SRC/ssytrf_rook.f(3)

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version 3.12.1 · 4 versions
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💅 SRC/ssytrf_rook.f(3) — like, the Library Functions Manual entry, bestie

okay so picture this: you opened the manual for SRC/ssytrf_rook.f(3) and it's giving "big LAPACK energy, zero vibes." not anymore. we're doing this together. 🫶

✨ SYNOPSIS ✨

Functions/Subroutines

  • subroutine ssytrf_rook (uplo, n, a, lda, ipiv, work, lwork, info) — literally the whole point of this page, it's SSYTRF_ROOK 👑

🎀 Function/Subroutine Documentation 🎀

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

SSYTRF_ROOK

🌸 Purpose 🌸

okay bestie, listen up. SSYTRF_ROOK computes the factorization of a real symmetric matrix A using the bounded Bunch-Kaufman () diagonal pivoting method. no cap, that's the whole gig.

the form of the factorization is:

   A = U*D*U**T  or  A = L*D*L**T

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. iconic honestly. ✨

this is the blocked version of the algorithm, calling Level 3 BLAS. she's efficient, she's got main character energy. 💅

💖 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 order of the matrix A. N >= 0. (yes, zero is allowed, she's flexible 🧚)

  • A

A is REAL array, dimension (LDA,N)

On entry, the symmetric 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. (she simply does not look at the other half, boundaries 💀)

On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L (see below for further details — yes there's more, keep reading 🙈).

  • LDA

LDA is INTEGER the leading dimension of the array A. LDA >= max(1,N). don't try her with anything smaller.

  • IPIV

IPIV is INTEGER array, dimension (N) details of the interchanges and the block structure of D. this is the messy part, stay with me:

If UPLO = 'U':

  • 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 IPIV(k) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were interchanged, and D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

If UPLO = 'L':

  • 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 IPIV(k) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were interchanged, and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

see? negative means she paired up. it's giving buddy system. 🫶

  • WORK

WORK is REAL array, dimension (MAX(1,LWORK)). on exit, if INFO = 0, WORK(1) returns the optimal LWORK. she tells you what she wants, queen behavior.

  • LWORK

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

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. so like, -1 is the "just asking, don't yell at me" mode. 🎀

  • INFO

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 that last one is NOT a drill. INFO > 0 means she finished the job but D is singular and if you go solve a system with that, you get division by zero. read the room. 💀

👑 Author 👑

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

the whole squad showed up. ✨

🦋 Further Details 🦋

If UPLO = 'U', then A = U*D*U**T, 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). (yes she's writing over your matrix, it's fine, it's on purpose 🌈)

If UPLO = 'L', then A = L*D*L**T, 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).

no cap, that's the whole structure. read it twice, it slaps the second time. 🔥

💜 Contributors 💜

  • June 2016, Igor Kozachenko, Computer Science Division, University of California, Berkeley
  • September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

legends, all of them. 🎀

📍 Definition at line 207 of file ssytrf_rook.f.

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. (she didn't write herself, a robot did, and honestly? slay.)

okay that's the whole page bestie, you're welcome. this was LAPACK, Version 3.12.0, entry SRC/ssytrf_rook.f(3) — go forth and factor some symmetric matrices, and remember: LDA >= max(1,N). periodt. 💅✨🦋🌸

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