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

💅 NAME 💅

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

okay so bestie, this is a page from the Library Functions Manual and it's literally all about one little file, sspsv.f 🎀 — blessed Fortran source that lives deep in the LAPACK build tree. Come with me, it's gonna slay.

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✨ SYNOPSIS ✨

Functions/Subroutines

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

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🦋 Function/Subroutine Documentation 🦋

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

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

🧠 Purpose

!>
!> SSPSV computes the solution to 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.
!>
!> 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, D is symmetric and block diagonal with 1-by-1
!> and 2-by-2 diagonal blocks.  The factored form of A is then used to
!> solve the system of equations A * X = B.
!>

periodt. that's the whole vibe: factor first, solve second 💅

🌸 Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

bestie, you literally pick a side: 'U' for the upper triangle, 'L' for the lower one. choose wisely 🫶

N

!>          N is INTEGER
!>          The number of linear equations, i.e., the order of the
!>          matrix A.  N >= 0.
!>

the number of linear equations — aka the order of matrix A. and yes, N >= 0, no cap.

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>

how many right hand sides you got, aka how many columns matrix B has. NRHS >= 0 ✨

AP

!>          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, 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 SSPTRF, stored as
!>          a packed triangular matrix in the same storage format as A.
!>

okay this one is the main character 👑 — dimension (N*(N+1)/2), packed columnwise into one linear array. on entry it's your triangle of A, on exit it's the block diagonal matrix D plus the multipliers from SSPTRF, chillin' in the same storage format. glow-up complete 💖

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D, as
!>          determined by SSPTRF.  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.
!>

dimension (N), and it's giving receipts 📋 — all the interchange details and the block structure of D, straight from SSPTRF. positive IPIV(k) means 1-by-1 block, and the negative twin situation depends on whether UPLO = 'U' (check k-1) or UPLO = 'L' (check k+1). iykyk 😌

B

!>          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.
!>

comes in as the right hand side, leaves as the solution matrix X when INFO = 0. literally a transformation arc 🦋

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

leading dimension of B, and it's gotta be LDB >= max(1,N). respect the constraint or don't bother 💀

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.
!>

the vibe check of the whole operation 🚨 — 0 slays, < 0 means argument -i was illegal, and > 0 means D(i,i) is exactly zero: the factorization finished but D is exactly singular so the solution could NOT be computed. tragic, but the function is telling you honestly 🫶

🎀 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 = aji)
!>                 a44
!>
!>  Packed storage of the upper triangle of A:
!>
!>  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
!>

see? N = 4, UPLO = 'U', and the whole upper triangle gets flattened into that one array. the way it just lines up perfectly — obsessed 🥹✨

Definition at line 161 of file sspsv.f.

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📓 Author

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page bestie, no notes 💅

cute little sign-off: this was LAPACK, Version 3.12.0 — handed to you from /home/abui...RC/sspsv.f(3). go solve something symmetric and iconic 🌈⭐