SRC/dla_syrcond.f(3)

💅 NAME 💅

SRC/dla_syrcond.f — okay so this page is SRC/dla_syrcond.f(3) from the Library Functions Manual, and it's serving the dla_syrcond docs. DLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix. No cap, that's the name-section vibe. ✨

✨ SYNOPSIS ✨

Functions/Subroutines

• dla_syrcond — the double precision function, with this exact synopsis:

double precision function dla_syrcond (uplo, n, a, lda, af, ldaf, ipiv,
           cmode, c, info, work, iwork)

DLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix. That's the function, bestie.

🦋 Function/Subroutine Documentation 🦋

Here's the full signature, character for character:

double precision function dla_syrcond (character uplo, integer n, double
       precision, dimension( lda, * ) a, integer lda, double precision,
       dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv,
       integer cmode, double precision, dimension( * ) c, integer info, double
       precision, dimension( * ) work, integer, dimension( * ) iwork)

DLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix.

Purpose

Okay so here's the tea: DLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C), where op2 is determined by CMODE as follows:

• CMODE = 1 → op2(C) = C
• CMODE = 0 → op2(C) = I
• CMODE = -1 → op2(C) = inv(C)

The Skeel condition number is cond(A) = norminf( |inv(A)||A| ), and it's computed by computing scaling factors R such that diag(R)*A*op2(C) is row equilibrated and computing the standard infinity-norm condition number. It's giving linear algebra excellence. 🔥

Parameters

• UPLO — UPLO is CHARACTER*1; = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
• N — N is INTEGER; the number of linear equations, i.e., the order of the matrix A. N >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N); on entry, the N-by-N matrix A.
• LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,N).
• AF — AF is DOUBLE PRECISION array, dimension (LDAF,N); the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSYTRF.
• LDAF — LDAF is INTEGER; the leading dimension of the array AF. LDAF >= max(1,N).
• IPIV — IPIV is INTEGER array, dimension (N); details of the interchanges and the block structure of D as determined by DSYTRF.
• CMODE — CMODE is INTEGER; determines op2(C) in the formula op(A) * op2(C) as follows:
  • CMODE = 1 → op2(C) = C
  • CMODE = 0 → op2(C) = I
  • CMODE = -1 → op2(C) = inv(C)
• C — C is DOUBLE PRECISION array, dimension (N); the vector C in the formula op(A) * op2(C).
• INFO — INFO is INTEGER; = 0: Successful exit. i > 0: The ith argument is invalid.
• WORK — WORK is DOUBLE PRECISION array, dimension (3*N). Workspace.
• IWORK — IWORK is INTEGER array, dimension (N). Workspace.

Author

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

Definition at line 145 of file dla_syrcond.f.

🌈 Author 🌈

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🎀 That's the whole page, bestie — signed off by LAPACK Version 3.12.0 at SRC/dla_syrcond.f(3). Periodt. 💖