LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ 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 *
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
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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