LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ 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* .. Executable Statements ..
152*
153 eps = dlamch( 'Epsilon' )
154 rmax = max( rcond, rcondc )
155 rmin = min( rcond, rcondc )
156*
157* Do the easy cases first.
158*
159 IF( rmin.LT.zero ) THEN
160*
161* Invalid value for RCOND or RCONDC, return 1/EPS.
162*
163 rat = one / eps
164*
165 ELSE IF( rmin.GT.zero ) THEN
166*
167* Both estimates are positive, return RMAX/RMIN - 1.
168*
169 rat = rmax / rmin - one
170*
171 ELSE IF( rmax.EQ.zero ) THEN
172*
173* Both estimates zero.
174*
175 rat = zero
176*
177 ELSE
178*
179* One estimate is zero, the other is non-zero. If the matrix is
180* ill-conditioned, return the nonzero estimate multiplied by
181* 1/EPS; if the matrix is badly scaled, return the nonzero
182* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
183* element in absolute value in A.
184*
185 smlnum = dlamch( 'Safe minimum' )
186 bignum = one / smlnum
187 anorm = dlantr( 'M', uplo, diag, n, n, a, lda, work )
188*
189 rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
190 END IF
191*
192 RETURN
193*
194* End of DTRT06
195*
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
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:140
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