CSYSV_ROOK(3)

💖 CSYSV_ROOK(3) 💖

Okay bestie, welcome to the LAPACK Library Functions Manual page for CSYSV_ROOK. The page tag is /home/abui...sysv_rook.f(3) — that's the header/footer file vibe. This routine is iconic: it solves a complex symmetric linear system, and yes, you're gonna understand every parameter. 🫶

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/csysv_rook.f — that's the source file this page is serving, periodt.

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine CSYSV_ROOK — computes the solution to system of linear equations A * X = B for SY matrices. Slay.

       subroutine CSYSV_ROOK (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork,
           info)

💅 Function/Subroutine Documentation 💅

⭐ subroutine CSYSV_ROOK ⭐

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

CSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices. That's the whole main character energy.

🔥 Purpose 🔥

CSYSV_ROOK computes the solution to a complex 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.

CSYTRF_ROOK is called to compute the factorization of a complex symmetric matrix A using the bounded Bunch-Kaufman () diagonal pivoting method. (Yes, the empty () is literally there, iykyk.)

The factored form of A is then used to solve the system of equations A * X = B by calling CSYTRS_ROOK.

🌈 Parameters 🌈

• UPLO — UPLO is CHARACTER*1.
  • = 'U': the upper triangle of A is stored.
  • = 'L': the lower triangle of A is stored.
• N — N is INTEGER. It's the number of linear equations, i.e. the order of the matrix A. Constraint: N >= 0.
• NRHS — NRHS is INTEGER. It's the number of right hand sides, i.e. the number of columns of the matrix B. Constraint: NRHS >= 0.
• A — A is COMPLEX array, dimension (LDA,N).
  • On entry, it's 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, this holds 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 CSYTRF_ROOK.
• LDA — LDA is INTEGER. It's the leading dimension of the array A. Constraint: LDA >= max(1,N).
• IPIV — IPIV is INTEGER array, dimension (N). It holds details of the interchanges and the block structure of D, as determined by CSYTRF_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 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.
• B — B is COMPLEX array, dimension (LDB,NRHS).
  • On entry, it's the N-by-NRHS right hand side matrix B.
  • On exit, if INFO = 0, it's the N-by-NRHS solution matrix X.
• LDB — LDB is INTEGER. It's the leading dimension of the array B. Constraint: LDB >= max(1,N).
• WORK — WORK is COMPLEX array, dimension (MAX(1,LWORK)).
  • On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER. It's the length of WORK. Constraint: LWORK >= 1, and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for CSYTRF_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.
• 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.

👑 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 at line 202 of file csysv_rook.f.

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, that's the whole page. Sign-off source/version: LAPACK Version 3.12.0; file tag: /home/abui...sysv_rook.f(3); date: not printed on this page (so I'm not inventing one, periodt). Bye, slay, go solve that symmetric system. 💅✨