zhesvx.c
Go to the documentation of this file.
00001 /* zhesvx.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 
00021 /* Subroutine */ int zhesvx_(char *fact, char *uplo, integer *n, integer *
00022         nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer *
00023         ldaf, integer *ipiv, doublecomplex *b, integer *ldb, doublecomplex *x, 
00024          integer *ldx, doublereal *rcond, doublereal *ferr, doublereal *berr, 
00025         doublecomplex *work, integer *lwork, doublereal *rwork, integer *info)
00026 {
00027     /* System generated locals */
00028     integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, 
00029             x_offset, i__1, i__2;
00030 
00031     /* Local variables */
00032     integer nb;
00033     extern logical lsame_(char *, char *);
00034     doublereal anorm;
00035     extern doublereal dlamch_(char *);
00036     logical nofact;
00037     extern /* Subroutine */ int xerbla_(char *, integer *);
00038     extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
00039             integer *, integer *);
00040     extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, 
00041             integer *, doublereal *);
00042     extern /* Subroutine */ int zhecon_(char *, integer *, doublecomplex *, 
00043             integer *, integer *, doublereal *, doublereal *, doublecomplex *, 
00044              integer *), zherfs_(char *, integer *, integer *, 
00045             doublecomplex *, integer *, doublecomplex *, integer *, integer *, 
00046              doublecomplex *, integer *, doublecomplex *, integer *, 
00047             doublereal *, doublereal *, doublecomplex *, doublereal *, 
00048             integer *), zhetrf_(char *, integer *, doublecomplex *, 
00049             integer *, integer *, doublecomplex *, integer *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *, 
00050             integer *, doublecomplex *, integer *), zhetrs_(char *, 
00051             integer *, integer *, doublecomplex *, integer *, integer *, 
00052             doublecomplex *, integer *, integer *);
00053     integer lwkopt;
00054     logical lquery;
00055 
00056 
00057 /*  -- LAPACK driver routine (version 3.2) -- */
00058 /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
00059 /*     November 2006 */
00060 
00061 /*     .. Scalar Arguments .. */
00062 /*     .. */
00063 /*     .. Array Arguments .. */
00064 /*     .. */
00065 
00066 /*  Purpose */
00067 /*  ======= */
00068 
00069 /*  ZHESVX uses the diagonal pivoting factorization to compute the */
00070 /*  solution to a complex system of linear equations A * X = B, */
00071 /*  where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS */
00072 /*  matrices. */
00073 
00074 /*  Error bounds on the solution and a condition estimate are also */
00075 /*  provided. */
00076 
00077 /*  Description */
00078 /*  =========== */
00079 
00080 /*  The following steps are performed: */
00081 
00082 /*  1. If FACT = 'N', the diagonal pivoting method is used to factor A. */
00083 /*     The form of the factorization is */
00084 /*        A = U * D * U**H,  if UPLO = 'U', or */
00085 /*        A = L * D * L**H,  if UPLO = 'L', */
00086 /*     where U (or L) is a product of permutation and unit upper (lower) */
00087 /*     triangular matrices, and D is Hermitian and block diagonal with */
00088 /*     1-by-1 and 2-by-2 diagonal blocks. */
00089 
00090 /*  2. If some D(i,i)=0, so that D is exactly singular, then the routine */
00091 /*     returns with INFO = i. Otherwise, the factored form of A is used */
00092 /*     to estimate the condition number of the matrix A.  If the */
00093 /*     reciprocal of the condition number is less than machine precision, */
00094 /*     INFO = N+1 is returned as a warning, but the routine still goes on */
00095 /*     to solve for X and compute error bounds as described below. */
00096 
00097 /*  3. The system of equations is solved for X using the factored form */
