TESTING/LIN/slarhs.f(3)

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version 3.12.1 · 3 versions
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okay bestie, you're looking at the manual page for TESTING/LIN/slarhs.f from the LAPACK Library Functions Manual, and it's lowkey a whole backstage pass to how LAPACK sets up linear-system test problems. 💅✨

💖 NAME 💖

TESTING/LIN/slarhs.f

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

subroutine slarhs (path, xtype, uplo, trans, m, n, kl, ku, nrhs, a, lda,
    x, ldx, b, ldb, iseed, info)
    SLARHS

🌟 Function/Subroutine Documentation 🌟

subroutine slarhs (character*3 path, character xtype, character uplo,
    character trans, integer m, integer n, integer kl, integer ku, integer
    nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldx, *
    ) x, integer ldx, real, dimension( ldb, * ) b, integer ldb, integer,
    dimension( 4 ) iseed, integer info)
    SLARHS

🎯 Purpose

SLARHS chooses a set of NRHS random solution vectors and sets up the right hand sides for the linear system

op(A) * X = B,

where op(A) = A or A**T, depending on TRANS. no cap, that's the whole assignment 💫

🧸 Parameters

PATH

PATH is CHARACTER*3.

The type of the real matrix A. PATH may be given in any combination of upper and lower case. Valid types include:

  • xGE: General m x n matrix
  • xGB: General banded matrix
  • xPO: Symmetric positive definite, 2-D storage
  • xPP: Symmetric positive definite packed
  • xPB: Symmetric positive definite banded
  • xSY: Symmetric indefinite, 2-D storage
  • xSP: Symmetric indefinite packed
  • xSB: Symmetric indefinite banded
  • xTR: Triangular
  • xTP: Triangular packed
  • xTB: Triangular banded
  • xQR: General m x n matrix
  • xLQ: General m x n matrix
  • xQL: General m x n matrix
  • xRQ: General m x n matrix

where the leading character indicates the precision. 🎀

XTYPE

XTYPE is CHARACTER*1.

Specifies how the exact solution X will be determined:

  • = 'N': New solution; generate a random X.
  • = 'C': Computed; use value of X on entry.

UPLO

UPLO is CHARACTER*1.

Specifies whether the upper or lower triangular part of the matrix A is stored, if A is symmetric.

  • = 'U': Upper triangular
  • = 'L': Lower triangular

TRANS

TRANS is CHARACTER*1.

Used only if A is nonsymmetric; specifies the operation applied to the matrix A.

  • = 'N': B := A * X (No transpose)
  • = 'T': B := A**T * X (Transpose)
  • = 'C': B := A**H * X (Conjugate transpose = Transpose)

M

M is INTEGER.

The number of rows of the matrix A. M >= 0. 🫶

N

N is INTEGER.

The number of columns of the matrix A. N >= 0. 🫶

KL

KL is INTEGER.

Used only if A is a band matrix; specifies the number of subdiagonals of A if A is a general band matrix or if A is symmetric or triangular and UPLO = 'L'; specifies the number of superdiagonals of A if A is symmetric or triangular and UPLO = 'U'. 0 <= KL <= M-1.

KU

KU is INTEGER.

Used only if A is a general band matrix or if A is triangular.

If PATH = xGB, specifies the number of superdiagonals of A, and 0 <= KU <= N-1.

If PATH = xTR, xTP, or xTB, specifies whether or not the matrix has unit diagonal:

  • = 1: matrix has non-unit diagonal (default)
  • = 2: matrix has unit diagonal

NRHS

NRHS is INTEGER.

The number of right hand side vectors in the system A*X = B.

A

A is REAL array, dimension (LDA,N).

The test matrix whose type is given by PATH.

LDA

LDA is INTEGER.

The leading dimension of the array A.

If PATH = xGB, LDA >= KL+KU+1.

If PATH = xPB, xSB, xHB, or xTB, LDA >= KL+1.

Otherwise, LDA >= max(1,M).

X

X is a REAL array (it's giving input/output energy), dimension (LDX,NRHS).

On entry, if XTYPE = 'C' (for 'Computed'), then X contains the exact solution to the system of linear equations.

On exit, if XTYPE = 'N' (for 'New'), then X is initialized with random values.

LDX

LDX is INTEGER.

The leading dimension of the array X. If TRANS = 'N', LDX >= max(1,N); if TRANS = 'T', LDX >= max(1,M).

B

B is REAL array, dimension (LDB,NRHS).

The right hand side vector(s) for the system of equations, computed from B = op(A) * X, where op(A) is determined by TRANS.

LDB

LDB is INTEGER.

The leading dimension of the array B. If TRANS = 'N', LDB >= max(1,M); if TRANS = 'T', LDB >= max(1,N).

ISEED

ISEED is INTEGER array, dimension (4).

The seed vector for the random number generator (used in SLATMS). Modified on exit. 🌀

INFO

INFO is INTEGER.

  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

🫶 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 203 of file slarhs.f.

👑 Author 👑

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