/* Subroutine */ int dlaein_(logical *rightv, logical *noinit, integer *n, doublereal *h__, integer *ldh, doublereal *wr, doublereal *wi, doublereal *vr, doublereal *vi, doublereal *b, integer *ldb, doublereal *work, doublereal *eps3, doublereal *smlnum, doublereal * bignum, integer *info) { /* System generated locals */ integer b_dim1, b_offset, h_dim1, h_offset, i__1, i__2, i__3, i__4; doublereal d__1, d__2, d__3, d__4; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ integer i__, j; doublereal w, x, y; integer i1, i2, i3; doublereal w1, ei, ej, xi, xr, rec; integer its, ierr; doublereal temp, norm, vmax; extern doublereal dnrm2_(integer *, doublereal *, integer *); extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); doublereal scale; extern doublereal dasum_(integer *, doublereal *, integer *); char trans[1]; doublereal vcrit, rootn, vnorm; extern doublereal dlapy2_(doublereal *, doublereal *); doublereal absbii, absbjj; extern integer idamax_(integer *, doublereal *, integer *); extern /* Subroutine */ int dladiv_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *), dlatrs_( char *, char *, char *, char *, integer *, doublereal *, integer * , doublereal *, doublereal *, doublereal *, integer *); char normin[1]; doublereal nrmsml, growto; /* -- LAPACK auxiliary routine (version 3.4.2) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* September 2012 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Parameter adjustments */ h_dim1 = *ldh; h_offset = 1 + h_dim1; h__ -= h_offset; --vr; --vi; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; --work; /* Function Body */ *info = 0; /* GROWTO is the threshold used in the acceptance test for an */ /* eigenvector. */ rootn = sqrt((doublereal) (*n)); growto = .1 / rootn; /* Computing MAX */ d__1 = 1.; d__2 = *eps3 * rootn; // , expr subst nrmsml = max(d__1,d__2) * *smlnum; /* Form B = H - (WR,WI)*I (except that the subdiagonal elements and */ /* the imaginary parts of the diagonal elements are not stored). */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { b[i__ + j * b_dim1] = h__[i__ + j * h_dim1]; /* L10: */ } b[j + j * b_dim1] = h__[j + j * h_dim1] - *wr; /* L20: */ } if (*wi == 0.) { /* Real eigenvalue. */ if (*noinit) { /* Set initial vector. */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { vr[i__] = *eps3; /* L30: */ } } else { /* Scale supplied initial vector. */ vnorm = dnrm2_(n, &vr[1], &c__1); d__1 = *eps3 * rootn / max(vnorm,nrmsml); dscal_(n, &d__1, &vr[1], &c__1); } if (*rightv) { /* LU decomposition with partial pivoting of B, replacing zero */ /* pivots by EPS3. */ i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { ei = h__[i__ + 1 + i__ * h_dim1]; if ((d__1 = b[i__ + i__ * b_dim1], abs(d__1)) < abs(ei)) { /* Interchange rows and eliminate. */ x = b[i__ + i__ * b_dim1] / ei; b[i__ + i__ * b_dim1] = ei; i__2 = *n; for (j = i__ + 1; j <= i__2; ++j) { temp = b[i__ + 1 + j * b_dim1]; b[i__ + 1 + j * b_dim1] = b[i__ + j * b_dim1] - x * temp; b[i__ + j * b_dim1] = temp; /* L40: */ } } else { /* Eliminate without interchange. */ if (b[i__ + i__ * b_dim1] == 0.) { b[i__ + i__ * b_dim1] = *eps3; } x = ei / b[i__ + i__ * b_dim1]; if (x != 0.) { i__2 = *n; for (j = i__ + 1; j <= i__2; ++j) { b[i__ + 1 + j * b_dim1] -= x * b[i__ + j * b_dim1] ; /* L50: */ } } } /* L60: */ } if (b[*n + *n * b_dim1] == 0.) { b[*n + *n * b_dim1] = *eps3; } *(unsigned char *)trans = 'N'; } else { /* UL decomposition with partial pivoting of B, replacing zero */ /* pivots by EPS3. */ for (j = *n; j >= 2; --j) { ej = h__[j + (j - 1) * h_dim1]; if ((d__1 = b[j + j * b_dim1], abs(d__1)) < abs(ej)) { /* Interchange columns and eliminate. */ x = b[j + j * b_dim1] / ej; b[j + j * b_dim1] = ej; i__1 = j - 1; for (i__ = 1; i__ <= i__1; ++i__) { temp = b[i__ + (j - 1) * b_dim1]; b[i__ + (j - 1) * b_dim1] = b[i__ + j * b_dim1] - x * temp; b[i__ + j * b_dim1] = temp; /* L70: */ } } else { /* Eliminate without interchange. */ if (b[j + j * b_dim1] == 0.) { b[j + j * b_dim1] = *eps3; } x = ej / b[j + j * b_dim1]; if (x != 0.) { i__1 = j - 1; for (i__ = 1; i__ <= i__1; ++i__) { b[i__ + (j - 1) * b_dim1] -= x * b[i__ + j * b_dim1]; /* L80: */ } } } /* L90: */ } if (b[b_dim1 + 1] == 0.) { b[b_dim1 + 1] = *eps3; } *(unsigned char *)trans = 'T'; } *(unsigned char *)normin = 'N'; i__1 = *n; for (its = 1; its <= i__1; ++its) { /* Solve U*x = scale*v for a right eigenvector */ /* or U**T*x = scale*v for a left eigenvector, */ /* overwriting x on v. */ dlatrs_("Upper", trans, "Nonunit", normin, n, &b[b_offset], ldb, & vr[1], &scale, &work[1], &ierr); *(unsigned char *)normin = 'Y'; /* Test for sufficient growth in the norm of v. */ vnorm = dasum_(n, &vr[1], &c__1); if (vnorm >= growto * scale) { goto L120; } /* Choose new orthogonal starting vector and try again. */ temp = *eps3 / (rootn + 1.); vr[1] = *eps3; i__2 = *n; for (i__ = 2; i__ <= i__2; ++i__) { vr[i__] = temp; /* L100: */ } vr[*n - its + 1] -= *eps3 * rootn; /* L110: */ } /* Failure to find eigenvector in N iterations. */ *info = 1; L120: /* Normalize eigenvector. */ i__ = idamax_(n, &vr[1], &c__1); d__2 = 1. / (d__1 = vr[i__], abs(d__1)); dscal_(n, &d__2, &vr[1], &c__1); } else { /* Complex eigenvalue. */ if (*noinit) { /* Set initial vector. */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { vr[i__] = *eps3; vi[i__] = 0.; /* L130: */ } } else { /* Scale supplied initial vector. */ d__1 = dnrm2_(n, &vr[1], &c__1); d__2 = dnrm2_(n, &vi[1], &c__1); norm = dlapy2_(&d__1, &d__2); rec = *eps3 * rootn / max(norm,nrmsml); dscal_(n, &rec, &vr[1], &c__1); dscal_(n, &rec, &vi[1], &c__1); } if (*rightv) { /* LU decomposition with partial pivoting of B, replacing zero */ /* pivots by EPS3. */ /* The imaginary part of the (i,j)-th element of U is stored in */ /* B(j+1,i). */ b[b_dim1 + 2] = -(*wi); i__1 = *n; for (i__ = 2; i__ <= i__1; ++i__) { b[i__ + 1 + b_dim1] = 0.; /* L140: */ } i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { absbii = dlapy2_(&b[i__ + i__ * b_dim1], &b[i__ + 1 + i__ * b_dim1]); ei = h__[i__ + 1 + i__ * h_dim1]; if (absbii < abs(ei)) { /* Interchange rows and eliminate. */ xr = b[i__ + i__ * b_dim1] / ei; xi = b[i__ + 1 + i__ * b_dim1] / ei; b[i__ + i__ * b_dim1] = ei; b[i__ + 1 + i__ * b_dim1] = 0.; i__2 = *n; for (j = i__ + 1; j <= i__2; ++j) { temp = b[i__ + 1 + j * b_dim1]; b[i__ + 1 + j * b_dim1] = b[i__ + j * b_dim1] - xr * temp; b[j + 1 + (i__ + 1) * b_dim1] = b[j + 1 + i__ * b_dim1] - xi * temp; b[i__ + j * b_dim1] = temp; b[j + 1 + i__ * b_dim1] = 0.; /* L150: */ } b[i__ + 2 + i__ * b_dim1] = -(*wi); b[i__ + 1 + (i__ + 1) * b_dim1] -= xi * *wi; b[i__ + 2 + (i__ + 1) * b_dim1] += xr * *wi; } else { /* Eliminate without interchanging rows. */ if (absbii == 0.) { b[i__ + i__ * b_dim1] = *eps3; b[i__ + 1 + i__ * b_dim1] = 0.; absbii = *eps3; } ei = ei / absbii / absbii; xr = b[i__ + i__ * b_dim1] * ei; xi = -b[i__ + 1 + i__ * b_dim1] * ei; i__2 = *n; for (j = i__ + 1; j <= i__2; ++j) { b[i__ + 1 + j * b_dim1] = b[i__ + 1 + j * b_dim1] - xr * b[i__ + j * b_dim1] + xi * b[j + 1 + i__ * b_dim1]; b[j + 1 + (i__ + 1) * b_dim1] = -xr * b[j + 1 + i__ * b_dim1] - xi * b[i__ + j * b_dim1]; /* L160: */ } b[i__ + 2 + (i__ + 1) * b_dim1] -= *wi; } /* Compute 1-norm of offdiagonal elements of i-th row. */ i__2 = *n - i__; i__3 = *n - i__; work[i__] = dasum_(&i__2, &b[i__ + (i__ + 1) * b_dim1], ldb) + dasum_(&i__3, &b[i__ + 2 + i__ * b_dim1], &c__1); /* L170: */ } if (b[*n + *n * b_dim1] == 0. && b[*n + 1 + *n * b_dim1] == 0.) { b[*n + *n * b_dim1] = *eps3; } work[*n] = 0.; i1 = *n; i2 = 1; i3 = -1; } else { /* UL decomposition with partial pivoting of conjg(B), */ /* replacing zero pivots by EPS3. */ /* The imaginary part of the (i,j)-th element of U is stored in */ /* B(j+1,i). */ b[*n + 1 + *n * b_dim1] = *wi; i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { b[*n + 1 + j * b_dim1] = 0.; /* L180: */ } for (j = *n; j >= 2; --j) { ej = h__[j + (j - 1) * h_dim1]; absbjj = dlapy2_(&b[j + j * b_dim1], &b[j + 1 + j * b_dim1]); if (absbjj < abs(ej)) { /* Interchange columns and eliminate */ xr = b[j + j * b_dim1] / ej; xi = b[j + 1 + j * b_dim1] / ej; b[j + j * b_dim1] = ej; b[j + 1 + j * b_dim1] = 0.; i__1 = j - 1; for (i__ = 1; i__ <= i__1; ++i__) { temp = b[i__ + (j - 1) * b_dim1]; b[i__ + (j - 1) * b_dim1] = b[i__ + j * b_dim1] - xr * temp; b[j + i__ * b_dim1] = b[j + 1 + i__ * b_dim1] - xi * temp; b[i__ + j * b_dim1] = temp; b[j + 1 + i__ * b_dim1] = 0.; /* L190: */ } b[j + 1 + (j - 1) * b_dim1] = *wi; b[j - 1 + (j - 1) * b_dim1] += xi * *wi; b[j + (j - 1) * b_dim1] -= xr * *wi; } else { /* Eliminate without interchange. */ if (absbjj == 0.) { b[j + j * b_dim1] = *eps3; b[j + 1 + j * b_dim1] = 0.; absbjj = *eps3; } ej = ej / absbjj / absbjj; xr = b[j + j * b_dim1] * ej; xi = -b[j + 1 + j * b_dim1] * ej; i__1 = j - 1; for (i__ = 1; i__ <= i__1; ++i__) { b[i__ + (j - 1) * b_dim1] = b[i__ + (j - 1) * b_dim1] - xr * b[i__ + j * b_dim1] + xi * b[j + 1 + i__ * b_dim1]; b[j + i__ * b_dim1] = -xr * b[j + 1 + i__ * b_dim1] - xi * b[i__ + j * b_dim1]; /* L200: */ } b[j + (j - 1) * b_dim1] += *wi; } /* Compute 1-norm of offdiagonal elements of j-th column. */ i__1 = j - 1; i__2 = j - 1; work[j] = dasum_(&i__1, &b[j * b_dim1 + 1], &c__1) + dasum_(& i__2, &b[j + 1 + b_dim1], ldb); /* L210: */ } if (b[b_dim1 + 1] == 0. && b[b_dim1 + 2] == 0.) { b[b_dim1 + 1] = *eps3; } work[1] = 0.; i1 = 1; i2 = *n; i3 = 1; } i__1 = *n; for (its = 1; its <= i__1; ++its) { scale = 1.; vmax = 1.; vcrit = *bignum; /* Solve U*(xr,xi) = scale*(vr,vi) for a right eigenvector, */ /* or U**T*(xr,xi) = scale*(vr,vi) for a left eigenvector, */ /* overwriting (xr,xi) on (vr,vi). */ i__2 = i2; i__3 = i3; for (i__ = i1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__3) { if (work[i__] > vcrit) { rec = 1. / vmax; dscal_(n, &rec, &vr[1], &c__1); dscal_(n, &rec, &vi[1], &c__1); scale *= rec; vmax = 1.; vcrit = *bignum; } xr = vr[i__]; xi = vi[i__]; if (*rightv) { i__4 = *n; for (j = i__ + 1; j <= i__4; ++j) { xr = xr - b[i__ + j * b_dim1] * vr[j] + b[j + 1 + i__ * b_dim1] * vi[j]; xi = xi - b[i__ + j * b_dim1] * vi[j] - b[j + 1 + i__ * b_dim1] * vr[j]; /* L220: */ } } else { i__4 = i__ - 1; for (j = 1; j <= i__4; ++j) { xr = xr - b[j + i__ * b_dim1] * vr[j] + b[i__ + 1 + j * b_dim1] * vi[j]; xi = xi - b[j + i__ * b_dim1] * vi[j] - b[i__ + 1 + j * b_dim1] * vr[j]; /* L230: */ } } w = (d__1 = b[i__ + i__ * b_dim1], abs(d__1)) + (d__2 = b[i__ + 1 + i__ * b_dim1], abs(d__2)); if (w > *smlnum) { if (w < 1.) { w1 = abs(xr) + abs(xi); if (w1 > w * *bignum) { rec = 1. / w1; dscal_(n, &rec, &vr[1], &c__1); dscal_(n, &rec, &vi[1], &c__1); xr = vr[i__]; xi = vi[i__]; scale *= rec; vmax *= rec; } } /* Divide by diagonal element of B. */ dladiv_(&xr, &xi, &b[i__ + i__ * b_dim1], &b[i__ + 1 + i__ * b_dim1], &vr[i__], &vi[i__]); /* Computing MAX */ d__3 = (d__1 = vr[i__], abs(d__1)) + (d__2 = vi[i__], abs( d__2)); vmax = max(d__3,vmax); vcrit = *bignum / vmax; } else { i__4 = *n; for (j = 1; j <= i__4; ++j) { vr[j] = 0.; vi[j] = 0.; /* L240: */ } vr[i__] = 1.; vi[i__] = 1.; scale = 0.; vmax = 1.; vcrit = *bignum; } /* L250: */ } /* Test for sufficient growth in the norm of (VR,VI). */ vnorm = dasum_(n, &vr[1], &c__1) + dasum_(n, &vi[1], &c__1); if (vnorm >= growto * scale) { goto L280; } /* Choose a new orthogonal starting vector and try again. */ y = *eps3 / (rootn + 1.); vr[1] = *eps3; vi[1] = 0.; i__3 = *n; for (i__ = 2; i__ <= i__3; ++i__) { vr[i__] = y; vi[i__] = 0.; /* L260: */ } vr[*n - its + 1] -= *eps3 * rootn; /* L270: */ } /* Failure to find eigenvector in N iterations */ *info = 1; L280: /* Normalize eigenvector. */ vnorm = 0.; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MAX */ d__3 = vnorm; d__4 = (d__1 = vr[i__], abs(d__1)) + (d__2 = vi[i__] , abs(d__2)); // , expr subst vnorm = max(d__3,d__4); /* L290: */ } d__1 = 1. / vnorm; dscal_(n, &d__1, &vr[1], &c__1); d__1 = 1. / vnorm; dscal_(n, &d__1, &vi[1], &c__1); } return 0; /* End of DLAEIN */ }
/* Subroutine */ int dtrcon_(char *norm, char *uplo, char *diag, integer *n, doublereal *a, integer *lda, doublereal *rcond, doublereal *work, integer *iwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1; doublereal d__1; /* Local variables */ integer ix, kase, kase1; doublereal scale; extern logical lsame_(char *, char *); integer isave[3]; extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *, integer *); doublereal anorm; logical upper; doublereal xnorm; extern /* Subroutine */ int dlacn2_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *); extern doublereal dlamch_(char *); extern integer idamax_(integer *, doublereal *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *); extern doublereal dlantr_(char *, char *, char *, integer *, integer *, doublereal *, integer *, doublereal *); doublereal ainvnm; extern /* Subroutine */ int dlatrs_(char *, char *, char *, char *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *); logical onenrm; char normin[1]; doublereal smlnum; logical nounit; /* -- LAPACK routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH. */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* DTRCON estimates the reciprocal of the condition number of a */ /* triangular matrix A, in either the 1-norm or the infinity-norm. */ /* The norm of A is computed and an estimate is obtained for */ /* norm(inv(A)), then the reciprocal of the condition number is */ /* computed as */ /* RCOND = 1 / ( norm(A) * norm(inv(A)) ). */ /* Arguments */ /* ========= */ /* NORM (input) CHARACTER*1 */ /* Specifies whether the 1-norm condition number or the */ /* infinity-norm condition number is required: */ /* = '1' or 'O': 1-norm; */ /* = 'I': Infinity-norm. */ /* UPLO (input) CHARACTER*1 */ /* = 'U': A is upper triangular; */ /* = 'L': A is lower triangular. */ /* DIAG (input) CHARACTER*1 */ /* = 'N': A is non-unit triangular; */ /* = 'U': A is unit triangular. */ /* N (input) INTEGER */ /* The order of the matrix A. N >= 0. */ /* A (input) DOUBLE PRECISION array, dimension (LDA,N) */ /* The triangular matrix A. If UPLO = 'U', the leading N-by-N */ /* upper triangular part of the array A contains the upper */ /* triangular matrix, and the strictly lower triangular part of */ /* A is not referenced. If UPLO = 'L', the leading N-by-N lower */ /* triangular part of the array A contains the lower triangular */ /* matrix, and the strictly upper triangular part of A is not */ /* referenced. If DIAG = 'U', the diagonal elements of A are */ /* also not referenced and are assumed to be 1. */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,N). */ /* RCOND (output) DOUBLE PRECISION */ /* The reciprocal of the condition number of the matrix A, */ /* computed as RCOND = 1/(norm(A) * norm(inv(A))). */ /* WORK (workspace) DOUBLE PRECISION array, dimension (3*N) */ /* IWORK (workspace) INTEGER array, dimension (N) */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --work; --iwork; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O"); nounit = lsame_(diag, "N"); if (! onenrm && ! lsame_(norm, "I")) { *info = -1; } else if (! upper && ! lsame_(uplo, "L")) { *info = -2; } else if (! nounit && ! lsame_(diag, "U")) { *info = -3; } else if (*n < 0) { *info = -4; } else if (*lda < max(1,*n)) { *info = -6; } if (*info != 0) { i__1 = -(*info); xerbla_("DTRCON", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { *rcond = 1.; return 0; } *rcond = 0.; smlnum = dlamch_("Safe minimum") * (doublereal) max(1,*n); /* Compute the norm of the triangular matrix A. */ anorm = dlantr_(norm, uplo, diag, n, n, &a[a_offset], lda, &work[1]); /* Continue only if ANORM > 0. */ if (anorm > 0.) { /* Estimate the norm of the inverse of A. */ ainvnm = 0.; *(unsigned char *)normin = 'N'; if (onenrm) { kase1 = 1; } else { kase1 = 2; } kase = 0; L10: dlacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave); if (kase != 0) { if (kase == kase1) { /* Multiply by inv(A). */ dlatrs_(uplo, "No transpose", diag, normin, n, &a[a_offset], lda, &work[1], &scale, &work[(*n << 1) + 1], info); } else { /* Multiply by inv(A'). */ dlatrs_(uplo, "Transpose", diag, normin, n, &a[a_offset], lda, &work[1], &scale, &work[(*n << 1) + 1], info); } *(unsigned char *)normin = 'Y'; /* Multiply by 1/SCALE if doing so will not cause overflow. */ if (scale != 1.) { ix = idamax_(n, &work[1], &c__1); xnorm = (d__1 = work[ix], abs(d__1)); if (scale < xnorm * smlnum || scale == 0.) { goto L20; } drscl_(n, &scale, &work[1], &c__1); } goto L10; } /* Compute the estimate of the reciprocal condition number. */ if (ainvnm != 0.) { *rcond = 1. / anorm / ainvnm; } } L20: return 0; /* End of DTRCON */ } /* dtrcon_ */
