SRC/csysv.f(3)

🌈 SRC/csysv.f — Library Functions Manual 🌈

💖 NAME 💖

SRC/csysv.f — that's the icon we're talking about, bestie. Periodt. 💅

✨ 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 ✨

🫶 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 ✨

💡 Purpose

Okay bestie, here's the whole vibe: 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. No cap. 🦋

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. 💖

🎀 Parameters

• UPLO — CHARACTER*1. = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored. 💅
• N — INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0. ✨
• NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. 🎀
• A — 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. 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,N). 🦋
• IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D, as determined by CSYTRF. 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 — 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. 🌸
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N). 🫶
• WORK — COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. ⭐
• LWORK — 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. 💀
• INFO — 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 csysv.f. 🎀

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code.

Byeee 💜 — LAPACK Version 3.12.0, source/footer SRC/csysv.f(3), and the footer didn't hand me a date so I'm not inventing one 🎀.