#include "blaswrap.h" /* dtpt06.f -- translated by f2c (version 20061008). You must link the resulting object file with libf2c: on Microsoft Windows system, link with libf2c.lib; on Linux or Unix systems, link with .../path/to/libf2c.a -lm or, if you install libf2c.a in a standard place, with -lf2c -lm -- in that order, at the end of the command line, as in cc *.o -lf2c -lm Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., http://www.netlib.org/f2c/libf2c.zip */ #include "f2c.h" /* Subroutine */ int dtpt06_(doublereal *rcond, doublereal *rcondc, char * uplo, char *diag, integer *n, doublereal *ap, doublereal *work, doublereal *rat) { /* System generated locals */ doublereal d__1, d__2; /* Local variables */ static doublereal eps, rmin, rmax, anorm; extern /* Subroutine */ int dlabad_(doublereal *, doublereal *); extern doublereal dlamch_(char *); static doublereal bignum; extern doublereal dlantp_(char *, char *, char *, integer *, doublereal *, doublereal *); static doublereal smlnum; /* -- LAPACK test routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= DTPT06 computes a test ratio comparing RCOND (the reciprocal condition number of a triangular matrix A) and RCONDC, the estimate computed by DTPCON. 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. Arguments ========= RCOND (input) 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)) ). RCONDC (input) DOUBLE PRECISION The estimate of the reciprocal condition number computed by DTPCON. UPLO (input) CHARACTER Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular DIAG (input) CHARACTER Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular N (input) INTEGER The order of the matrix A. N >= 0. AP (input) DOUBLE PRECISION 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. WORK (workspace) DOUBLE PRECISION array, dimension (N) RAT (output) 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. ===================================================================== Parameter adjustments */ --work; --ap; /* Function Body */ eps = dlamch_("Epsilon"); rmax = max(*rcond,*rcondc); rmin = min(*rcond,*rcondc); /* Do the easy cases first. */ if (rmin < 0.) { /* Invalid value for RCOND or RCONDC, return 1/EPS. */ *rat = 1. / eps; } else if (rmin > 0.) { /* Both estimates are positive, return RMAX/RMIN - 1. */ *rat = rmax / rmin - 1.; } else if (rmax == 0.) { /* Both estimates zero. */ *rat = 0.; } else { /* One estimate is zero, the other is non-zero. If the matrix is ill-conditioned, return the nonzero estimate multiplied by 1/EPS; if the matrix is badly scaled, return the nonzero estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum element in absolute value in A. */ smlnum = dlamch_("Safe minimum"); bignum = 1. / smlnum; dlabad_(&smlnum, &bignum); anorm = dlantp_("M", uplo, diag, n, &ap[1], &work[1]); /* Computing MIN */ d__1 = bignum / max(1.,anorm), d__2 = 1. / eps; *rat = rmax * min(d__1,d__2); } return 0; /* End of DTPT06 */ } /* dtpt06_ */