/* Subroutine */ int dchktr_(logical *dotype, integer *nn, integer *nval, integer *nnb, integer *nbval, integer *nns, integer *nsval, doublereal *thresh, logical *tsterr, integer *nmax, doublereal *a, doublereal *ainv, doublereal *b, doublereal *x, doublereal *xact, doublereal *work, doublereal *rwork, integer *iwork, integer *nout) { /* Initialized data */ static integer iseedy[4] = { 1988,1989,1990,1991 }; static char uplos[1*2] = "U" "L"; static char transs[1*3] = "N" "T" "C"; /* Format strings */ static char fmt_9999[] = "(\002 UPLO='\002,a1,\002', DIAG='\002,a1,\002'" ", N=\002,i5,\002, NB=\002,i4,\002, type \002,i2,\002, test(\002," "i2,\002)= \002,g12.5)"; static char fmt_9998[] = "(\002 UPLO='\002,a1,\002', TRANS='\002,a1,\002" "', DIAG='\002,a1,\002', N=\002,i5,\002, NB=\002,i4,\002, type" " \002,i2,\002, test(\002,i2,\002)= \002,g12" ".5)"; static char fmt_9997[] = "(\002 NORM='\002,a1,\002', UPLO ='\002,a1,\002" "', N=\002,i5,\002,\002,11x,\002 type \002,i2,\002, test(\002,i2" ",\002)=\002,g12.5)"; static char fmt_9996[] = "(1x,a6,\002( '\002,a1,\002', '\002,a1,\002', " "'\002,a1,\002', '\002,a1,\002',\002,i5,\002, ... ), type \002,i2," "\002, test(\002,i2,\002)=\002,g12.5)"; /* System generated locals */ address a__1[2], a__2[3], a__3[4]; integer i__1, i__2, i__3[2], i__4, i__5[3], i__6[4]; char ch__1[2], ch__2[3], ch__3[4]; /* Builtin functions */ /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen), s_cat(char *, char **, integer *, integer *, ftnlen); integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); /* Local variables */ integer i__, k, n, nb, in, lda, inb; char diag[1]; integer imat, info; char path[3]; integer irhs, nrhs; char norm[1], uplo[1]; integer nrun; extern /* Subroutine */ int alahd_(integer *, char *); integer idiag; doublereal scale; extern /* Subroutine */ int dget04_(integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *); integer nfail, iseed[4]; extern logical lsame_(char *, char *); doublereal rcond, anorm; integer itran; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *), dtrt01_(char *, char *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *), dtrt02_(char *, char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *), dtrt03_(char *, char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *), dtrt05_(char *, char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *), dtrt06_( doublereal *, doublereal *, char *, char *, integer *, doublereal *, integer *, doublereal *, doublereal *); char trans[1]; integer iuplo, nerrs; doublereal dummy; char xtype[1]; extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *); doublereal rcondc; extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), dlarhs_(char *, char *, char *, char *, integer *, integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, integer *); doublereal rcondi; extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer *, integer *); doublereal rcondo; extern doublereal dlantr_(char *, char *, char *, integer *, integer *, doublereal *, integer *, doublereal *); doublereal ainvnm; extern /* Subroutine */ int dlatrs_(char *, char *, char *, char *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *), dlattr_( integer *, char *, char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *), dtrcon_(char *, char *, char *, integer * , doublereal *, integer *, doublereal *, doublereal *, integer *, integer *), xlaenv_(integer *, integer *), derrtr_(char *, integer *), dtrrfs_(char *, char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), dtrtri_(char *, char *, integer *, doublereal *, integer *, integer *); doublereal result[9]; extern /* Subroutine */ int dtrtrs_(char *, char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *); /* Fortran I/O blocks */ static cilist io___27 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___36 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___38 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___40 = { 0, 0, 0, fmt_9996, 0 }; static cilist io___41 = { 0, 0, 0, fmt_9996, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* DCHKTR tests DTRTRI, -TRS, -RFS, and -CON, and DLATRS */ /* Arguments */ /* ========= */ /* DOTYPE (input) LOGICAL array, dimension (NTYPES) */ /* The matrix types to be used for testing. Matrices of type j */ /* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */ /* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */ /* NN (input) INTEGER */ /* The number of values of N contained in the vector NVAL. */ /* NVAL (input) INTEGER array, dimension (NN) */ /* The values of the matrix column dimension N. */ /* NNB (input) INTEGER */ /* The number of values of NB contained in the vector NBVAL. */ /* NBVAL (input) INTEGER array, dimension (NNB) */ /* The values of the blocksize NB. */ /* NNS (input) INTEGER */ /* The number of values of NRHS contained in the vector NSVAL. */ /* NSVAL (input) INTEGER array, dimension (NNS) */ /* The values of the number of right hand sides NRHS. */ /* THRESH (input) DOUBLE PRECISION */ /* The threshold value for the test ratios. A result is */ /* included in the output file if RESULT >= THRESH. To have */ /* every test ratio printed, use THRESH = 0. */ /* TSTERR (input) LOGICAL */ /* Flag that indicates whether error exits are to be tested. */ /* NMAX (input) INTEGER */ /* The leading dimension of the work arrays. */ /* NMAX >= the maximum value of N in NVAL. */ /* A (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) */ /* AINV (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) */ /* B (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX) */ /* where NSMAX is the largest entry in NSVAL. */ /* X (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX) */ /* XACT (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX) */ /* WORK (workspace) DOUBLE PRECISION array, dimension */ /* (NMAX*max(3,NSMAX)) */ /* RWORK (workspace) DOUBLE PRECISION array, dimension */ /* (max(NMAX,2*NSMAX)) */ /* IWORK (workspace) INTEGER array, dimension (NMAX) */ /* NOUT (input) INTEGER */ /* The unit number for output. