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

okay bestie, first things first: this page is from the Library Functions Manual, page /home/abui...RC/dppsv.f(3), and it’s all about the LAPACK routine DPPSV. it’s giving linear-algebra main character energy, no cap 💅

✨ NAME ✨

the file path, exactly as given:

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

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

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

💖 Function/Subroutine Documentation 💖

🎀 subroutine DPPSV 🎀

here’s the full signature, copied exactly so you can trust it:

subroutine DPPSV (character uplo, integer n, integer nrhs, double precision, dimension( * ) ap, double precision, dimension( ldb, * ) b, integer ldb, integer info)

and the one-liner is literally: DPPSV computes the solution to system of linear equations A * X = B for OTHER matrices.

🦋 Purpose 🦋

okay so DPPSV computes the solution to a real system of linear equations

A * X = B,

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

the Cholesky decomposition is used to factor A as

A = U**T* U,  if UPLO = 'U', or
A = L * L**T,  if UPLO = 'L',

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

✨ 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.
• AP — DOUBLE PRECISION array, dimension (N*(N+1)/2). on entry, the upper or lower triangle of the symmetric 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**T*U or A = L*L**T, in the same storage format as A.
• B — DOUBLE PRECISION 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).
• INFO — 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.

🦋 Further Details 🦋

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

two-dimensional storage of the symmetric 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 dppsv.f.

👑 Author 👑

generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie — footer vibes are LAPACK Version 3.12.0, page /home/abui...RC/dppsv.f(3), and you absolutely ate that linear algebra read 💖✨