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

🎀 /home/abui...RC/cppsv.f(3) — Library Functions Manual 🎀

okay bestie, welcome to CPPSV 💖 this page is from the Library Functions Manual, and it’s all about a very specific little LAPACK workhorse. no cap, the facts are all here — just with way more sparkle ✨

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🦋 NAME 🦋

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cppsv.f

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✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

• subroutine CPPSV (uplo, n, nrhs, ap, b, ldb, info) — CPPSV computes the solution to system of linear equations A * X = B for OTHER matrices

subroutine CPPSV (uplo, n, nrhs, ap, b, ldb, info)
     CPPSV computes the solution to system of linear equations A * X = B
     for OTHER matrices

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🧚 Function/Subroutine Documentation 🧚

subroutine CPPSV (character uplo, integer n, integer nrhs, complex,
     dimension( * ) ap, complex, dimension( ldb, * ) b, integer ldb, integer
     info)

CPPSV computes the solution to system of linear equations A * X = B for OTHER matrices. periodt 💅

🌟 Purpose 🌟

okay so here’s the main-character energy: CPPSV computes the solution to a complex system of linear equations

A * X = B,

where A is an N-by-N Hermitian positive definite matrix stored in packed format and X and B are N-by-NRHS matrices. slay 🫶

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. iconic 🔥

💅 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.
• AP — AP is COMPLEX array, dimension (N*(N+1)/2)
  • On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
    • if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    • if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
  • See below for further details.
  • On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, in the same storage format as A.
• 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).
• INFO — 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.

bestie, that INFO > 0 case is the “it did not work, do not trust the solution” vibe 😭 the factorization could not be completed, and the solution has not been computed. no cap.

👑 Author 👑

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

🦋 Further Details 🦋

The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U':

Two-dimensional storage of the Hermitian matrix A:

    a11 a12 a13 a14
        a22 a23 a24
            a33 a34     (aij = conjg(aji))
                a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

Definition at line 143 of file cppsv.f.

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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bye bestie 💖 this adorable little page is signed off with LAPACK Version 3.12.0 and the path /home/abui...RC/cppsv.f(3) — that’s the whole footer vibe, and it ate ✨👑