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Scalars in Common .. */ /* .. */ /* .. Common blocks .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Data statements .. */ /* Parameter adjustments */ --iwork; --rwork; --work; --xact; --x; --b; --ainv; --a; --nsval; --nbval; --nval; --dotype; /* Function Body */ /* .. */ /* .. Executable Statements .. */ /* Initialize constants and the random number seed. */ s_copy(path, "Double precision", (ftnlen)1, (ftnlen)16); s_copy(path + 1, "TR", (ftnlen)2, (ftnlen)2); nrun = 0; nfail = 0; nerrs = 0; for (i__ = 1; i__ <= 4; ++i__) { iseed[i__ - 1] = iseedy[i__ - 1]; /* L10: */ } /* Test the error exits */ if (*tsterr) { derrtr_(path, nout); } infoc_1.infot = 0; xlaenv_(&c__2, &c__2); i__1 = *nn; for (in = 1; in <= i__1; ++in) { /* Do for each value of N in NVAL */ n = nval[in]; lda = max(1,n); *(unsigned char *)xtype = 'N'; for (imat = 1; imat <= 10; ++imat) { /* Do the tests only if DOTYPE( IMAT ) is true. */ if (! dotype[imat]) { goto L80; } for (iuplo = 1; iuplo <= 2; ++iuplo) { /* Do first for UPLO = 'U', then for UPLO = 'L' */ *(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1]; /* Call DLATTR to generate a triangular test matrix. */ s_copy(srnamc_1.srnamt, "DLATTR", (ftnlen)6, (ftnlen)6); dlattr_(&imat, uplo, "No transpose", diag, iseed, &n, &a[1], & lda, &x[1], &work[1], &info); /* Set IDIAG = 1 for non-unit matrices, 2 for unit. */ if (lsame_(diag, "N")) { idiag = 1; } else { idiag = 2; } i__2 = *nnb; for (inb = 1; inb <= i__2; ++inb) { /* Do for each blocksize in NBVAL */ nb = nbval[inb]; xlaenv_(&c__1, &nb); /* + TEST 1 */ /* Form the inverse of A. */ dlacpy_(uplo, &n, &n, &a[1], &lda, &ainv[1], &lda); s_copy(srnamc_1.srnamt, "DTRTRI", (ftnlen)6, (ftnlen)6); dtrtri_(uplo, diag, &n, &ainv[1], &lda, &info); /* Check error code from DTRTRI. */ if (info != 0) { /* Writing concatenation */ i__3[0] = 1, a__1[0] = uplo; i__3[1] = 1, a__1[1] = diag; s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); alaerh_(path, "DTRTRI", &info, &c__0, ch__1, &n, &n, & c_n1, &c_n1, &nb, &imat, &nfail, &nerrs, nout); } /* Compute the infinity-norm condition number of A. */ anorm = dlantr_("I", uplo, diag, &n, &n, &a[1], &lda, & rwork[1]); ainvnm = dlantr_("I", uplo, diag, &n, &n, &ainv[1], &lda, &rwork[1]); if (anorm <= 0. || ainvnm <= 0.) { rcondi = 1.; } else { rcondi = 1. / anorm / ainvnm; } /* Compute the residual for the triangular matrix times */ /* its inverse. Also compute the 1-norm condition number */ /* of A. */ dtrt01_(uplo, diag, &n, &a[1], &lda, &ainv[1], &lda, & rcondo, &rwork[1], result); /* Print the test ratio if it is .GE. THRESH. */ if (result[0] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___27.ciunit = *nout; s_wsfe(&io___27); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, diag, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&nb, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&c__1, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[0], (ftnlen)sizeof( doublereal)); e_wsfe(); ++nfail; } ++nrun; /* Skip remaining tests if not the first block size. */ if (inb != 1) { goto L60; } i__4 = *nns; for (irhs = 1; irhs <= i__4; ++irhs) { nrhs = nsval[irhs]; *(unsigned char *)xtype = 'N'; for (itran = 1; itran <= 3; ++itran) { /* Do for op(A) = A, A**T, or A**H. */ *(unsigned char *)trans = *(unsigned char *)& transs[itran - 1]; if (itran == 1) { *(unsigned char *)norm = 'O'; rcondc = rcondo; } else { *(unsigned char *)norm = 'I'; rcondc = rcondi; } /* + TEST 2 */ /* Solve and compute residual for op(A)*x = b. */ s_copy(srnamc_1.srnamt, "DLARHS", (ftnlen)6, ( ftnlen)6); dlarhs_(path, xtype, uplo, trans, &n, &n, &c__0, & idiag, &nrhs, &a[1], &lda, &xact[1], &lda, &b[1], &lda, iseed, &info); *(unsigned char *)xtype = 'C'; dlacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], & lda); s_copy(srnamc_1.srnamt, "DTRTRS", (ftnlen)6, ( ftnlen)6); dtrtrs_(uplo, trans, diag, &n, &nrhs, &a[1], &lda, &x[1], &lda, &info); /* Check error code from DTRTRS. */ if (info != 0) { /* Writing concatenation */ i__5[0] = 1, a__2[0] = uplo; i__5[1] = 1, a__2[1] = trans; i__5[2] = 1, a__2[2] = diag; s_cat(ch__2, a__2, i__5, &c__3, (ftnlen)3); alaerh_(path, "DTRTRS", &info, &c__0, ch__2, & n, &n, &c_n1, &c_n1, &nrhs, &imat, & nfail, &nerrs, nout); } /* This line is needed on a Sun SPARCstation. */ if (n > 0) { dummy = a[1]; } dtrt02_(uplo, trans, diag, &n, &nrhs, &a[1], &lda, &x[1], &lda, &b[1], &lda, &work[1], & result[1]); /* + TEST 3 */ /* Check solution from generated exact solution. */ dget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[2]); /* + TESTS 4, 5, and 6 */ /* Use iterative refinement to improve the solution */ /* and compute error bounds. */ s_copy(srnamc_1.srnamt, "DTRRFS", (ftnlen)6, ( ftnlen)6); dtrrfs_(uplo, trans, diag, &n, &nrhs, &a[1], &lda, &b[1], &lda, &x[1], &lda, &rwork[1], & rwork[nrhs + 