LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches

◆ 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*
dlamch
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
dlabad
subroutine dlabad(SMALL, LARGE)
DLABAD
Definition: dlabad.f:74
dlantr
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
Here is the call graph for this function:
Here is the caller graph for this function: