SRC/zposv.f(3)

💖 NAME 💖

okay bestie, welcome to SRC/zposv.f from the Library Functions Manual — manual name folded in right near the top like a little bow 🎀. This is the LAPACK page for the zposv subroutine, and it is highkey giving “solve the system, serve the solution” main-character energy. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

The one and only subroutine on deck:

       subroutine zposv (uplo, n, nrhs, a, lda, b, ldb, info)
            ZPOSV computes the solution to system of linear equations A * X = B
           for PO matrices

🦋 Function/Subroutine Documentation 🦋

Here is the full signature, copied exactly because we do not play with code:

   subroutine zposv (character uplo, integer n, integer nrhs, complex*16,
       dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b,
       integer ldb, integer info)
        ZPOSV computes the solution to system of linear equations A * X = B for
       PO matrices

ZPOSV computes the solution to system of linear equations A * X = B for PO matrices. Periodt. 💜

🎀 Purpose 🎀

okay so the whole point: ZPOSV computes the solution to a complex system of linear equations

A * X = B,

where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices. Iconic linear algebra behavior. 🦋

The Cholesky decomposition is used to factor A as

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

where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B. Slay. ✨

🍓 Parameters 🍓

• UPLO — is CHARACTER*1.
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
• NRHS — is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
• A — is COMPLEX*16 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 factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H.
• LDA — is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• 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 — is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• INFO — is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, the leading principal minor of order i of A is not positive, so the factorization could not be completed, and the solution has not been computed.

💜 Author 💜

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

Definition at line 129 of file zposv.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 — this page is from LAPACK Version 3.12.0, SRC/zposv.f(3). bye bestie, go solve something cute 🫶✨