 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dtrt06()

 subroutine dtrt06 ( double precision RCOND, double precision RCONDC, character UPLO, character DIAG, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) WORK, double precision RAT )

DTRT06

Purpose:
``` DTRT06 computes a test ratio comparing RCOND (the reciprocal
condition number of a triangular matrix A) and RCONDC, the estimate
computed by DTRCON.  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 DTRCON.``` [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 DOUBLE PRECISION 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] WORK ` WORK 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 119 of file dtrt06.f.

121 *
122 * -- LAPACK test routine --
123 * -- LAPACK is a software package provided by Univ. of Tennessee, --
124 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125 *
126 * .. Scalar Arguments ..
127  CHARACTER DIAG, UPLO
128  INTEGER LDA, N
129  DOUBLE PRECISION RAT, RCOND, RCONDC
130 * ..
131 * .. Array Arguments ..
132  DOUBLE PRECISION A( LDA, * ), WORK( * )
133 * ..
134 *
135 * =====================================================================
136 *
137 * .. Parameters ..
138  DOUBLE PRECISION ZERO, ONE
139  parameter( zero = 0.0d+0, one = 1.0d+0 )
140 * ..
141 * .. Local Scalars ..
142  DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
143 * ..
144 * .. External Functions ..
145  DOUBLE PRECISION DLAMCH, DLANTR
146  EXTERNAL dlamch, dlantr
147 * ..
148 * .. Intrinsic Functions ..
149  INTRINSIC max, min
150 * ..
151 * .. External Subroutines ..
153 * ..
154 * .. Executable Statements ..
155 *
156  eps = dlamch( 'Epsilon' )
157  rmax = max( rcond, rcondc )
158  rmin = min( rcond, rcondc )
159 *
160 * Do the easy cases first.
161 *
162  IF( rmin.LT.zero ) THEN
163 *
164 * Invalid value for RCOND or RCONDC, return 1/EPS.
165 *
166  rat = one / eps
167 *
168  ELSE IF( rmin.GT.zero ) THEN
169 *
170 * Both estimates are positive, return RMAX/RMIN - 1.
171 *
172  rat = rmax / rmin - one
173 *
174  ELSE IF( rmax.EQ.zero ) THEN
175 *
176 * Both estimates zero.
177 *
178  rat = zero
179 *
180  ELSE
181 *
182 * One estimate is zero, the other is non-zero. If the matrix is
183 * ill-conditioned, return the nonzero estimate multiplied by
184 * 1/EPS; if the matrix is badly scaled, return the nonzero
185 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
186 * element in absolute value in A.
187 *
188  smlnum = dlamch( 'Safe minimum' )
189  bignum = one / smlnum
190  CALL dlabad( smlnum, bignum )
191  anorm = dlantr( 'M', uplo, diag, n, n, a, lda, work )
192 *
193  rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
194  END IF
195 *
196  RETURN
197 *
198 * End of DTRT06
199 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69