chptri.c
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00001 /* chptri.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 complex c_b2 = {0.f,0.f};
00019 static integer c__1 = 1;
00020 
00021 /* Subroutine */ int chptri_(char *uplo, integer *n, complex *ap, integer *
00022         ipiv, complex *work, integer *info)
00023 {
00024     /* System generated locals */
00025     integer i__1, i__2, i__3;
00026     real r__1;
00027     complex q__1, q__2;
00028 
00029     /* Builtin functions */
00030     double c_abs(complex *);
00031     void r_cnjg(complex *, complex *);
00032 
00033     /* Local variables */
00034     real d__;
00035     integer j, k;
00036     real t, ak;
00037     integer kc, kp, kx, kpc, npp;
00038     real akp1;
00039     complex temp, akkp1;
00040     extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer 
00041             *, complex *, integer *);
00042     extern logical lsame_(char *, char *);
00043     extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, 
00044             complex *, integer *), chpmv_(char *, integer *, complex *, 
00045             complex *, complex *, integer *, complex *, complex *, integer *), cswap_(integer *, complex *, integer *, complex *, 
00046             integer *);
00047     integer kstep;
00048     logical upper;
00049     extern /* Subroutine */ int xerbla_(char *, integer *);
00050     integer kcnext;
00051 
00052 
00053 /*  -- LAPACK routine (version 3.2) -- */
00054 /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
00055 /*     November 2006 */
00056 
00057 /*     .. Scalar Arguments .. */
00058 /*     .. */
00059 /*     .. Array Arguments .. */
00060 /*     .. */
00061 
00062 /*  Purpose */
00063 /*  ======= */
00064 
00065 /*  CHPTRI computes the inverse of a complex Hermitian indefinite matrix */
00066 /*  A in packed storage using the factorization A = U*D*U**H or */
00067 /*  A = L*D*L**H computed by CHPTRF. */
00068 
00069 /*  Arguments */
00070 /*  ========= */
00071 
00072 /*  UPLO    (input) CHARACTER*1 */
00073 /*          Specifies whether the details of the factorization are stored */
00074 /*          as an upper or lower triangular matrix. */
00075 /*          = 'U':  Upper triangular, form is A = U*D*U**H; */
00076 /*          = 'L':  Lower triangular, form is A = L*D*L**H. */
00077 
00078 /*  N       (input) INTEGER */
00079 /*          The order of the matrix A.  N >= 0. */
00080 
00081 /*  AP      (input/output) COMPLEX array, dimension (N*(N+1)/2) */
00082 /*          On entry, the block diagonal matrix D and the multipliers */
00083 /*          used to obtain the factor U or L as computed by CHPTRF, */
00084 /*          stored as a packed triangular matrix. */
00085 
00086 /*          On exit, if INFO = 0, the (Hermitian) inverse of the original */
00087 /*          matrix, stored as a packed triangular matrix. The j-th column */
00088 /*          of inv(A) is stored in the array AP as follows: */
00089 /*          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j; */
00090 /*          if UPLO = 'L', */
00091 /*             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n. */
00092 
00093 /*  IPIV    (input) INTEGER array, dimension (N) */
00094 /*          Details of the interchanges and the block structure of D */
00095 /*          as determined by CHPTRF. */
00096 
00097 /*  WORK    (workspace) COMPLEX array, dimension (N) */
00098 
00099 /*  INFO    (output) INTEGER */
00100 /*          = 0: successful exit */
00101 /*          < 0: if INFO = -i, the i-th argument had an illegal value */
00102 /*          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its */
00103 /*               inverse could not be computed. */
00104 
00105 /*  ===================================================================== */
00106 
00107 /*     .. Parameters .. */
00108 /*     .. */
00109 /*     .. Local Scalars .. */
00110 /*     .. */