00098 /*     of A. */
00099 
00100 /*  4. Iterative refinement is applied to improve the computed solution */
00101 /*     matrix and calculate error bounds and backward error estimates */
00102 /*     for it. */
00103 
00104 /*  Arguments */
00105 /*  ========= */
00106 
00107 /*  FACT    (input) CHARACTER*1 */
00108 /*          Specifies whether or not the factored form of A has been */
00109 /*          supplied on entry. */
00110 /*          = 'F':  On entry, AF and IPIV contain the factored form */
00111 /*                  of A.  A, AF and IPIV will not be modified. */
00112 /*          = 'N':  The matrix A will be copied to AF and factored. */
00113 
00114 /*  UPLO    (input) CHARACTER*1 */
00115 /*          = 'U':  Upper triangle of A is stored; */
00116 /*          = 'L':  Lower triangle of A is stored. */
00117 
00118 /*  N       (input) INTEGER */
00119 /*          The number of linear equations, i.e., the order of the */
00120 /*          matrix A.  N >= 0. */
00121 
00122 /*  NRHS    (input) INTEGER */
00123 /*          The number of right hand sides, i.e., the number of columns */
00124 /*          of the matrices B and X.  NRHS >= 0. */
00125 
00126 /*  A       (input) COMPLEX*16 array, dimension (LDA,N) */
00127 /*          The Hermitian matrix A.  If UPLO = 'U', the leading N-by-N */
00128 /*          upper triangular part of A contains the upper triangular part */
00129 /*          of the matrix A, and the strictly lower triangular part of A */
00130 /*          is not referenced.  If UPLO = 'L', the leading N-by-N lower */
00131 /*          triangular part of A contains the lower triangular part of */
00132 /*          the matrix A, and the strictly upper triangular part of A is */
00133 /*          not referenced. */
00134 
00135 /*  LDA     (input) INTEGER */
00136 /*          The leading dimension of the array A.  LDA >= max(1,N). */
00137 
00138 /*  AF      (input or output) COMPLEX*16 array, dimension (LDAF,N) */
00139 /*          If FACT = 'F', then AF is an input argument and on entry */
00140 /*          contains the block diagonal matrix D and the multipliers used */
00141 /*          to obtain the factor U or L from the factorization */
00142 /*          A = U*D*U**H or A = L*D*L**H as computed by ZHETRF. */
00143 
00144 /*          If FACT = 'N', then AF is an output argument and on exit */
00145 /*          returns the block diagonal matrix D and the multipliers used */
00146 /*          to obtain the factor U or L from the factorization */
00147 /*          A = U*D*U**H or A = L*D*L**H. */
00148 
00149 /*  LDAF    (input) INTEGER */
00150 /*          The leading dimension of the array AF.  LDAF >= max(1,N). */
00151 
00152 /*  IPIV    (input or output) INTEGER array, dimension (N) */
00153 /*          If FACT = 'F', then IPIV is an input argument and on entry */
00154 /*          contains details of the interchanges and the block structure */
00155 /*          of D, as determined by ZHETRF. */
00156 /*          If IPIV(k) > 0, then rows and columns k and IPIV(k) were */
00157 /*          interchanged and D(k,k) is a 1-by-1 diagonal block. */
00158 /*          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and */
00159 /*          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */
00160 /*          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) = */
00161 /*          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were */
00162 /*          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */
00163 
00164 /*          If FACT = 'N', then IPIV is an output argument and on exit */
00165 /*          contains details of the interchanges and the block structure */
00166 /*          of D, as determined by ZHETRF. */
00167 
00168 /*  B       (input) COMPLEX*16 array, dimension (LDB,NRHS) */
00169 /*          The N-by-NRHS right hand side matrix B. */
00170 
00171 /*  LDB     (input) INTEGER */
00172 /*          The leading dimension of the array B.  LDB >= max(1,N). */
