LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dtbt06()

 subroutine dtbt06 ( double precision RCOND, double precision RCONDC, character UPLO, character DIAG, integer N, integer KD, double precision, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) WORK, double precision RAT )

DTBT06

Purpose:
``` DTBT06 computes a test ratio comparing RCOND (the reciprocal
condition number of a triangular matrix A) and RCONDC, the estimate
computed by DTBCON.  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 DTBCON.``` [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] KD ``` KD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.``` [in] AB ``` AB is DOUBLE PRECISION array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).``` [in] LDAB ``` LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.``` [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 123 of file dtbt06.f.

125*
126* -- LAPACK test routine --
127* -- LAPACK is a software package provided by Univ. of Tennessee, --
128* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129*
130* .. Scalar Arguments ..
131 CHARACTER DIAG, UPLO
132 INTEGER KD, LDAB, N
133 DOUBLE PRECISION RAT, RCOND, RCONDC
134* ..
135* .. Array Arguments ..
136 DOUBLE PRECISION AB( LDAB, * ), WORK( * )
137* ..
138*
139* =====================================================================
140*
141* .. Parameters ..
142 DOUBLE PRECISION ZERO, ONE
143 parameter( zero = 0.0d+0, one = 1.0d+0 )
144* ..
145* .. Local Scalars ..
146 DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
147* ..
148* .. External Functions ..
149 DOUBLE PRECISION DLAMCH, DLANTB
150 EXTERNAL dlamch, dlantb
151* ..
152* .. Intrinsic Functions ..
153 INTRINSIC max, min
154* ..
155* .. External Subroutines ..
157* ..
158* .. Executable Statements ..
159*
160 eps = dlamch( 'Epsilon' )
161 rmax = max( rcond, rcondc )
162 rmin = min( rcond, rcondc )
163*
164* Do the easy cases first.
165*
166 IF( rmin.LT.zero ) THEN
167*
168* Invalid value for RCOND or RCONDC, return 1/EPS.
169*
170 rat = one / eps
171*
172 ELSE IF( rmin.GT.zero ) THEN
173*
174* Both estimates are positive, return RMAX/RMIN - 1.
175*
176 rat = rmax / rmin - one
177*
178 ELSE IF( rmax.EQ.zero ) THEN
179*
180* Both estimates zero.
181*
182 rat = zero
183*
184 ELSE
185*
186* One estimate is zero, the other is non-zero. If the matrix is
187* ill-conditioned, return the nonzero estimate multiplied by
188* 1/EPS; if the matrix is badly scaled, return the nonzero
189* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
190* element in absolute value in A.
191*
192 smlnum = dlamch( 'Safe minimum' )
193 bignum = one / smlnum
194 CALL dlabad( smlnum, bignum )
195 anorm = dlantb( 'M', uplo, diag, n, kd, ab, ldab, work )
196*
197 rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
198 END IF
199*
200 RETURN
201*
202* End of DTBT06
203*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69