00111 /*     .. External Functions .. */
00112 /*     .. */
00113 /*     .. External Subroutines .. */
00114 /*     .. */
00115 /*     .. Intrinsic Functions .. */
00116 /*     .. */
00117 /*     .. Executable Statements .. */
00118 
00119 /*     Test the input parameters. */
00120 
00121     /* Parameter adjustments */
00122     --work;
00123     --ipiv;
00124     --ap;
00125 
00126     /* Function Body */
00127     *info = 0;
00128     upper = lsame_(uplo, "U");
00129     if (! upper && ! lsame_(uplo, "L")) {
00130         *info = -1;
00131     } else if (*n < 0) {
00132         *info = -2;
00133     }
00134     if (*info != 0) {
00135         i__1 = -(*info);
00136         xerbla_("CHPTRI", &i__1);
00137         return 0;
00138     }
00139 
00140 /*     Quick return if possible */
00141 
00142     if (*n == 0) {
00143         return 0;
00144     }
00145 
00146 /*     Check that the diagonal matrix D is nonsingular. */
00147 
00148     if (upper) {
00149 
00150 /*        Upper triangular storage: examine D from bottom to top */
00151 
00152         kp = *n * (*n + 1) / 2;
00153         for (*info = *n; *info >= 1; --(*info)) {
00154             i__1 = kp;
00155             if (ipiv[*info] > 0 && (ap[i__1].r == 0.f && ap[i__1].i == 0.f)) {
00156                 return 0;
00157             }
00158             kp -= *info;
00159 /* L10: */
00160         }
00161     } else {
00162 
00163 /*        Lower triangular storage: examine D from top to bottom. */
00164 
00165         kp = 1;
00166         i__1 = *n;
00167         for (*info = 1; *info <= i__1; ++(*info)) {
00168             i__2 = kp;
00169             if (ipiv[*info] > 0 && (ap[i__2].r == 0.f && ap[i__2].i == 0.f)) {
00170                 return 0;
00171             }
00172             kp = kp + *n - *info + 1;
00173 /* L20: */
00174         }
00175     }
00176     *info = 0;
00177 
00178     if (upper) {
00179 
00180 /*        Compute inv(A) from the factorization A = U*D*U'. */
00181 
00182 /*        K is the main loop index, increasing from 1 to N in steps of */
00183 /*        1 or 2, depending on the size of the diagonal blocks. */
00184 
00185         k = 1;
00186         kc = 1;
00187 L30:
00188 
00189 /*        If K > N, exit from loop. */
00190 
00191         if (k > *n) {
00192             goto L50;
00193         }
00194 
00195         kcnext = kc + k;
00196         if (ipiv[k] > 0) {
00197 
00198 /*           1 x 1 diagonal block */
00199 
00200 /*           Invert the diagonal block. */
00201 
00202             i__1 = kc + k - 1;
00203             i__2 = kc + k - 1;
00204             r__1 = 1.f / ap[i__2].r;
00205             ap[i__1].r = r__1, ap[i__1].i = 0.f;
00206 
00207 /*           Compute column K of the inverse. */
00208 
00209             if (k > 1) {
00210                 i__1 = k - 1;
00211                 ccopy_(&i__1, &ap[kc], &c__1, &work[1], &c__1);
00212                 i__1 = k - 1;
00213                 q__1.r = -1.f, q__1.i = -0.f;
00214                 chpmv_(uplo, &i__1, &q__1, &ap[1], &work[1], &c__1, &c_b2, &
00215                         ap[kc], &c__1);
00216                 i__1 = kc + k - 1;
00217                 i__2 = kc + k - 1;
00218                 i__3 = k - 1;
00219                 cdotc_(&q__2, &i__3, &work[1], &c__1, &ap[kc], &c__1);
00220                 r__1 = q__2.r;
00221                 q__1.r = ap[i__2].r - r__1, q__1.i = ap[i__2].i;
00222                 ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00223             }
00224             kstep = 1;
00225         } else {
00226 
00227 /*           2 x 2 diagonal block */
00228 
00229 /*           Invert the diagonal block. */
00230 
00231             t = c_abs(&ap[kcnext + k - 1]);
00232             i__1 = kc + k - 1;
00233             ak = ap[i__1].r / t;
00234             i__1 = kcnext + k;
00235             akp1 = ap[i__1].r / t;
00236             i__1 = kcnext + k - 1;
