zhptri.c
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00001 /* zhptri.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 doublecomplex c_b2 = {0.,0.};
00019 static integer c__1 = 1;
00020 
00021 /* Subroutine */ int zhptri_(char *uplo, integer *n, doublecomplex *ap, 
00022         integer *ipiv, doublecomplex *work, integer *info)
00023 {
00024     /* System generated locals */
00025     integer i__1, i__2, i__3;
00026     doublereal d__1;
00027     doublecomplex z__1, z__2;
00028 
00029     /* Builtin functions */
00030     double z_abs(doublecomplex *);
00031     void d_cnjg(doublecomplex *, doublecomplex *);
00032 
00033     /* Local variables */
00034     doublereal d__;
00035     integer j, k;
00036     doublereal t, ak;
00037     integer kc, kp, kx, kpc, npp;
00038     doublereal akp1;
00039     doublecomplex temp, akkp1;
00040     extern logical lsame_(char *, char *);
00041     extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, 
00042             doublecomplex *, integer *, doublecomplex *, integer *);
00043     integer kstep;
00044     logical upper;
00045     extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 
00046             doublecomplex *, integer *), zhpmv_(char *, integer *, 
00047             doublecomplex *, doublecomplex *, doublecomplex *, integer *, 
00048             doublecomplex *, doublecomplex *, integer *), zswap_(
00049             integer *, doublecomplex *, integer *, doublecomplex *, integer *)
00050             , xerbla_(char *, integer *);
00051     integer kcnext;
00052 
00053 
00054 /*  -- LAPACK routine (version 3.2) -- */
00055 /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
00056 /*     November 2006 */
00057 
00058 /*     .. Scalar Arguments .. */
00059 /*     .. */
00060 /*     .. Array Arguments .. */
00061 /*     .. */
00062 
00063 /*  Purpose */
00064 /*  ======= */
00065 
00066 /*  ZHPTRI computes the inverse of a complex Hermitian indefinite matrix */
00067 /*  A in packed storage using the factorization A = U*D*U**H or */
00068 /*  A = L*D*L**H computed by ZHPTRF. */
00069 
00070 /*  Arguments */
00071 /*  ========= */
00072 
00073 /*  UPLO    (input) CHARACTER*1 */
00074 /*          Specifies whether the details of the factorization are stored */
00075 /*          as an upper or lower triangular matrix. */
00076 /*          = 'U':  Upper triangular, form is A = U*D*U**H; */
00077 /*          = 'L':  Lower triangular, form is A = L*D*L**H. */
00078 
00079 /*  N       (input) INTEGER */
00080 /*          The order of the matrix A.  N >= 0. */
00081 
00082 /*  AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) */
00083 /*          On entry, the block diagonal matrix D and the multipliers */
00084 /*          used to obtain the factor U or L as computed by ZHPTRF, */
00085 /*          stored as a packed triangular matrix. */
00086 
00087 /*          On exit, if INFO = 0, the (Hermitian) inverse of the original */
00088 /*          matrix, stored as a packed triangular matrix. The j-th column */
00089 /*          of inv(A) is stored in the array AP as follows: */
00090 /*          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j; */
00091 /*          if UPLO = 'L', */
00092 /*             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n. */
00093 
00094 /*  IPIV    (input) INTEGER array, dimension (N) */
00095 /*          Details of the interchanges and the block structure of D */
00096 /*          as determined by ZHPTRF. */
00097 
00098 /*  WORK    (workspace) COMPLEX*16 array, dimension (N) */
00099 
00100 /*  INFO    (output) INTEGER */
00101 /*          = 0: successful exit */
00102 /*          < 0: if INFO = -i, the i-th argument had an illegal value */
00103 /*          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its */
00104 /*               inverse could not be computed. */
00105 
00106 /*  ===================================================================== */
