 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ ztpt06()

 subroutine ztpt06 ( double precision RCOND, double precision RCONDC, character UPLO, character DIAG, integer N, complex*16, dimension( * ) AP, double precision, dimension( * ) RWORK, double precision RAT )

ZTPT06

Purpose:
``` ZTPT06 computes a test ratio comparing RCOND (the reciprocal
condition number of the triangular matrix A) and RCONDC, the estimate
computed by ZTPCON.  Information about the triangular matrix 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 ZTPCON.``` [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 COMPLEX*16 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] 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 114 of file ztpt06.f.

114 *
115 * -- LAPACK test routine (version 3.7.0) --
116 * -- LAPACK is a software package provided by Univ. of Tennessee, --
117 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118 * December 2016
119 *
120 * .. Scalar Arguments ..
121  CHARACTER diag, uplo
122  INTEGER n
123  DOUBLE PRECISION rat, rcond, rcondc
124 * ..
125 * .. Array Arguments ..
126  DOUBLE PRECISION rwork( * )
127  COMPLEX*16 ap( * )
128 * ..
129 *
130 * =====================================================================
131 *
132 * .. Parameters ..
133  DOUBLE PRECISION zero, one
134  parameter( zero = 0.0d+0, one = 1.0d+0 )
135 * ..
136 * .. Local Scalars ..
137  DOUBLE PRECISION anorm, bignum, eps, rmax, rmin
138 * ..
139 * .. External Functions ..
140  DOUBLE PRECISION dlamch, zlantp
141  EXTERNAL dlamch, zlantp
142 * ..
143 * .. Intrinsic Functions ..
144  INTRINSIC max, min
145 * ..
146 * .. Executable Statements ..
147 *
148  eps = dlamch( 'Epsilon' )
149  rmax = max( rcond, rcondc )
150  rmin = min( rcond, rcondc )
151 *
152 * Do the easy cases first.
153 *
154  IF( rmin.LT.zero ) THEN
155 *
156 * Invalid value for RCOND or RCONDC, return 1/EPS.
157 *
158  rat = one / eps
159 *
160  ELSE IF( rmin.GT.zero ) THEN
161 *
162 * Both estimates are positive, return RMAX/RMIN - 1.
163 *
164  rat = rmax / rmin - one
165 *
166  ELSE IF( rmax.EQ.zero ) THEN
167 *
168 * Both estimates zero.
169 *
170  rat = zero
171 *
172  ELSE
173 *
174 * One estimate is zero, the other is non-zero. If the matrix is
175 * ill-conditioned, return the nonzero estimate multiplied by
176 * 1/EPS; if the matrix is badly scaled, return the nonzero
177 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
178 * element in absolute value in A.
179 *
180  bignum = one / dlamch( 'Safe minimum' )
181  anorm = zlantp( 'M', uplo, diag, n, ap, rwork )
182 *
183  rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
184  END IF
185 *
186  RETURN
187 *
188 * End of ZTPT06
189 *
double precision function zlantp(NORM, UPLO, DIAG, N, AP, WORK)
ZLANTP 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 matrix supplied in packed form.
Definition: zlantp.f:127
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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