00237             q__1.r = ap[i__1].r / t, q__1.i = ap[i__1].i / t;
00238             akkp1.r = q__1.r, akkp1.i = q__1.i;
00239             d__ = t * (ak * akp1 - 1.f);
00240             i__1 = kc + k - 1;
00241             r__1 = akp1 / d__;
00242             ap[i__1].r = r__1, ap[i__1].i = 0.f;
00243             i__1 = kcnext + k;
00244             r__1 = ak / d__;
00245             ap[i__1].r = r__1, ap[i__1].i = 0.f;
00246             i__1 = kcnext + k - 1;
00247             q__2.r = -akkp1.r, q__2.i = -akkp1.i;
00248             q__1.r = q__2.r / d__, q__1.i = q__2.i / d__;
00249             ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00250 
00251 /*           Compute columns K and K+1 of the inverse. */
00252 
00253             if (k > 1) {
00254                 i__1 = k - 1;
00255                 ccopy_(&i__1, &ap[kc], &c__1, &work[1], &c__1);
00256                 i__1 = k - 1;
00257                 q__1.r = -1.f, q__1.i = -0.f;
00258                 chpmv_(uplo, &i__1, &q__1, &ap[1], &work[1], &c__1, &c_b2, &
00259                         ap[kc], &c__1);
00260                 i__1 = kc + k - 1;
00261                 i__2 = kc + k - 1;
00262                 i__3 = k - 1;
00263                 cdotc_(&q__2, &i__3, &work[1], &c__1, &ap[kc], &c__1);
00264                 r__1 = q__2.r;
00265                 q__1.r = ap[i__2].r - r__1, q__1.i = ap[i__2].i;
00266                 ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00267                 i__1 = kcnext + k - 1;
00268                 i__2 = kcnext + k - 1;
00269                 i__3 = k - 1;
00270                 cdotc_(&q__2, &i__3, &ap[kc], &c__1, &ap[kcnext], &c__1);
00271                 q__1.r = ap[i__2].r - q__2.r, q__1.i = ap[i__2].i - q__2.i;
00272                 ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00273                 i__1 = k - 1;
00274                 ccopy_(&i__1, &ap[kcnext], &c__1, &work[1], &c__1);
00275                 i__1 = k - 1;
00276                 q__1.r = -1.f, q__1.i = -0.f;
00277                 chpmv_(uplo, &i__1, &q__1, &ap[1], &work[1], &c__1, &c_b2, &
00278                         ap[kcnext], &c__1);
00279                 i__1 = kcnext + k;
00280                 i__2 = kcnext + k;
00281                 i__3 = k - 1;
00282                 cdotc_(&q__2, &i__3, &work[1], &c__1, &ap[kcnext], &c__1);
00283                 r__1 = q__2.r;
00284                 q__1.r = ap[i__2].r - r__1, q__1.i = ap[i__2].i;
00285                 ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00286             }
00287             kstep = 2;
00288             kcnext = kcnext + k + 1;
00289         }
00290 
00291         kp = (i__1 = ipiv[k], abs(i__1));
00292         if (kp != k) {
00293 
00294 /*           Interchange rows and columns K and KP in the leading */
00295 /*           submatrix A(1:k+1,1:k+1) */
00296 
00297             kpc = (kp - 1) * kp / 2 + 1;
00298             i__1 = kp - 1;
00299             cswap_(&i__1, &ap[kc], &c__1, &ap[kpc], &c__1);
00300             kx = kpc + kp - 1;
00301             i__1 = k - 1;
00302             for (j = kp + 1; j <= i__1; ++j) {
00303                 kx = kx + j - 1;
00304                 r_cnjg(&q__1, &ap[kc + j - 1]);
00305                 temp.r = q__1.r, temp.i = q__1.i;
00306                 i__2 = kc + j - 1;
00307                 r_cnjg(&q__1, &ap[kx]);
00308                 ap[i__2].r = q__1.r, ap[i__2].i = q__1.i;
00309                 i__2 = kx;
00310                 ap[i__2].r = temp.r, ap[i__2].i = temp.i;
00311 /* L40: */
00312             }
00313             i__1 = kc + kp - 1;
00314             r_cnjg(&q__1, &ap[kc + kp - 1]);
00315             ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00316             i__1 = kc + k - 1;
00317             temp.r = ap[i__1].r, temp.i = ap[i__1].i;
00318             i__1 = kc + k - 1;
00319             i__2 = kpc + kp - 1;
