LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dtpt06()

 subroutine dtpt06 ( double precision RCOND, double precision RCONDC, character UPLO, character DIAG, integer N, double precision, dimension( * ) AP, double precision, dimension( * ) WORK, double precision RAT )

DTPT06

Purpose:
``` DTPT06 computes a test ratio comparing RCOND (the reciprocal
condition number of a triangular matrix A) and RCONDC, the estimate
computed by DTPCON.  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 DTPCON.``` [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 DOUBLE PRECISION 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 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 110 of file dtpt06.f.

111*
112* -- LAPACK test routine --
113* -- LAPACK is a software package provided by Univ. of Tennessee, --
114* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
115*
116* .. Scalar Arguments ..
117 CHARACTER DIAG, UPLO
118 INTEGER N
119 DOUBLE PRECISION RAT, RCOND, RCONDC
120* ..
121* .. Array Arguments ..
122 DOUBLE PRECISION AP( * ), WORK( * )
123* ..
124*
125* =====================================================================
126*
127* .. Parameters ..
128 DOUBLE PRECISION ZERO, ONE
129 parameter( zero = 0.0d+0, one = 1.0d+0 )
130* ..
131* .. Local Scalars ..
132 DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
133* ..
134* .. External Functions ..
135 DOUBLE PRECISION DLAMCH, DLANTP
136 EXTERNAL dlamch, dlantp
137* ..
138* .. Intrinsic Functions ..
139 INTRINSIC max, min
140* ..
141* .. External Subroutines ..
143* ..
144* .. Executable Statements ..
145*
146 eps = dlamch( 'Epsilon' )
147 rmax = max( rcond, rcondc )
148 rmin = min( rcond, rcondc )
149*
150* Do the easy cases first.
151*
152 IF( rmin.LT.zero ) THEN
153*
154* Invalid value for RCOND or RCONDC, return 1/EPS.
155*
156 rat = one / eps
157*
158 ELSE IF( rmin.GT.zero ) THEN
159*
160* Both estimates are positive, return RMAX/RMIN - 1.
161*
162 rat = rmax / rmin - one
163*
164 ELSE IF( rmax.EQ.zero ) THEN
165*
166* Both estimates zero.
167*
168 rat = zero
169*
170 ELSE
171*
172* One estimate is zero, the other is non-zero. If the matrix is
173* ill-conditioned, return the nonzero estimate multiplied by
174* 1/EPS; if the matrix is badly scaled, return the nonzero
175* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
176* element in absolute value in A.
177*
178 smlnum = dlamch( 'Safe minimum' )
179 bignum = one / smlnum
180 CALL dlabad( smlnum, bignum )
181 anorm = dlantp( 'M', uplo, diag, n, ap, work )
182*
183 rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
184 END IF
185*
186 RETURN
187*
188* End of DTPT06
189*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69