00173 
00174 /*  X       (output) COMPLEX*16 array, dimension (LDX,NRHS) */
00175 /*          If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X. */
00176 
00177 /*  LDX     (input) INTEGER */
00178 /*          The leading dimension of the array X.  LDX >= max(1,N). */
00179 
00180 /*  RCOND   (output) DOUBLE PRECISION */
00181 /*          The estimate of the reciprocal condition number of the matrix */
00182 /*          A.  If RCOND is less than the machine precision (in */
00183 /*          particular, if RCOND = 0), the matrix is singular to working */
00184 /*          precision.  This condition is indicated by a return code of */
00185 /*          INFO > 0. */
00186 
00187 /*  FERR    (output) DOUBLE PRECISION array, dimension (NRHS) */
00188 /*          The estimated forward error bound for each solution vector */
00189 /*          X(j) (the j-th column of the solution matrix X). */
00190 /*          If XTRUE is the true solution corresponding to X(j), FERR(j) */
00191 /*          is an estimated upper bound for the magnitude of the largest */
00192 /*          element in (X(j) - XTRUE) divided by the magnitude of the */
00193 /*          largest element in X(j).  The estimate is as reliable as */
00194 /*          the estimate for RCOND, and is almost always a slight */
00195 /*          overestimate of the true error. */
00196 
00197 /*  BERR    (output) DOUBLE PRECISION array, dimension (NRHS) */
00198 /*          The componentwise relative backward error of each solution */
00199 /*          vector X(j) (i.e., the smallest relative change in */
00200 /*          any element of A or B that makes X(j) an exact solution). */
00201 
00202 /*  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) */
00203 /*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
00204 
00205 /*  LWORK   (input) INTEGER */
00206 /*          The length of WORK.  LWORK >= max(1,2*N), and for best */
00207 /*          performance, when FACT = 'N', LWORK >= max(1,2*N,N*NB), where */
00208 /*          NB is the optimal blocksize for ZHETRF. */
00209 
00210 /*          If LWORK = -1, then a workspace query is assumed; the routine */
00211 /*          only calculates the optimal size of the WORK array, returns */
00212 /*          this value as the first entry of the WORK array, and no error */
00213 /*          message related to LWORK is issued by XERBLA. */
00214 
00215 /*  RWORK   (workspace) DOUBLE PRECISION array, dimension (N) */
00216 
00217 /*  INFO    (output) INTEGER */
00218 /*          = 0: successful exit */
00219 /*          < 0: if INFO = -i, the i-th argument had an illegal value */
00220 /*          > 0: if INFO = i, and i is */
00221 /*                <= N:  D(i,i) is exactly zero.  The factorization */
00222 /*                       has been completed but the factor D is exactly */
00223 /*                       singular, so the solution and error bounds could */
00224 /*                       not be computed. RCOND = 0 is returned. */
00225 /*                = N+1: D is nonsingular, but RCOND is less than machine */
00226 /*                       precision, meaning that the matrix is singular */
00227 /*                       to working precision.  Nevertheless, the */
00228 /*                       solution and error bounds are computed because */
00229 /*                       there are a number of situations where the */
00230 /*                       computed solution can be more accurate than the */
00231 /*                       value of RCOND would suggest. */
00232 
00233 /*  ===================================================================== */
00234 
00235 /*     .. Parameters .. */
00236 /*     .. */
00237 /*     .. Local Scalars .. */
00238 /*     .. */
00239 /*     .. External Functions .. */
00240 /*     .. */
00241 /*     .. External Subroutines .. */
00242 /*     .. */
00243 /*     .. Intrinsic Functions .. */
00244 /*     .. */
