LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

◆ ctrt06()

 subroutine ctrt06 ( real RCOND, real RCONDC, character UPLO, character DIAG, integer N, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) RWORK, real RAT )

CTRT06

Purpose:
``` CTRT06 computes a test ratio comparing RCOND (the reciprocal
condition number of a triangular matrix A) and RCONDC, the estimate
computed by CTRCON.  Information about the triangular matrix A is
used if one estimate is zero and the other is non-zero to decide if
underflow in the estimate is justified.```
Parameters
 [in] RCOND ``` RCOND is REAL The estimate of the reciprocal condition number obtained by forming the explicit inverse of the matrix A and computing RCOND = 1/( norm(A) * norm(inv(A)) ).``` [in] RCONDC ``` RCONDC is REAL The estimate of the reciprocal condition number computed by CTRCON.``` [in] UPLO ``` UPLO is CHARACTER Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular``` [in] DIAG ``` DIAG is CHARACTER Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] A ``` A is COMPLEX 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.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [out] RWORK ` RWORK is REAL array, dimension (N)` [out] RAT ``` RAT is REAL The test ratio. If both RCOND and RCONDC are nonzero, RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1. If RAT = 0, the two estimates are exactly the same.```
Date
December 2016

Definition at line 124 of file ctrt06.f.

124 *
125 * -- LAPACK test routine (version 3.7.0) --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 * December 2016
129 *
130 * .. Scalar Arguments ..
131  CHARACTER diag, uplo
132  INTEGER lda, n
133  REAL rat, rcond, rcondc
134 * ..
135 * .. Array Arguments ..
136  REAL rwork( * )
137  COMPLEX a( lda, * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  REAL zero, one
144  parameter( zero = 0.0e+0, one = 1.0e+0 )
145 * ..
146 * .. Local Scalars ..
147  REAL anorm, bignum, eps, rmax, rmin
148 * ..
149 * .. External Functions ..
150  REAL clantr, slamch
151  EXTERNAL clantr, slamch
152 * ..
153 * .. Intrinsic Functions ..
154  INTRINSIC max, min
155 * ..
156 * .. Executable Statements ..
157 *
158  eps = slamch( 'Epsilon' )
159  rmax = max( rcond, rcondc )
160  rmin = min( rcond, rcondc )
161 *
162 * Do the easy cases first.
163 *
164  IF( rmin.LT.zero ) THEN
165 *
166 * Invalid value for RCOND or RCONDC, return 1/EPS.
167 *
168  rat = one / eps
169 *
170  ELSE IF( rmin.GT.zero ) THEN
171 *
172 * Both estimates are positive, return RMAX/RMIN - 1.
173 *
174  rat = rmax / rmin - one
175 *
176  ELSE IF( rmax.EQ.zero ) THEN
177 *
178 * Both estimates zero.
179 *
180  rat = zero
181 *
182  ELSE
183 *
184 * One estimate is zero, the other is non-zero. If the matrix is
185 * ill-conditioned, return the nonzero estimate multiplied by
186 * 1/EPS; if the matrix is badly scaled, return the nonzero
187 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
188 * element in absolute value in A.
189 *
190  bignum = one / slamch( 'Safe minimum' )
191  anorm = clantr( 'M', uplo, diag, n, n, a, lda, rwork )
192 *
193  rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
194  END IF
195 *
196  RETURN
197 *
198 * End of CTRT06
199 *
real function clantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
CLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.
Definition: clantr.f:144
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
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