csptri.c
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00001 /* csptri.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_b1 = {1.f,0.f};
00019 static complex c_b2 = {0.f,0.f};
00020 static integer c__1 = 1;
00021 
00022 /* Subroutine */ int csptri_(char *uplo, integer *n, complex *ap, integer *
00023         ipiv, complex *work, integer *info)
00024 {
00025     /* System generated locals */
00026     integer i__1, i__2, i__3;
00027     complex q__1, q__2, q__3;
00028 
00029     /* Builtin functions */
00030     void c_div(complex *, complex *, complex *);
00031 
00032     /* Local variables */
00033     complex d__;
00034     integer j, k;
00035     complex t, ak;
00036     integer kc, kp, kx, kpc, npp;
00037     complex akp1, temp, akkp1;
00038     extern logical lsame_(char *, char *);
00039     extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, 
00040             complex *, integer *);
00041     extern /* Complex */ VOID cdotu_(complex *, integer *, complex *, integer 
00042             *, complex *, integer *);
00043     extern /* Subroutine */ int cswap_(integer *, complex *, integer *, 
00044             complex *, integer *);
00045     integer kstep;
00046     extern /* Subroutine */ int cspmv_(char *, integer *, complex *, complex *
00047 , complex *, integer *, complex *, complex *, integer *);
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 /*  CSPTRI computes the inverse of a complex symmetric indefinite matrix */
00066 /*  A in packed storage using the factorization A = U*D*U**T or */
00067 /*  A = L*D*L**T computed by CSPTRF. */
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**T; */
00076 /*          = 'L':  Lower triangular, form is A = L*D*L**T. */
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 CSPTRF, */
00084 /*          stored as a packed triangular matrix. */
00085 
00086 /*          On exit, if INFO = 0, the (symmetric) 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 CSPTRF. */
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_("CSPTRI", &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             c_div(&q__1, &c_b1, &ap[kc + k - 1]);
00204             ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00205 
00206 /*           Compute column K of the inverse. */
00207 
00208             if (k > 1) {
00209                 i__1 = k - 1;
00210                 ccopy_(&i__1, &ap[kc], &c__1, &work[1], &c__1);
00211                 i__1 = k - 1;
00212                 q__1.r = -1.f, q__1.i = -0.f;
00213                 cspmv_(uplo, &i__1, &q__1, &ap[1], &work[1], &c__1, &c_b2, &
00214                         ap[kc], &c__1);
00215                 i__1 = kc + k - 1;
00216                 i__2 = kc + k - 1;
00217                 i__3 = k - 1;
00218                 cdotu_(&q__2, &i__3, &work[1], &c__1, &ap[kc], &c__1);
00219                 q__1.r = ap[i__2].r - q__2.r, q__1.i = ap[i__2].i - q__2.i;
00220                 ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00221             }
00222             kstep = 1;
00223         } else {
00224 
00225 /*           2 x 2 diagonal block */
00226 
00227 /*           Invert the diagonal block. */
00228 
00229             i__1 = kcnext + k - 1;
00230             t.r = ap[i__1].r, t.i = ap[i__1].i;
00231             c_div(&q__1, &ap[kc + k - 1], &t);
00232             ak.r = q__1.r, ak.i = q__1.i;
00233             c_div(&q__1, &ap[kcnext + k], &t);
00234             akp1.r = q__1.r, akp1.i = q__1.i;
00235             c_div(&q__1, &ap[kcnext + k - 1], &t);
00236             akkp1.r = q__1.r, akkp1.i = q__1.i;
00237             q__3.r = ak.r * akp1.r - ak.i * akp1.i, q__3.i = ak.r * akp1.i + 
00238                     ak.i * akp1.r;
00239             q__2.r = q__3.r - 1.f, q__2.i = q__3.i - 0.f;
00240             q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r * q__2.i + t.i 
00241                     * q__2.r;
00242             d__.r = q__1.r, d__.i = q__1.i;
00243             i__1 = kc + k - 1;
00244             c_div(&q__1, &akp1, &d__);
00245             ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00246             i__1 = kcnext + k;
00247             c_div(&q__1, &ak, &d__);
00248             ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00249             i__1 = kcnext + k - 1;
00250             q__2.r = -akkp1.r, q__2.i = -akkp1.i;
00251             c_div(&q__1, &q__2, &d__);
00252             ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00253 
00254 /*           Compute columns K and K+1 of the inverse. */
00255 
00256             if (k > 1) {
00257                 i__1 = k - 1;
