 LAPACK  3.8.0 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.```
Date
December 2016

Definition at line 123 of file dtrt06.f.

123 *
124 * -- LAPACK test routine (version 3.7.0) --
125 * -- LAPACK is a software package provided by Univ. of Tennessee, --
126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127 * December 2016
128 *
129 * .. Scalar Arguments ..
130  CHARACTER diag, uplo
131  INTEGER lda, n
132  DOUBLE PRECISION rat, rcond, rcondc
133 * ..
134 * .. Array Arguments ..
135  DOUBLE PRECISION a( lda, * ), work( * )
136 * ..
137 *
138 * =====================================================================
139 *
140 * .. Parameters ..
141  DOUBLE PRECISION zero, one
142  parameter( zero = 0.0d+0, one = 1.0d+0 )
143 * ..
144 * .. Local Scalars ..
145  DOUBLE PRECISION anorm, bignum, eps, rmax, rmin, smlnum
146 * ..
147 * .. External Functions ..
148  DOUBLE PRECISION dlamch, dlantr
149  EXTERNAL dlamch, dlantr
150 * ..
151 * .. Intrinsic Functions ..
152  INTRINSIC max, min
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL dlabad
156 * ..
157 * .. Executable Statements ..
158 *
159  eps = dlamch( 'Epsilon' )
160  rmax = max( rcond, rcondc )
161  rmin = min( rcond, rcondc )
162 *
163 * Do the easy cases first.
164 *
165  IF( rmin.LT.zero ) THEN
166 *
167 * Invalid value for RCOND or RCONDC, return 1/EPS.
168 *
169  rat = one / eps
170 *
171  ELSE IF( rmin.GT.zero ) THEN
172 *
173 * Both estimates are positive, return RMAX/RMIN - 1.
174 *
175  rat = rmax / rmin - one
176 *
177  ELSE IF( rmax.EQ.zero ) THEN
178 *
179 * Both estimates zero.
180 *
181  rat = zero
182 *
183  ELSE
184 *
185 * One estimate is zero, the other is non-zero. If the matrix is
186 * ill-conditioned, return the nonzero estimate multiplied by
187 * 1/EPS; if the matrix is badly scaled, return the nonzero
188 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
189 * element in absolute value in A.
190 *
191  smlnum = dlamch( 'Safe minimum' )
192  bignum = one / smlnum
193  CALL dlabad( smlnum, bignum )
194  anorm = dlantr( 'M', uplo, diag, n, n, a, lda, work )
195 *
196  rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
197  END IF
198 *
199  RETURN
200 *
201 * End of DTRT06
202 *
subroutine dlabad(SMALL, LARGE)
DLABAD
Definition: dlabad.f:76
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
double precision function dlantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
DLANTR 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: dlantr.f:143
Here is the call graph for this function:
Here is the caller graph for this function: