CHETRF(3)

💅 CHETRF(3) — like, the whole entire chetrf.f situation 🎀

okay bestie so this is a page from the Library Functions Manual and the file it lives in is literally:

/home/abui...RC/chetrf.f(3)

yes the path is giving ellipsis-core, that's just how it printed, we move 💀

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines

subroutine CHETRF (uplo, n, a, lda, ipiv, work, lwork, info)

CHETRF 🫶

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🦋 Function/Subroutine Documentation 🦋

subroutine CHETRF (character uplo, integer n, complex, dimension( lda, * )
a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * )
work, integer lwork, integer info)

CHETRF ✨

👑 Purpose:

!> !> CHETRF computes the factorization of a complex Hermitian matrix A !> using the Bunch-Kaufman diagonal pivoting method. The form of the !> factorization is !> !> A = U*D*UH or A = L*D*LH !> !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and D is Hermitian and block diagonal with !> 1-by-1 and 2-by-2 diagonal blocks. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS. !>

so basically: give it a complex Hermitian matrix, it hands you back the Bunch-Kaufman factorization, blocked version, Level 3 BLAS, main character energy fr 🔥

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💖 Parameters 💖

• UPLO — ngl this one decides which triangle of A we're even looking at:

!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>

• N — the order of the matrix A. N >= 0.

!> N is INTEGER !> The order of the matrix A. N >= 0. !>

• A — COMPLEX array, dimension (LDA,N). the moment of truth 🫶

!> A is COMPLEX array, dimension (LDA,N) !> On entry, the Hermitian matrix A. If UPLO = 'U', the leading !> N-by-N upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced. !> !> On exit, the block diagonal matrix D and the multipliers used !> to obtain the factor U or L (see below for further details). !>

• LDA — the leading dimension of the array A. LDA >= max(1,N).

!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>

• IPIV — INTEGER array, dimension (N). this is the receipts for all the interchanges and the block structure of D 📋

!> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D. !> If IPIV(k) > 0, then rows and columns k and IPIV(k) were !> interchanged and D(k,k) is a 1-by-1 diagonal block. !> If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and !> columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) !> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = !> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were !> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. !>

• WORK — COMPLEX array, dimension (MAX(1,LWORK)). on exit, if INFO = 0, then WORK(1) returns the optimal LWORK 🎀

!> WORK is COMPLEX array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>

• LWORK — INTEGER, the length of WORK. LWORK >=1. for best performance, LWORK >= N*NB, where NB is the block size returned by ILAENV.

!> LWORK is INTEGER !> The length of WORK. LWORK >=1. For best performance !> LWORK >= N*NB, where NB is the block size returned by ILAENV. !>

• INFO — INTEGER, the vibe check at the end:

!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) is exactly zero. The factorization !> has been completed, but the block diagonal matrix D is !> exactly singular, and division by zero will occur if it !> is used to solve a system of equations. !>

⚠️ bestie listen to me: INFO > 0 means D is exactly singular — the factorization finished but if you try to solve a system of equations with it you get division by zero. that's not a drill, that's a real trap 💀

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🧚 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

(iconic quartet, no notes 👑)

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🔥 Further Details:

!> !> If UPLO = 'U', then A = U*D*UH, where !> U = P(n)U(n) ... P(k)U(k) ..., !> i.e., U is a product of terms P(k)U(k), where k decreases from n to !> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as !> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I v 0 ) k-s !> U(k) = ( 0 I 0 ) s !> ( 0 0 I ) n-k !> k-s s n-k !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). !> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), !> and A(k,k), and v overwrites A(1:k-2,k-1:k). !> !> If UPLO = 'L', then A = LD*LH, where !> L = P(1)L(1) ... P(k)L(k)* ..., !> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to !> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as !> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I 0 0 ) k-1 !> L(k) = ( 0 I 0 ) s !> ( 0 v I ) n-k-s+1 !> k-1 s n-k-s+1 !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). !> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), !> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). !>

like, the way that s = 1 and s = 2 just change which bits get overwritten is honestly so satisfying once it clicks 💅

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Definition at line 176 of file chetrf.f. 🦋

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🌈 Author (the meta one)

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page bestie, mwah 🫶 — this was LAPACK, Version 3.12.0, and the file was literally /home/abui...RC/chetrf.f(3) the entire time. slay, go factor something Hermitian 💖✨