 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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 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
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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