 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ ztbt06()

 subroutine ztbt06 ( double precision RCOND, double precision RCONDC, character UPLO, character DIAG, integer N, integer KD, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) RWORK, double precision RAT )

ZTBT06

Purpose:
``` ZTBT06 computes a test ratio comparing RCOND (the reciprocal
condition number of a triangular matrix A) and RCONDC, the estimate
computed by ZTBCON.  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 ZTBCON.``` [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*16 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 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 128 of file ztbt06.f.

128 *
129 * -- LAPACK test routine (version 3.7.0) --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 * December 2016
133 *
134 * .. Scalar Arguments ..
135  CHARACTER diag, uplo
136  INTEGER kd, ldab, n
137  DOUBLE PRECISION rat, rcond, rcondc
138 * ..
139 * .. Array Arguments ..
140  DOUBLE PRECISION rwork( * )
141  COMPLEX*16 ab( ldab, * )
142 * ..
143 *
144 * =====================================================================
145 *
146 * .. Parameters ..
147  DOUBLE PRECISION zero, one
148  parameter( zero = 0.0d+0, one = 1.0d+0 )
149 * ..
150 * .. Local Scalars ..
151  DOUBLE PRECISION anorm, bignum, eps, rmax, rmin
152 * ..
153 * .. External Functions ..
154  DOUBLE PRECISION dlamch, zlantb
155  EXTERNAL dlamch, zlantb
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC max, min
159 * ..
160 * .. Executable Statements ..
161 *
162  eps = dlamch( 'Epsilon' )
163  rmax = max( rcond, rcondc )
164  rmin = min( rcond, rcondc )
165 *
166 * Do the easy cases first.
167 *
168  IF( rmin.LT.zero ) THEN
169 *
170 * Invalid value for RCOND or RCONDC, return 1/EPS.
171 *
172  rat = one / eps
173 *
174  ELSE IF( rmin.GT.zero ) THEN
175 *
176 * Both estimates are positive, return RMAX/RMIN - 1.
177 *
178  rat = rmax / rmin - one
179 *
180  ELSE IF( rmax.EQ.zero ) THEN
181 *
182 * Both estimates zero.
183 *
184  rat = zero
185 *
186  ELSE
187 *
188 * One estimate is zero, the other is non-zero. If the matrix is
189 * ill-conditioned, return the nonzero estimate multiplied by
190 * 1/EPS; if the matrix is badly scaled, return the nonzero
191 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
192 * element in absolute value in A.
193 *
194  bignum = one / dlamch( 'Safe minimum' )
195  anorm = zlantb( 'M', uplo, diag, n, kd, ab, ldab, rwork )
196 *
197  rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
198  END IF
199 *
200  RETURN
201 *
202 * End of ZTBT06
203 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
double precision function zlantb(NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
ZLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.
Definition: zlantb.f:143
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