LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine stpt06 ( real RCOND, real RCONDC, character UPLO, character DIAG, integer N, real, dimension( * ) AP, real, dimension( * ) WORK, real RAT )

STPT06

Purpose:
``` STPT06 computes a test ratio comparing RCOND (the reciprocal
condition number of a triangular matrix A) and RCONDC, the estimate
computed by STPCON.  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 STPCON.``` [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] AP ``` AP is REAL array, dimension (N*(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.``` [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
November 2011

Definition at line 113 of file stpt06.f.

113 *
114 * -- LAPACK test routine (version 3.4.0) --
115 * -- LAPACK is a software package provided by Univ. of Tennessee, --
116 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117 * November 2011
118 *
119 * .. Scalar Arguments ..
120  CHARACTER diag, uplo
121  INTEGER n
122  REAL rat, rcond, rcondc
123 * ..
124 * .. Array Arguments ..
125  REAL ap( * ), work( * )
126 * ..
127 *
128 * =====================================================================
129 *
130 * .. Parameters ..
131  REAL zero, one
132  parameter ( zero = 0.0e+0, one = 1.0e+0 )
133 * ..
134 * .. Local Scalars ..
135  REAL anorm, bignum, eps, rmax, rmin, smlnum
136 * ..
137 * .. External Functions ..
138  REAL slamch, slantp
139  EXTERNAL slamch, slantp
140 * ..
141 * .. Intrinsic Functions ..
142  INTRINSIC max, min
143 * ..
144 * .. External Subroutines ..
146 * ..
147 * .. Executable Statements ..
148 *
149  eps = slamch( 'Epsilon' )
150  rmax = max( rcond, rcondc )
151  rmin = min( rcond, rcondc )
152 *
153 * Do the easy cases first.
154 *
155  IF( rmin.LT.zero ) THEN
156 *
157 * Invalid value for RCOND or RCONDC, return 1/EPS.
158 *
159  rat = one / eps
160 *
161  ELSE IF( rmin.GT.zero ) THEN
162 *
163 * Both estimates are positive, return RMAX/RMIN - 1.
164 *
165  rat = rmax / rmin - one
166 *
167  ELSE IF( rmax.EQ.zero ) THEN
168 *
169 * Both estimates zero.
170 *
171  rat = zero
172 *
173  ELSE
174 *
175 * One estimate is zero, the other is non-zero. If the matrix is
176 * ill-conditioned, return the nonzero estimate multiplied by
177 * 1/EPS; if the matrix is badly scaled, return the nonzero
178 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
179 * element in absolute value in A.
180 *
181  smlnum = slamch( 'Safe minimum' )
182  bignum = one / smlnum
183  CALL slabad( smlnum, bignum )
184  anorm = slantp( 'M', uplo, diag, n, ap, work )
185 *
186  rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
187  END IF
188 *
189  RETURN
190 *
191 * End of STPT06
192 *