SRC/dsysv_aa.f(3)

💅 SRC/dsysv_aa.f — Library Functions Manual 🎀

okay so bestie, you've pulled up the man page for SRC/dsysv_aa.f, and honestly? she's a whole vibe. buckle up. 🦋

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✨ NAME ✨

SRC/dsysv_aa.f — literally just the file itself, that's the name, no notes 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

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

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👑 Function/Subroutine Documentation 👑

subroutine dsysv_aa (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)

ngl the signature is long enough to need its own zip code, but she said what she said. DSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices. periodt. 💖

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.
!>
!> Aasen's algorithm is used to factor A as
!>    A = U**T * T * U,  if UPLO = 'U', or
!>    A = L * T * L**T,  if UPLO = 'L',
!> where U (or L) is a product of permutation and unit upper (lower)
!> triangular matrices, and T is symmetric tridiagonal. The factored
!> form of A is then used to solve the system of equations A * X = B.
!>

so like, Aasen's algorithm is the main character here — she factors A into A = U**T * T * U when UPLO = 'U', or A = L * T * L**T when UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric tridiagonal ✨. then that factored form gets used to solve A * X = B. iconic behaviour, truly. 🧚

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💜 Parameters 💜

UPLO

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

character ✨one✨, and she only accepts two moods: 'U' means the upper triangle of A is stored, 'L' means the lower triangle of A is stored. pick a lane bestie 🎀

N

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

integer, the number of linear equations — aka the order of the matrix A — and N >= 0. no negative N energy allowed 🙈

NRHS

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

integer, the number of right hand sides, i.e. the number of columns of the matrix B. NRHS >= 0, always. 🫶

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 tridiagonal matrix T and the
!>          multipliers used to obtain the factor U or L from the
!>          factorization A = U**T*T*U or A = L*T*L**T as computed by
!>          DSYTRF.
!>

double precision array, dimension (LDA,N). on entry she'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. if UPLO = 'L', it flips: the leading N-by-N lower triangular part holds the lower triangular part of the matrix A, and the strictly upper triangular part is not referenced. 💅

on exit, if INFO = 0, you get the tridiagonal matrix T and the multipliers used to obtain the factor U or L from the factorization A = U**T*T*U or A = L*T*L**T as computed by DSYTRF. she really did that. 🌟

LDA

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

integer, the leading dimension of the array A. rule: LDA >= max(1,N). not a suggestion, it's a lifestyle 🎀

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i.e.,
!>          the row and column k of A were interchanged with the
!>          row and column IPIV(k).
!>

integer array, dimension (N). on exit she's holding the details of the interchanges, i.e. the row and column k of A were interchanged with the row and column IPIV(k). tea. ☕

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.
!>

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. glow-up of the century 🔥

LDB

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

integer, the leading dimension of the array B, and LDB >= max(1,N) — same rules as her sister LDA, no cap 💖

WORK

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

double precision array, dimension (MAX(1,LWORK)). on exit, if INFO = 0, WORK(1) returns the optimal LWORK. she's helpful like that 🫶

LWORK

!>          LWORK is INTEGER
!>          The length of WORK.  LWORK >= MAX(1,2*N,3*N-2), and for
!>          the best performance, LWORK >= MAX(1,N*NB), where NB is
!>          the optimal blocksize for DSYTRF_AA.
!>
!>          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.
!>

integer, the length of WORK. minimum is LWORK >= MAX(1,2*N,3*N-2), and for the best performance you want LWORK >= MAX(1,N*NB), where NB is the optimal blocksize for DSYTRF_AA. treat her right and she'll perform 💅

oh and — 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. sneaky little shortcut, love that for you 😌

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.
!>

integer, and she's the vibe check at the end:

• = 0: successful exit 🎉 slay
• < 0: if INFO = -i, the i-th argument had an illegal value 💀 someone misbehaved
• > 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. 😭 devastating, but at least she told you

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🎀 Author 🎀

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

the whole squad collaborated, we love a group project that actually worked 🫶✨

Definition at line 160 of file dsysv_aa.f.

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🌈 Author (the meta one) 🌈

Generated automatically by Doxygen for LAPACK from the source code. no human wrote this section, the robot did it, and honestly? she ate 🤖💅

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and that's the whole page bestie!! 🌸 this lil gem is LAPACK, Version 3.12.0, and it lives at SRC/dsysv_aa.f(3) — go forth and solve those symmetric systems, ily, bye!! 💖🎀🦋👑⭐