SRC/slatdf.f(3)

💖 NAME 💖

okay bestie, this is the manual page for SRC/slatdf.f, and the manual name is SRC/slatdf.f(3) — yes, it's the whole page for the slatdf subroutine. LAPACK girlies rise ✨

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine slatdf (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv)

This icon is the slatdf subroutine: SLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate. periodt 🌈

🧚 Function/Subroutine Documentation 🧚

Here's the full signature, character-for-character bestie:

   subroutine slatdf (integer ijob, integer n, real, dimension( ldz, * ) z,
       integer ldz, real, dimension( * ) rhs, real rdsum, real rdscal, integer,
       dimension( * ) ipiv, integer, dimension( * ) jpiv)

And the summary again: SLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.

🎯 Purpose:

okay so the whole plot: SLATDF uses the LU factorization of the n-by-n matrix Z computed by SGETC2 and computes a contribution to the reciprocal Dif-estimate by solving Z * x = b for x, and choosing the r.h.s. b such that the norm of x is as large as possible. On entry RHS = b holds the contribution from earlier solved sub-systems, and on return RHS = x.

The factorization of Z returned by SGETC2 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. the vibe check:
  • IJOB = 2: First compute an approximative null-vector e of Z using SGECON, 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 are chosen as either +1 or -1 (Default).
• N — N is INTEGER. The number of columns of the matrix Z.
• Z — Z is REAL array, dimension (LDZ, N). On entry, the LU part of the factorization of the n-by-n matrix Z computed by SGETC2: Z = P * L * U * Q.
• LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDA >= max(1, N).
• RHS — RHS is REAL 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 STGSYL, 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 STGSY2 is called by STGSYL.
• 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 STGSY2 is called by STGSYL.
• 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. [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. [2] Peter Poromaa, On Efficient and Robust Estimators for the Separation between two Regular Matrix Pairs with Applications in Condition Estimation. Report IMINF-95.05, Departement of Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.

Definition at line 169 of file slatdf.f.

📝 Author

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