LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ ztrt06()

 subroutine ztrt06 ( double precision rcond, double precision rcondc, character uplo, character diag, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) rwork, double precision rat )

ZTRT06

Purpose:
``` ZTRT06 computes a test ratio comparing RCOND (the reciprocal
condition number of a triangular matrix A) and RCONDC, the estimate
computed by ZTRCON.  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 DOUBLE PRECISION 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 DOUBLE PRECISION The estimate of the reciprocal condition number computed by ZTRCON.``` [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*16 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 DOUBLE PRECISION array, dimension (N)` [out] RAT ``` RAT is DOUBLE PRECISION 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.```

Definition at line 120 of file ztrt06.f.

122*
123* -- LAPACK test routine --
124* -- LAPACK is a software package provided by Univ. of Tennessee, --
125* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126*
127* .. Scalar Arguments ..
128 CHARACTER DIAG, UPLO
129 INTEGER LDA, N
130 DOUBLE PRECISION RAT, RCOND, RCONDC
131* ..
132* .. Array Arguments ..
133 DOUBLE PRECISION RWORK( * )
134 COMPLEX*16 A( LDA, * )
135* ..
136*
137* =====================================================================
138*
139* .. Parameters ..
140 DOUBLE PRECISION ZERO, ONE
141 parameter( zero = 0.0d+0, one = 1.0d+0 )
142* ..
143* .. Local Scalars ..
144 DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN
145* ..
146* .. External Functions ..
147 DOUBLE PRECISION DLAMCH, ZLANTR
148 EXTERNAL dlamch, zlantr
149* ..
150* .. Intrinsic Functions ..
151 INTRINSIC max, min
152* ..
153* .. Executable Statements ..
154*
155 eps = dlamch( 'Epsilon' )
156 rmax = max( rcond, rcondc )
157 rmin = min( rcond, rcondc )
158*
159* Do the easy cases first.
160*
161 IF( rmin.LT.zero ) THEN
162*
163* Invalid value for RCOND or RCONDC, return 1/EPS.
164*
165 rat = one / eps
166*
167 ELSE IF( rmin.GT.zero ) THEN
168*
169* Both estimates are positive, return RMAX/RMIN - 1.
170*
171 rat = rmax / rmin - one
172*
173 ELSE IF( rmax.EQ.zero ) THEN
174*
175* Both estimates zero.
176*
177 rat = zero
178*
179 ELSE
180*
181* One estimate is zero, the other is non-zero. If the matrix is
182* ill-conditioned, return the nonzero estimate multiplied by
183* 1/EPS; if the matrix is badly scaled, return the nonzero
184* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
185* element in absolute value in A.
186*
187 bignum = one / dlamch( 'Safe minimum' )
188 anorm = zlantr( 'M', uplo, diag, n, n, a, lda, rwork )
189*
190 rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
191 END IF
192*
193 RETURN
194*
195* End of ZTRT06
196*
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
double precision function zlantr(norm, uplo, diag, m, n, a, lda, work)
ZLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition zlantr.f:142
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