SRC/clatdf.f(3)

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💖 SRC/clatdf.f(3) 💖

okay so bestie, welcome to the Library Functions Manual page for SRC/clatdf.f. This is LAPACK lore, and the whole vibe is CLATDF doing its reciprocal Dif-estimate thing. No cap, it’s giving main character energy ✨

✨ NAME ✨

SRC/clatdf.f

🌸 SYNOPSIS 🌸

Functions/Subroutines

  • subroutine clatdf (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv) — CLATDF 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 clatdf (integer ijob, integer n, complex, dimension( ldz, * ) z,
       integer ldz, complex, dimension( * ) rhs, real rdsum, real rdscal,
       integer, dimension( * ) ipiv, integer, dimension( * ) jpiv)

CLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate. That’s the synopsis vibe, and the details are right below 👇

🎀 Purpose 🎀

CLATDF 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 CGETC2. On entry RHS = f holds the contribution from earlier solved sub-systems, and on return RHS = x.

The factorization of Z returned by CGETC2 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 CGECON, 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 array, dimension (LDZ, N). On entry, the LU part of the factorization of the n-by-n matrix Z computed by CGETC2: Z = P * L * U * Q.
  • LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDA >= max(1, N).
  • RHS — RHS is COMPLEX 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 REAL. On entry, the sum of squares of computed contributions to the Dif-estimate under computation by CTGSYL, 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 CTGSY2 is called by CTGSYL.
  • RDSCAL — RDSCAL is REAL. 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 CTGSY2 is called by CTGSYL.
  • 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 clatdf.f.

🧚 Author 🧚

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