SRC/dsysv.f(3)

💅 SRC/dsysv.f — from the Library Functions Manual ✨

okay bestie, buckle up 🎀 this one is a whole LAPACK situation and it's actually kind of iconic.

🌸 NAME 🌸

SRC/dsysv.f — and yes that's the entire name section, she's mysterious like that 💅

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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 🌈

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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:

!>
!> 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.
!>
!> 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.
!>

literally the whole plot: factor A with diagonal pivoting, then use that factored form to solve the system. main character energy fr fr ✨

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🎀 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.
!>

💖 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.
!>

ngl, she comes in as your symmetric matrix and leaves as the D-plus-multipliers situation. glow-up 💅

💖 LDA

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

💖 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.
!>

this is the receipts of every swap that went down, courtesy of DSYTRF 🔥

💖 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.
!>

she walks in as B and struts out as X. periodt. 👑

💖 LDB

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

💖 WORK

!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!>

💖 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.
!>

bestie listen 👀 — LWORK = -1 is the workspace-query era. she does NOT solve anything, she just sizes up the WORK array, drops that value in WORK(1), and XERBLA stays completely silent about it. no error, no drama 🫶

💖 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.
!>

💀 INFO > 0 is the bad-ending timeline: D(i,i) is exactly zero, the factorization finished but D is exactly singular, so no solution could be computed. not slay, but at least you know.

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🧚 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. (yes, the robot wrote this one, she just formatted it 🎀)

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LAPACK · Version 3.12.0 · SRC/dsysv.f(3)

that's the whole page bestie, go solve your symmetric systems, ily, bye 💖✨🦋🌸🍓