LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ 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.```

Definition at line 111 of file ztpt06.f.

112*
113* -- LAPACK test routine --
114* -- LAPACK is a software package provided by Univ. of Tennessee, --
115* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
116*
117* .. Scalar Arguments ..
118 CHARACTER DIAG, UPLO
119 INTEGER N
120 DOUBLE PRECISION RAT, RCOND, RCONDC
121* ..
122* .. Array Arguments ..
123 DOUBLE PRECISION RWORK( * )
124 COMPLEX*16 AP( * )
125* ..
126*
127* =====================================================================
128*
129* .. Parameters ..
130 DOUBLE PRECISION ZERO, ONE
131 parameter( zero = 0.0d+0, one = 1.0d+0 )
132* ..
133* .. Local Scalars ..
134 DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN
135* ..
136* .. External Functions ..
137 DOUBLE PRECISION DLAMCH, ZLANTP
138 EXTERNAL dlamch, zlantp
139* ..
140* .. Intrinsic Functions ..
141 INTRINSIC max, min
142* ..
143* .. Executable Statements ..
144*
145 eps = dlamch( 'Epsilon' )
146 rmax = max( rcond, rcondc )
147 rmin = min( rcond, rcondc )
148*
149* Do the easy cases first.
150*
151 IF( rmin.LT.zero ) THEN
152*
153* Invalid value for RCOND or RCONDC, return 1/EPS.
154*
155 rat = one / eps
156*
157 ELSE IF( rmin.GT.zero ) THEN
158*
159* Both estimates are positive, return RMAX/RMIN - 1.
160*
161 rat = rmax / rmin - one
162*
163 ELSE IF( rmax.EQ.zero ) THEN
164*
165* Both estimates zero.
166*
167 rat = zero
168*
169 ELSE
170*
171* One estimate is zero, the other is non-zero. If the matrix is
172* ill-conditioned, return the nonzero estimate multiplied by
173* 1/EPS; if the matrix is badly scaled, return the nonzero
174* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
175* element in absolute value in A.
176*
177 bignum = one / dlamch( 'Safe minimum' )
178 anorm = zlantp( 'M', uplo, diag, n, ap, rwork )
179*
180 rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
181 END IF
182*
183 RETURN
184*
185* End of ZTPT06
186*
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
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,...
Definition zlantp.f:125
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