LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ dtbt06()

subroutine dtbt06 ( double precision  RCOND,
double precision  RCONDC,
character  UPLO,
character  DIAG,
integer  N,
integer  KD,
double precision, dimension( ldab, * )  AB,
integer  LDAB,
double precision, dimension( * )  WORK,
double precision  RAT 
)

DTBT06

Purpose:
 DTBT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by DTBCON.  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
          DTBCON.
[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 DOUBLE PRECISION 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]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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 123 of file dtbt06.f.

125*
126* -- LAPACK test routine --
127* -- LAPACK is a software package provided by Univ. of Tennessee, --
128* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129*
130* .. Scalar Arguments ..
131 CHARACTER DIAG, UPLO
132 INTEGER KD, LDAB, N
133 DOUBLE PRECISION RAT, RCOND, RCONDC
134* ..
135* .. Array Arguments ..
136 DOUBLE PRECISION AB( LDAB, * ), WORK( * )
137* ..
138*
139* =====================================================================
140*
141* .. Parameters ..
142 DOUBLE PRECISION ZERO, ONE
143 parameter( zero = 0.0d+0, one = 1.0d+0 )
144* ..
145* .. Local Scalars ..
146 DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
147* ..
148* .. External Functions ..
149 DOUBLE PRECISION DLAMCH, DLANTB
150 EXTERNAL dlamch, dlantb
151* ..
152* .. Intrinsic Functions ..
153 INTRINSIC max, min
154* ..
155* .. External Subroutines ..
156 EXTERNAL dlabad
157* ..
158* .. Executable Statements ..
159*
160 eps = dlamch( 'Epsilon' )
161 rmax = max( rcond, rcondc )
162 rmin = min( rcond, rcondc )
163*
164* Do the easy cases first.
165*
166 IF( rmin.LT.zero ) THEN
167*
168* Invalid value for RCOND or RCONDC, return 1/EPS.
169*
170 rat = one / eps
171*
172 ELSE IF( rmin.GT.zero ) THEN
173*
174* Both estimates are positive, return RMAX/RMIN - 1.
175*
176 rat = rmax / rmin - one
177*
178 ELSE IF( rmax.EQ.zero ) THEN
179*
180* Both estimates zero.
181*
182 rat = zero
183*
184 ELSE
185*
186* One estimate is zero, the other is non-zero. If the matrix is
187* ill-conditioned, return the nonzero estimate multiplied by
188* 1/EPS; if the matrix is badly scaled, return the nonzero
189* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
190* element in absolute value in A.
191*
192 smlnum = dlamch( 'Safe minimum' )
193 bignum = one / smlnum
194 CALL dlabad( smlnum, bignum )
195 anorm = dlantb( 'M', uplo, diag, n, kd, ab, ldab, work )
196*
197 rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
198 END IF
199*
200 RETURN
201*
202* End of DTBT06
203*
dlamch
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
dlabad
subroutine dlabad(SMALL, LARGE)
DLABAD
Definition: dlabad.f:74
dlantb
double precision function dlantb(NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
DLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlantb.f:140
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