SRC/ctrcon.f(3)

🌸 NAME 🌸

okay so bestie, this is SRC/ctrcon.f(3) from the Library Functions Manual — the page for SRC/ctrcon.f 💅 no cap, we're getting into ctrcon and it's lowkey iconic.

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine ctrcon (norm, uplo, diag, n, a, lda, rcond, work, rwork,
    info)

CTRCON

📚 Function/Subroutine Documentation 📚

🧚 subroutine ctrcon 🧚

subroutine ctrcon (character norm, character uplo, character diag, integer
    n, complex, dimension( lda, * ) a, integer lda, real rcond, complex,
    dimension( * ) work, real, dimension( * ) rwork, integer info)

CTRCON

🎯 Purpose 🎯

okay so CTRCON estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm. It computes the norm of A and gets an estimate for norm(inv(A)), then the reciprocal of the condition number is computed as:

RCOND = 1 / ( norm(A) * norm(inv(A)) ).

🔥 Parameters 🔥

• NORM — NORM is CHARACTER*1. Specifies whether you want the 1-norm condition number or the infinity-norm condition number:
  • = '1' or 'O': 1-norm;
  • = 'I': Infinity-norm.
• UPLO — UPLO is CHARACTER*1:
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• DIAG — DIAG is CHARACTER*1:
  • = 'N': A is non-unit triangular;
  • = 'U': A is unit triangular.
• N — N is INTEGER. The order of the matrix A. N >= 0.
• A — A is COMPLEX array, dimension (LDA,N). The triangular matrix A.
  • If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced.
  • If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced.
  • If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• RCOND — RCOND is REAL. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
• WORK — WORK is COMPLEX array, dimension (2*N).
• RWORK — RWORK is REAL array, dimension (N).
• INFO — INFO is INTEGER:
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

✨ Author ✨

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

Definition at line 135 of file ctrcon.f.

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole vibe: LAPACK, Version 3.12.0, page SRC/ctrcon.f(3) — byeee, drink water and slay your condition numbers 💖✨