LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ ctbt06()

subroutine ctbt06 ( real  rcond,
real  rcondc,
character  uplo,
character  diag,
integer  n,
integer  kd,
complex, dimension( ldab, * )  ab,
integer  ldab,
real, dimension( * )  rwork,
real  rat 
)

CTBT06

Purpose:
 CTBT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by CTBCON.  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
          CTBCON.
[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]KD
          KD is INTEGER
          The number of superdiagonals or subdiagonals of the
          triangular band matrix A.  KD >= 0.
[in]AB
          AB is COMPLEX array, dimension (LDAB,N)
          The upper or lower triangular band matrix A, stored in the
          first kd+1 rows of the array. The j-th column of A is stored
          in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.
[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 124 of file ctbt06.f.

126*
127* -- LAPACK test routine --
128* -- LAPACK is a software package provided by Univ. of Tennessee, --
129* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130*
131* .. Scalar Arguments ..
132 CHARACTER DIAG, UPLO
133 INTEGER KD, LDAB, N
134 REAL RAT, RCOND, RCONDC
135* ..
136* .. Array Arguments ..
137 REAL RWORK( * )
138 COMPLEX AB( LDAB, * )
139* ..
140*
141* =====================================================================
142*
143* .. Parameters ..
144 REAL ZERO, ONE
145 parameter( zero = 0.0e+0, one = 1.0e+0 )
146* ..
147* .. Local Scalars ..
148 REAL ANORM, BIGNUM, EPS, RMAX, RMIN
149* ..
150* .. External Functions ..
151 REAL CLANTB, SLAMCH
152 EXTERNAL clantb, slamch
153* ..
154* .. Intrinsic Functions ..
155 INTRINSIC max, min
156* ..
157* .. Executable Statements ..
158*
159 eps = slamch( 'Epsilon' )
160 rmax = max( rcond, rcondc )
161 rmin = min( rcond, rcondc )
162*
163* Do the easy cases first.
164*
165 IF( rmin.LT.zero ) THEN
166*
167* Invalid value for RCOND or RCONDC, return 1/EPS.
168*
169 rat = one / eps
170*
171 ELSE IF( rmin.GT.zero ) THEN
172*
173* Both estimates are positive, return RMAX/RMIN - 1.
174*
175 rat = rmax / rmin - one
176*
177 ELSE IF( rmax.EQ.zero ) THEN
178*
179* Both estimates zero.
180*
181 rat = zero
182*
183 ELSE
184*
185* One estimate is zero, the other is non-zero. If the matrix is
186* ill-conditioned, return the nonzero estimate multiplied by
187* 1/EPS; if the matrix is badly scaled, return the nonzero
188* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
189* element in absolute value in A.
190*
191 bignum = one / slamch( 'Safe minimum' )
192 anorm = clantb( 'M', uplo, diag, n, kd, ab, ldab, rwork )
193*
194 rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
195 END IF
196*
197 RETURN
198*
199* End of CTBT06
200*
slamch
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
clantb
real function clantb(norm, uplo, diag, n, k, ab, ldab, work)
CLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition clantb.f:141
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