00001 /* slatdf.f -- translated by f2c (version 20061008). 00002 You must link the resulting object file with libf2c: 00003 on Microsoft Windows system, link with libf2c.lib; 00004 on Linux or Unix systems, link with .../path/to/libf2c.a -lm 00005 or, if you install libf2c.a in a standard place, with -lf2c -lm 00006 -- in that order, at the end of the command line, as in 00007 cc *.o -lf2c -lm 00008 Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., 00009 00010 http://www.netlib.org/f2c/libf2c.zip 00011 */ 00012 00013 #include "f2c.h" 00014 #include "blaswrap.h" 00015 00016 /* Table of constant values */ 00017 00018 static integer c__1 = 1; 00019 static integer c_n1 = -1; 00020 static real c_b23 = 1.f; 00021 static real c_b37 = -1.f; 00022 00023 /* Subroutine */ int slatdf_(integer *ijob, integer *n, real *z__, integer * 00024 ldz, real *rhs, real *rdsum, real *rdscal, integer *ipiv, integer * 00025 jpiv) 00026 { 00027 /* System generated locals */ 00028 integer z_dim1, z_offset, i__1, i__2; 00029 real r__1; 00030 00031 /* Builtin functions */ 00032 double sqrt(doublereal); 00033 00034 /* Local variables */ 00035 integer i__, j, k; 00036 real bm, bp, xm[8], xp[8]; 00037 integer info; 00038 real temp; 00039 extern doublereal sdot_(integer *, real *, integer *, real *, integer *); 00040 real work[32]; 00041 extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); 00042 real pmone; 00043 extern doublereal sasum_(integer *, real *, integer *); 00044 real sminu; 00045 integer iwork[8]; 00046 extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 00047 integer *), saxpy_(integer *, real *, real *, integer *, real *, 00048 integer *); 00049 real splus; 00050 extern /* Subroutine */ int sgesc2_(integer *, real *, integer *, real *, 00051 integer *, integer *, real *), sgecon_(char *, integer *, real *, 00052 integer *, real *, real *, real *, integer *, integer *), 00053 slassq_(integer *, real *, integer *, real *, real *), slaswp_( 00054 integer *, real *, integer *, integer *, integer *, integer *, 00055 integer *); 00056 00057 00058 /* -- LAPACK auxiliary routine (version 3.2) -- */ 00059 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00060 /* November 2006 */ 00061 00062 /* .. Scalar Arguments .. */ 00063 /* .. */ 00064 /* .. Array Arguments .. */ 00065 /* .. */ 00066 00067 /* Purpose */ 00068 /* ======= */ 00069 00070 /* SLATDF uses the LU factorization of the n-by-n matrix Z computed by */ 00071 /* SGETC2 and computes a contribution to the reciprocal Dif-estimate */ 00072 /* by solving Z * x = b for x, and choosing the r.h.s. b such that */ 00073 /* the norm of x is as large as possible. On entry RHS = b holds the */ 00074 /* contribution from earlier solved sub-systems, and on return RHS = x. */ 00075 00076 /* The factorization of Z returned by SGETC2 has the form Z = P*L*U*Q, */ 00077 /* where P and Q are permutation matrices. L is lower triangular with */ 00078 /* unit diagonal elements and U is upper triangular. */ 00079 00080 /* Arguments */ 00081 /* ========= */ 00082 00083 /* IJOB (input) INTEGER */ 00084 /* IJOB = 2: First compute an approximative null-vector e */ 00085 /* of Z using SGECON, e is normalized and solve for */ 00086 /* Zx = +-e - f with the sign giving the greater value */ 00087 /* of 2-norm(x). About 5 times as expensive as Default. */ 00088 /* IJOB .ne. 2: Local look ahead strategy where all entries of */ 00089 /* the r.h.s. b is choosen as either +1 or -1 (Default). */ 00090 00091 /* N (input) INTEGER */ 00092 /* The number of columns of the matrix Z. */ 00093 00094 /* Z (input) REAL