SRC/sppsv.f(3)

🌸 NAME 🌸

SRC/sppsv.f — that's the name, bestie, and also the whole vibe. This is the Library Functions Manual page for SRC/sppsv.f(3), and it's fully about the sppsv subroutine.

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✨ SYNOPSIS ✨

Functions/Subroutines

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

👑 Function/Subroutine Documentation 👑

subroutine sppsv (character uplo, integer n, integer nrhs, real, dimension( * ) ap, real, dimension( ldb, * ) b, integer ldb, integer info)

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

🎀 Purpose:

Okay so SPPSV 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 — 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.
• AP — is REAL 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 — is REAL 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.

🦋 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 sppsv.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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Cute little footer sign-off, bestie: LAPACK Version 3.12.0, source SRC/sppsv.f(3) — that's the version/source/date footer energy, periodt. 💅✨🎀