LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ dtrt06()

subroutine dtrt06 ( double precision  RCOND,
double precision  RCONDC,
character  UPLO,
character  DIAG,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  WORK,
double precision  RAT 
)

DTRT06

Purpose:
 DTRT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by DTRCON.  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
          DTRCON.
[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 DOUBLE PRECISION 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]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 119 of file dtrt06.f.

121 *
122 * -- LAPACK test routine --
123 * -- LAPACK is a software package provided by Univ. of Tennessee, --
124 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125 *
126 * .. Scalar Arguments ..
127  CHARACTER DIAG, UPLO
128  INTEGER LDA, N
129  DOUBLE PRECISION RAT, RCOND, RCONDC
130 * ..
131 * .. Array Arguments ..
132  DOUBLE PRECISION A( LDA, * ), WORK( * )
133 * ..
134 *
135 * =====================================================================
136 *
137 * .. Parameters ..
138  DOUBLE PRECISION ZERO, ONE
139  parameter( zero = 0.0d+0, one = 1.0d+0 )
140 * ..
141 * .. Local Scalars ..
142  DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
143 * ..
144 * .. External Functions ..
145  DOUBLE PRECISION DLAMCH, DLANTR
146  EXTERNAL dlamch, dlantr
147 * ..
148 * .. Intrinsic Functions ..
149  INTRINSIC max, min
150 * ..
151 * .. External Subroutines ..
152  EXTERNAL dlabad
153 * ..
154 * .. Executable Statements ..
155 *
156  eps = dlamch( 'Epsilon' )
157  rmax = max( rcond, rcondc )
158  rmin = min( rcond, rcondc )
159 *
160 * Do the easy cases first.
161 *
162  IF( rmin.LT.zero ) THEN
163 *
164 * Invalid value for RCOND or RCONDC, return 1/EPS.
165 *
166  rat = one / eps
167 *
168  ELSE IF( rmin.GT.zero ) THEN
169 *
170 * Both estimates are positive, return RMAX/RMIN - 1.
171 *
172  rat = rmax / rmin - one
173 *
174  ELSE IF( rmax.EQ.zero ) THEN
175 *
176 * Both estimates zero.
177 *
178  rat = zero
179 *
180  ELSE
181 *
182 * One estimate is zero, the other is non-zero. If the matrix is
183 * ill-conditioned, return the nonzero estimate multiplied by
184 * 1/EPS; if the matrix is badly scaled, return the nonzero
185 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
186 * element in absolute value in A.
187 *
188  smlnum = dlamch( 'Safe minimum' )
189  bignum = one / smlnum
190  CALL dlabad( smlnum, bignum )
191  anorm = dlantr( 'M', uplo, diag, n, n, a, lda, work )
192 *
193  rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
194  END IF
195 *
196  RETURN
197 *
198 * End of DTRT06
199 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine dlabad(SMALL, LARGE)
DLABAD
Definition: dlabad.f:74
double precision function dlantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
DLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlantr.f:141
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