array, dimension (LDZ, N) */ 00095 /* On entry, the LU part of the factorization of the n-by-n */ 00096 /* matrix Z computed by SGETC2: Z = P * L * U * Q */ 00097 00098 /* LDZ (input) INTEGER */ 00099 /* The leading dimension of the array Z. LDA >= max(1, N). */ 00100 00101 /* RHS (input/output) REAL array, dimension N. */ 00102 /* On entry, RHS contains contributions from other subsystems. */ 00103 /* On exit, RHS contains the solution of the subsystem with */ 00104 /* entries acoording to the value of IJOB (see above). */ 00105 00106 /* RDSUM (input/output) REAL */ 00107 /* On entry, the sum of squares of computed contributions to */ 00108 /* the Dif-estimate under computation by STGSYL, where the */ 00109 /* scaling factor RDSCAL (see below) has been factored out. */ 00110 /* On exit, the corresponding sum of squares updated with the */ 00111 /* contributions from the current sub-system. */ 00112 /* If TRANS = 'T' RDSUM is not touched. */ 00113 /* NOTE: RDSUM only makes sense when STGSY2 is called by STGSYL. */ 00114 00115 /* RDSCAL (input/output) REAL */ 00116 /* On entry, scaling factor used to prevent overflow in RDSUM. */ 00117 /* On exit, RDSCAL is updated w.r.t. the current contributions */ 00118 /* in RDSUM. */ 00119 /* If TRANS = 'T', RDSCAL is not touched. */ 00120 /* NOTE: RDSCAL only makes sense when STGSY2 is called by */ 00121 /* STGSYL. */ 00122 00123 /* IPIV (input) INTEGER array, dimension (N). */ 00124 /* The pivot indices; for 1 <= i <= N, row i of the */ 00125 /* matrix has been interchanged with row IPIV(i). */ 00126 00127 /* JPIV (input) INTEGER array, dimension (N). */ 00128 /* The pivot indices; for 1 <= j <= N, column j of the */ 00129 /* matrix has been interchanged with column JPIV(j). */ 00130 00131 /* Further Details */ 00132 /* =============== */ 00133 00134 /* Based on contributions by */ 00135 /* Bo Kagstrom and Peter Poromaa, Department of Computing Science, */ 00136 /* Umea University, S-901 87 Umea, Sweden. */ 00137 00138 /* This routine is a further developed implementation of algorithm */ 00139 /* BSOLVE in [1] using complete pivoting in the LU factorization. */ 00140 00141 /* [1] Bo Kagstrom and Lars Westin, */ 00142 /* Generalized Schur Methods with Condition Estimators for */ 00143 /* Solving the Generalized Sylvester Equation, IEEE Transactions */ 00144 /* on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751. */ 00145 00146 /* [2] Peter Poromaa, */ 00147 /* On Efficient and Robust Estimators for the Separation */ 00148 /* between two Regular Matrix Pairs with Applications in */ 00149 /* Condition Estimation. Report IMINF-95.05, Departement of */ 00150 /* Computing Science, Umea University, S-901 87 Umea, Sweden, 1995. */ 00151 00152 /* ===================================================================== */ 00153 00154 /* .. Parameters .. */ 00155 /* .. */ 00156 /* .. Local Scalars .. */ 00157 /* .. */ 00158 /* .. Local Arrays .. */ 00159 /* .. */ 00160 /* .. External Subroutines .. */ 00161 /* .. */ 00162 /* .. External Functions .. */ 00163 /* .. */ 00164 /* .. Intrinsic Functions .. */ 00165 /* .. */ 00166 /* .. Executable Statements .. */ 00167 00168 /* Parameter adjustments */ 00169 z_dim1 = *ldz; 00170 z_offset = 1 + z_dim1; 00171 z__ -= z_offset; 00172 --rhs; 00173 --ipiv; 00174 --jpiv; 00175 00176 /* Function Body */ 00177 if (*ijob != 2) { 00178 00179 /* Apply permutations IPIV to RHS */ 00180 00181 i__1 = *n - 1; 00182 slaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &ipiv[1], &c__1); 00183 00184 /* Solve for L-part choosing RHS either to +1 or -1. */ 00185 00186 