00320             ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
00321             i__1 = kpc + kp - 1;
00322             ap[i__1].r = temp.r, ap[i__1].i = temp.i;
00323             if (kstep == 2) {
00324                 i__1 = kc + k + k - 1;
00325                 temp.r = ap[i__1].r, temp.i = ap[i__1].i;
00326                 i__1 = kc + k + k - 1;
00327                 i__2 = kc + k + kp - 1;
00328                 ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
00329                 i__1 = kc + k + kp - 1;
00330                 ap[i__1].r = temp.r, ap[i__1].i = temp.i;
00331             }
00332         }
00333 
00334         k += kstep;
00335         kc = kcnext;
00336         goto L30;
00337 L50:
00338 
00339         ;
00340     } else {
00341 
00342 /*        Compute inv(A) from the factorization A = L*D*L'. */
00343 
00344 /*        K is the main loop index, increasing from 1 to N in steps of */
00345 /*        1 or 2, depending on the size of the diagonal blocks. */
00346 
00347         npp = *n * (*n + 1) / 2;
00348         k = *n;
00349         kc = npp;
00350 L60:
00351 
00352 /*        If K < 1, exit from loop. */
00353 
00354         if (k < 1) {
00355             goto L80;
00356         }
00357 
00358         kcnext = kc - (*n - k + 2);
00359         if (ipiv[k] > 0) {
00360 
00361 /*           1 x 1 diagonal block */
00362 
00363 /*           Invert the diagonal block. */
00364 
00365             i__1 = kc;
00366             i__2 = kc;
00367             r__1 = 1.f / ap[i__2].r;
00368             ap[i__1].r = r__1, ap[i__1].i = 0.f;
00369 
00370 /*           Compute column K of the inverse. */
00371 
00372             if (k < *n) {
00373                 i__1 = *n - k;
00374                 ccopy_(&i__1, &ap[kc + 1], &c__1, &work[1], &c__1);
00375                 i__1 = *n - k;
00376                 q__1.r = -1.f, q__1.i = -0.f;
00377                 chpmv_(uplo, &i__1, &q__1, &ap[kc + *n - k + 1], &work[1], &
00378                         c__1, &c_b2, &ap[kc + 1], &c__1);
00379                 i__1 = kc;
00380                 i__2 = kc;
00381                 i__3 = *n - k;
00382                 cdotc_(&q__2, &i__3, &work[1], &c__1, &ap[kc + 1], &c__1);
00383                 r__1 = q__2.r;
00384                 q__1.r = ap[i__2].r - r__1, q__1.i = ap[i__2].i;
00385                 ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00386             }
00387             kstep = 1;
00388         } else {
00389 
00390 /*           2 x 2 diagonal block */
00391 
00392 /*           Invert the diagonal block. */
00393 
00394             t = c_abs(&ap[kcnext + 1]);
00395             i__1 = kcnext;
00396             ak = ap[i__1].r / t;
00397             i__1 = kc;
00398             akp1 = ap[i__1].r / t;
00399             i__1 = kcnext + 1;
00400             q__1.r = ap[i__1].r / t, q__1.i = ap[i__1].i / t;
00401             akkp1.r = q__1.r, akkp1.i = q__1.i;
00402             d__ = t * (ak * akp1 - 1.f);
00403             i__1 = kcnext;
00404             r__1 = akp1 / d__;
00405             ap[i__1].r = r__1, ap[i__1].i = 0.f;
00406             i__1 = kc;
00407             r__1 = ak / d__;
00408             ap[i__1].r = r__1, ap[i__1].i = 0.f;
00409             i__1 = kcnext + 1;
00410             q__2.r = -akkp1.r, q__2.i = -akkp1.i;
00411             q__1.r = q__2.r / d__, q__1.i = q__2.i / d__;
00412             ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00413 
00414 /*           Compute columns K-1 and K of the inverse. */
00415 
00416             if (k < *n) {
00417                 i__1 = *n - k;
00418                 ccopy_(&i__1, &ap[kc + 1], &c__1, &work[1], &c__1);
00419                 i__1 = *n - k;
00420                 q__1.r = -1.f, q__1.i = -0.f;
00421                 chpmv_(uplo, &i__1, &q__1, &ap[kc + (*n - k + 1)], &work[1], &
00422                         c__1, &c_b2, &ap[kc + 1], &c__1);