00107 
00108 /*     .. Parameters .. */
00109 /*     .. */
00110 /*     .. Local Scalars .. */
00111 /*     .. */
00112 /*     .. External Functions .. */
00113 /*     .. */
00114 /*     .. External Subroutines .. */
00115 /*     .. */
00116 /*     .. Intrinsic Functions .. */
00117 /*     .. */
00118 /*     .. Executable Statements .. */
00119 
00120 /*     Test the input parameters. */
00121 
00122     /* Parameter adjustments */
00123     --work;
00124     --ipiv;
00125     --ap;
00126 
00127     /* Function Body */
00128     *info = 0;
00129     upper = lsame_(uplo, "U");
00130     if (! upper && ! lsame_(uplo, "L")) {
00131         *info = -1;
00132     } else if (*n < 0) {
00133         *info = -2;
00134     }
00135     if (*info != 0) {
00136         i__1 = -(*info);
00137         xerbla_("ZHPTRI", &i__1);
00138         return 0;
00139     }
00140 
00141 /*     Quick return if possible */
00142 
00143     if (*n == 0) {
00144         return 0;
00145     }
00146 
00147 /*     Check that the diagonal matrix D is nonsingular. */
00148 
00149     if (upper) {
00150 
00151 /*        Upper triangular storage: examine D from bottom to top */
00152 
00153         kp = *n * (*n + 1) / 2;
00154         for (*info = *n; *info >= 1; --(*info)) {
00155             i__1 = kp;
00156             if (ipiv[*info] > 0 && (ap[i__1].r == 0. && ap[i__1].i == 0.)) {
00157                 return 0;
00158             }
00159             kp -= *info;
00160 /* L10: */
00161         }
00162     } else {
00163 
00164 /*        Lower triangular storage: examine D from top to bottom. */
00165 
00166         kp = 1;
00167         i__1 = *n;
00168         for (*info = 1; *info <= i__1; ++(*info)) {
00169             i__2 = kp;
00170             if (ipiv[*info] > 0 && (ap[i__2].r == 0. && ap[i__2].i == 0.)) {
00171                 return 0;
00172             }
00173             kp = kp + *n - *info + 1;
00174 /* L20: */
00175         }
00176     }
00177     *info = 0;
00178 
00179     if (upper) {
00180 
00181 /*        Compute inv(A) from the factorization A = U*D*U'. */
00182 
00183 /*        K is the main loop index, increasing from 1 to N in steps of */
00184 /*        1 or 2, depending on the size of the diagonal blocks. */
00185 
00186         k = 1;
00187         kc = 1;
00188 L30:
00189 
00190 /*        If K > N, exit from loop. */
00191 
00192         if (k > *n) {
00193             goto L50;
00194         }
00195 
00196         kcnext = kc + k;
00197         if (ipiv[k] > 0) {
00198 
00199 /*           1 x 1 diagonal block */
00200 
00201 /*           Invert the diagonal block. */
00202 
00203             i__1 = kc + k - 1;
00204             i__2 = kc + k - 1;
00205             d__1 = 1. / ap[i__2].r;
00206             ap[i__1].r = d__1, ap[i__1].i = 0.;
00207 
00208 /*           Compute column K of the inverse. */
00209 
00210             if (k > 1) {
00211                 i__1 = k - 1;
00212                 zcopy_(&i__1, &ap[kc], &c__1, &work[1], &c__1);
00213                 i__1 = k - 1;
00214                 z__1.r = -1., z__1.i = -0.;
00215                 zhpmv_(uplo, &i__1, &z__1, &ap[1], &work[1], &c__1, &c_b2, &
00216                         ap[kc], &c__1);
00217                 i__1 = kc + k - 1;
00218                 i__2 = kc + k - 1;
00219                 i__3 = k - 1;
00220                 zdotc_(&z__2, &i__3, &work[1], &c__1, &ap[kc], &c__1);
00221                 d__1 = z__2.r;
00222                 z__1.r = ap[i__2].r - d__1, z__1.i = ap[i__2].i;
00223                 ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
00224             }
00225             kstep = 1;
00226         } else {
00227 
00228 /*           2 x 2 diagonal block */
00229 
00230 /*           Invert the diagonal block. */
00231 
00232             t = z_abs(&ap[kcnext + k - 1]);
00233             i__1 = kc + k - 1;
00234             ak = ap[i__1].r / t;
00235             i__1 = kcnext + k;
