#include "f2c.h" #include "blaswrap.h" /* Subroutine */ int stpt06_(real *rcond, real *rcondc, char *uplo, char * diag, integer *n, real *ap, real *work, real *rat) { /* System generated locals */ real r__1, r__2; /* Local variables */ real eps, rmin, rmax, anorm; extern /* Subroutine */ int slabad_(real *, real *); extern doublereal slamch_(char *); real bignum; extern doublereal slantp_(char *, char *, char *, integer *, real *, real *); real smlnum; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* 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. */ /* Arguments */ /* ========= */ /* RCOND (input) 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)) ). */ /* RCONDC (input) REAL */ /* The estimate of the reciprocal condition number computed by */ /* STPCON. */ /* 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) 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. */ /* WORK (workspace) REAL array, dimension (N) */ /* RAT (output) 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. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Executable Statements .. */ /* Parameter adjustments */ --work; --ap; /* Function Body */ eps = slamch_("Epsilon"); rmax = dmax(*rcond,*rcondc); rmin = dmin(*rcond,*rcondc); /* Do the easy cases first. */ if (rmin < 0.f) { /* Invalid value for RCOND or RCONDC, return 1/EPS. */ *rat = 1.f / eps; } else if (rmin > 0.f) { /* Both estimates are positive, return RMAX/RMIN - 1. */ *rat = rmax / rmin - 1.f; } else if (rmax == 0.f) { /* Both estimates zero. */ *rat = 0.f; } 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 = slamch_("Safe minimum"); bignum = 1.f / smlnum; slabad_(&smlnum, &bignum); anorm = slantp_("M", uplo, diag, n, &ap[1], &work[1]); /* Computing MIN */ r__1 = bignum / dmax(1.f,anorm), r__2 = 1.f / eps; *rat = rmax * dmin(r__1,r__2); } return 0; /* End of STPT06 */ } /* stpt06_ */