SRC/chesv.f(3)

💖 NAME 💖

Okay so bestie, this page is for SRC/chesv.f(3) from the Library Functions Manual, and our main character is chesv — a Fortran subroutine that computes solutions to systems of linear equations for Hermitian (HE) matrices. It’s giving math girlie with main character energy. 💅

---

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine chesv (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) — CHESV computes the solution to system of linear equations A * X = B for HE matrices. 🫶

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

---

🌸 Function/Subroutine Documentation 🌸

🌈 subroutine chesv 🌈

subroutine chesv (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)

CHESV computes the solution to system of linear equations A * X = B for HE matrices. ✨

🎀 Purpose

CHESV computes the solution to a complex system of linear equations

A * X = B,

where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS matrices.

The diagonal pivoting method is used to factor A as

A = U * D * U**H,  if UPLO = 'U', or
A = L * D * L**H,  if UPLO = 'L',

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian 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 — 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 array, dimension (LDA,N). On entry, the Hermitian 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**H or A = L*D*L**H as computed by CHETRF. 🎀
• 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 CHETRF. 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.
• 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 CHETRF. 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 chesv.f.

---

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

---

And that’s the whole vibe, bestie: this page is serving LAPACK Version 3.12.0, source SRC/chesv.f(3) — iconic, mathy, and fully documented. Periodt. 💅✨🌸