zspsvx.c
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00001 /* zspsvx.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 
00020 /* Subroutine */ int zspsvx_(char *fact, char *uplo, integer *n, integer *
00021         nrhs, doublecomplex *ap, doublecomplex *afp, integer *ipiv, 
00022         doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, 
00023         doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex *
00024         work, doublereal *rwork, integer *info)
00025 {
00026     /* System generated locals */
00027     integer b_dim1, b_offset, x_dim1, x_offset, i__1;
00028 
00029     /* Local variables */
00030     extern logical lsame_(char *, char *);
00031     doublereal anorm;
00032     extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 
00033             doublecomplex *, integer *);
00034     extern doublereal dlamch_(char *);
00035     logical nofact;
00036     extern /* Subroutine */ int xerbla_(char *, integer *), zlacpy_(
00037             char *, integer *, integer *, doublecomplex *, integer *, 
00038             doublecomplex *, integer *);
00039     extern doublereal zlansp_(char *, char *, integer *, doublecomplex *, 
00040             doublereal *);
00041     extern /* Subroutine */ int zspcon_(char *, integer *, doublecomplex *, 
00042             integer *, doublereal *, doublereal *, doublecomplex *, integer *), zsprfs_(char *, integer *, integer *, doublecomplex *, 
00043             doublecomplex *, integer *, doublecomplex *, integer *, 
00044             doublecomplex *, integer *, doublereal *, doublereal *, 
00045             doublecomplex *, doublereal *, integer *), zsptrf_(char *, 
00046              integer *, doublecomplex *, integer *, integer *), 
00047             zsptrs_(char *, integer *, integer *, doublecomplex *, integer *, 
00048             doublecomplex *, integer *, integer *);
00049 
00050 
00051 /*  -- LAPACK driver routine (version 3.2) -- */
00052 /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
00053 /*     November 2006 */
00054 
00055 /*     .. Scalar Arguments .. */
00056 /*     .. */
00057 /*     .. Array Arguments .. */
00058 /*     .. */
00059 
00060 /*  Purpose */
00061 /*  ======= */
00062 
00063 /*  ZSPSVX uses the diagonal pivoting factorization A = U*D*U**T or */
00064 /*  A = L*D*L**T to compute the solution to a complex system of linear */
00065 /*  equations A * X = B, where A is an N-by-N symmetric matrix stored */
00066 /*  in packed format and X and B are N-by-NRHS matrices. */
00067 
00068 /*  Error bounds on the solution and a condition estimate are also */
00069 /*  provided. */
00070 
00071 /*  Description */
00072 /*  =========== */
00073 
00074 /*  The following steps are performed: */
00075 
00076 /*  1. If FACT = 'N', the diagonal pivoting method is used to factor A as */
00077 /*        A = U * D * U**T,  if UPLO = 'U', or */
00078 /*        A = L * D * L**T,  if UPLO = 'L', */
00079 /*     where U (or L) is a product of permutation and unit upper (lower) */
00080 /*     triangular matrices and D is symmetric and block diagonal with */
00081 /*     1-by-1 and 2-by-2 diagonal blocks. */
00082 
00083 /*  2. If some D(i,i)=0, so that D is exactly singular, then the routine */
00084 /*     returns with INFO = i. Otherwise, the factored form of A is used */
00085 /*     to estimate the condition number of the matrix A.  If the */
00086 /*     reciprocal of the condition number is less than machine precision, */
00087 /*     INFO = N+1 is returned as a warning, but the routine still goes on */
00088 /*     to solve for X and compute error bounds as described below. */
00089 
00090 /*  3. The system of equations is solved for X using the factored form */
00091 /*     of A. */
00092 
00093 /*  4. Iterative refinement is applied to improve the computed solution */
00094 /*     matrix and calculate error bounds and backward error estimates */
00095 /*     for it. */
00096 
00097 /*  Arguments */
00098 /*  ========= */
00099 
00100 /*  FACT    (input) CHARACTER*1 */
00101 /*          Specifies whether or not the factored form of A has been */
00102 /*          supplied on entry. */
00103 /*          = 'F':  On entry, AFP and IPIV contain the factored form */
00104 /*                  of A.  AP, AFP and IPIV will not be modified. */
00105 /*          = 'N':  The matrix A will be copied to AFP and factored. */
00106 
00107 /*  UPLO    (input) CHARACTER*1 */
00108 /*          = 'U':  Upper triangle of A is stored; */
00109 /*          = 'L':  Lower triangle of A is stored. */
00110 
00111 /*  N       (input) INTEGER */
00112 /*          The number of linear equations, i.e., the order of the */
00113 /*          matrix A.  N >= 0. */
00114 
