LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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◆ ctbt06()

 subroutine ctbt06 ( real rcond, real rcondc, character uplo, character diag, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) rwork, real rat )

CTBT06

Purpose:
``` CTBT06 computes a test ratio comparing RCOND (the reciprocal
condition number of a triangular matrix A) and RCONDC, the estimate
computed by CTBCON.  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 REAL 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 REAL The estimate of the reciprocal condition number computed by CTBCON.``` [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 COMPLEX 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] RWORK ` RWORK is REAL array, dimension (N)` [out] RAT ``` RAT is REAL 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 124 of file ctbt06.f.

126*
127* -- LAPACK test routine --
128* -- LAPACK is a software package provided by Univ. of Tennessee, --
129* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130*
131* .. Scalar Arguments ..
132 CHARACTER DIAG, UPLO
133 INTEGER KD, LDAB, N
134 REAL RAT, RCOND, RCONDC
135* ..
136* .. Array Arguments ..
137 REAL RWORK( * )
138 COMPLEX AB( LDAB, * )
139* ..
140*
141* =====================================================================
142*
143* .. Parameters ..
144 REAL ZERO, ONE
145 parameter( zero = 0.0e+0, one = 1.0e+0 )
146* ..
147* .. Local Scalars ..
148 REAL ANORM, BIGNUM, EPS, RMAX, RMIN
149* ..
150* .. External Functions ..
151 REAL CLANTB, SLAMCH
152 EXTERNAL clantb, slamch
153* ..
154* .. Intrinsic Functions ..
155 INTRINSIC max, min
156* ..
157* .. Executable Statements ..
158*
159 eps = slamch( '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 bignum = one / slamch( 'Safe minimum' )
192 anorm = clantb( 'M', uplo, diag, n, kd, ab, ldab, rwork )
193*
194 rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
195 END IF
196*
197 RETURN
198*
199* End of CTBT06
200*
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
real function clantb(norm, uplo, diag, n, k, ab, ldab, work)
CLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition clantb.f:141
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