LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ ctrt06()

subroutine ctrt06 ( real  rcond,
real  rcondc,
character  uplo,
character  diag,
integer  n,
complex, dimension( lda, * )  a,
integer  lda,
real, dimension( * )  rwork,
real  rat 
)

CTRT06

Purpose:
 CTRT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by CTRCON.  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
          CTRCON.
[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]A
          A is COMPLEX array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading n by n
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced.  If UPLO = 'L', the leading n by n lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[out]RWORK
          RWORK 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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 120 of file ctrt06.f.

122*
123* -- LAPACK test routine --
124* -- LAPACK is a software package provided by Univ. of Tennessee, --
125* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126*
127* .. Scalar Arguments ..
128 CHARACTER DIAG, UPLO
129 INTEGER LDA, N
130 REAL RAT, RCOND, RCONDC
131* ..
132* .. Array Arguments ..
133 REAL RWORK( * )
134 COMPLEX A( LDA, * )
135* ..
136*
137* =====================================================================
138*
139* .. Parameters ..
140 REAL ZERO, ONE
141 parameter( zero = 0.0e+0, one = 1.0e+0 )
142* ..
143* .. Local Scalars ..
144 REAL ANORM, BIGNUM, EPS, RMAX, RMIN
145* ..
146* .. External Functions ..
147 REAL CLANTR, SLAMCH
148 EXTERNAL clantr, slamch
149* ..
150* .. Intrinsic Functions ..
151 INTRINSIC max, min
152* ..
153* .. Executable Statements ..
154*
155 eps = slamch( 'Epsilon' )
156 rmax = max( rcond, rcondc )
157 rmin = min( rcond, rcondc )
158*
159* Do the easy cases first.
160*
161 IF( rmin.LT.zero ) THEN
162*
163* Invalid value for RCOND or RCONDC, return 1/EPS.
164*
165 rat = one / eps
166*
167 ELSE IF( rmin.GT.zero ) THEN
168*
169* Both estimates are positive, return RMAX/RMIN - 1.
170*
171 rat = rmax / rmin - one
172*
173 ELSE IF( rmax.EQ.zero ) THEN
174*
175* Both estimates zero.
176*
177 rat = zero
178*
179 ELSE
180*
181* One estimate is zero, the other is non-zero. If the matrix is
182* ill-conditioned, return the nonzero estimate multiplied by
183* 1/EPS; if the matrix is badly scaled, return the nonzero
184* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
185* element in absolute value in A.
186*
187 bignum = one / slamch( 'Safe minimum' )
188 anorm = clantr( 'M', uplo, diag, n, n, a, lda, rwork )
189*
190 rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
191 END IF
192*
193 RETURN
194*
195* End of CTRT06
196*
slamch
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
clantr
real function clantr(norm, uplo, diag, m, n, a, lda, work)
CLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition clantr.f:142
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