00258                 ccopy_(&i__1, &ap[kc], &c__1, &work[1], &c__1);
00259                 i__1 = k - 1;
00260                 q__1.r = -1.f, q__1.i = -0.f;
00261                 cspmv_(uplo, &i__1, &q__1, &ap[1], &work[1], &c__1, &c_b2, &
00262                         ap[kc], &c__1);
00263                 i__1 = kc + k - 1;
00264                 i__2 = kc + k - 1;
00265                 i__3 = k - 1;
00266                 cdotu_(&q__2, &i__3, &work[1], &c__1, &ap[kc], &c__1);
00267                 q__1.r = ap[i__2].r - q__2.r, q__1.i = ap[i__2].i - q__2.i;
00268                 ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00269                 i__1 = kcnext + k - 1;
00270                 i__2 = kcnext + k - 1;
00271                 i__3 = k - 1;
00272                 cdotu_(&q__2, &i__3, &ap[kc], &c__1, &ap[kcnext], &c__1);
00273                 q__1.r = ap[i__2].r - q__2.r, q__1.i = ap[i__2].i - q__2.i;
00274                 ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00275                 i__1 = k - 1;
00276                 ccopy_(&i__1, &ap[kcnext], &c__1, &work[1], &c__1);
00277                 i__1 = k - 1;
00278                 q__1.r = -1.f, q__1.i = -0.f;
00279                 cspmv_(uplo, &i__1, &q__1, &ap[1], &work[1], &c__1, &c_b2, &
00280                         ap[kcnext], &c__1);
00281                 i__1 = kcnext + k;
00282                 i__2 = kcnext + k;
00283                 i__3 = k - 1;
00284                 cdotu_(&q__2, &i__3, &work[1], &c__1, &ap[kcnext], &c__1);
00285                 q__1.r = ap[i__2].r - q__2.r, q__1.i = ap[i__2].i - q__2.i;
00286                 ap[i__1].r = q__1.r, ap[i__1].i = q__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             cswap_(&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                 i__2 = kc + j - 1;
00306                 temp.r = ap[i__2].r, temp.i = ap[i__2].i;
00307                 i__2 = kc + j - 1;
00308                 i__3 = kx;
00309                 ap[i__2].r = ap[i__3].r, ap[i__2].i = ap[i__3].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 + k - 1;
00315             temp.r = ap[i__1].r, temp.i = ap[i__1].i;
00316             i__1 = kc + k - 1;
00317             i__2 = kpc + kp - 1;
00318             ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
00319             i__1 = kpc + kp - 1;
00320             ap[i__1].r = temp.r, ap[i__1].i = temp.i;
00321             if (kstep == 2) {
00322                 i__1 = kc + k + k - 1;
00323                 temp.r = ap[i__1].r, temp.i = ap[i__1].i;
00324                 i__1 = kc + k + k - 1;
00325                 i__2 = kc + k + kp - 1;
00326                 ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
00327                 i__1 = kc + k + kp - 1;
00328                 ap[i__1].r = temp.r, ap[i__1].i = temp.i;
00329             }
00330         }
00331 
00332         k += kstep;
00333         kc = kcnext;
00334         goto L30;
00335 L50:
00336 
00337         ;
00338     } else {
00339 
00340 /*        Compute inv(A) from the factorization A = L*D*L'. */
00341 
00342 /*        K is the main loop index, increasing from 1 to N in steps of */
00343 /*        1 or 2, depending on the size of the diagonal blocks. */
00344 
00345         npp = *n * (*n + 1) / 2;
00346         k = *n;
00347         kc = npp;
00348 L60:
00349 
00350 /*        If K < 1, exit from loop. */
00351 
00352         if (k < 1) {
00353             goto L80;
00354         }
00355 
00356         kcnext = kc - (*n - k + 2);
00357         if (ipiv[k] > 0) {
00358 
00359 /*           1 x 1 diagonal block */
00360 
00361 /*           Invert the diagonal block. */
00362 
00363             i__1 = kc;
00364             c_div(&q__1, &c_b1, &ap[kc]);
00365             ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00366 
00367 /*           Compute column K of the inverse. */
00368 
00369             if (k < *n) {
00370                 i__1 = *n - k;
00371                 ccopy_(&i__1, &ap[kc + 1], &c__1, &work[1], &c__1);
00372                 i__1 = *n - k;
00373                 q__1.r = -1.f, q__1.i = -0.f;
00374                 cspmv_(uplo, &i__1, &q__1, &ap[kc + *n - k + 1], &work[1], &
00375                         c__1, &c_b2, &ap[kc + 1], &c__1);
00376                 i__1 = kc;
00377                 i__2 = kc;
00378                 i__3 = *n - k;
00379                 cdotu_(&q__2, &i__3, &work[1], &c__1, &ap[kc + 1], &c__1);
00380                 q__1.r = ap[i__2].r - q__2.r, q__1.i = ap[i__2].i - q__2.i;
00381                 ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00382             }
