#include #include #include #include #include #ifdef complex #undef complex #endif #ifdef I #undef I #endif #if defined(_WIN64) typedef long long BLASLONG; typedef unsigned long long BLASULONG; #else typedef long BLASLONG; typedef unsigned long BLASULONG; #endif #ifdef LAPACK_ILP64 typedef BLASLONG blasint; #if defined(_WIN64) #define blasabs(x) llabs(x) #else #define blasabs(x) labs(x) #endif #else typedef int blasint; #define blasabs(x) abs(x) #endif typedef blasint integer; typedef unsigned int uinteger; typedef char *address; typedef short int shortint; typedef float real; typedef double doublereal; typedef struct { real r, i; } complex; typedef struct { doublereal r, i; } doublecomplex; #ifdef _MSC_VER static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;} static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;} static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;} static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;} #else static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;} static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;} static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;} static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;} #endif #define pCf(z) (*_pCf(z)) #define pCd(z) (*_pCd(z)) typedef int logical; typedef short int shortlogical; typedef char logical1; typedef char integer1; #define TRUE_ (1) #define FALSE_ (0) /* Extern is for use with -E */ #ifndef Extern #define Extern extern #endif /* I/O stuff */ typedef int flag; typedef int ftnlen; typedef int ftnint; /*external read, write*/ typedef struct { flag cierr; ftnint ciunit; flag ciend; char *cifmt; ftnint cirec; } cilist; /*internal read, write*/ typedef struct { flag icierr; char *iciunit; flag iciend; char *icifmt; ftnint icirlen; ftnint icirnum; } icilist; /*open*/ typedef struct { flag oerr; ftnint ounit; char *ofnm; ftnlen ofnmlen; char *osta; char *oacc; char *ofm; ftnint orl; char *oblnk; } olist; /*close*/ typedef struct { flag cerr; ftnint cunit; char *csta; } cllist; /*rewind, backspace, endfile*/ typedef struct { flag aerr; ftnint aunit; } alist; /* inquire */ typedef struct { flag inerr; ftnint inunit; char *infile; ftnlen infilen; ftnint *inex; /*parameters in standard's order*/ ftnint *inopen; ftnint *innum; ftnint *innamed; char *inname; ftnlen innamlen; char *inacc; ftnlen inacclen; char *inseq; ftnlen inseqlen; char *indir; ftnlen indirlen; char *infmt; ftnlen infmtlen; char *inform; ftnint informlen; char *inunf; ftnlen inunflen; ftnint *inrecl; ftnint *innrec; char *inblank; ftnlen inblanklen; } inlist; #define VOID void union Multitype { /* for multiple entry points */ integer1 g; shortint h; integer i; /* longint j; */ real r; doublereal d; complex c; doublecomplex z; }; typedef union Multitype Multitype; struct Vardesc { /* for Namelist */ char *name; char *addr; ftnlen *dims; int type; }; typedef struct Vardesc Vardesc; struct Namelist { char *name; Vardesc **vars; int nvars; }; typedef struct Namelist Namelist; #define abs(x) ((x) >= 0 ? (x) : -(x)) #define dabs(x) (fabs(x)) #define f2cmin(a,b) ((a) <= (b) ? (a) : (b)) #define f2cmax(a,b) ((a) >= (b) ? (a) : (b)) #define dmin(a,b) (f2cmin(a,b)) #define dmax(a,b) (f2cmax(a,b)) #define bit_test(a,b) ((a) >> (b) & 1) #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b))) #define bit_set(a,b) ((a) | ((uinteger)1 << (b))) #define abort_() { sig_die("Fortran abort routine called", 1); } #define c_abs(z) (cabsf(Cf(z))) #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); } #ifdef _MSC_VER #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);} #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);} #else #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);} #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);} #endif #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));} #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));} #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));} //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));} #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));} #define d_abs(x) (fabs(*(x))) #define d_acos(x) (acos(*(x))) #define d_asin(x) (asin(*(x))) #define d_atan(x) (atan(*(x))) #define d_atn2(x, y) (atan2(*(x),*(y))) #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); } #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); } #define d_cos(x) (cos(*(x))) #define d_cosh(x) (cosh(*(x))) #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 ) #define d_exp(x) (exp(*(x))) #define d_imag(z) (cimag(Cd(z))) #define r_imag(z) (cimagf(Cf(z))) #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define d_log(x) (log(*(x))) #define d_mod(x, y) (fmod(*(x), *(y))) #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x))) #define d_nint(x) u_nint(*(x)) #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a))) #define d_sign(a,b) u_sign(*(a),*(b)) #define r_sign(a,b) u_sign(*(a),*(b)) #define d_sin(x) (sin(*(x))) #define d_sinh(x) (sinh(*(x))) #define d_sqrt(x) (sqrt(*(x))) #define d_tan(x) (tan(*(x))) #define d_tanh(x) (tanh(*(x))) #define i_abs(x) abs(*(x)) #define i_dnnt(x) ((integer)u_nint(*(x))) #define i_len(s, n) (n) #define i_nint(x) ((integer)u_nint(*(x))) #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b))) #define pow_dd(ap, bp) ( pow(*(ap), *(bp))) #define pow_si(B,E) spow_ui(*(B),*(E)) #define pow_ri(B,E) spow_ui(*(B),*(E)) #define pow_di(B,E) dpow_ui(*(B),*(E)) #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));} #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));} #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));} #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; } #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d)))) #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; } #define sig_die(s, kill) { exit(1); } #define s_stop(s, n) {exit(0);} static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n"; #define z_abs(z) (cabs(Cd(z))) #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));} #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));} #define myexit_() break; #define mycycle() continue; #define myceiling(w) {ceil(w)} #define myhuge(w) {HUGE_VAL} //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);} #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)} /* procedure parameter types for -A and -C++ */ #define F2C_proc_par_types 1 #ifdef __cplusplus typedef logical (*L_fp)(...); #else typedef logical (*L_fp)(); #endif static float spow_ui(float x, integer n) { float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static double dpow_ui(double x, integer n) { double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #ifdef _MSC_VER static _Fcomplex cpow_ui(complex x, integer n) { complex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i; for(u = n; ; ) { if(u & 01) pow.r *= x.r, pow.i *= x.i; if(u >>= 1) x.r *= x.r, x.i *= x.i; else break; } } _Fcomplex p={pow.r, pow.i}; return p; } #else static _Complex float cpow_ui(_Complex float x, integer n) { _Complex float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif #ifdef _MSC_VER static _Dcomplex zpow_ui(_Dcomplex x, integer n) { _Dcomplex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1]; for(u = n; ; ) { if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1]; if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1]; else break; } } _Dcomplex p = {pow._Val[0], pow._Val[1]}; return p; } #else static _Complex double zpow_ui(_Complex double x, integer n) { _Complex double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif static integer pow_ii(integer x, integer n) { integer pow; unsigned long int u; if (n <= 0) { if (n == 0 || x == 1) pow = 1; else if (x != -1) pow = x == 0 ? 1/x : 0; else n = -n; } if ((n > 0) || !