SRC/dla_gercond.f(3)

💅 SRC/dla_gercond.f

okay so bestie, this page is from the Library Functions Manual and honestly it's a whole vibe — it's all about one little function that does some very serious math. Let me walk you through it 🫶

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines

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

DLA_GERCOND estimates the Skeel condition number for a general matrix. that's it, that's the tweet 💅

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🌸 Function/Subroutine Documentation 🌸

double precision function dla_gercond (character trans, 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_GERCOND estimates the Skeel condition number for a general matrix. no cap, that's literally what it does ✨

💖 Purpose

!> !> DLA_GERCOND 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 cond(A) = norminf( |inv(A)||A| ) !> is computed by computing scaling factors R such that !> diag(R)*A*op2(C) is row equilibrated and computing the standard !> infinity-norm condition number. !>

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👑 Parameters

• TRANS — so this one's a CHARACTER*1 and it specifies the form of the system of equations, okay? here's the tea:

!>       = 'N':  A * X = B     (No transpose)
!>       = 'T':  A**T * X = B  (Transpose)
!>       = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)

lowkey iconic that 'C' is just transpose again, iykyk 😭

• N — N is INTEGER, and it's the number of linear equations, i.e., the order of the matrix A. and bestie: N >= 0. periodt.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). on entry, it's the N-by-N matrix A. main character energy fr 💜
• LDA — LDA is INTEGER, the leading dimension of the array A. and it's giving LDA >= max(1,N). no exceptions 💅
• AF — AF is DOUBLE PRECISION array, dimension (LDAF,N). these are the factors L and U from the factorization A = P*L*U as computed by DGETRF. slay 🎀
• LDAF — LDAF is INTEGER, the leading dimension of the array AF. LDAF >= max(1,N). yes ma'am ✨
• IPIV — IPIV is INTEGER array, dimension (N). these are the pivot indices from the factorization A = P*L*U as computed by DGETRF; row i of the matrix was interchanged with row IPIV(i). it's giving very organized chaos 🌀
• CMODE — CMODE is INTEGER and it determines op2(C) in the formula op(A) * op2(C), like so:

!>     CMODE =  1    op2(C) = C
!>     CMODE =  0    op2(C) = I
!>     CMODE = -1    op2(C) = inv(C)

• C — C is DOUBLE PRECISION array, dimension (N). it's the vector C in the formula op(A) * op2(C). the moment 🫶
• INFO — INFO is INTEGER, and here's the vibe check:

!>       = 0:  Successful exit.
!>     i > 0:  The ith argument is invalid.

so 0 means we ate and left no crumbs, and anything i > 0 means the *i*th argument is invalid 🙈

• WORK — WORK is DOUBLE PRECISION array, dimension (3*N). it's workspace, bestie. don't touch it, it's doing its job 💀
• IWORK — IWORK is INTEGER array, dimension (N). also workspace. also doing its job. 🌈

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⭐ Author

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

Definition at line 149 of file dla_gercond.f. go look, it's literally right there 👑

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💫 Sign-off

this page was generated automatically by Doxygen for LAPACK from the source code — so like, don't come for me about the formatting, a robot made it 🤖✨ it's LAPACK Version 3.12.0, and yeah, that's the whole thing. hope this helped bestie, go forth and estimate those condition numbers responsibly 💖🦋🍓