1], &work[1], &iwork[1], & info); /* Check error code from DTRRFS. */ if (info != 0) { /* Writing concatenation */ i__5[0] = 1, a__2[0] = uplo; i__5[1] = 1, a__2[1] = trans; i__5[2] = 1, a__2[2] = diag; s_cat(ch__2, a__2, i__5, &c__3, (ftnlen)3); alaerh_(path, "DTRRFS", &info, &c__0, ch__2, & n, &n, &c_n1, &c_n1, &nrhs, &imat, & nfail, &nerrs, nout); } dget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[3]); dtrt05_(uplo, trans, diag, &n, &nrhs, &a[1], &lda, &b[1], &lda, &x[1], &lda, &xact[1], &lda, &rwork[1], &rwork[nrhs + 1], &result[4]); /* Print information about the tests that did not */ /* pass the threshold. */ for (k = 2; k <= 6; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___36.ciunit = *nout; s_wsfe(&io___36); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, trans, (ftnlen)1); do_fio(&c__1, diag, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&nrhs, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&imat, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&k, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&result[k - 1], ( ftnlen)sizeof(doublereal)); e_wsfe(); ++nfail; } /* L20: */ } nrun += 5; /* L30: */ } /* L40: */ } /* + TEST 7 */ /* Get an estimate of RCOND = 1/CNDNUM. */ for (itran = 1; itran <= 2; ++itran) { if (itran == 1) { *(unsigned char *)norm = 'O'; rcondc = rcondo; } else { *(unsigned char *)norm = 'I'; rcondc = rcondi; } s_copy(srnamc_1.srnamt, "DTRCON", (ftnlen)6, (ftnlen) 6); dtrcon_(norm, uplo, diag, &n, &a[1], &lda, &rcond, & work[1], &iwork[1], &info); /* Check error code from DTRCON. */ if (info != 0) { /* Writing concatenation */ i__5[0] = 1, a__2[0] = norm; i__5[1] = 1, a__2[1] = uplo; i__5[2] = 1, a__2[2] = diag; s_cat(ch__2, a__2, i__5, &c__3, (ftnlen)3); alaerh_(path, "DTRCON", &info, &c__0, ch__2, &n, & n, &c_n1, &c_n1, &c_n1, &imat, &nfail, & nerrs, nout); } dtrt06_(&rcond, &rcondc, uplo, diag, &n, &a[1], &lda, &rwork[1], &result[6]); /* Print the test ratio if it is .GE. THRESH. */ if (result[6] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___38.ciunit = *nout; s_wsfe(&io___38); do_fio(&c__1, norm, (ftnlen)1); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&imat, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&c__7, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&result[6], (ftnlen)sizeof( doublereal)); e_wsfe(); ++nfail; } ++nrun; /* L50: */ } L60: ; } /* L70: */ } L80: ; } /* Use pathological test matrices to test DLATRS. */ for (imat = 11; imat <= 18; ++imat) { /* Do the tests only if DOTYPE( IMAT ) is true. */ if (! dotype[imat]) { goto L110; } for (iuplo = 1; iuplo <= 2; ++iuplo) { /* Do first for UPLO = 'U', then for UPLO = 'L' */ *(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1]; for (itran = 1; itran <= 3; ++itran) { /* Do for op(A) = A, A**T, and A**H. */ *(unsigned char *)trans = *(unsigned char *)&transs[itran - 1]; /* Call DLATTR to generate a triangular test matrix. */ s_copy(srnamc_1.srnamt, "DLATTR", (ftnlen)6, (ftnlen)6); dlattr_(&imat, uplo, trans, diag, iseed, &n, &a[1], &lda, &x[1], &work[1], &info); /* + TEST 8 */ /* Solve the system op(A)*x = b. */ s_copy(srnamc_1.srnamt, "DLATRS", (ftnlen)6, (ftnlen)6); dcopy_(&n, &x[1], &c__1, &b[1], &c__1); dlatrs_(uplo, trans, diag, "N", &n, &a[1], &lda, &b[1], & scale, &rwork[1], &info); /* Check error code from DLATRS. */ if (info != 0) { /* Writing concatenation */ i__6[0] = 1, a__3[0] = uplo; i__6[1] = 1, a__3[1] = trans; i__6[2] = 1, a__3[2] = diag; i__6[3] = 1, a__3[3] = "N"; s_cat(ch__3, a__3, i__6, &c__4, (ftnlen)4); alaerh_(path, "DLATRS", &info, &c__0, ch__3, &n, &n, & c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); } dtrt03_(uplo, trans, diag, &n, &c__1, &a[1], &lda, &scale, &rwork[1], &c_b101, &b[1], &lda, &x[1], &lda, & work[1], &result[7]); /* + TEST 9 */ /* Solve op(A)*X = b again with NORMIN = 'Y'. */ dcopy_(&n, &x[1], &c__1, &b[n + 1], &c__1); dlatrs_(uplo, trans, diag, "Y", &n, &a[1], &lda, &b[n + 1] , &scale, &rwork[1], &info); /* Check error code from DLATRS. */ if (info != 0) { /* Writing concatenation */ i__6[0] = 1, a__3[0] = uplo; i__6[1] = 1, a__3[1] = trans; i__6[2] = 1, a__3[2] = diag; i__6[3] = 1, a__3[3] = "Y"; s_cat(ch__3, a__3, i__6, &c__4, (ftnlen)4); alaerh_(path, "DLATRS", &info, &c__0, ch__3, &n, &n, & c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); } dtrt03_(uplo, trans, diag, &n, &c__1, &a[1], &lda, &scale, &rwork[1], &c_b101, &b[n + 1], &lda, &x[1], &lda, &work[1], &result[8]); /* Print information about the tests that did not pass */ /* the threshold. */ if (result[7] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___40.ciunit = *nout; s_wsfe(&io___40); do_fio(&c__1, "DLATRS", (ftnlen)6); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, trans, (ftnlen)1); do_fio(&c__1, diag, (ftnlen)1); do_fio(&c__1, "N", (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&c__8, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[7], (ftnlen)sizeof( doublereal)); e_wsfe(); ++nfail; } if (result[8] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___41.ciunit = *nout; s_wsfe(&io___41); do_fio(&c__1, "DLATRS", (ftnlen)6); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, trans, (ftnlen)1); do_fio(&c__1, diag, (ftnlen)1); do_fio(&c__1, "Y", (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&c__9, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[8], (ftnlen)sizeof( doublereal)); e_wsfe(); ++nfail; } nrun += 2; /* L90: */ } /* L100: */ } L110: ; } /* L120: */ } /* Print a summary of the results. */ alasum_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of DCHKTR */ } /* dchktr_ */