00245 /*     .. Executable Statements .. */
00246 
00247 /*     Test the input parameters. */
00248 
00249     /* Parameter adjustments */
00250     a_dim1 = *lda;
00251     a_offset = 1 + a_dim1;
00252     a -= a_offset;
00253     af_dim1 = *ldaf;
00254     af_offset = 1 + af_dim1;
00255     af -= af_offset;
00256     --ipiv;
00257     b_dim1 = *ldb;
00258     b_offset = 1 + b_dim1;
00259     b -= b_offset;
00260     x_dim1 = *ldx;
00261     x_offset = 1 + x_dim1;
00262     x -= x_offset;
00263     --ferr;
00264     --berr;
00265     --work;
00266     --rwork;
00267 
00268     /* Function Body */
00269     *info = 0;
00270     nofact = lsame_(fact, "N");
00271     lquery = *lwork == -1;
00272     if (! nofact && ! lsame_(fact, "F")) {
00273         *info = -1;
00274     } else if (! lsame_(uplo, "U") && ! lsame_(uplo, 
00275             "L")) {
00276         *info = -2;
00277     } else if (*n < 0) {
00278         *info = -3;
00279     } else if (*nrhs < 0) {
00280         *info = -4;
00281     } else if (*lda < max(1,*n)) {
00282         *info = -6;
00283     } else if (*ldaf < max(1,*n)) {
00284         *info = -8;
00285     } else if (*ldb < max(1,*n)) {
00286         *info = -11;
00287     } else if (*ldx < max(1,*n)) {
00288         *info = -13;
00289     } else /* if(complicated condition) */ {
00290 /* Computing MAX */
00291         i__1 = 1, i__2 = *n << 1;
00292         if (*lwork < max(i__1,i__2) && ! lquery) {
00293             *info = -18;
00294         }
00295     }
00296 
00297     if (*info == 0) {
00298 /* Computing MAX */
00299         i__1 = 1, i__2 = *n << 1;
00300         lwkopt = max(i__1,i__2);
00301         if (nofact) {
00302             nb = ilaenv_(&c__1, "ZHETRF", uplo, n, &c_n1, &c_n1, &c_n1);
00303 /* Computing MAX */
00304             i__1 = lwkopt, i__2 = *n * nb;
00305             lwkopt = max(i__1,i__2);
00306         }
00307         work[1].r = (doublereal) lwkopt, work[1].i = 0.;
00308     }
00309 
00310     if (*info != 0) {
00311         i__1 = -(*info);
00312         xerbla_("ZHESVX", &i__1);
00313         return 0;
00314     } else if (lquery) {
00315         return 0;
00316     }
00317 
00318     if (nofact) {
00319 
00320 /*        Compute the factorization A = U*D*U' or A = L*D*L'. */
00321 
00322         zlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
00323         zhetrf_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &work[1], lwork, 
00324                 info);
00325 
00326 /*        Return if INFO is non-zero. */
00327 
00328         if (*info > 0) {
00329             *rcond = 0.;
00330             return 0;
00331         }
00332     }
00333 
00334 /*     Compute the norm of the matrix A. */
00335 
00336     anorm = zlanhe_("I", uplo, n, &a[a_offset], lda, &rwork[1]);
00337 
00338 /*     Compute the reciprocal of the condition number of A. */
00339 
00340     zhecon_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &anorm, rcond, &work[1], 
00341             info);
00342 
00343 /*     Compute the solution vectors X. */
00344 
00345     zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
00346     zhetrs_(uplo, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx, 
00347             info);
00348 
00349 /*     Use iterative refinement to improve the computed solutions and */
00350 /*     compute error bounds and backward error estimates for them. */
00351 
00352     zherfs_(uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &ipiv[1], 
00353             &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1]
00354 , &rwork[1], info);
00355 
00356 /*     Set INFO = N+1 if the matrix is singular to working precision. */
00357 
00358     if (*rcond < dlamch_("Epsilon")) {
00359         *info = *n + 1;
00360     }
00361 
00362     work[1].r = (doublereal) lwkopt, work[1].i = 0.;
00363 
00364     return 0;
00365 
00366 /*     End of ZHESVX */
00367 
00368 } /* zhesvx_ */


swiftnav
Author(s):
autogenerated on Sat Jun 8 2019 18:56:37