(n == 0 || x == 1 || x != -1)) { u = n; for(pow = 1; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static integer dmaxloc_(double *w, integer s, integer e, integer *n) { double m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static integer smaxloc_(float *w, integer s, integer e, integer *n) { float m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) { integer n = *n_, incx = *incx_, incy = *incy_, i; #ifdef _MSC_VER _Fcomplex zdotc = {0.0, 0.0}; if (incx == 1 && incy == 1) { for (i=0;i \brief \b CSYTRI_3X */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download CSYTRI_3X + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE CSYTRI_3X( UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO ) */ /* CHARACTER UPLO */ /* INTEGER INFO, LDA, N, NB */ /* INTEGER IPIV( * ) */ /* COMPLEX*16 A( LDA, * ), E( * ), WORK( N+NB+1, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > CSYTRI_3X computes the inverse of a complex symmetric indefinite */ /* > matrix A using the factorization computed by CSYTRF_RK or CSYTRF_BK: */ /* > */ /* > A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T), */ /* > */ /* > where U (or L) is unit upper (or lower) triangular matrix, */ /* > U**T (or L**T) is the transpose of U (or L), P is a permutation */ /* > matrix, P**T is the transpose of P, and D is symmetric and block */ /* > diagonal with 1-by-1 and 2-by-2 diagonal blocks. */ /* > */ /* > This is the blocked version of the algorithm, calling Level 3 BLAS. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] UPLO */ /* > \verbatim */ /* > UPLO is CHARACTER*1 */ /* > Specifies whether the details of the factorization are */ /* > stored as an upper or lower triangular matrix. */ /* > = 'U': Upper triangle of A is stored; */ /* > = 'L': Lower triangle of A is stored. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix A. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is COMPLEX array, dimension (LDA,N) */ /* > On entry, diagonal of the block diagonal matrix D and */ /* > factors U or L as computed by CSYTRF_RK and CSYTRF_BK: */ /* > a) ONLY diagonal elements of the symmetric block diagonal */ /* > matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); */ /* > (superdiagonal (or subdiagonal) elements of D */ /* > should be provided on entry in array E), and */ /* > b) If UPLO = 'U': factor U in the superdiagonal part of A. */ /* > If UPLO = 'L': factor L in the subdiagonal part of A. */ /* > */ /* > On exit, if INFO = 0, the symmetric inverse of the original */ /* > matrix. */ /* > If UPLO = 'U': the upper triangular part of the inverse */ /* > is formed and the part of A below the diagonal is not */ /* > referenced; */ /* > If UPLO = 'L': the lower triangular part of the inverse */ /* > is formed and the part of A above the diagonal is not */ /* > referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in] E */ /* > \verbatim */ /* > E is COMPLEX array, dimension (N) */ /* > On entry, contains the superdiagonal (or subdiagonal) */ /* > elements of the symmetric block diagonal matrix D */ /* > with 1-by-1 or 2-by-2 diagonal blocks, where */ /* > If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) not referenced; */ /* > If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) not referenced. */ /* > */ /* > NOTE: For 1-by-1 diagonal block D(k), where */ /* > 1 <= k <= N, the element E(k) is not referenced in both */ /* > UPLO = 'U' or UPLO = 'L' cases. */ /* > \endverbatim */ /* > */ /* > \param[in] IPIV */ /* > \verbatim */ /* > IPIV is INTEGER array, dimension (N) */ /* > Details of the interchanges and the block structure of D */ /* > as determined by CSYTRF_RK or CSYTRF_BK. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is COMPLEX array, dimension (N+NB+1,NB+3). */ /* > \endverbatim */ /* > */ /* > \param[in] NB */ /* > \verbatim */ /* > NB is INTEGER */ /* > Block size. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if INFO = -i, the i-th argument had an illegal value */ /* > > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its */ /* > inverse could not be computed. