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

💅 NAME

okay so bestie, this is the manual page for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ssysv.f — like yes that's a whole entire path and it's giving "my home address on the first day of school" 🏠✨ but that's literally the name of this thing, no cap.

This is part of the LAPACK Library Functions Manual, and it's about one specific little icon: the SSYSV subroutine. 🎀

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines

• subroutine SSYSV (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) — and like, what does it do? It SSYSV computes the solution to system of linear equations A * X = B for SY matrices. that's the whole vibe. 💫

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🔥 Function/Subroutine Documentation 🔥

🫶 the full signature (yes, all of it)

subroutine SSYSV (character uplo, integer n, integer nrhs, real, dimension(
    lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension(
    ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork,
    integer info)

and again, for the people in the back: SSYSV computes the solution to system of linear equations A * X = B for SY matrices. 👑

🦋 Purpose

so here's the tea, bestie — SSYSV computes the solution to a real system of linear equations

   A * X = B,

where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices. like, it's solving for X, that's the whole plot. 😌

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. The factored form of A is then used to solve the system of equations A * X = B. slay, honestly. 💅

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🌈 Parameters

🍓 UPLO

UPLO is CHARACTER*1 and it's literally just "which triangle of A are we even looking at":

• = 'U': Upper triangle of A is stored;
• = 'L': Lower triangle of A is stored.

pick one, bestie, don't be indecisive. 🙈

🍓 N

N is INTEGER — the number of linear equations, i.e., the order of the matrix A. constraint era: N >= 0. ✨

🍓 NRHS

NRHS is INTEGER — the number of right hand sides, i.e., the number of columns of the matrix B. also NRHS >= 0. so many right-hand sides, so little time. 😭

🍓 A

A is REAL array, dimension (LDA,N).

On entry, it's the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced (it's just sitting there, unbothered, not invited to the function 🧚). If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

On exit, if INFO = 0, you get 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 SSYTRF. glow-up complete. ⭐

🍓 LDA

LDA is INTEGER — the leading dimension of the array A. rule of law: LDA >= max(1,N). 👑

🍓 IPIV

IPIV is INTEGER array, dimension (N) — details of the interchanges and the block structure of D, as determined by SSYTRF. and this part is lowkey the whole lore, so pay attention:

• 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.

see? 2-by-2 blocks are the main characters here. 💀

🍓 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. it literally transforms. ate and left no crumbs. 🔥

🍓 LDB

LDB is INTEGER — the leading dimension of the array B, and LDB >= max(1,N). yes we're checking again. 💜

🍓 WORK

WORK is REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. it's the little helper that could. 🫶

🍓 LWORK

LWORK is INTEGER — the length of WORK. LWORK >= 1, and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for SSYTRF.

• for LWORK < N, TRS will be done with Level BLAS 2
• for LWORK >= N, TRS will be done with Level BLAS 3

and, iconic behaviour: if LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. so it's like asking "how much room do I need" and it just tells you instead of screaming. 🌸

🍓 INFO

INFO is INTEGER and it's the vibe check at the end:

• = 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. 😭 like it tried, it finished the factorization, and then there was just... no solution. tragic.

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💖 Author

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

📍 Definition at line 169 of file ssysv.f.

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👑 Author

Generated automatically by Doxygen for LAPACK from the source code. so nobody hand-wrote this one, a robot did it, and honestly? respect. 🤖✨

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and that's the whole page, bestie!! 💖 LAPACK, Version 3.12.0, live from /home/abui...RC/ssysv.f(3) — go forth and solve your symmetric systems. mwah. 🎀🦋💅