/home/abui...RC/csysv.f(3)

💅 NAME 💅

ok so bestie, this is the manual page for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/csysv.f — from the Library Functions Manual, page csysv.f(3). it's a whole LAPACK situation and we're gonna get through it together, i promise 🫶

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✨ SYNOPSIS ✨

Functions/Subroutines

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

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

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🦋 Function/Subroutine Documentation 🦋

subroutine CSYSV (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 computes the solution to system of linear equations A * X = B for SY matrices. no cap, that's literally the whole gig 💖

🌸 Purpose 🌸

ok so picture this: CSYSV 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. main character matrices fr 🎀

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. the factored form of A is then used to solve the system of equations A * X = B. iconic behaviour honestly 👑

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🌈 Parameters 🌈

• UPLO — UPLO is CHARACTER*1, and it's giving "which triangle are we even talking about":
  • = '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 COMPLEX 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. (the other half is literally not invited to the party 🙈)
  • 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 CSYTRF. ✨
• LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,N).
• IPIV — IPIV is INTEGER array, dimension (N). deets on the interchanges and the block structure of D, as determined by CSYTRF. so:
  • 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 UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
  • if UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) 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, the N-by-NRHS right hand side matrix B.
  • On exit, if INFO = 0, the N-by-NRHS solution matrix X. the glow-up is real 🌟
• LDB — LDB is INTEGER. the leading dimension of the array B. 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. the length of WORK. LWORK >= 1, and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for CSYTRF.
  • for LWORK < N, TRS will be done with Level BLAS 2
  • for LWORK >= N, TRS will be done with Level BLAS 3
  • 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. (yes, -1 is the "just tell me how much room i need" mode, it's a vibe check not a real call 💀)
• 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. 😭 that one hurts

heads up bestie: INFO > 0 means the routine did finish the factorization, but D came out exactly singular — so there's no solution to hand back. don't go looking for one.

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👑 Author 👑

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

Definition at line 169 of file csysv.f.

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🌸 Author (the meta one) 🌸

Generated automatically by Doxygen for LAPACK from the source code. it wrote its own about-me, obsessed 🤖✨

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that's the whole page, bestie — go forth and solve your complex symmetric systems 💖

LAPACK — Version 3.12.0 🦋 mwah, thanks for reading, ilysm 🫶