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date June 2017 */ /* > \ingroup complexSYcomputational */ /* > \par Contributors: */ /* ================== */ /* > \verbatim */ /* > */ /* > June 2017, Igor Kozachenko, */ /* > Computer Science Division, */ /* > University of California, Berkeley */ /* > */ /* > \endverbatim */ /* ===================================================================== */ /* Subroutine */ int csytri_3x_(char *uplo, integer *n, complex *a, integer * lda, complex *e, integer *ipiv, complex *work, integer *nb, integer * info) { /* System generated locals */ integer a_dim1, a_offset, work_dim1, work_offset, i__1, i__2, i__3, i__4, i__5, i__6; complex q__1, q__2, q__3; /* Local variables */ integer invd; complex akkp1; extern /* Subroutine */ int csyswapr_(char *, integer *, complex *, integer *, integer *, integer *); complex d__; integer i__, j, k; complex t; extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *); extern logical lsame_(char *, char *); extern /* Subroutine */ int ctrmm_(char *, char *, char *, char *, integer *, integer *, complex *, complex *, integer *, complex *, integer *); logical upper; complex ak, u01_i_j__; integer u11; complex u11_i_j__; integer ip; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); integer icount; extern /* Subroutine */ int ctrtri_(char *, char *, integer *, complex *, integer *, integer *); integer nnb, cut; complex akp1, u01_ip1_j__, u11_ip1_j__; /* -- LAPACK computational routine (version 3.7.1) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* June 2017 */ /* ===================================================================== */ /* Test the input parameters. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --e; --ipiv; work_dim1 = *n + *nb + 1; work_offset = 1 + work_dim1 * 1; work -= work_offset; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*lda < f2cmax(1,*n)) { *info = -4; } /* Quick return if possible */ if (*info != 0) { i__1 = -(*info); xerbla_("CSYTRI_3X", &i__1, (ftnlen)9); return 0; } if (*n == 0) { return 0; } /* Workspace got Non-diag elements of D */ i__1 = *n; for (k = 1; k <= i__1; ++k) { i__2 = k + work_dim1; i__3 = k; work[i__2].r = e[i__3].r, work[i__2].i = e[i__3].i; } /* Check that the diagonal matrix D is nonsingular. */ if (upper) { /* Upper triangular storage: examine D from bottom to top */ for (*info = *n; *info >= 1; --(*info)) { i__1 = *info + *info * a_dim1; if (ipiv[*info] > 0 && (a[i__1].r == 0.f && a[i__1].i == 0.f)) { return 0; } } } else { /* Lower triangular storage: examine D from top to bottom. */ i__1 = *n; for (*info = 1; *info <= i__1; ++(*info)) { i__2 = *info + *info * a_dim1; if (ipiv[*info] > 0 && (a[i__2].r == 0.f && a[i__2].i == 0.f)) { return 0; } } } *info = 0; /* Splitting Workspace */ /* U01 is a block ( N, NB+1 ) */ /* The first element of U01 is in WORK( 1, 1 ) */ /* U11 is a block ( NB+1, NB+1 ) */ /* The first element of U11 is in WORK( N+1, 1 ) */ u11 = *n; /* INVD is a block ( N, 2 ) */ /* The first element of INVD is in WORK( 1, INVD ) */ invd = *nb + 2; if (upper) { /* Begin Upper */ /* invA = P * inv(U**T) * inv(D) * inv(U) * P**T. */ ctrtri_(uplo, "U", n, &a[a_offset], lda, info); /* inv(D) and inv(D) * inv(U) */ k = 1; while(k <= *n) { if (ipiv[k] > 0) { /* 1 x 1 diagonal NNB */ i__1 = k + invd * work_dim1; c_div(&q__1, &c_b1, &a[k + k * a_dim1]); work[i__1].r = q__1.r, work[i__1].i = q__1.i; i__1 = k + (invd + 1) * work_dim1; work[i__1].r = 0.f, work[i__1].i = 0.f; } else { /* 2 x 2 diagonal NNB */ i__1 = k + 1 + work_dim1; t.r = work[i__1].r, t.i = work[i__1].i; c_div(&q__1, &a[k + k * a_dim1], &t); ak.r = q__1.r, ak.i = q__1.i; c_div(&q__1, &a[k + 1 + (k + 1) * a_dim1], &t); akp1.r = q__1.r, akp1.i = q__1.i; c_div(&q__1, &work[k + 1 + work_dim1], &t); akkp1.r = q__1.r, akkp1.i = q__1.i; q__3.r = ak.r * akp1.r - ak.i * akp1.i, q__3.i = ak.r * akp1.i + ak.i * akp1.r; q__2.r = q__3.r - 1.f, q__2.i = q__3.i + 0.f; q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r * q__2.i + t.i * q__2.r; d__.r = q__1.r, d__.i = q__1.i; i__1 = k + invd * work_dim1; c_div(&q__1, &akp1, &d__); work[i__1].r = q__1.r, work[i__1].i = q__1.i; i__1 = k + 1 + (invd + 1) * work_dim1; c_div(&q__1, &ak, &d__); work[i__1].r = q__1.r, work[i__1].i = q__1.i; i__1 = k + (invd + 1) * work_dim1; q__2.r = -akkp1.r, q__2.i = -akkp1.i; c_div(&q__1, &q__2, &d__); work[i__1].r = q__1.r, work[i__1].i = q__1.i; i__1 = k + 1 + invd * work_dim1; i__2 = k + (invd + 1) * work_dim1; work[i__1].r = work[i__2].r, work[i__1].i = work[i__2].i; ++k; } ++k; } /* inv(U**T) = (inv(U))**T */ /* inv(U**T) * inv(D) * inv(U) */ cut = *n; while(cut > 0) { nnb = *nb; if (cut <= nnb) { nnb = cut; } else { icount = 0; /* count negative elements, */ i__1 = cut; for (i__ = cut + 1 - nnb; i__ <= i__1; ++i__) { if (ipiv[i__] < 0) { ++icount; } } /* need a even number for a clear cut */ if (icount % 2 == 1) { ++nnb; } } cut -= nnb; /* U01 Block */ i__1 = cut; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = nnb; for (j = 1; j <= i__2; ++j) { i__3 = i__ + j * work_dim1; i__4 = i__ + (cut + j) * a_dim1; work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i; } } /* U11 Block */ i__1 = nnb; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = u11 + i__ + i__ * work_dim1; work[i__2].r = 1.f, work[i__2].i = 0.f; i__2 = i__ - 1; for (j = 1; j <= i__2; ++j) { i__3 = u11 + i__ + j * work_dim1; work[i__3].r = 0.f, work[i__3].i = 0.f; } i__2 = nnb; for (j = i__ + 1; j <= i__2; ++j) { i__3 = u11 + i__ + j * work_dim1; i__4 = cut + i__ + (cut + j) * a_dim1; work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i; } } /* invD * U01 */ i__ = 1; while(i__ <= cut) { if (ipiv[i__] > 0) { i__1 = nnb; for (j = 1; j <= i__1; ++j) { i__2 = i__ + j * work_dim1; i__3 = i__ + invd * work_dim1; i__4 = i__ + j * work_dim1; q__1.r = work[i__3].r * work[i__4].r - work[i__3].i * work[i__4].i, q__1.i = work[i__3].r * work[ i__4].i + work[i__3].i * work[i__4].r; work[i__2].r = q__1.r, work[i__2].i = q__1.i; } } else { i__1 = nnb; for (j = 1; j <= i__1; ++j) { i__2 = i__ + j * work_dim1; u01_i_j__.r = work[i__2].r, u01_i_j__.i = work[i__2] .i; i__2 = i__ + 1 + j * work_dim1; u01_ip1_j__.r = work[i__2].r, u01_ip1_j__.i = work[ i__2].i; i__2 = i__ + j * work_dim1; i__3 = i__ + invd * work_dim1; q__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i * u01_i_j__.i, q__2.i = work[i__3].r * u01_i_j__.i + work[i__3].i * u01_i_j__.r; i__4 = i__ + (invd + 1) * work_dim1; q__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i * u01_ip1_j__.i, q__3.i = work[i__4].r * u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; work[i__2].r = q__1.r, work[i__2].i = q__1.i; i__2 = i__ + 1 + j * work_dim1; i__3 = i__ + 1 + invd * work_dim1; q__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i * u01_i_j__.i, q__2.i = work[i__3].r * u01_i_j__.i + work[i__3].i * u01_i_j__.r; i__4 = i__ + 1 + (invd + 1) * work_dim1; q__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i * u01_ip1_j__.i, q__3.i = work[i__4].r * u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; work[i__2].r = q__1.r, work[i__2].i = q__1.i; } ++i__; } ++i__; } /* invD1 * U11 */ i__ = 1; while(i__ <= nnb) { if (ipiv[cut + i__] > 0) { i__1 = nnb; for (j = i__; j <= i__1; ++j) { i__2 = u11 + i__ + j * work_dim1; i__3 = cut + i__ + invd * work_dim1; i__4 = u11 + i__ + j * work_dim1; q__1.r = work[i__3].r * work[i__4].r - work[i__3].i * work[i__4].i, q__1.i = work[i__3].r * work[ i__4].i + work[i__3].i * work[i__4].r; work[i__2].r = q__1.r, work[i__2].i = q__1.i; } } else { i__1 = nnb; for (j = i__; j <= i__1; ++j) { i__2 = u11 + i__ + j * work_dim1; u11_i_j__.r = work[i__2].r, u11_i_j__.i = work[i__2] .i; i__2 = u11 + i__ + 1 + j * work_dim1; u11_ip1_j__.r = work[i__2].r, u11_ip1_j__.i = work[ i__2].i; i__2 = u11 + i__ + j * work_dim1; i__3 = cut + i__ + invd * work_dim1; i__4 = u11 + i__ + j * work_dim1; q__2.r = work[i__3].r * work[i__4].r - work[i__3].i * work[i__4].i, q__2.i = work[i__3].r * work[ i__4].i + work[i__3].i * work[i__4].r; i__5 = cut + i__ + (invd + 1) * work_dim1; i__6 = u11 + i__ + 1 + j * work_dim1; q__3.r = work[i__5].r * work[i__6].r - work[i__5].i * work[i__6].i, q__3.i = work[i__5].r * work[ i__6].i + work[i__5].i * work[i__6].r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; work[i__2].r = q__1.r, work[i__2].i = q__1.i; i__2 = u11 + i__ + 1 + j * work_dim1; i__3 = cut + i__ + 1 + invd * work_dim1; q__2.r = work[i__3].r * u11_i_j__.r - work[i__3].i * u11_i_j__.i, q__2.i = work[i__3].r * u11_i_j__.i + work[i__3].i * u11_i_j__.r; i__4 = cut + i__ + 1 + (invd + 1) * work_dim1; q__3.r = work[i__4].r * u11_ip1_j__.r - work[i__4].i * u11_ip1_j__.i, q__3.i = work[i__4].r * u11_ip1_j__.i + work[i__4].i * u11_ip1_j__.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; work[i__2].r = q__1.r, work[i__2].i = q__1.i; } ++i__; } ++i__; } /* U11**T * invD1 * U11 -> U11 */ i__1 = *n + *nb + 1; ctrmm_("L", "U", "T", "U", &nnb, &nnb, &c_b1, &a[cut + 1 + (cut + 1) * a_dim1], lda, &work[u11 + 1 + work_dim1], &i__1); i__1 = nnb; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = nnb; for (j = i__; j <= i__2; ++j) { i__3 = cut + i__ + (cut + j) * a_dim1; i__4 = u11 + i__ + j * work_dim1; a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i; } } /* U01**T * invD * U01 -> A( CUT+I, CUT+J ) */ i__1 = *n + *nb + 1; i__2 = *n + *nb + 1; cgemm_("T", "N", &nnb, &nnb, &cut, &c_b1, &a[(cut + 1) * a_dim1 + 1], lda, &work[work_offset], &i__1, &c_b2, &work[u11 + 1 + work_dim1], &i__2); /* U11 = U11**T * invD1 * U11 + U01**T * invD * U01 */ i__1 = nnb; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = nnb; for (j = i__; j <= i__2; ++j) { i__3 = cut + i__ + (cut + j) * a_dim1; i__4 = cut + i__ + (cut + j) * a_dim1; i__5 = u11 + i__ + j * work_dim1; q__1.r = a[i__4].r + work[i__5].r, q__1.i = a[i__4].i + work[i__5].i; a[i__3].r = q__1.r, a[i__3].i = q__1.i; } } /* U01 = U00**T * invD0 * U01 */ i__1 = *n + *nb + 1; ctrmm_("L", uplo, "T", "U", &cut, &nnb, &c_b1, &a[a_offset], lda, &work[work_offset], &i__1); /* Update U01 */ i__1 = cut; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = nnb; for (j = 1; j <= i__2; ++j) { i__3 = i__ + (cut + j) * a_dim1; i__4 = i__ + j * work_dim1; a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i; } } /* Next Block */ } /* Apply PERMUTATIONS P and P**T: */ /* P * inv(U**T) * inv(D) * inv(U) * P**T. */ /* Interchange rows and columns I and IPIV(I) in reverse order */ /* from the formation order of IPIV vector for Upper case. */ /* ( We can use a loop over IPIV with increment 1, */ /* since the ABS value of IPIV(I) represents the row (column) */ /* index of the interchange with row (column) i in both 1x1 */ /* and 2x2 pivot cases, i.e. we don't need separate code branches */ /* for 1x1 and 2x2 pivot cases ) */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { ip = (i__2 = ipiv[i__], abs(i__2)); if (ip != i__) { if (i__ < ip) { csyswapr_(uplo, n, &a[a_offset], lda, &i__, &ip); } if (i__ > ip) { csyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__); } } } } else { /* Begin Lower */ /* inv A = P * inv(L**T) * inv(D) * inv(L) * P**T. */ ctrtri_(uplo, "U", n, &a[a_offset], lda, info); /* inv(D) and inv(D) * inv(L) */ k = *n; while(k >= 1) { if (ipiv[k] > 0) { /* 1 x 1 diagonal NNB */ i__1 = k + invd * work_dim1; c_div(&q__1, &c_b1, &a[k + k * a_dim1]); work[i__1].r = q__1.r, work[i__1].i = q__1.i; i__1 = k + (invd + 1) * work_dim1; work[i__1].r = 0.f, work[i__1].i = 0.f; } else { /* 2 x 2 diagonal NNB */ i__1 = k - 1 + work_dim1; t.r = work[i__1].r, t.i = work[i__1].i; c_div(&q__1, &a[k - 1 + (k - 1) * a_dim1], &t); ak.r = q__1.r, ak.i = q__1.i; c_div(&q__1, &a[k + k * a_dim1], &t); akp1.r = q__1.r, akp1.i = q__1.i; c_div(&q__1, &work[k - 1 + work_dim1], &t); akkp1.r = q__1.r, akkp1.i = q__1.i; q__3.r = ak.r * akp1.r - ak.i * akp1.i, q__3.i = ak.r * akp1.i + ak.i * akp1.r; q__2.r = q__3.r - 1.f, q__2.i = q__3.i + 0.f; q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r * q__2.i + t.i * q__2.r; d__.r = q__1.r, d__.i = q__1.i; i__1 = k - 1 + invd * work_dim1; c_div(&q__1, &akp1, &d__); work[i__1].r = q__1.r, work[i__1].i = q__1.i; i__1 = k + invd * work_dim1; c_div(&q__1, &ak, &d__); work[i__1].r = q__1.r, work[i__1].i = q__1.i; i__1 = k + (invd + 1) * work_dim1; q__2.r = -akkp1.r, q__2.i = -akkp1.i; c_div(&q__1, &q__2, &d__); work[i__1].r = q__1.r, work[i__1].i = q__1.i; i__1 = k - 1 + (invd + 1) * work_dim1; i__2 = k + (invd + 1) * work_dim1; work[i__1].r = work[i__2].r, work[i__1].i = work[i__2].i; --k; } --k; } /* inv(L**T) = (inv(L))**T */ /* inv(L**T) * inv(D) * inv(L) */ cut = 0; while(cut < *n) { nnb = *nb; if (cut + nnb > *n) { nnb = *n - cut; } else { icount = 0; /* count negative elements, */ i__1 = cut + nnb; for (i__ = cut + 1; i__ <= i__1; ++i__) { if (ipiv[i__] < 0) { ++icount; } } /* need a even number for a clear cut */ if (icount % 2 == 1) { ++nnb; } } /* L21 Block */ i__1 = *n - cut - nnb; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = nnb; for (j = 1; j <= i__2; ++j) { i__3 = i__ + j * work_dim1; i__4 = cut + nnb + i__ + (cut + j) * a_dim1; work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i; } } /* L11 Block */ i__1 = nnb; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = u11 + i__ + i__ * work_dim1; work[i__2].r = 1.f, work[i__2].i = 0.f; i__2 = nnb; for (j = i__ + 1; j <= i__2; ++j) { i__3 = u11 + i__ + j * work_dim1; work[i__3].r = 0.f, work[i__3].i = 0.f; } i__2 = i__ - 1; for (j = 1; j <= i__2; ++j) { i__3 = u11 + i__ + j * work_dim1; i__4 = cut + i__ + (cut + j) * a_dim1; work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i; } } /* invD*L21 */ i__ = *n - cut - nnb; while(i__ >= 1) { if (ipiv[cut + nnb + i__] > 0) { i__1 = nnb; for (j = 1; j <= i__1; ++j) { i__2 = i__ + j * work_dim1; i__3 = cut + nnb + i__ + invd * work_dim1; i__4 = i__ + j * work_dim1; q__1.r = work[i__3].r * work[i__4].r - work[i__3].i * work[i__4].i, q__1.i = work[i__3].r * work[ i__4].i + work[i__3].i * work[i__4].r; work[i__2].r = q__1.r, work[i__2].i = q__1.i; } } else { i__1 = nnb; for (j = 1; j <= i__1; ++j) { i__2 = i__ + j * work_dim1; u01_i_j__.r = work[i__2].r, u01_i_j__.i = work[i__2] .i; i__2 = i__ - 1 + j * work_dim1; u01_ip1_j__.r = work[i__2].r, u01_ip1_j__.i = work[ i__2].i; i__2 = i__ + j * work_dim1; i__3 = cut + nnb + i__ + invd * work_dim1; q__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i * u01_i_j__.i, q__2.i = work[i__3].r * u01_i_j__.i + work[i__3].i * u01_i_j__.r; i__4 = cut + nnb + i__ + (invd + 1) * work_dim1; q__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i * u01_ip1_j__.i, q__3.i = work[i__4].r * u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; work[i__2].r = q__1.r, work[i__2].i = q__1.i; i__2 = i__ - 1 + j * work_dim1; i__3 = cut + nnb + i__ - 1 + (invd + 1) * work_dim1; q__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i * u01_i_j__.i, q__2.i = work[i__3].r * u01_i_j__.i + work[i__3].i * u01_i_j__.r; i__4 = cut + nnb + i__ - 1 + invd * work_dim1; q__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i * u01_ip1_j__.i, q__3.i = work[i__4].r * u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; work[i__2].r = q__1.r, work[i__2].i = q__1.i; } --i__; } --i__; } /* invD1*L11 */ i__ = nnb; while(i__ >= 1) { if (ipiv[cut + i__] > 0) { i__1 = nnb; for (j = 1; j <= i__1; ++j) { i__2 = u11 + i__ + j * work_dim1; i__3 = cut + i__ + invd * work_dim1; i__4 = u11 + i__ + j * work_dim1; q__1.r = work[i__3].r * work[i__4].r - work[i__3].i * work[i__4].i, q__1.i = work[i__3].r * work[ i__4].i + work[i__3].i * work[i__4].r; work[i__2].r = q__1.r, work[i__2].i = q__1.i; } } else { i__1 = nnb; for (j = 1; j <= i__1; ++j) { i__2 = u11 + i__ + j * work_dim1; u11_i_j__.r = work[i__2].r, u11_i_j__.i = work[i__2] .i; i__2 = u11 + i__ - 1 + j * work_dim1; u11_ip1_j__.r = work[i__2].r, u11_ip1_j__.i = work[ i__2].i; i__2 = u11 + i__ + j * work_dim1; i__3 = cut + i__ + invd * work_dim1; i__4 = u11 + i__ + j * work_dim1; q__2.r = work[i__3].r * work[i__4].r - work[i__3].i * work[i__4].i, q__2.i = work[i__3].r * work[ i__4].i + work[i__3].i * work[i__4].r; i__5 = cut + i__ + (invd + 1) * work_dim1; q__3.r = work[i__5].r * u11_ip1_j__.r - work[i__5].i * u11_ip1_j__.i, q__3.i = work[i__5].r * u11_ip1_j__.i + work[i__5].i * u11_ip1_j__.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; work[i__2].r = q__1.r, work[i__2].i = q__1.i; i__2 = u11 + i__ - 1 + j * work_dim1; i__3 = cut + i__ - 1 + (invd + 1) * work_dim1; q__2.r = work[i__3].r * u11_i_j__.r - work[i__3].i * u11_i_j__.i, q__2.i = work[i__3].r * u11_i_j__.i + work[i__3].i * u11_i_j__.r; i__4 = cut + i__ - 1 + invd * work_dim1; q__3.r = work[i__4].r * u11_ip1_j__.r - work[i__4].i * u11_ip1_j__.i, q__3.i = work[i__4].r * u11_ip1_j__.i + work[i__4].i * u11_ip1_j__.r; q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i; work[i__2].r = q__1.r, work[i__2].i = q__1.i; } --i__; } --i__; } /* L11**T * invD1 * L11 -> L11 */ i__1 = *n + *nb + 1; ctrmm_("L", uplo, "T", "U", &nnb, &nnb, &c_b1, &a[cut + 1 + (cut + 1) * a_dim1], lda, &work[u11 + 1 + work_dim1], &i__1); i__1 = nnb; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; for (j = 1; j <= i__2; ++j) { i__3 = cut + i__ + (cut + j) * a_dim1; i__4 = u11 + i__ + j * work_dim1; a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i; } } if (cut + nnb < *n) { /* L21**T * invD2*L21 -> A( CUT+I, CUT+J ) */ i__1 = *n - nnb - cut; i__2 = *n + *nb + 1; i__3 = *n + *nb + 1; cgemm_("T", "N", &nnb, &nnb, &i__1, &c_b1, &a[cut + nnb + 1 + (cut + 1) * a_dim1], lda, &work[work_offset], &i__2, & c_b2, &work[u11 + 1 + work_dim1], &i__3); /* L11 = L11**T * invD1 * L11 + U01**T * invD * U01 */ i__1 = nnb; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; for (j = 1; j <= i__2; ++j) { i__3 = cut + i__ + (cut + j) * a_dim1; i__4 = cut + i__ + (cut + j) * a_dim1; i__5 = u11 + i__ + j * work_dim1; q__1.r = a[i__4].r + work[i__5].r, q__1.i = a[i__4].i + work[i__5].i; a[i__3].r = q__1.r, a[i__3].i = q__1.i; } } /* L01 = L22**T * invD2 * L21 */ i__1 = *n - nnb - cut; i__2 = *n + *nb + 1; ctrmm_("L", uplo, "T", "U", &i__1, &nnb, &c_b1, &a[cut + nnb + 1 + (cut + nnb + 1) * a_dim1], lda, &work[ work_offset], &i__2); /* Update L21 */ i__1 = *n - cut - nnb; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = nnb; for (j = 1; j <= i__2; ++j) { i__3 = cut + nnb + i__ + (cut + j) * a_dim1; i__4 = i__ + j * work_dim1; a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i; } } } else { /* L11 = L11**T * invD1 * L11 */ i__1 = nnb; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; for (j = 1; j <= i__2; ++j) { i__3 = cut + i__ + (cut + j) * a_dim1; i__4 = u11 + i__ + j * work_dim1; a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i; } } } /* Next Block */ cut += nnb; } /* Apply PERMUTATIONS P and P**T: */ /* P * inv(L**T) * inv(D) * inv(L) * P**T. */ /* Interchange rows and columns I and IPIV(I) in reverse order */ /* from the formation order of IPIV vector for Lower case. */ /* ( We can use a loop over IPIV with increment -1, */ /* since the ABS value of IPIV(I) represents the row (column) */ /* index of the interchange with row (column) i in both 1x1 */ /* and 2x2 pivot cases, i.e. we don't need separate code branches */ /* for 1x1 and 2x2 pivot cases ) */ for (i__ = *n; i__ >= 1; --i__) { ip = (i__1 = ipiv[i__], abs(i__1)); if (ip != i__) { if (i__ < ip) { csyswapr_(uplo, n, &a[a_offset], lda, &i__, &ip); } if (i__ > ip) { csyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__); } } } } return 0; /* End of CSYTRI_3X */ } /* csytri_3x__ */