SRC/zlatdf.f(3)

📦
version 3.12.1 · 4 versions
, in arch rolling

🌸 SRC/zlatdf.f 🌸

okay so this page is from the Library Functions Manual, and it’s all about the file SRC/zlatdf.f and its subroutine zlatdf. Buckle up bestie, it’s giving numerical linear algebra with main character energy. 💖

✨ NAME ✨

SRC/zlatdf.f

That’s the name, no cap. 💅

🌈 SYNOPSIS 🌈

🎀 Functions/Subroutines 🎀

  • subroutine zlatdf (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv) — ZLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.

💖 Function/Subroutine Documentation 💖

subroutine zlatdf (integer ijob, integer n, complex*16, dimension( ldz, * )
       z, integer ldz, complex*16, dimension( * ) rhs, double precision rdsum,
       double precision rdscal, integer, dimension( * ) ipiv, integer,
       dimension( * ) jpiv)

ZLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.

✨ Purpose ✨

lowkey the whole point: ZLATDF computes the contribution to the reciprocal Dif-estimate by solving for x in Z * x = b, where b is chosen such that the norm of x is as large as possible. It is assumed that LU decomposition of Z has been computed by ZGETC2. On entry RHS = f holds the contribution from earlier solved sub-systems, and on return RHS = x.

The factorization of Z returned by ZGETC2 has the form Z = P * L * U * Q, where P and Q are permutation matrices. L is lower triangular with unit diagonal elements and U is upper triangular.

🍓 Parameters 🍓

IJOB

IJOB is INTEGER.

  • IJOB = 2: First compute an approximative null-vector e of Z using ZGECON, e is normalized and solve for Zx = +-e - f with the sign giving the greater value of 2-norm(x). About 5 times as expensive as Default.
  • IJOB .ne. 2: Local look ahead strategy where all entries of the r.h.s. b is chosen as either +1 or -1. Default.

N

N is INTEGER.

The number of columns of the matrix Z.

Z

Z is COMPLEX*16 array, dimension (LDZ, N).

On entry, the LU part of the factorization of the n-by-n matrix Z computed by ZGETC2: Z = P * L * U * Q.

LDZ

LDZ is INTEGER.

The leading dimension of the array Z. LDA >= max(1, N). Yes bestie, the original says LDA right there — we keep it exactly as written. 💅

RHS

RHS is COMPLEX*16 array, dimension (N).

On entry, RHS contains contributions from other subsystems. On exit, RHS contains the solution of the subsystem with entries according to the value of IJOB (see above).

RDSUM

RDSUM is DOUBLE PRECISION.

On entry, the sum of squares of computed contributions to the Dif-estimate under computation by ZTGSYL, where the scaling factor RDSCAL (see below) has been factored out. On exit, the corresponding sum of squares updated with the contributions from the current sub-system. If TRANS = 'T' RDSUM is not touched.

NOTE: RDSUM only makes sense when ZTGSY2 is called by CTGSYL.

RDSCAL

RDSCAL is DOUBLE PRECISION.

On entry, scaling factor used to prevent overflow in RDSUM. On exit, RDSCAL is updated w.r.t. the current contributions in RDSUM. If TRANS = 'T', RDSCAL is not touched.

NOTE: RDSCAL only makes sense when ZTGSY2 is called by ZTGSYL.

IPIV

IPIV is INTEGER array, dimension (N).

The pivot indices; for 1 <= i <= N, row i of the matrix has been interchanged with row IPIV(i).

JPIV

JPIV is INTEGER array, dimension (N).

The pivot indices; for 1 <= j <= N, column j of the matrix has been interchanged with column JPIV(j).

🌟 Author 🌟

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

💜 Further Details 💜

This routine is a further developed implementation of algorithm BSOLVE in [1] using complete pivoting in the LU factorization.

🫶 Contributors 🫶

Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

📚 References 📚

  • [1] Bo Kagstrom and Lars Westin, Generalized Schur Methods with Condition Estimators for Solving the Generalized Sylvester Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751.
  • [2] Peter Poromaa, On Efficient and Robust Estimators for the Separation between two Regular Matrix Pairs with Applications in Condition Estimation. Report UMINF-95.05, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.

Definition at line 167 of file zlatdf.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

okay bye bestie — this iconic little page is LAPACK Version 3.12.0, source SRC/zlatdf.f(3), and that’s the whole vibe ✨💅🫶

📦 where this page comes from