00236             akp1 = ap[i__1].r / t;
00237             i__1 = kcnext + k - 1;
00238             z__1.r = ap[i__1].r / t, z__1.i = ap[i__1].i / t;
00239             akkp1.r = z__1.r, akkp1.i = z__1.i;
00240             d__ = t * (ak * akp1 - 1.);
00241             i__1 = kc + k - 1;
00242             d__1 = akp1 / d__;
00243             ap[i__1].r = d__1, ap[i__1].i = 0.;
00244             i__1 = kcnext + k;
00245             d__1 = ak / d__;
00246             ap[i__1].r = d__1, ap[i__1].i = 0.;
00247             i__1 = kcnext + k - 1;
00248             z__2.r = -akkp1.r, z__2.i = -akkp1.i;
00249             z__1.r = z__2.r / d__, z__1.i = z__2.i / d__;
00250             ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
00251 
00252 /*           Compute columns K and K+1 of the inverse. */
00253 
00254             if (k > 1) {
00255                 i__1 = k - 1;
00256                 zcopy_(&i__1, &ap[kc], &c__1, &work[1], &c__1);
00257                 i__1 = k - 1;
00258                 z__1.r = -1., z__1.i = -0.;
00259                 zhpmv_(uplo, &i__1, &z__1, &ap[1], &work[1], &c__1, &c_b2, &
00260                         ap[kc], &c__1);
00261                 i__1 = kc + k - 1;
00262                 i__2 = kc + k - 1;
00263                 i__3 = k - 1;
00264                 zdotc_(&z__2, &i__3, &work[1], &c__1, &ap[kc], &c__1);
00265                 d__1 = z__2.r;
00266                 z__1.r = ap[i__2].r - d__1, z__1.i = ap[i__2].i;
00267                 ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
00268                 i__1 = kcnext + k - 1;
00269                 i__2 = kcnext + k - 1;
00270                 i__3 = k - 1;
00271                 zdotc_(&z__2, &i__3, &ap[kc], &c__1, &ap[kcnext], &c__1);
00272                 z__1.r = ap[i__2].r - z__2.r, z__1.i = ap[i__2].i - z__2.i;
00273                 ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
00274                 i__1 = k - 1;
00275                 zcopy_(&i__1, &ap[kcnext], &c__1, &work[1], &c__1);
00276                 i__1 = k - 1;
00277                 z__1.r = -1., z__1.i = -0.;
00278                 zhpmv_(uplo, &i__1, &z__1, &ap[1], &work[1], &c__1, &c_b2, &
00279                         ap[kcnext], &c__1);
00280                 i__1 = kcnext + k;
00281                 i__2 = kcnext + k;
00282                 i__3 = k - 1;
00283                 zdotc_(&z__2, &i__3, &work[1], &c__1, &ap[kcnext], &c__1);
00284                 d__1 = z__2.r;
00285                 z__1.r = ap[i__2].r - d__1, z__1.i = ap[i__2].i;
00286                 ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
00287             }
00288             kstep = 2;
00289             kcnext = kcnext + k + 1;
00290         }
00291 
00292         kp = (i__1 = ipiv[k], abs(i__1));
00293         if (kp != k) {
00294 
00295 /*           Interchange rows and columns K and KP in the leading */
00296 /*           submatrix A(1:k+1,1:k+1) */
00297 
00298             kpc = (kp - 1) * kp / 2 + 1;
00299             i__1 = kp - 1;
00300             zswap_(&i__1, &ap[kc], &c__1, &ap[kpc], &c__1);
00301             kx = kpc + kp - 1;
00302             i__1 = k - 1;
00303             for (j = kp + 1; j <= i__1; ++j) {
00304                 kx = kx + j - 1;
00305                 d_cnjg(&z__1, &ap[kc + j - 1]);
00306                 temp.r = z__1.r, temp.i = z__1.i;
00307                 i__2 = kc + j - 1;
00308                 d_cnjg(&z__1, &ap[kx]);
00309                 ap[i__2].r = z__1.r, ap[i__2].i = z__1.i;
00310                 i__2 = kx;
00311                 ap[i__2].r = temp.r, ap[i__2].i = temp.i;
00312 /* L40: */
00313             }
00314             i__1 = kc + kp - 1;
00315             d_cnjg(&z__1, &ap[kc + kp - 1]);
00316             ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
00317             i__1 = kc + k - 1;
00318             temp.r = ap[i__1].r, temp.i = ap[i__1].i;
00319             i__1 = kc + k - 1;
