LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
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.
Date
November 2011

Definition at line 127 of file dtbt06.f.

127 *
128 * -- LAPACK test routine (version 3.4.0) --
129 * -- LAPACK is a software package provided by Univ. of Tennessee, --
130 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131 * November 2011
132 *
133 * .. Scalar Arguments ..
134  CHARACTER diag, uplo
135  INTEGER kd, ldab, n
136  DOUBLE PRECISION rat, rcond, rcondc
137 * ..
138 * .. Array Arguments ..
139  DOUBLE PRECISION ab( ldab, * ), work( * )
140 * ..
141 *
142 * =====================================================================
143 *
144 * .. Parameters ..
145  DOUBLE PRECISION zero, one
146  parameter ( zero = 0.0d+0, one = 1.0d+0 )
147 * ..
148 * .. Local Scalars ..
149  DOUBLE PRECISION anorm, bignum, eps, rmax, rmin, smlnum
150 * ..
151 * .. External Functions ..
152  DOUBLE PRECISION dlamch, dlantb
153  EXTERNAL dlamch, dlantb
154 * ..
155 * .. Intrinsic Functions ..
156  INTRINSIC max, min
157 * ..
158 * .. External Subroutines ..
159  EXTERNAL dlabad
160 * ..
161 * .. Executable Statements ..
162 *
163  eps = dlamch( 'Epsilon' )
164  rmax = max( rcond, rcondc )
165  rmin = min( rcond, rcondc )
166 *
167 * Do the easy cases first.
168 *
169  IF( rmin.LT.zero ) THEN
170 *
171 * Invalid value for RCOND or RCONDC, return 1/EPS.
172 *
173  rat = one / eps
174 *
175  ELSE IF( rmin.GT.zero ) THEN
176 *
177 * Both estimates are positive, return RMAX/RMIN - 1.
178 *
179  rat = rmax / rmin - one
180 *
181  ELSE IF( rmax.EQ.zero ) THEN
182 *
183 * Both estimates zero.
184 *
185  rat = zero
186 *
187  ELSE
188 *
189 * One estimate is zero, the other is non-zero. If the matrix is
190 * ill-conditioned, return the nonzero estimate multiplied by
191 * 1/EPS; if the matrix is badly scaled, return the nonzero
192 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
193 * element in absolute value in A.
194 *
195  smlnum = dlamch( 'Safe minimum' )
196  bignum = one / smlnum
197  CALL dlabad( smlnum, bignum )
198  anorm = dlantb( 'M', uplo, diag, n, kd, ab, ldab, work )
199 *
200  rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
201  END IF
202 *
203  RETURN
204 *
205 * End of DTBT06
206 *
dlamch
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
dlabad
subroutine dlabad(SMALL, LARGE)
DLABAD
Definition: dlabad.f:76
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, or the element of largest absolute value of a triangular band matrix.
Definition: dlantb.f:142

Here is the call graph for this function:

Here is the caller graph for this function: