LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ stbt06()

subroutine stbt06 ( real  RCOND,
real  RCONDC,
character  UPLO,
character  DIAG,
integer  N,
integer  KD,
real, dimension( ldab, * )  AB,
integer  LDAB,
real, dimension( * )  WORK,
real  RAT 
)

STBT06

Purpose:
 STBT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by STBCON.  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
          STBCON.
[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 REAL 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 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 123 of file stbt06.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  REAL RAT, RCOND, RCONDC
134 * ..
135 * .. Array Arguments ..
136  REAL AB( LDAB, * ), WORK( * )
137 * ..
138 *
139 * =====================================================================
140 *
141 * .. Parameters ..
142  REAL ZERO, ONE
143  parameter( zero = 0.0e+0, one = 1.0e+0 )
144 * ..
145 * .. Local Scalars ..
146  REAL ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
147 * ..
148 * .. External Functions ..
149  REAL SLAMCH, SLANTB
150  EXTERNAL slamch, slantb
151 * ..
152 * .. Intrinsic Functions ..
153  INTRINSIC max, min
154 * ..
155 * .. External Subroutines ..
156  EXTERNAL slabad
157 * ..
158 * .. Executable Statements ..
159 *
160  eps = slamch( '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 = slamch( 'Safe minimum' )
193  bignum = one / smlnum
194  CALL slabad( smlnum, bignum )
195  anorm = slantb( '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 STBT06
203 *
subroutine slabad(SMALL, LARGE)
SLABAD
Definition: slabad.f:74
real function slantb(NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
SLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slantb.f:140
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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