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

💖 NAME 💖

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

Bestie, this is the dsysv.f(3) page from the Library Functions Manual, filed under /home/abui...RC/dsysv.f(3). It's literally the home of DSYSV, and it's giving symmetric linear solver main character energy. 💅

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine DSYSV (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork,
    info)
     DSYSV computes the solution to system of linear equations A * X = B
    for SY matrices

• subroutine DSYSV (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) — DSYSV computes the solution to system of linear equations A * X = B for SY matrices. Periodt. 💖

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🎀 Function/Subroutine Documentation 🎀

subroutine DSYSV (character uplo, integer n, integer nrhs, double precision,
    dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double
    precision, dimension( ldb, * ) b, integer ldb, double precision,
    dimension( * ) work, integer lwork, integer info)

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

🌸 Purpose 🌸

Okay so, DSYSV 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. Iconic.

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. No cap, that's the whole vibe. ✨

💅 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. Slay.

🌸 NRHS 🌸

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

🎀 A 🎀

A is DOUBLE PRECISION array, dimension (LDA,N).

On entry, 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. 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, 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 DSYTRF. IYKYK.

🧚 LDA 🧚

LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). Respect the leading dimension, bestie.

💜 IPIV 💜

IPIV is INTEGER array, dimension (N).

Details of the interchanges and the block structure of D, as determined by DSYTRF.

• 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.

That's the pivot gossip, and it's all in the details. 💅

🌈 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. Main character transformation. ✨

⭐ LDB ⭐

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

🫶 WORK 🫶

WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)).

On exit, if INFO = 0, WORK(1) returns the optimal LWORK. Little workspace, big reveal.

🔥 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 DSYTRF.

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

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 if you're doing a lil workspace peek, LWORK = -1 is the move. 👑

💀 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.

Heads up, bestie: if INFO > 0, D is exactly singular and the solution could not be computed. That's not a vibe, that's a real status. 😭

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 169 of file dsysv.f.

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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Sign-off, bestie: this footer says LAPACK, Version 3.12.0, and the page path /home/abui...RC/dsysv.f(3). There's no extra date listed, so that's the whole cute little ending. Mwah. 💋🎀