SSYTRS_3(3)

💖 NAME 💖

okay bestie, so this page is ssytrs_3.f(3) and it lives in the Library Functions Manual — very demure, very Fortran. the star of the show is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ssytrs_3.f

that's the actual file, no cap. 💅

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

subroutine SSYTRS_3 (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info)

that's the vibe-check version. the full glow-up signature is down in the docs section 🫶 it's SSYTRS_3 and honestly? it ate.

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🦋 Function/Subroutine Documentation 🦋

subroutine SSYTRS_3 (character uplo, integer n, integer nrhs, real,
    dimension( lda, * ) a, integer lda, real, dimension( * ) e, integer,
    dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, integer
    info)

SSYTRS_3 — literally the whole point of this page. 🎀

🔥 Purpose 🔥

so what does it do? it solves a system of linear equations A * X = B with a real symmetric matrix A, using the factorization computed by SSYTRF_RK or SSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is a unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. 💀 the math is mathing.

and this algorithm is using Level 3 BLAS. periodt. 👑

🌈 Parameters 🌈

💜 UPLO

UPLO is CHARACTER*1. it tells you whether the details of the factorization are stored as an upper or lower triangular matrix:

• = 'U': upper triangular, form is A = P*U*D*(U**T)*(P**T);
• = 'L': lower triangular, form is A = P*L*D*(L**T)*(P**T).

💜 N

N is INTEGER. 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.

💜 A

A is REAL array, dimension (LDA,N). it holds the diagonal of the block diagonal matrix D and the factors U or L as computed by SSYTRF_RK and SSYTRF_BK:

• a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and
• b) if UPLO = 'U': factor U in the superdiagonal part of A. if UPLO = 'L': factor L in the subdiagonal part of A.

💜 LDA

LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,N). don't skip this one fr fr 🙈

💜 E

E is REAL array, dimension (N). on entry, it contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where:

• if UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
• if UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: for 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases. iykyk 👀

💜 IPIV

IPIV is INTEGER array, dimension (N). the details of the interchanges and the block structure of D as determined by SSYTRF_RK or SSYTRF_BK. 🧚

💜 B

B is REAL array, dimension (LDB,NRHS). on entry, the right hand side matrix B. on exit, the solution matrix X. the literal main character transformation 💫

💜 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 😭

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👑 Author 👑

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

🍓 Contributors 🍓

• June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley
• September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

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⭐ Definition at line 163 of file ssytrs_3.f. ⭐

🎀 Author (the auto-generated one) 🎀

Generated automatically by Doxygen for LAPACK from the source code. not a human, just a little robot doing its thing 🤖💖

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cute sign-off: this whole page came to you from LAPACK, Version 3.12.0, and the file is /home/abui.../ssytrs_3.f(3). slay, go solve something symmetric bestie 🌸🫶💜