LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ 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 * .. External Subroutines ..
142  EXTERNAL slabad
143 * ..
144 * .. Executable Statements ..
145 *
146  eps = slamch( 'Epsilon' )
147  rmax = max( rcond, rcondc )
148  rmin = min( rcond, rcondc )
149 *
150 * Do the easy cases first.
151 *
152  IF( rmin.LT.zero ) THEN
153 *
154 * Invalid value for RCOND or RCONDC, return 1/EPS.
155 *
156  rat = one / eps
157 *
158  ELSE IF( rmin.GT.zero ) THEN
159 *
160 * Both estimates are positive, return RMAX/RMIN - 1.
161 *
162  rat = rmax / rmin - one
163 *
164  ELSE IF( rmax.EQ.zero ) THEN
165 *
166 * Both estimates zero.
167 *
168  rat = zero
169 *
170  ELSE
171 *
172 * One estimate is zero, the other is non-zero. If the matrix is
173 * ill-conditioned, return the nonzero estimate multiplied by
174 * 1/EPS; if the matrix is badly scaled, return the nonzero
175 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
176 * element in absolute value in A.
177 *
178  smlnum = slamch( 'Safe minimum' )
179  bignum = one / smlnum
180  CALL slabad( smlnum, bignum )
181  anorm = slantp( 'M', uplo, diag, n, ap, work )
182 *
183  rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
184  END IF
185 *
186  RETURN
187 *
188 * End of STPT06
189 *
subroutine slabad(SMALL, LARGE)
SLABAD
Definition: slabad.f:74
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
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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