SSYSV_ROOK(3)

📦 version 3.12.0, in opensuse-leap 16.0

🦋 ssysv_rook.f(3) — LAPACK manual, bestie edition 🦋

okay so this page lives in the LAPACK library manual and it's literally all about ssysv_rook.f, no cap. Grab a snack, we're doing linear algebra 💅

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ssysv_rook.f

that's the file, that's the whole name section, she's an icon of brevity 🎀

🌸 SYNOPSIS 🌸

Functions/Subroutines

  • subroutine SSYSV_ROOK (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) — SSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices ✨

👑 Function/Subroutine Documentation 👑

subroutine SSYSV_ROOK (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork, integer info)

SSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices. that's the whole vibe, and honestly? she ate 💅

🧚 Purpose:

!>
!> SSYSV_ROOK computes the solution to a real system of linear
!> equations
!>    A * X = B,
!> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
!> matrices.
!>
!> The diagonal pivoting method is used to factor A as
!>    A = U * D * U**T,  if UPLO = 'U', or
!>    A = L * D * L**T,  if UPLO = 'L',
!> 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.
!>
!> SSYTRF_ROOK is called to compute the factorization of a real
!> symmetric matrix A using the bounded Bunch-Kaufman () diagonal
!> pivoting method.
!>
!> The factored form of A is then used to solve the system
!> of equations A * X = B by calling SSYTRS_ROOK.
!>

so like, quick translation bestie: it factors A with the diagonal pivoting method, then solves A * X = B with it. SSYTRF_ROOK does the factoring (bounded Bunch-Kaufman () diagonal pivoting, iykyk), and SSYTRS_ROOK does the solving. two besties, one job 🫶

🌈 Parameters 🌈

UPLO

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

literally just tells it which triangle of A you bothered to store. pick your fighter 💀

N

!>          N is INTEGER
!>          The number of linear equations, i.e., the order of the
!>          matrix A.  N >= 0.
!>

the number of linear equations, aka the order of matrix A. N >= 0, periodt.

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>

the number of right hand sides — which is just how many columns B has. NRHS >= 0 🌸

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.
!>
!>          On exit, if INFO = 0, the block diagonal matrix D and the
!>          multipliers used to obtain the factor U or L from the
!>          factorization A = U*D*U**T or A = L*D*L**T as computed by
!>          SSYTRF_ROOK.
!>

okay so on entry it's your symmetric matrix A. if UPLO = 'U', only the leading N-by-N upper triangular part matters and the strictly lower triangular part is not referenced. if UPLO = 'L', flip it — the leading N-by-N lower triangular part matters and the strictly upper triangular part is not referenced.

on exit, if INFO = 0, you get back the block diagonal matrix D plus the multipliers that make the factor U or L from A = U*D*U**T or A = L*D*L**T, exactly as SSYTRF_ROOK computed them. she recycles, we love her ♻️

LDA

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

leading dimension of A. LDA >= max(1,N). no notes.

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D,
!>          as determined by SSYTRF_ROOK.
!>
!>          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 inerchaged,
!>               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 inerchaged,
!>               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
!>

IPIV is an INTEGER array of dimension (N) and it's the receipts 📝 — the details of the interchanges and the block structure of D, as determined by SSYTRF_ROOK.

if UPLO = 'U':

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

if UPLO = 'L':

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

(yes "inerchaged" is in the original, she's quirky like that, we keep her exactly as she is 🙈)

B

!>          B is REAL array, dimension (LDB,NRHS)
!>          On entry, the N-by-NRHS right hand side matrix B.
!>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
!>

on entry: the N-by-NRHS right hand side matrix B. on exit, if INFO = 0: the N-by-NRHS solution matrix X. glow-up arc, honestly ✨

LDB

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

leading dimension of B. LDB >= max(1,N) 💜

WORK

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

workspace, dimension (MAX(1,LWORK)). on exit, if INFO = 0, WORK(1) hands you the optimal LWORK. she's helpful like that 🫶

LWORK

!>          LWORK is INTEGER
!>          The length of WORK.  LWORK >= 1, and for best performance
!>          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
!>          SSYTRF_ROOK.
!>
!>          TRS will be done with Level 2 BLAS
!>
!>          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.
!>

the length of WORK. LWORK >= 1, and for best performance LWORK >= max(1,N*NB) where NB is the optimal blocksize for SSYTRF_ROOK. also: TRS will be done with Level 2 BLAS 👀

if LWORK = -1 it's a workspace query — the routine only calculates the optimal size of the WORK array, returns that value as the first entry of the WORK array, and XERBLA will not issue any error message related to LWORK. it's giving "just asking, not committing" 💅

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, so the solution could not be computed.
!>
  • = 0 — successful exit, slay 🎉
  • < 0 — if INFO = -i, the i-th argument had an illegal value, oops
  • > 0 — if INFO = i, D(i,i) is exactly zero. the factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed 😭

🍓 Author 🍓

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

⭐ Contributors: ⭐

!>
!>   April 2012, 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 💖

Definition at line 202 of file ssysv_rook.f.

🙈 Author (again, doxygen's turn) 🙈

Generated automatically by Doxygen for LAPACK from the source code.

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