SRC/zsysv.f(3)

okay bestie, this is SRC/zsysv.f(3) from the Library Functions Manual — and no cap, it's giving complex symmetric solver realness. 💅✨

🌸 NAME 🌸

SRC/zsysv.f — that's the name, and that's the whole name. Periodt. 💖

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

🧚 Function/Subroutine Documentation 🧚

🦋 subroutine zsysv 🦋

okay here's the full signature, bestie — copied exactly, no edits, no "fixing" the vibe:

   subroutine zsysv (character uplo, integer n, integer nrhs, complex*16,
       dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,
       complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( *
       ) work, integer lwork, integer info)

and the headline is literally: ZSYSV computes the solution to system of linear equations A * X = B for SY matrices. 🫶

🔮 Purpose 🔮

okay so the glow-up here: ZSYSV 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. periodt. 💖

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. slay. 🌈

🎀 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 COMPLEX*16 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 ZSYTRF.

• 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 ZSYTRF. 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*16 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 COMPLEX*16 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 ZSYTRF.
  • 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.

• 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.

Definition at line 169 of file zsysv.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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that's the whole page, bestie — signed off with LAPACK Version 3.12.0 and source SRC/zsysv.f(3), and the page didn't hand me a date so I'm not inventing one. mwah 💋✨