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

🎀 /home/abui...RC/dspsv.f(3) 🎀

okay bestie, welcome to the Library Functions Manual page for /home/abui...RC/dspsv.f(3) — yes, with the dramatic ellipsis, we are keeping it exactly. This is LAPACK business and the vibe is very “linear algebra main character.” 💅

✨ NAME ✨

The name/path on this page is exactly:

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

No cap, that’s the whole NAME section. 🫶

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🌸 SYNOPSIS 🌸

Functions/Subroutines

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

That summary line literally says for OTHER matrices — we are preserving the mystery wording, bestie. 🔥

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🦋 Function/Subroutine Documentation 🦋

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

The one-liner is:

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

Including the iconic OTHER matrices phrase. She said what she said. 💀

Purpose:

DSPSV solves a real system of linear equations:

A * X = B,

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

The diagonal pivoting method is used to factor A as:

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

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. Then the factored form of A is used to solve the system of equations A * X = B. It’s giving factorize, solve, serve. 💅

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, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as a packed triangular matrix in the same storage format as A. 🫶

• IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D, as determined by DSPTRF.
  • If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block.
  • If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
  • If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
• 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, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed. 😭

Author

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

The author gang ate. 👑

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 = aji)
                 a44

Packed storage of the upper triangle of A:

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

That’s the whole visual, bestie. A little triangular moment. 🌈

Definition at line 161 of file dspsv.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Doxygen said “I’ll handle the paperwork,” and honestly? Iconic. 🎀

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Alright bestie, cute sign-off time: this footer tea is LAPACK, Version 3.12.0, page /home/abui...RC/dspsv.f(3). The source/version is right there; the provided footer doesn’t show a separate date, so I’m not inventing one — we keep it honest in this group chat. 🫶💖✨