SRC/dsysv_rook.f(3)

💖 SRC/dsysv_rook.f 💖

okay bestie, this is the Library Functions Manual page for SRC/dsysv_rook.f — LAPACK's symmetric-system solver has entered the chat, and she's giving very much main character energy. 🫶

🌸 NAME 🌸

SRC/dsysv_rook.f

✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

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

• dsysv_rook — DSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices. 💅

🦋 Function/Subroutine Documentation 🦋

subroutine dsysv_rook (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, integer lwork, integer info)

DSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices. 🔥

🎀 Purpose 🎀

Okay so <pink>DSYSV_ROOK</pink> 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. ✨

DSYTRF_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 DSYTRS_ROOK. 🔥

🌸 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 number of linear equations, i.e., the order of the matrix A. N >= 0. 🎀
• NRHS — NRHS is INTEGER.
  • The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. 🌈
• A — A is DOUBLE PRECISION 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 DSYTRF_ROOK. 💖
• LDA — LDA is INTEGER.
  • The leading dimension of the array A. LDA >= max(1,N). ✨
• IPIV — IPIV is INTEGER array, dimension (N).
  • Details of the interchanges and the block structure of D, as determined by DSYTRF_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. 😭
• B — B is DOUBLE PRECISION 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. 🦋
• LDB — LDB is INTEGER.
  • The leading dimension of the array B. LDB >= max(1,N). 🌟
• WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)).
  • On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 💜
• 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 DSYTRF_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 dsysv_rook.f.

🧚 Author 🧚

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