zspcon.c
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00001 /* zspcon.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 zspcon_(char *uplo, integer *n, doublecomplex *ap, 
00021         integer *ipiv, doublereal *anorm, doublereal *rcond, doublecomplex *
00022         work, integer *info)
00023 {
00024     /* System generated locals */
00025     integer i__1, i__2;
00026 
00027     /* Local variables */
00028     integer i__, ip, kase;
00029     extern logical lsame_(char *, char *);
00030     integer isave[3];
00031     logical upper;
00032     extern /* Subroutine */ int zlacn2_(integer *, doublecomplex *, 
00033             doublecomplex *, doublereal *, integer *, integer *), xerbla_(
00034             char *, integer *);
00035     doublereal ainvnm;
00036     extern /* Subroutine */ int zsptrs_(char *, integer *, integer *, 
00037             doublecomplex *, integer *, doublecomplex *, integer *, integer *);
00038 
00039 
00040 /*  -- LAPACK routine (version 3.2) -- */
00041 /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
00042 /*     November 2006 */
00043 
00044 /*     Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. */
00045 
00046 /*     .. Scalar Arguments .. */
00047 /*     .. */
00048 /*     .. Array Arguments .. */
00049 /*     .. */
00050 
00051 /*  Purpose */
00052 /*  ======= */
00053 
00054 /*  ZSPCON estimates the reciprocal of the condition number (in the */
00055 /*  1-norm) of a complex symmetric packed matrix A using the */
00056 /*  factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF. */
00057 
00058 /*  An estimate is obtained for norm(inv(A)), and the reciprocal of the */
00059 /*  condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). */
00060 
00061 /*  Arguments */
00062 /*  ========= */
00063 
00064 /*  UPLO    (input) CHARACTER*1 */
00065 /*          Specifies whether the details of the factorization are stored */
00066 /*          as an upper or lower triangular matrix. */
00067 /*          = 'U':  Upper triangular, form is A = U*D*U**T; */
00068 /*          = 'L':  Lower triangular, form is A = L*D*L**T. */
00069 
00070 /*  N       (input) INTEGER */
00071 /*          The order of the matrix A.  N >= 0. */
00072 
00073 /*  AP      (input) COMPLEX*16 array, dimension (N*(N+1)/2) */
00074 /*          The block diagonal matrix D and the multipliers used to */
00075 /*          obtain the factor U or L as computed by ZSPTRF, stored as a */
00076 /*          packed triangular matrix. */
00077 
00078 /*  IPIV    (input) INTEGER array, dimension (N) */
00079 /*          Details of the interchanges and the block structure of D */
00080 /*          as determined by ZSPTRF. */
00081 
00082 /*  ANORM   (input) DOUBLE PRECISION */
00083 /*          The 1-norm of the original matrix A. */
00084 
00085 /*  RCOND   (output) DOUBLE PRECISION */
00086 /*          The reciprocal of the condition number of the matrix A, */
00087 /*          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an */
00088 /*          estimate of the 1-norm of inv(A) computed in this routine. */
00089 
00090 /*  WORK    (workspace) COMPLEX*16 array, dimension (2*N) */
00091 
00092 /*  INFO    (output) INTEGER */
00093 /*          = 0:  successful exit */
00094 /*          < 0:  if INFO = -i, the i-th argument had an illegal value */
00095 
00096 /*  ===================================================================== */
00097 
00098 /*     .. Parameters .. */
00099 /*     .. */
00100 /*     .. Local Scalars .. */
00101 /*     .. */
00102 /*     .. Local Arrays .. */
00103 /*     .. */
00104 /*     .. External Functions .. */
00105 /*     .. */
00106 /*     .. External Subroutines .. */
00107 /*     .. */
00108 /*     .. Executable Statements .. */
00109 
00110 /*     Test the input parameters. */
00111 
00112     /* Parameter adjustments */
00113     --work;
00114     --ipiv;
00115     --ap;
00116 
00117     /* Function Body */
00118     *info = 0;
00119     upper = lsame_(uplo, "U");
00120     if (! upper && ! lsame_(uplo, "L")) {
00121         *info = -1;
00122     } else if (*n < 0) {
00123         *info = -2;
00124     } else if (*anorm < 0.) {
00125         *info = -5;
00126     }
00127     if (*info != 0) {
00128         i__1 = -(*info);
00129         xerbla_("ZSPCON", &i__1);
00130         return 0;
00131     }
00132 
00133 /*     Quick return if possible */
00134 
00135     *rcond = 0.;
00136     if (*n == 0) {
00137         *rcond = 1.;
00138         return 0;
00139     } else if (*anorm <= 0.) {
00140         return 0;
00141     }
00142 
00143 /*     Check that the diagonal matrix D is nonsingular. */
00144 
00145     if (upper) {
00146 
00147 /*        Upper triangular storage: examine D from bottom to top */
00148 
00149         ip = *n * (*n + 1) / 2;
00150         for (i__ = *n; i__ >= 1; --i__) {
00151             i__1 = ip;
00152             if (ipiv[i__] > 0 && (ap[i__1].r == 0. && ap[i__1].i == 0.)) {
00153                 return 0;
00154             }
00155             ip -= i__;
00156 /* L10: */
00157         }
00158     } else {
00159 
00160 /*        Lower triangular storage: examine D from top to bottom. */
00161 
00162         ip = 1;
00163         i__1 = *n;
00164         for (i__ = 1; i__ <= i__1; ++i__) {
00165             i__2 = ip;
00166             if (ipiv[i__] > 0 && (ap[i__2].r == 0. && ap[i__2].i == 0.)) {
00167                 return 0;
00168             }
00169             ip = ip + *n - i__ + 1;
00170 /* L20: */
00171         }
00172     }
00173 
00174 /*     Estimate the 1-norm of the inverse. */
00175 
00176     kase = 0;
00177 L30:
00178     zlacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave);
00179     if (kase != 0) {
00180 
00181 /*        Multiply by inv(L*D*L') or inv(U*D*U'). */
00182 
00183         zsptrs_(uplo, n, &c__1, &ap[1], &ipiv[1], &work[1], n, info);
00184         goto L30;
00185     }
00186 
00187 /*     Compute the estimate of the reciprocal condition number. */
00188 
00189     if (ainvnm != 0.) {
00190         *rcond = 1. / ainvnm / *anorm;
00191     }
00192 
00193     return 0;
00194 
00195 /*     End of ZSPCON */
00196 
00197 } /* zspcon_ */


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autogenerated on Sat Jun 8 2019 18:56:43