ZLAIC1(3)

🎀 NAME 🎀

Manual name: zlaic1(3) — straight out of the Library Functions Manual, bestie 💅

The file path is literally: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zlaic1.f

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

       subroutine ZLAIC1 (job, j, x, sest, w, gamma, sestpr, s, c)
           ZLAIC1 applies one step of incremental condition estimation.

🫶 Function/Subroutine Documentation 🫶

The full signature, no cap:

   subroutine ZLAIC1 (integer job, integer j, complex*16, dimension( j ) x,
       double precision sest, complex*16, dimension( j ) w, complex*16 gamma,
       double precision sestpr, complex*16 s, complex*16 c)

ZLAIC1 applies one step of incremental condition estimation. Iconic. ✨

🌸 Purpose 🌸

Okay so here's the whole math vibe, preserved exactly because we do not play with the details:

!>
!> ZLAIC1 applies one step of incremental condition estimation in
!> its simplest version:
!>
!> Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j
!> lower triangular matrix L, such that
!>          twonorm(L*x) = sest
!> Then ZLAIC1 computes sestpr, s, c such that
!> the vector
!>                 [ s*x ]
!>          xhat = [  c  ]
!> is an approximate singular vector of
!>                 [ L       0  ]
!>          Lhat = [ w**H gamma ]
!> in the sense that
!>          twonorm(Lhat*xhat) = sestpr.
!>
!> Depending on JOB, an estimate for the largest or smallest singular
!> value is computed.
!>
!> Note that [s c]**H and sestpr**2 is an eigenpair of the system
!>
!>     diag(sest*sest, 0) + [alpha  gamma] * [ conjg(alpha) ]
!>                                           [ conjg(gamma) ]
!>
!> where  alpha =  x**H * w.
!>

So yeah: depending on JOB, you're getting an estimate for either the largest or smallest singular value. Main character estimation energy. 👑

💖 Parameters 💖

• JOB — JOB is INTEGER. = 1: an estimate for the largest singular value is computed. = 2: an estimate for the smallest singular value is computed. 🦋
• J — J is INTEGER. Length of X and W. 📏
• X — X is COMPLEX*16 array, dimension (J). The j-vector x. 🍓
• SEST — SEST is DOUBLE PRECISION. Estimated singular value of j by j matrix L. 🌟
• W — W is COMPLEX*16 array, dimension (J). The j-vector w. 🧚
• GAMMA — GAMMA is COMPLEX*16. The diagonal element gamma. 💫
• SESTPR — SESTPR is DOUBLE PRECISION. Estimated singular value of (j+1) by (j+1) matrix Lhat. 🔥
• S — S is COMPLEX*16. Sine needed in forming xhat. 🌈
• C — C is COMPLEX*16. Cosine needed in forming xhat. 🎀

👑 Author 👑

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

Definition at line 134 of file zlaic1.f. 📌

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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Byeee bestie 🫶 this little cutie is LAPACK, Version 3.12.0, and the footer points at /home/abui...RC/zlaic1.f(3). Mwah 💋✨