 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ stbt06()

 subroutine stbt06 ( real RCOND, real RCONDC, character UPLO, character DIAG, integer N, integer KD, real, dimension( ldab, * ) AB, integer LDAB, real, dimension( * ) WORK, real RAT )

STBT06

Purpose:
``` STBT06 computes a test ratio comparing RCOND (the reciprocal
condition number of a triangular matrix A) and RCONDC, the estimate
computed by STBCON.  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 STBCON.``` [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 REAL 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 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.```
Date
December 2016

Definition at line 127 of file stbt06.f.

127 *
128 * -- LAPACK test routine (version 3.7.0) --
129 * -- LAPACK is a software package provided by Univ. of Tennessee, --
130 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131 * December 2016
132 *
133 * .. Scalar Arguments ..
134  CHARACTER diag, uplo
135  INTEGER kd, ldab, n
136  REAL rat, rcond, rcondc
137 * ..
138 * .. Array Arguments ..
139  REAL ab( ldab, * ), work( * )
140 * ..
141 *
142 * =====================================================================
143 *
144 * .. Parameters ..
145  REAL zero, one
146  parameter( zero = 0.0e+0, one = 1.0e+0 )
147 * ..
148 * .. Local Scalars ..
149  REAL anorm, bignum, eps, rmax, rmin, smlnum
150 * ..
151 * .. External Functions ..
152  REAL slamch, slantb
153  EXTERNAL slamch, slantb
154 * ..
155 * .. Intrinsic Functions ..
156  INTRINSIC max, min
157 * ..
158 * .. External Subroutines ..
160 * ..
161 * .. Executable Statements ..
162 *
163  eps = slamch( 'Epsilon' )
164  rmax = max( rcond, rcondc )
165  rmin = min( rcond, rcondc )
166 *
167 * Do the easy cases first.
168 *
169  IF( rmin.LT.zero ) THEN
170 *
171 * Invalid value for RCOND or RCONDC, return 1/EPS.
172 *
173  rat = one / eps
174 *
175  ELSE IF( rmin.GT.zero ) THEN
176 *
177 * Both estimates are positive, return RMAX/RMIN - 1.
178 *
179  rat = rmax / rmin - one
180 *
181  ELSE IF( rmax.EQ.zero ) THEN
182 *
183 * Both estimates zero.
184 *
185  rat = zero
186 *
187  ELSE
188 *
189 * One estimate is zero, the other is non-zero. If the matrix is
190 * ill-conditioned, return the nonzero estimate multiplied by
191 * 1/EPS; if the matrix is badly scaled, return the nonzero
192 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
193 * element in absolute value in A.
194 *
195  smlnum = slamch( 'Safe minimum' )
196  bignum = one / smlnum
197  CALL slabad( smlnum, bignum )
198  anorm = slantb( 'M', uplo, diag, n, kd, ab, ldab, work )
199 *
200  rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
201  END IF
202 *
203  RETURN
204 *
205 * End of STBT06
206 *
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69