00115 /*  NRHS    (input) INTEGER */
00116 /*          The number of right hand sides, i.e., the number of columns */
00117 /*          of the matrices B and X.  NRHS >= 0. */
00118 
00119 /*  AP      (input) COMPLEX*16 array, dimension (N*(N+1)/2) */
00120 /*          The upper or lower triangle of the symmetric matrix A, packed */
00121 /*          columnwise in a linear array.  The j-th column of A is stored */
00122 /*          in the array AP as follows: */
00123 /*          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
00124 /*          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */
00125 /*          See below for further details. */
00126 
00127 /*  AFP     (input or output) COMPLEX*16 array, dimension (N*(N+1)/2) */
00128 /*          If FACT = 'F', then AFP is an input argument and on entry */
00129 /*          contains the block diagonal matrix D and the multipliers used */
00130 /*          to obtain the factor U or L from the factorization */
00131 /*          A = U*D*U**T or A = L*D*L**T as computed by ZSPTRF, stored as */
00132 /*          a packed triangular matrix in the same storage format as A. */
00133 
00134 /*          If FACT = 'N', then AFP is an output argument and on exit */
00135 /*          contains the block diagonal matrix D and the multipliers used */
00136 /*          to obtain the factor U or L from the factorization */
00137 /*          A = U*D*U**T or A = L*D*L**T as computed by ZSPTRF, stored as */
00138 /*          a packed triangular matrix in the same storage format as A. */
00139 
00140 /*  IPIV    (input or output) INTEGER array, dimension (N) */
00141 /*          If FACT = 'F', then IPIV is an input argument and on entry */
00142 /*          contains details of the interchanges and the block structure */
00143 /*          of D, as determined by ZSPTRF. */
00144 /*          If IPIV(k) > 0, then rows and columns k and IPIV(k) were */
00145 /*          interchanged and D(k,k) is a 1-by-1 diagonal block. */
00146 /*          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and */
00147 /*          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */
00148 /*          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) = */
00149 /*          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were */
00150 /*          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */
00151 
00152 /*          If FACT = 'N', then IPIV is an output argument and on exit */
00153 /*          contains details of the interchanges and the block structure */
00154 /*          of D, as determined by ZSPTRF. */
00155 
00156 /*  B       (input) COMPLEX*16 array, dimension (LDB,NRHS) */
00157 /*          The N-by-NRHS right hand side matrix B. */
00158 
00159 /*  LDB     (input) INTEGER */
00160 /*          The leading dimension of the array B.  LDB >= max(1,N). */
00161 
00162 /*  X       (output) COMPLEX*16 array, dimension (LDX,NRHS) */
00163 /*          If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X. */
00164 
00165 /*  LDX     (input) INTEGER */
00166 /*          The leading dimension of the array X.  LDX >= max(1,N). */
00167 
00168 /*  RCOND   (output) DOUBLE PRECISION */
00169 /*          The estimate of the reciprocal condition number of the matrix */
00170 /*          A.  If RCOND is less than the machine precision (in */
00171 /*          particular, if RCOND = 0), the matrix is singular to working */
00172 /*          precision.  This condition is indicated by a return code of */
00173 /*          INFO > 0. */
00174 
00175 /*  FERR    (output) DOUBLE PRECISION array, dimension (NRHS) */
00176 /*          The estimated forward error bound for each solution vector */
00177 /*          X(j) (the j-th column of the solution matrix X). */
00178 /*          If XTRUE is the true solution corresponding to X(j), FERR(j) */
00179 /*          is an estimated upper bound for the magnitude of the largest */
00180 /*          element in (X(j) - XTRUE) divided by the magnitude of the */
00181 /*          largest element in X(j).  The estimate is as reliable as */
00182 /*          the estimate for RCOND, and is almost always a slight */
00183 /*          overestimate of the true error. */
00184 
00185 /*  BERR    (output) DOUBLE PRECISION array, dimension (NRHS) */
00186 /*          The componentwise relative backward error of each solution */
00187 /*          vector X(j) (i.e., the smallest relative change in */
00188 /*          any element of A or B that makes X(j) an exact solution). */
00189 
00190 /*  WORK    (workspace) COMPLEX*16 array, dimension (2*N) */
00191 
00192 /*  RWORK   (workspace) DOUBLE PRECISION array, dimension (N) */
00193 
00194 /*  INFO    (output) INTEGER */