00423                 i__1 = kc;
00424                 i__2 = kc;
00425                 i__3 = *n - k;
00426                 cdotc_(&q__2, &i__3, &work[1], &c__1, &ap[kc + 1], &c__1);
00427                 r__1 = q__2.r;
00428                 q__1.r = ap[i__2].r - r__1, q__1.i = ap[i__2].i;
00429                 ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00430                 i__1 = kcnext + 1;
00431                 i__2 = kcnext + 1;
00432                 i__3 = *n - k;
00433                 cdotc_(&q__2, &i__3, &ap[kc + 1], &c__1, &ap[kcnext + 2], &
00434                         c__1);
00435                 q__1.r = ap[i__2].r - q__2.r, q__1.i = ap[i__2].i - q__2.i;
00436                 ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00437                 i__1 = *n - k;
00438                 ccopy_(&i__1, &ap[kcnext + 2], &c__1, &work[1], &c__1);
00439                 i__1 = *n - k;
00440                 q__1.r = -1.f, q__1.i = -0.f;
00441                 chpmv_(uplo, &i__1, &q__1, &ap[kc + (*n - k + 1)], &work[1], &
00442                         c__1, &c_b2, &ap[kcnext + 2], &c__1);
00443                 i__1 = kcnext;
00444                 i__2 = kcnext;
00445                 i__3 = *n - k;
00446                 cdotc_(&q__2, &i__3, &work[1], &c__1, &ap[kcnext + 2], &c__1);
00447                 r__1 = q__2.r;
00448                 q__1.r = ap[i__2].r - r__1, q__1.i = ap[i__2].i;
00449                 ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00450             }
00451             kstep = 2;
00452             kcnext -= *n - k + 3;
00453         }
00454 
00455         kp = (i__1 = ipiv[k], abs(i__1));
00456         if (kp != k) {
00457 
00458 /*           Interchange rows and columns K and KP in the trailing */
00459 /*           submatrix A(k-1:n,k-1:n) */
00460 
00461             kpc = npp - (*n - kp + 1) * (*n - kp + 2) / 2 + 1;
00462             if (kp < *n) {
00463                 i__1 = *n - kp;
00464                 cswap_(&i__1, &ap[kc + kp - k + 1], &c__1, &ap[kpc + 1], &
00465                         c__1);
00466             }
00467             kx = kc + kp - k;
00468             i__1 = kp - 1;
00469             for (j = k + 1; j <= i__1; ++j) {
00470                 kx = kx + *n - j + 1;
00471                 r_cnjg(&q__1, &ap[kc + j - k]);
00472                 temp.r = q__1.r, temp.i = q__1.i;
00473                 i__2 = kc + j - k;
00474                 r_cnjg(&q__1, &ap[kx]);
00475                 ap[i__2].r = q__1.r, ap[i__2].i = q__1.i;
00476                 i__2 = kx;
00477                 ap[i__2].r = temp.r, ap[i__2].i = temp.i;
00478 /* L70: */
00479             }
00480             i__1 = kc + kp - k;
00481             r_cnjg(&q__1, &ap[kc + kp - k]);
00482             ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00483             i__1 = kc;
00484             temp.r = ap[i__1].r, temp.i = ap[i__1].i;
00485             i__1 = kc;
00486             i__2 = kpc;
00487             ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
00488             i__1 = kpc;
00489             ap[i__1].r = temp.r, ap[i__1].i = temp.i;
00490             if (kstep == 2) {
00491                 i__1 = kc - *n + k - 1;
00492                 temp.r = ap[i__1].r, temp.i = ap[i__1].i;
00493                 i__1 = kc - *n + k - 1;
00494                 i__2 = kc - *n + kp - 1;
00495                 ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
00496                 i__1 = kc - *n + kp - 1;
00497                 ap[i__1].r = temp.r, ap[i__1].i = temp.i;
00498             }
00499         }
00500 
00501         k -= kstep;
00502         kc = kcnext;
00503         goto L60;
00504 L80:
00505         ;
00506     }
00507 
00508     return 0;
00509 
00510 /*     End of CHPTRI */
00511 
00512 } /* chptri_ */

swiftnav
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autogenerated on Sat Jun 8 2019 18:55:29