00320             i__2 = kpc + kp - 1;
00321             ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
00322             i__1 = kpc + kp - 1;
00323             ap[i__1].r = temp.r, ap[i__1].i = temp.i;
00324             if (kstep == 2) {
00325                 i__1 = kc + k + k - 1;
00326                 temp.r = ap[i__1].r, temp.i = ap[i__1].i;
00327                 i__1 = kc + k + k - 1;
00328                 i__2 = kc + k + kp - 1;
00329                 ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
00330                 i__1 = kc + k + kp - 1;
00331                 ap[i__1].r = temp.r, ap[i__1].i = temp.i;
00332             }
00333         }
00334 
00335         k += kstep;
00336         kc = kcnext;
00337         goto L30;
00338 L50:
00339 
00340         ;
00341     } else {
00342 
00343 /*        Compute inv(A) from the factorization A = L*D*L'. */
00344 
00345 /*        K is the main loop index, increasing from 1 to N in steps of */
00346 /*        1 or 2, depending on the size of the diagonal blocks. */
00347 
00348         npp = *n * (*n + 1) / 2;
00349         k = *n;
00350         kc = npp;
00351 L60:
00352 
00353 /*        If K < 1, exit from loop. */
00354 
00355         if (k < 1) {
00356             goto L80;
00357         }
00358 
00359         kcnext = kc - (*n - k + 2);
00360         if (ipiv[k] > 0) {
00361 
00362 /*           1 x 1 diagonal block */
00363 
00364 /*           Invert the diagonal block. */
00365 
00366             i__1 = kc;
00367             i__2 = kc;
00368             d__1 = 1. / ap[i__2].r;
00369             ap[i__1].r = d__1, ap[i__1].i = 0.;
00370 
00371 /*           Compute column K of the inverse. */
00372 
00373             if (k < *n) {
00374                 i__1 = *n - k;
00375                 zcopy_(&i__1, &ap[kc + 1], &c__1, &work[1], &c__1);
00376                 i__1 = *n - k;
00377                 z__1.r = -1., z__1.i = -0.;
00378                 zhpmv_(uplo, &i__1, &z__1, &ap[kc + *n - k + 1], &work[1], &
00379                         c__1, &c_b2, &ap[kc + 1], &c__1);
00380                 i__1 = kc;
00381                 i__2 = kc;
00382                 i__3 = *n - k;
00383                 zdotc_(&z__2, &i__3, &work[1], &c__1, &ap[kc + 1], &c__1);
00384                 d__1 = z__2.r;
00385                 z__1.r = ap[i__2].r - d__1, z__1.i = ap[i__2].i;
00386                 ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
00387             }
00388             kstep = 1;
00389         } else {
00390 
00391 /*           2 x 2 diagonal block */
00392 
00393 /*           Invert the diagonal block. */
00394 
00395             t = z_abs(&ap[kcnext + 1]);
00396             i__1 = kcnext;
00397             ak = ap[i__1].r / t;
00398             i__1 = kc;
00399             akp1 = ap[i__1].r / t;
00400             i__1 = kcnext + 1;
00401             z__1.r = ap[i__1].r / t, z__1.i = ap[i__1].i / t;
00402             akkp1.r = z__1.r, akkp1.i = z__1.i;
00403             d__ = t * (ak * akp1 - 1.);
00404             i__1 = kcnext;
00405             d__1 = akp1 / d__;
00406             ap[i__1].r = d__1, ap[i__1].i = 0.;
00407             i__1 = kc;
00408             d__1 = ak / d__;
00409             ap[i__1].r = d__1, ap[i__1].i = 0.;
00410             i__1 = kcnext + 1;
00411             z__2.r = -akkp1.r, z__2.i = -akkp1.i;
00412             z__1.r = z__2.r / d__, z__1.i = z__2.i / d__;
00413             ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
00414 
00415 /*           Compute columns K-1 and K of the inverse. */
00416 
00417             if (k < *n) {
00418                 i__1 = *n - k;
00419                 zcopy_(&i__1, &ap[kc + 1], &c__1, &work[1], &c__1);
00420                 i__1 = *n - k;
00421                 z__1.r = -1., z__1.i = -0.;
00422                 zhpmv_(uplo, &i__1, &z__1, &ap[kc + (*n - k + 1)], &work[1], &
00423                         c__1, &c_b2, &ap[kc + 1], &c__1);
