/home/abui...trf_rook.f(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 NAME 💖

okay so bestie, this page is all about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ssytrf_rook.f — yes that's the whole entire path, she's got a long name and she's serving it, we love a full-address moment ✨ (the manpage itself lives at /home/abui...trf_rook.f(3) under Library Functions Manual, iykyk).

🦋 SYNOPSIS 🦋

Functions/Subroutines

  • subroutine SSYTRF_ROOK (uplo, n, a, lda, ipiv, work, lwork, info) — that's her, that's the girl, 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 so, SSYTRF_ROOK computes the factorization of a real symmetric matrix A using the bounded Bunch-Kaufman () diagonal pivoting method. 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. no cap, that's the whole vibe 💫

This is the blocked version of the algorithm, calling Level 3 BLAS. she's the leveled-up version, main character energy fr fr 🔥

🎀 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. zero is allowed bestie, she can be empty, it's fine 🌈
  • 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. (so like, only one half of her gets read, the other half is literally just vibing and being ignored 🙈) On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L (see below for further details). 💖
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). don't skimp on LDA or it's gonna be a whole thing 😭
  • IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D. this is the lore, pay attention 👀
    • 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, 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, D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
  • 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 actually needed, iconic 🫶
  • 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 -1 is the "just tell me how much room you need, no drama" option 💫
  • 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. ⚠️ like, the factorization finished, but she's singular and dividing by her is gonna explode
real talk: that INFO > 0 case is not a cute warning. D is exactly singular and using her to solve a system means division by zero. don't do it bestie 😭

👑 Author 👑

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

🔥 Further Details 🔥

the whole structural breakdown, here we go, this is the part where she gets specific 💅

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).

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).

🧚 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

Definition at line 207 of file ssytrf_rook.f. 📍

🍓 Author 🍓

Generated automatically by Doxygen for LAPACK from the source code. (she's auto-generated, she didn't write herself, but she ate anyway 💅)

cute little sign-off bestie: this iconic specimen is from LAPACK, Version 3.12.0, and the page footer also shouts out /home/abui...trf_rook.f(3). go forth and factorize responsibly 🎀🦋💜
📦 where this page comes from