SRC/dppsv.f(3)

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version 3.12.1 · 7 versions
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💅 SRC/dppsv.f(3) — Library Functions Manual ✨

okay so bestie, this is the dppsv page, and it is literally giving “LAPACK function that solves a real linear system with a packed symmetric positive definite matrix.” Let’s get into it 🫶

✨ NAME ✨

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

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

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. 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.

AP

AP is 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

B is 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

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.

✨ 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.

and that’s the whole vibe check, bestie 💖 Footer recap: LAPACK Version 3.12.0, page SRC/dppsv.f(3), and there is no date listed — so I’m not making one up. ✨💅

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