functions Manual ✨

okay so welcome to the dlasq2.f page in the Library Functions Manual — the page file is /home/abui...RC/dlasq2.f(3). bestie, this is the LAPACK routine that does the eigenvalue thing, and yes it’s giving main-character numerical linear algebra energy. 🫶

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlasq2.f

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine DLASQ2 (n, z, info)

DLASQ2 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.

🦋 Function/Subroutine Documentation 🦋

subroutine DLASQ2 (integer n, double precision, dimension( * ) z, integer
    info)

DLASQ2 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.

🎯 Purpose: 🎯

okay so the purpose is literally this: DLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd array Z to high relative accuracy. Those eigenvalues are computed to high relative accuracy in the absence of denormalization, underflow and overflow. 💖

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: DLASQ2 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 DLASQ3. 🫶

🎀 Parameters 🎀

• N — N is INTEGER. The number of rows and columns in the matrix. N >= 0. 💅
• Z — Z is DOUBLE PRECISION 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. So:
  • = 0: successful exit. slay. ✅
  • < 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 dlasq2.f. 📌

Definition at line 111 of file dlasq2.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie that’s the whole page 💖 — kisses from LAPACK, Version 3.12.0, and the page file is /home/abui...RC/dlasq2.f(3). periodt. 💅✨