pmone = -1.f; 00187 00188 i__1 = *n - 1; 00189 for (j = 1; j <= i__1; ++j) { 00190 bp = rhs[j] + 1.f; 00191 bm = rhs[j] - 1.f; 00192 splus = 1.f; 00193 00194 /* Look-ahead for L-part RHS(1:N-1) = + or -1, SPLUS and */ 00195 /* SMIN computed more efficiently than in BSOLVE [1]. */ 00196 00197 i__2 = *n - j; 00198 splus += sdot_(&i__2, &z__[j + 1 + j * z_dim1], &c__1, &z__[j + 1 00199 + j * z_dim1], &c__1); 00200 i__2 = *n - j; 00201 sminu = sdot_(&i__2, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1], 00202 &c__1); 00203 splus *= rhs[j]; 00204 if (splus > sminu) { 00205 rhs[j] = bp; 00206 } else if (sminu > splus) { 00207 rhs[j] = bm; 00208 } else { 00209 00210 /* In this case the updating sums are equal and we can */ 00211 /* choose RHS(J) +1 or -1. The first time this happens */ 00212 /* we choose -1, thereafter +1. This is a simple way to */ 00213 /* get good estimates of matrices like Byers well-known */ 00214 /* example (see [1]). (Not done in BSOLVE.) */ 00215 00216 rhs[j] += pmone; 00217 pmone = 1.f; 00218 } 00219 00220 /* Compute the remaining r.h.s. */ 00221 00222 temp = -rhs[j]; 00223 i__2 = *n - j; 00224 saxpy_(&i__2, &temp, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1], 00225 &c__1); 00226 00227 /* L10: */ 00228 } 00229 00230 /* Solve for U-part, look-ahead for RHS(N) = +-1. This is not done */ 00231 /* in BSOLVE and will hopefully give us a better estimate because */ 00232 /* any ill-conditioning of the original matrix is transfered to U */ 00233 /* and not to L. U(N, N) is an approximation to sigma_min(LU). */ 00234 00235 i__1 = *n - 1; 00236 scopy_(&i__1, &rhs[1], &c__1, xp, &c__1); 00237 xp[*n - 1] = rhs[*n] + 1.f; 00238 rhs[*n] += -1.f; 00239 splus = 0.f; 00240 sminu = 0.f; 00241 for (i__ = *n; i__ >= 1; --i__) { 00242 temp = 1.f / z__[i__ + i__ * z_dim1]; 00243 xp[i__ - 1] *= temp; 00244 rhs[i__] *= temp; 00245 i__1 = *n; 00246 for (k = i__ + 1; k <= i__1; ++k) { 00247 xp[i__ - 1] -= xp[k - 1] * (z__[i__ + k * z_dim1] * temp); 00248 rhs[i__] -= rhs[k] * (z__[i__ + k * z_dim1] * temp); 00249 /* L20: */ 00250 } 00251 splus += (r__1 = xp[i__ - 1], dabs(r__1)); 00252 sminu += (r__1 = rhs[i__], dabs(r__1)); 00253 /* L30: */ 00254 } 00255 if (splus > sminu) { 00256 scopy_(n, xp, &c__1, &rhs[1], &c__1); 00257 } 00258 00259 /* Apply the permutations JPIV to the computed solution (RHS) */ 00260 00261 i__1 = *n - 1; 00262 slaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &jpiv[1], &c_n1); 00263 00264 /* Compute the sum of squares */ 00265 00266 slassq_(n, &rhs[1], &c__1, rdscal, rdsum); 00267 00268 } else { 00269 00270 /* IJOB = 2, Compute approximate nullvector XM of Z */ 00271 00272 sgecon_("I", n, &z__[z_offset], ldz, &c_b23, &temp, work, iwork, & 00273 info); 00274 scopy_(n, &work[*n], &c__1, xm, &c__1); 00275 00276 /* Compute RHS */ 00277 00278 i__1 = *n - 1; 00279 slaswp_(&c__1, xm, ldz, &c__1, &i__1, &ipiv[1], &c_n1); 00280 temp = 1.f / sqrt(sdot_(n, xm, &c__1, xm, &c__1)); 00281 sscal_(n, &temp, xm, &c__1); 00282 scopy_(n, xm, &c__1, xp, &c__1); 00283 saxpy_(n, &c_b23, &rhs[1], &c__1, xp, &c__1); 00284 saxpy_(n, &c_b37, xm, &c__1, &rhs[1], &c__1); 00285 sgesc2_(n, &z__[z_offset], ldz, &rhs[1], &ipiv[1], &jpiv[1], &temp); 00286 sgesc2_(n, &z__[z_offset], ldz, xp, &ipiv[1], &jpiv[1], &temp); 00287 if (sasum_(n, xp, &c__1) > sasum_(n, &rhs[1], &c__1)) { 00288 scopy_(n, xp, &c__1, &rhs[1], &c__1); 00289 } 00290 00291 /* Compute the sum of squares */ 00292 00293 slassq_(n, &rhs[1], &c__1, rdscal, rdsum); 00294 00295 } 00296 00297 return 0; 00298 00299 /* End of SLATDF */ 00300 00301 } /* slatdf_ */