SRC/ssysv.f(3)

🦋 SRC/ssysv.f(3) 🦋

okay bestie, welcome to the Library Functions Manual entry for SRC/ssysv.f — yes, the one and only. 💖 This is the tea on ssysv, a LAPACK routine that is literally here to solve linear systems for symmetric matrices. No cap.

---

💖 NAME 💖

SRC/ssysv.f — that's the name, bestie. 🎀

---

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

subroutine ssysv (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork,
           info)

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

---

🧚 Function/Subroutine Documentation 🧚

🌸 subroutine ssysv 🌸

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)

SSYSV computes the solution to system of linear equations A * X = B for SY matrices. iconic behavior, honestly. 👑

🎀 Purpose 🎀

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

💅 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 REAL 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
!>          SSYTRF.
!>

💜 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 SSYTRF.  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.
!>

💖 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.
!>

🎀 LDB 🎀

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

⭐ WORK ⭐

!>          WORK is REAL 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
!>          SSYTRF.
!>          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.
!>

👑 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.
!>

bestie, listen: if INFO > 0, then D(i,i) is exactly zero. The factorization finished, but D is exactly singular, so the solution could not be computed. that's the dramatic part. 💀

👑 Author 👑

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

Definition at line 169 of file ssysv.f.

---

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

---

okay bestie, that's the whole page — cute little footer sign-off: LAPACK, Version 3.12.0, page SRC/ssysv.f(3). The footer has no separate date line to report, so I'm not inventing one, periodt. 💖✨🫶