# zlarhs.f - Man Page

TESTING/LIN/zlarhs.f

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine zlarhs (character*3 path, character xtype, character uplo, character trans, integer m, integer n, integer kl, integer ku, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldx, * ) x, integer ldx, complex*16, dimension( ldb, * ) b, integer ldb, integer, dimension( 4 ) iseed, integer info)

**ZLARHS**

**Purpose:**

ZLARHS 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, A**T, or A**H, depending on TRANS.

**Parameters***PATH*PATH is CHARACTER*3 The type of the complex matrix A. PATH may be given in any combination of upper and lower case. Valid paths include xGE: General m x n matrix xGB: General banded matrix xPO: Hermitian positive definite, 2-D storage xPP: Hermitian positive definite packed xPB: Hermitian positive definite banded xHE: Hermitian indefinite, 2-D storage xHP: Hermitian indefinite packed xHB: Hermitian indefinite 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 Used only if A is symmetric or triangular; specifies whether the upper or lower triangular part of the matrix A is stored. = '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)

*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 COMPLEX*16 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 or output) COMPLEX*16 array, 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 COMPLEX*16 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 ZLATMS). 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 **206** of file **zlarhs.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlarhs(3) is an alias of zlarhs.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK