127 lines
3.7 KiB
FortranFixed
127 lines
3.7 KiB
FortranFixed
SUBROUTINE CTPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT )
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*
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* -- LAPACK test routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER DIAG, UPLO
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INTEGER N
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REAL RAT, RCOND, RCONDC
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* ..
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* .. Array Arguments ..
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REAL RWORK( * )
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COMPLEX AP( * )
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* ..
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*
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* Purpose
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* =======
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*
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* CTPT06 computes a test ratio comparing RCOND (the reciprocal
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* condition number of the triangular matrix A) and RCONDC, the estimate
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* computed by CTPCON. Information about the triangular matrix is used
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* if one estimate is zero and the other is non-zero to decide if
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* underflow in the estimate is justified.
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*
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* Arguments
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* =========
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*
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* RCOND (input) REAL
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* The estimate of the reciprocal condition number obtained by
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* forming the explicit inverse of the matrix A and computing
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* RCOND = 1/( norm(A) * norm(inv(A)) ).
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*
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* RCONDC (input) REAL
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* The estimate of the reciprocal condition number computed by
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* CTPCON.
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*
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* UPLO (input) CHARACTER
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* Specifies whether the matrix A is upper or lower triangular.
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* = 'U': Upper triangular
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* = 'L': Lower triangular
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*
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* DIAG (input) CHARACTER
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* Specifies whether or not the matrix A is unit triangular.
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* = 'N': Non-unit triangular
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* = 'U': Unit triangular
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*
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* N (input) INTEGER
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* The order of the matrix A. N >= 0.
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*
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* AP (input) COMPLEX array, dimension (N*(N+1)/2)
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* The upper or lower triangular matrix A, packed columnwise in
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* a linear array. The j-th column of A is stored in the array
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* AP as follows:
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* if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
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* if UPLO = 'L',
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* AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
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*
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* RWORK (workspace) REAL array, dimension (N)
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*
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* RAT (output) REAL
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* The test ratio. If both RCOND and RCONDC are nonzero,
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* RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
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* If RAT = 0, the two estimates are exactly the same.
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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* ..
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* .. Local Scalars ..
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REAL ANORM, BIGNUM, EPS, RMAX, RMIN
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* ..
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* .. External Functions ..
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REAL CLANTP, SLAMCH
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EXTERNAL CLANTP, SLAMCH
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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EPS = SLAMCH( 'Epsilon' )
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RMAX = MAX( RCOND, RCONDC )
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RMIN = MIN( RCOND, RCONDC )
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*
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* Do the easy cases first.
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*
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IF( RMIN.LT.ZERO ) THEN
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*
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* Invalid value for RCOND or RCONDC, return 1/EPS.
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*
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RAT = ONE / EPS
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*
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ELSE IF( RMIN.GT.ZERO ) THEN
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*
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* Both estimates are positive, return RMAX/RMIN - 1.
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*
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RAT = RMAX / RMIN - ONE
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*
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ELSE IF( RMAX.EQ.ZERO ) THEN
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*
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* Both estimates zero.
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*
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RAT = ZERO
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*
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ELSE
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*
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* One estimate is zero, the other is non-zero. If the matrix is
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* ill-conditioned, return the nonzero estimate multiplied by
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* 1/EPS; if the matrix is badly scaled, return the nonzero
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* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
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* element in absolute value in A.
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*
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BIGNUM = ONE / SLAMCH( 'Safe minimum' )
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ANORM = CLANTP( 'M', UPLO, DIAG, N, AP, RWORK )
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*
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RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) )
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END IF
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*
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RETURN
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*
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* End of CTPT06
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*
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END
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