00424                 i__1 = kc;
00425                 i__2 = kc;
00426                 i__3 = *n - k;
00427                 zdotc_(&z__2, &i__3, &work[1], &c__1, &ap[kc + 1], &c__1);
00428                 d__1 = z__2.r;
00429                 z__1.r = ap[i__2].r - d__1, z__1.i = ap[i__2].i;
00430                 ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
00431                 i__1 = kcnext + 1;
00432                 i__2 = kcnext + 1;
00433                 i__3 = *n - k;
00434                 zdotc_(&z__2, &i__3, &ap[kc + 1], &c__1, &ap[kcnext + 2], &
00435                         c__1);
00436                 z__1.r = ap[i__2].r - z__2.r, z__1.i = ap[i__2].i - z__2.i;
00437                 ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
00438                 i__1 = *n - k;
00439                 zcopy_(&i__1, &ap[kcnext + 2], &c__1, &work[1], &c__1);
00440                 i__1 = *n - k;
00441                 z__1.r = -1., z__1.i = -0.;
00442                 zhpmv_(uplo, &i__1, &z__1, &ap[kc + (*n - k + 1)], &work[1], &
00443                         c__1, &c_b2, &ap[kcnext + 2], &c__1);
00444                 i__1 = kcnext;
00445                 i__2 = kcnext;
00446                 i__3 = *n - k;
00447                 zdotc_(&z__2, &i__3, &work[1], &c__1, &ap[kcnext + 2], &c__1);
00448                 d__1 = z__2.r;
00449                 z__1.r = ap[i__2].r - d__1, z__1.i = ap[i__2].i;
00450                 ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
00451             }
00452             kstep = 2;
00453             kcnext -= *n - k + 3;
00454         }
00455 
00456         kp = (i__1 = ipiv[k], abs(i__1));
00457         if (kp != k) {
00458 
00459 /*           Interchange rows and columns K and KP in the trailing */
00460 /*           submatrix A(k-1:n,k-1:n) */
00461 
00462             kpc = npp - (*n - kp + 1) * (*n - kp + 2) / 2 + 1;
00463             if (kp < *n) {
00464                 i__1 = *n - kp;
00465                 zswap_(&i__1, &ap[kc + kp - k + 1], &c__1, &ap[kpc + 1], &
00466                         c__1);
00467             }
00468             kx = kc + kp - k;
00469             i__1 = kp - 1;
00470             for (j = k + 1; j <= i__1; ++j) {
00471                 kx = kx + *n - j + 1;
00472                 d_cnjg(&z__1, &ap[kc + j - k]);
00473                 temp.r = z__1.r, temp.i = z__1.i;
00474                 i__2 = kc + j - k;
00475                 d_cnjg(&z__1, &ap[kx]);
00476                 ap[i__2].r = z__1.r, ap[i__2].i = z__1.i;
00477                 i__2 = kx;
00478                 ap[i__2].r = temp.r, ap[i__2].i = temp.i;
00479 /* L70: */
00480             }
00481             i__1 = kc + kp - k;
00482             d_cnjg(&z__1, &ap[kc + kp - k]);
00483             ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
00484             i__1 = kc;
00485             temp.r = ap[i__1].r, temp.i = ap[i__1].i;
00486             i__1 = kc;
00487             i__2 = kpc;
00488             ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
00489             i__1 = kpc;
00490             ap[i__1].r = temp.r, ap[i__1].i = temp.i;
00491             if (kstep == 2) {
00492                 i__1 = kc - *n + k - 1;
00493                 temp.r = ap[i__1].r, temp.i = ap[i__1].i;
00494                 i__1 = kc - *n + k - 1;
00495                 i__2 = kc - *n + kp - 1;
00496                 ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
00497                 i__1 = kc - *n + kp - 1;
00498                 ap[i__1].r = temp.r, ap[i__1].i = temp.i;
00499             }
00500         }
00501 
00502         k -= kstep;
00503         kc = kcnext;
00504         goto L60;
00505 L80:
00506         ;
00507     }
00508 
00509     return 0;
00510 
00511 /*     End of ZHPTRI */
00512 
00513 } /* zhptri_ */

swiftnav
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autogenerated on Sat Jun 8 2019 18:56:39