/home/abui.../dlatrs3.f(3)

💅 NAME 💅

okay so bestie, this is the Library Functions Manual page for /home/abui.../dlatrs3.f(3), and the source file it’s serving looks like:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlatrs3.f

it’s giving “we are legally required to show the whole path” energy, and honestly? iconic. 🎀

---

🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

• subroutine DLATRS3 (uplo, trans, diag, normin, n, nrhs, a, lda, x, ldx, scale, cnorm, work, lwork, info) — DLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow.

---

🌸 Function/Subroutine Documentation 🌸

🫶 subroutine DLATRS3 🫶

meet the signature, bestie — copied exactly, no cap:

   subroutine DLATRS3 (character uplo, character trans, character diag,
       character normin, integer n, integer nrhs, double precision, dimension(
       lda, * ) a, integer lda, double precision, dimension( ldx, * ) x,
       integer ldx, double precision, dimension( * ) scale, double precision,
       dimension( * ) cnorm, double precision, dimension( * ) work, integer
       lwork, integer info)

DLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow.

🌟 Purpose: 🌟

okay so the whole point, literally:

!>
!> DLATRS3 solves one of the triangular systems
!>
!>    A * X = B * diag(scale)  or  A**T * X = B * diag(scale)
!>
!> with scaling to prevent overflow.  Here A is an upper or lower
!> triangular matrix, A**T denotes the transpose of A. X and B are
!> n by nrhs matrices and scale is an nrhs element vector of scaling
!> factors. A scaling factor scale(j) is usually less than or equal
!> to 1, chosen such that X(:,j) is less than the overflow threshold.
!> If the matrix A is singular (A(j,j) = 0 for some j), then
!> a non-trivial solution to A*X = 0 is returned. If the system is
!> so badly scaled that the solution cannot be represented as
!> (1/scale(k))*X(:,k), then x(:,k) = 0 and scale(k) is returned.
!>
!> This is a BLAS-3 version of LATRS for solving several right
!> hand sides simultaneously.
!>
!>

like, it’s solving A * X = B * diag(scale) or A**T * X = B * diag(scale), with scaling so nothing overflows. and if A(j,j) = 0 for some j, you get a non-trivial solution to A*X = 0. if it’s so badly scaled that the solution can’t be represented as (1/scale(k))*X(:,k), then x(:,k) = 0 and scale(k) is returned. periodt. 💅

🎀 Parameters 🎀

• UPLO — UPLO is CHARACTER*1. specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular. = 'L': Lower triangular.
• TRANS — TRANS is CHARACTER*1. specifies the operation applied to A. = 'N': Solve A * x = s*b (No transpose). = 'T': Solve A**T* x = s*b (Transpose). = 'C': Solve A**T* x = s*b (Conjugate transpose = Transpose).
• DIAG — DIAG is CHARACTER*1. specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular. = 'U': Unit triangular.
• NORMIN — NORMIN is CHARACTER*1. specifies whether CNORM has been set or not. = 'Y': CNORM contains the column norms on entry. = 'N': CNORM is not set on entry. On exit, the norms will be computed and stored in CNORM.
• N — N is INTEGER. the order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER. the number of columns of X. NRHS >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). the triangular matrix A. If UPLO = 'U', the leading n by n upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
• LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max (1,N).
• X — X is DOUBLE PRECISION array, dimension (LDX,NRHS). on entry, the right hand side B of the triangular system. on exit, X is overwritten by the solution matrix X.
• LDX — LDX is INTEGER. the leading dimension of the array X. LDX >= max (1,N).
• SCALE — SCALE is DOUBLE PRECISION array, dimension (NRHS). the scaling factor s(k) is for the triangular system A * x(:,k) = s(k)*b(:,k) or A**T* x(:,k) = s(k)*b(:,k). If SCALE = 0, the matrix A is singular or badly scaled. If A(j,j) = 0 is encountered, a non-trivial vector x(:,k) that is an exact or approximate solution to A*x(:,k) = 0 is returned. If the system so badly scaled that solution cannot be presented as x(:,k) * 1/s(k), then x(:,k) = 0 is returned.
• CNORM — CNORM is DOUBLE PRECISION array, dimension (N). If NORMIN = 'Y', CNORM is an input argument and CNORM(j) contains the norm of the off-diagonal part of the j-th column of A. If TRANS = 'N', CNORM(j) must be greater than or equal to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) must be greater than or equal to the 1-norm. If NORMIN = 'N', CNORM is an output argument and CNORM(j) returns the 1-norm of the offdiagonal part of the j-th column of A.
• WORK — WORK is DOUBLE PRECISION array, dimension (LWORK). on exit, if INFO = 0, WORK(1) returns the optimal size of WORK.
• LWORK — the page literally says LWORK LWORK is INTEGER, and then:

LWORK >= MAX(1, 2*NBA * MAX(NBA, MIN(NRHS,
32)), where NBA = (N + NB - 1)/NB and NB is the optimal block size.

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal dimensions 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.

🎀 Parameters 🎀

• INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -k, the k-th argument had an illegal value.

---

👑 Author 👑

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

---

🔥 Further Details: 🔥

Definition at line 227 of file dlatrs3.f.

---

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

---

byeee 💖 LAPACK, Version 3.12.0 — /home/abui.../dlatrs3.f(3) — that’s the footer vibe, periodt. 🎀