 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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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