laic1(3)

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version 3.12.1 · 9 versions
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💅 laic1(3) 💅

okay bestie, this is the Library Functions Manual page for laic1 — the header says laic1(3) and the footer says laic1(3), so we are folding that whole title vibe in right here. This is part 1, and more parts are literally coming, so don’t wander off 🫶

✨ NAME ✨

laic1 — laic1: condition estimate, step in gelsy

🦋 SYNOPSIS 🦋

💖 Functions 💖

  • subroutine claic1 (job, j, x, sest, w, gamma, sestpr, s, c) — CLAIC1 applies one step of incremental condition estimation.
  • subroutine dlaic1 (job, j, x, sest, w, gamma, sestpr, s, c) — DLAIC1 applies one step of incremental condition estimation.
  • subroutine slaic1 (job, j, x, sest, w, gamma, sestpr, s, c) — SLAIC1 applies one step of incremental condition estimation.
  • subroutine zlaic1 (job, j, x, sest, w, gamma, sestpr, s, c) — ZLAIC1 applies one step of incremental condition estimation.

🌸 Detailed Description 🌸

bestie, this section is literally empty on the original page — no extra deets here, no cap. Part 2 is still coming, so keep scrolling 💅✨

💖 Function Documentation 💖

okay bestie, this is the LAIC1 squad — claic1, dlaic1, slaic1, and zlaic1. Same job, different precision vibes, no cap. 💅

🌸 claic1 🌸

subroutine claic1 (integer job, integer j, complex, dimension( j ) x, real sest, complex, dimension( j ) w, complex gamma, real sestpr, complex s, complex c)

CLAIC1 applies one step of incremental condition estimation. iconic behavior, honestly.

🎀 Purpose 🎀

Okay so CLAIC1 does 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 CLAIC1 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. vibe check: JOB decides the whole plotline.

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.

🌈 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 array, dimension (J). The j-vector x.
  • SEST — SEST is REAL. Estimated singular value of j by j matrix L.
  • W — W is COMPLEX array, dimension (J). The j-vector w.
  • GAMMA — GAMMA is COMPLEX. The diagonal element gamma.
  • SESTPR — SESTPR is REAL. Estimated singular value of (j+1) by (j+1) matrix Lhat.
  • S — S is COMPLEX. Sine needed in forming xhat.
  • C — C is COMPLEX. Cosine needed in forming xhat.

👑 Author 👑

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

Definition: Definition at line 134 of file claic1.f.

🦋 dlaic1 🦋

subroutine dlaic1 (integer job, integer j, double precision, dimension( j ) x, double precision sest, double precision, dimension( j ) w, double precision gamma, double precision sestpr, double precision s, double precision c)

DLAIC1 applies one step of incremental condition estimation. double precision bestie has entered the chat.

🎀 Purpose 🎀

Okay so DLAIC1 does 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 DLAIC1 computes sestpr, s, c such that the vector

                 [ s*x ]
          xhat = [  c  ]

is an approximate singular vector of

                 [ L       0  ]
          Lhat = [ w**T gamma ]

in the sense that

          twonorm(Lhat*xhat) = sestpr.

Depending on JOB, an estimate for the largest or smallest singular value is computed. same energy, real-number edition.

Note that [s c]**T and sestpr**2 is an eigenpair of the system

    diag(sest*sest, 0) + [alpha  gamma] * [ alpha ]
                                           [ gamma ]

where alpha = x**T*w.

🌈 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 DOUBLE PRECISION array, dimension (J). The j-vector x.
  • SEST — SEST is DOUBLE PRECISION. Estimated singular value of j by j matrix L.
  • W — W is DOUBLE PRECISION array, dimension (J). The j-vector w.
  • GAMMA — GAMMA is DOUBLE PRECISION. The diagonal element gamma.
  • SESTPR — SESTPR is DOUBLE PRECISION. Estimated singular value of (j+1) by (j+1) matrix Lhat.
  • S — S is DOUBLE PRECISION. Sine needed in forming xhat.
  • C — C is DOUBLE PRECISION. Cosine needed in forming xhat.

👑 Author 👑

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

Definition: Definition at line 133 of file dlaic1.f.

🍓 slaic1 🍓

subroutine slaic1 (integer job, integer j, real, dimension( j ) x, real sest, real, dimension( j ) w, real gamma, real sestpr, real s, real c)

SLAIC1 applies one step of incremental condition estimation. single precision, still slaying.

🎀 Purpose 🎀

Okay so SLAIC1 does 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 SLAIC1 computes sestpr, s, c such that the vector

                 [ s*x ]
          xhat = [  c  ]

is an approximate singular vector of

                 [ L      0  ]
          Lhat = [ w**T gamma ]

in the sense that

          twonorm(Lhat*xhat) = sestpr.

Depending on JOB, an estimate for the largest or smallest singular value is computed. the real-real one, literally.

Note that [s c]**T and sestpr**2 is an eigenpair of the system

    diag(sest*sest, 0) + [alpha  gamma] * [ alpha ]
                                           [ gamma ]

where alpha = x**T*w.

🌈 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 REAL array, dimension (J). The j-vector x.
  • SEST — SEST is REAL. Estimated singular value of j by j matrix L.
  • W — W is REAL array, dimension (J). The j-vector w.
  • GAMMA — GAMMA is REAL. The diagonal element gamma.
  • SESTPR — SESTPR is REAL. Estimated singular value of (j+1) by (j+1) matrix Lhat.
  • S — S is REAL. Sine needed in forming xhat.
  • C — C is REAL. Cosine needed in forming xhat.

👑 Author 👑

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

Definition: Definition at line 133 of file slaic1.f.

💜 zlaic1 💜

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. complex*16 main character energy.

🎀 Purpose 🎀

Okay so ZLAIC1 does 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. conjugate-transpose girlies rise up.

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.

🌈 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: Definition at line 134 of file zlaic1.f.

👑 Author 👑

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💅 that's a wrap, bestie — this page is LAPACK Version 3.12.0, laic1(3), and the footer didn't give me a date so I'm not inventing one, periodt. 🫶✨

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