00195 /*          = 0: successful exit */
00196 /*          < 0: if INFO = -i, the i-th argument had an illegal value */
00197 /*          > 0:  if INFO = i, and i is */
00198 /*                <= N:  D(i,i) is exactly zero.  The factorization */
00199 /*                       has been completed but the factor D is exactly */
00200 /*                       singular, so the solution and error bounds could */
00201 /*                       not be computed. RCOND = 0 is returned. */
00202 /*                = N+1: D is nonsingular, but RCOND is less than machine */
00203 /*                       precision, meaning that the matrix is singular */
00204 /*                       to working precision.  Nevertheless, the */
00205 /*                       solution and error bounds are computed because */
00206 /*                       there are a number of situations where the */
00207 /*                       computed solution can be more accurate than the */
00208 /*                       value of RCOND would suggest. */
00209 
00210 /*  Further Details */
00211 /*  =============== */
00212 
00213 /*  The packed storage scheme is illustrated by the following example */
00214 /*  when N = 4, UPLO = 'U': */
00215 
00216 /*  Two-dimensional storage of the symmetric matrix A: */
00217 
00218 /*     a11 a12 a13 a14 */
00219 /*         a22 a23 a24 */
00220 /*             a33 a34     (aij = aji) */
00221 /*                 a44 */
00222 
00223 /*  Packed storage of the upper triangle of A: */
00224 
00225 /*  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] */
00226 
00227 /*  ===================================================================== */
00228 
00229 /*     .. Parameters .. */
00230 /*     .. */
00231 /*     .. Local Scalars .. */
00232 /*     .. */
00233 /*     .. External Functions .. */
00234 /*     .. */
00235 /*     .. External Subroutines .. */
00236 /*     .. */
00237 /*     .. Intrinsic Functions .. */
00238 /*     .. */
00239 /*     .. Executable Statements .. */
00240 
00241 /*     Test the input parameters. */
00242 
00243     /* Parameter adjustments */
00244     --ap;
00245     --afp;
00246     --ipiv;
00247     b_dim1 = *ldb;
00248     b_offset = 1 + b_dim1;
00249     b -= b_offset;
00250     x_dim1 = *ldx;
00251     x_offset = 1 + x_dim1;
00252     x -= x_offset;
00253     --ferr;
00254     --berr;
00255     --work;
00256     --rwork;
00257 
00258     /* Function Body */
00259     *info = 0;
00260     nofact = lsame_(fact, "N");
00261     if (! nofact && ! lsame_(fact, "F")) {
00262         *info = -1;
00263     } else if (! lsame_(uplo, "U") && ! lsame_(uplo, 
00264             "L")) {
00265         *info = -2;
00266     } else if (*n < 0) {
00267         *info = -3;
00268     } else if (*nrhs < 0) {
00269         *info = -4;
00270     } else if (*ldb < max(1,*n)) {
00271         *info = -9;
00272     } else if (*ldx < max(1,*n)) {
00273         *info = -11;
00274     }
00275     if (*info != 0) {
00276         i__1 = -(*info);
00277         xerbla_("ZSPSVX", &i__1);
00278         return 0;
00279     }
00280 
00281     if (nofact) {
00282 
00283 /*        Compute the factorization A = U*D*U' or A = L*D*L'. */
00284 
00285         i__1 = *n * (*n + 1) / 2;
00286         zcopy_(&i__1, &ap[1], &c__1, &afp[1], &c__1);
00287         zsptrf_(uplo, n, &afp[1], &ipiv[1], info);
00288 
00289 /*        Return if INFO is non-zero. */
00290 
00291         if (*info > 0) {
00292             *rcond = 0.;
00293             return 0;
00294         }
00295     }
00296 
00297 /*     Compute the norm of the matrix A. */
00298 
00299     anorm = zlansp_("I", uplo, n, &ap[1], &rwork[1]);
00300 
00301 /*     Compute the reciprocal of the condition number of A. */
00302 
00303     zspcon_(uplo, n, &afp[1], &ipiv[1], &anorm, rcond, &work[1], info);
00304 
00305 /*     Compute the solution vectors X. */
00306 
00307     zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
00308     zsptrs_(uplo, n, nrhs, &afp[1], &ipiv[1], &x[x_offset], ldx, info);
00309 
00310 /*     Use iterative refinement to improve the computed solutions and */
00311 /*     compute error bounds and backward error estimates for them. */
00312 
00313     zsprfs_(uplo, n, nrhs, &ap[1], &afp[1], &ipiv[1], &b[b_offset], ldb, &x[
00314             x_offset], ldx, &ferr[1], &berr[1], &work[1], &rwork[1], info);
00315 
00316 /*     Set INFO = N+1 if the matrix is singular to working precision. */
00317 
00318     if (*rcond < dlamch_("Epsilon")) {
00319         *info = *n + 1;
00320     }
00321 
00322     return 0;
00323 
00324 /*     End of ZSPSVX */
00325 
00326 } /* zspsvx_ */


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autogenerated on Sat Jun 8 2019 18:56:43