00383             kstep = 1;
00384         } else {
00385 
00386 /*           2 x 2 diagonal block */
00387 
00388 /*           Invert the diagonal block. */
00389 
00390             i__1 = kcnext + 1;
00391             t.r = ap[i__1].r, t.i = ap[i__1].i;
00392             c_div(&q__1, &ap[kcnext], &t);
00393             ak.r = q__1.r, ak.i = q__1.i;
00394             c_div(&q__1, &ap[kc], &t);
00395             akp1.r = q__1.r, akp1.i = q__1.i;
00396             c_div(&q__1, &ap[kcnext + 1], &t);
00397             akkp1.r = q__1.r, akkp1.i = q__1.i;
00398             q__3.r = ak.r * akp1.r - ak.i * akp1.i, q__3.i = ak.r * akp1.i + 
00399                     ak.i * akp1.r;
00400             q__2.r = q__3.r - 1.f, q__2.i = q__3.i - 0.f;
00401             q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r * q__2.i + t.i 
00402                     * q__2.r;
00403             d__.r = q__1.r, d__.i = q__1.i;
00404             i__1 = kcnext;
00405             c_div(&q__1, &akp1, &d__);
00406             ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00407             i__1 = kc;
00408             c_div(&q__1, &ak, &d__);
00409             ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00410             i__1 = kcnext + 1;
00411             q__2.r = -akkp1.r, q__2.i = -akkp1.i;
00412             c_div(&q__1, &q__2, &d__);
00413             ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00414 
00415 /*           Compute columns K-1 and K of the inverse. */
00416 
00417             if (k < *n) {
00418                 i__1 = *n - k;
00419                 ccopy_(&i__1, &ap[kc + 1], &c__1, &work[1], &c__1);
00420                 i__1 = *n - k;
00421                 q__1.r = -1.f, q__1.i = -0.f;
00422                 cspmv_(uplo, &i__1, &q__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                 cdotu_(&q__2, &i__3, &work[1], &c__1, &ap[kc + 1], &c__1);
00428                 q__1.r = ap[i__2].r - q__2.r, q__1.i = ap[i__2].i - q__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                 cdotu_(&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                 cspmv_(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                 cdotu_(&q__2, &i__3, &work[1], &c__1, &ap[kcnext + 2], &c__1);
00447                 q__1.r = ap[i__2].r - q__2.r, q__1.i = ap[i__2].i - q__2.i;
00448                 ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
00449             }
00450             kstep = 2;
00451             kcnext -= *n - k + 3;
00452         }
00453 
00454         kp = (i__1 = ipiv[k], abs(i__1));
00455         if (kp != k) {
00456 
00457 /*           Interchange rows and columns K and KP in the trailing */
00458 /*           submatrix A(k-1:n,k-1:n) */
00459 
00460             kpc = npp - (*n - kp + 1) * (*n - kp + 2) / 2 + 1;
00461             if (kp < *n) {
00462                 i__1 = *n - kp;
00463                 cswap_(&i__1, &ap[kc + kp - k + 1], &c__1, &ap[kpc + 1], &
00464                         c__1);
00465             }
00466             kx = kc + kp - k;
00467             i__1 = kp - 1;
00468             for (j = k + 1; j <= i__1; ++j) {
00469                 kx = kx + *n - j + 1;
00470                 i__2 = kc + j - k;
00471                 temp.r = ap[i__2].r, temp.i = ap[i__2].i;
00472                 i__2 = kc + j - k;
00473                 i__3 = kx;
00474                 ap[i__2].r = ap[i__3].r, ap[i__2].i = ap[i__3].i;
00475                 i__2 = kx;
00476                 ap[i__2].r = temp.r, ap[i__2].i = temp.i;
00477 /* L70: */
00478             }
00479             i__1 = kc;
00480             temp.r = ap[i__1].r, temp.i = ap[i__1].i;
00481             i__1 = kc;
00482             i__2 = kpc;
00483             ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
00484             i__1 = kpc;
00485             ap[i__1].r = temp.r, ap[i__1].i = temp.i;
00486             if (kstep == 2) {
00487                 i__1 = kc - *n + k - 1;
00488                 temp.r = ap[i__1].r, temp.i = ap[i__1].i;
00489                 i__1 = kc - *n + k - 1;
00490                 i__2 = kc - *n + kp - 1;
00491                 ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
00492                 i__1 = kc - *n + kp - 1;
00493                 ap[i__1].r = temp.r, ap[i__1].i = temp.i;
00494             }
00495         }
00496 
00497         k -= kstep;
00498         kc = kcnext;
00499         goto L60;
00500 L80:
00501         ;
00502     }
00503 
00504     return 0;
00505 
00506 /*     End of CSPTRI */
00507 
00508 } /* csptri_ */

swiftnav
Author(s):
autogenerated on Sat Jun 8 2019 18:55:33