/* Subroutine */ int dgecon_(char *norm, integer *n, doublereal *a, integer * lda, doublereal *anorm, doublereal *rcond, doublereal *work, integer * iwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1; doublereal d__1; /* Local variables */ doublereal sl; integer ix; doublereal su; integer kase, kase1; doublereal scale; extern logical lsame_(char *, char *); integer isave[3]; extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *, integer *), dlacn2_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *); extern doublereal dlamch_(char *); extern integer idamax_(integer *, doublereal *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *); doublereal ainvnm; extern /* Subroutine */ int dlatrs_(char *, char *, char *, char *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *); logical onenrm; char normin[1]; doublereal smlnum; /* -- LAPACK routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH. */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* DGECON estimates the reciprocal of the condition number of a general */ /* real matrix A, in either the 1-norm or the infinity-norm, using */ /* the LU factorization computed by DGETRF. */ /* An estimate is obtained for norm(inv(A)), and the reciprocal of the */ /* condition number is computed as */ /* RCOND = 1 / ( norm(A) * norm(inv(A)) ). */ /* Arguments */ /* ========= */ /* NORM (input) CHARACTER*1 */ /* Specifies whether the 1-norm condition number or the */ /* infinity-norm condition number is required: */ /* = '1' or 'O': 1-norm; */ /* = 'I': Infinity-norm. */ /* N (input) INTEGER */ /* The order of the matrix A. N >= 0. */ /* A (input) DOUBLE PRECISION array, dimension (LDA,N) */ /* The factors L and U from the factorization A = P*L*U */ /* as computed by DGETRF. */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,N). */ /* ANORM (input) DOUBLE PRECISION */ /* If NORM = '1' or 'O', the 1-norm of the original matrix A. */ /* If NORM = 'I', the infinity-norm of the original matrix A. */ /* RCOND (output) DOUBLE PRECISION */ /* The reciprocal of the condition number of the matrix A, */ /* computed as RCOND = 1/(norm(A) * norm(inv(A))). */ /* WORK (workspace) DOUBLE PRECISION array, dimension (4*N) */ /* IWORK (workspace) INTEGER array, dimension (N) */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --work; --iwork; /* Function Body */ *info = 0; onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O"); if (! onenrm && ! lsame_(norm, "I")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*lda < max(1,*n)) { *info = -4; } else if (*anorm < 0.) { *info = -5; } if (*info != 0) { i__1 = -(*info); xerbla_("DGECON", &i__1); return 0; } /* Quick return if possible */ *rcond = 0.; if (*n == 0) { *rcond = 1.; return 0; } else if (*anorm == 0.) { return 0; } smlnum = dlamch_("Safe minimum"); /* Estimate the norm of inv(A). */ ainvnm = 0.; *(unsigned char *)normin = 'N'; if (onenrm) { kase1 = 1; } else { kase1 = 2; } kase = 0; L10: dlacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave); if (kase != 0) { if (kase == kase1) { /* Multiply by inv(L). */ dlatrs_("Lower", "No transpose", "Unit", normin, n, &a[a_offset], lda, &work[1], &sl, &work[(*n << 1) + 1], info); /* Multiply by inv(U). */ dlatrs_("Upper", "No transpose", "Non-unit", normin, n, &a[ a_offset], lda, &work[1], &su, &work[*n * 3 + 1], info); } else { /* Multiply by inv(U'). */ dlatrs_("Upper", "Transpose", "Non-unit", normin, n, &a[a_offset], lda, &work[1], &su, &work[*n * 3 + 1], info); /* Multiply by inv(L'). */ dlatrs_("Lower", "Transpose", "Unit", normin, n, &a[a_offset], lda, &work[1], &sl, &work[(*n << 1) + 1], info); } /* Divide X by 1/(SL*SU) if doing so will not cause overflow. */ scale = sl * su; *(unsigned char *)normin = 'Y'; if (scale != 1.) { ix = idamax_(n, &work[1], &c__1); if (scale < (d__1 = work[ix], abs(d__1)) * smlnum || scale == 0.) { goto L20; } drscl_(n, &scale, &work[1], &c__1); } goto L10; } /* Compute the estimate of the reciprocal condition number. */ if (ainvnm != 0.) { *rcond = 1. / ainvnm / *anorm; } L20: return 0; /* End of DGECON */ } /* dgecon_ */
/* Subroutine */ int dpocon_(char *uplo, integer *n, doublereal *a, integer * lda, doublereal *anorm, doublereal *rcond, doublereal *work, integer * iwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1; doublereal d__1; /* Local variables */ integer ix, kase; doublereal scale; extern logical lsame_(char *, char *); integer isave[3]; extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *, integer *); logical upper; extern /* Subroutine */ int dlacn2_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *); extern doublereal dlamch_(char *); doublereal scalel; extern integer idamax_(integer *, doublereal *, integer *); doublereal scaleu; extern /* Subroutine */ int xerbla_(char *, integer *); doublereal ainvnm; extern /* Subroutine */ int dlatrs_(char *, char *, char *, char *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *); char normin[1]; doublereal smlnum; /* -- LAPACK routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH. */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* DPOCON estimates the reciprocal of the condition number (in the */ /* 1-norm) of a real symmetric positive definite matrix using the */ /* Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF. */ /* An estimate is obtained for norm(inv(A)), and the reciprocal of the */ /* condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). */ /* Arguments */ /* ========= */ /* UPLO (input) CHARACTER*1 */ /* = 'U': Upper triangle of A is stored; */ /* = 'L': Lower triangle of A is stored. */ /* N (input) INTEGER */ /* The order of the matrix A. N >= 0. */ /* A (input) DOUBLE PRECISION array, dimension (LDA,N) */ /* The triangular factor U or L from the Cholesky factorization */ /* A = U**T*U or A = L*L**T, as computed by DPOTRF. */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,N). */ /* ANORM (input) DOUBLE PRECISION */ /* The 1-norm (or infinity-norm) of the symmetric matrix A. */ /* RCOND (output) DOUBLE PRECISION */ /* The reciprocal of the condition number of the matrix A, */ /* computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an */ /* estimate of the 1-norm of inv(A) computed in this routine. */ /* WORK (workspace) DOUBLE PRECISION array, dimension (3*N) */ /* IWORK (workspace) INTEGER array, dimension (N) */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --work; --iwork; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*lda < max(1,*n)) { *info = -4; } else if (*anorm < 0.) { *info = -5; } if (*info != 0) { i__1 = -(*info); xerbla_("DPOCON", &i__1); return 0; } /* Quick return if possible */ *rcond = 0.; if (*n == 0) { *rcond = 1.; return 0; } else if (*anorm == 0.) { return 0; } smlnum = dlamch_("Safe minimum"); /* Estimate the 1-norm of inv(A). */ kase = 0; *(unsigned char *)normin = 'N'; L10: dlacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave); if (kase != 0) { if (upper) { /* Multiply by inv(U'). */ dlatrs_("Upper", "Transpose", "Non-unit", normin, n, &a[a_offset], lda, &work[1], &scalel, &work[(*n << 1) + 1], info); *(unsigned char *)normin = 'Y'; /* Multiply by inv(U). */ dlatrs_("Upper", "No transpose", "Non-unit", normin, n, &a[ a_offset], lda, &work[1], &scaleu, &work[(*n << 1) + 1], info); } else { /* Multiply by inv(L). */ dlatrs_("Lower", "No transpose", "Non-unit", normin, n, &a[ a_offset], lda, &work[1], &scalel, &work[(*n << 1) + 1], info); *(unsigned char *)normin = 'Y'; /* Multiply by inv(L'). */ dlatrs_("Lower", "Transpose", "Non-unit", normin, n, &a[a_offset], lda, &work[1], &scaleu, &work[(*n << 1) + 1], info); } /* Multiply by 1/SCALE if doing so will not cause overflow. */ scale = scalel * scaleu; if (scale != 1.) { ix = idamax_(n, &work[1], &c__1); if (scale < (d__1 = work[ix], abs(d__1)) * smlnum || scale == 0.) { goto L20; } drscl_(n, &scale, &work[1], &c__1); } goto L10; } /* Compute the estimate of the reciprocal condition number. */ if (ainvnm != 0.) { *rcond = 1. / ainvnm / *anorm; } L20: return 0; /* End of DPOCON */ } /* dpocon_ */
/* Subroutine */ int dtrcon_(char *norm, char *uplo, char *diag, integer *n, doublereal *a, integer *lda, doublereal *rcond, doublereal *work, integer *iwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1; doublereal d__1; /* Local variables */ integer ix, kase, kase1; doublereal scale; extern logical lsame_(char *, char *); integer isave[3]; extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *, integer *); doublereal anorm; logical upper; doublereal xnorm; extern /* Subroutine */ int dlacn2_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *); extern doublereal dlamch_(char *); extern integer idamax_(integer *, doublereal *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *); extern doublereal dlantr_(char *, char *, char *, integer *, integer *, doublereal *, integer *, doublereal *); doublereal ainvnm; extern /* Subroutine */ int dlatrs_(char *, char *, char *, char *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *); logical onenrm; char normin[1]; doublereal smlnum; logical nounit; /* -- LAPACK computational routine (version 3.4.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* November 2011 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --work; --iwork; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O"); nounit = lsame_(diag, "N"); if (! onenrm && ! lsame_(norm, "I")) { *info = -1; } else if (! upper && ! lsame_(uplo, "L")) { *info = -2; } else if (! nounit && ! lsame_(diag, "U")) { *info = -3; } else if (*n < 0) { *info = -4; } else if (*lda < max(1,*n)) { *info = -6; } if (*info != 0) { i__1 = -(*info); xerbla_("DTRCON", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { *rcond = 1.; return 0; } *rcond = 0.; smlnum = dlamch_("Safe minimum") * (doublereal) max(1,*n); /* Compute the norm of the triangular matrix A. */ anorm = dlantr_(norm, uplo, diag, n, n, &a[a_offset], lda, &work[1]); /* Continue only if ANORM > 0. */ if (anorm > 0.) { /* Estimate the norm of the inverse of A. */ ainvnm = 0.; *(unsigned char *)normin = 'N'; if (onenrm) { kase1 = 1; } else { kase1 = 2; } kase = 0; L10: dlacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave); if (kase != 0) { if (kase == kase1) { /* Multiply by inv(A). */ dlatrs_(uplo, "No transpose", diag, normin, n, &a[a_offset], lda, &work[1], &scale, &work[(*n << 1) + 1], info); } else { /* Multiply by inv(A**T). */ dlatrs_(uplo, "Transpose", diag, normin, n, &a[a_offset], lda, &work[1], &scale, &work[(*n << 1) + 1], info); } *(unsigned char *)normin = 'Y'; /* Multiply by 1/SCALE if doing so will not cause overflow. */ if (scale != 1.) { ix = idamax_(n, &work[1], &c__1); xnorm = (d__1 = work[ix], abs(d__1)); if (scale < xnorm * smlnum || scale == 0.) { goto L20; } drscl_(n, &scale, &work[1], &c__1); } goto L10; } /* Compute the estimate of the reciprocal condition number. */ if (ainvnm != 0.) { *rcond = 1. / anorm / ainvnm; } } L20: return 0; /* End of DTRCON */ }