LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ stpt06()

subroutine stpt06 ( real  rcond,
real  rcondc,
character  uplo,
character  diag,
integer  n,
real, dimension( * )  ap,
real, dimension( * )  work,
real  rat 
)

STPT06

Purpose:
 STPT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by STPCON.  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
          STPCON.
[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]AP
          AP is REAL array, dimension (N*(N+1)/2)
          The upper or lower triangular matrix A, packed columnwise in
          a linear array.  The j-th column of A is stored in the array
          AP as follows:
          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
          if UPLO = 'L',
             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
[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 110 of file stpt06.f.

111*
112* -- LAPACK test routine --
113* -- LAPACK is a software package provided by Univ. of Tennessee, --
114* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
115*
116* .. Scalar Arguments ..
117 CHARACTER DIAG, UPLO
118 INTEGER N
119 REAL RAT, RCOND, RCONDC
120* ..
121* .. Array Arguments ..
122 REAL AP( * ), WORK( * )
123* ..
124*
125* =====================================================================
126*
127* .. Parameters ..
128 REAL ZERO, ONE
129 parameter( zero = 0.0e+0, one = 1.0e+0 )
130* ..
131* .. Local Scalars ..
132 REAL ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
133* ..
134* .. External Functions ..
135 REAL SLAMCH, SLANTP
136 EXTERNAL slamch, slantp
137* ..
138* .. Intrinsic Functions ..
139 INTRINSIC max, min
140* ..
141* .. Executable Statements ..
142*
143 eps = slamch( 'Epsilon' )
144 rmax = max( rcond, rcondc )
145 rmin = min( rcond, rcondc )
146*
147* Do the easy cases first.
148*
149 IF( rmin.LT.zero ) THEN
150*
151* Invalid value for RCOND or RCONDC, return 1/EPS.
152*
153 rat = one / eps
154*
155 ELSE IF( rmin.GT.zero ) THEN
156*
157* Both estimates are positive, return RMAX/RMIN - 1.
158*
159 rat = rmax / rmin - one
160*
161 ELSE IF( rmax.EQ.zero ) THEN
162*
163* Both estimates zero.
164*
165 rat = zero
166*
167 ELSE
168*
169* One estimate is zero, the other is non-zero. If the matrix is
170* ill-conditioned, return the nonzero estimate multiplied by
171* 1/EPS; if the matrix is badly scaled, return the nonzero
172* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
173* element in absolute value in A.
174*
175 smlnum = slamch( 'Safe minimum' )
176 bignum = one / smlnum
177 anorm = slantp( 'M', uplo, diag, n, ap, work )
178*
179 rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
180 END IF
181*
182 RETURN
183*
184* End of STPT06
185*
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
real function slantp(norm, uplo, diag, n, ap, work)
SLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition slantp.f:124
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