SRC/dlatrs3.f(3)

💖 NAME 💖

SRC/dlatrs3.f — this is a LAPACK Library Functions Manual page, bestie, and it's all about the dlatrs3 subroutine. Lowkey 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 (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. Bestie, it's giving "linear algebra but make it not explode." 😭🔥

🔥 Purpose 🔥

So DLATRS3 solves one of these 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, and 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. Periodt. 🫶

🎀 Parameters 🎀

• UPLO — CHARACTER*1. Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular, = 'L': Lower triangular.
• TRANS — 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 — CHARACTER*1. Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular, = 'U': Unit triangular.
• NORMIN — 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 — INTEGER. The order of the matrix A. N >= 0.
• NRHS — INTEGER. The number of columns of X. NRHS >= 0.
• A — 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 — INTEGER. The leading dimension of the array A. LDA >= max (1,N).
• X — 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 — INTEGER. The leading dimension of the array X. LDX >= max (1,N).
• SCALE — 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 — 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 — DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal size of WORK.
• LWORK — INTEGER. The dimension of the array WORK. If MIN(N,NRHS) = 0, LWORK >= 1, else

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.

• INFO — 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 🌈

Nothing else is tucked under Further Details on this page, bestie — just the heading doing its thing. 🦋

Definition at line 232 of file dlatrs3.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

---

That's the whole page, bestie! 🫶 Signed off with LAPACK Version 3.12.0 and SRC/dlatrs3.f(3) — the footer doesn't give a separate date line beyond that source/version, so no cap. 💅✨