#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]/Cd(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 ZSYTRS */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZSYTRS + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) */ /* CHARACTER UPLO */ /* INTEGER INFO, LDA, LDB, N, NRHS */ /* INTEGER IPIV( * ) */ /* COMPLEX*16 A( LDA, * ), B( LDB, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZSYTRS solves a system of linear equations A*X = B with a complex */ /* > symmetric matrix A using the factorization A = U*D*U**T or */ /* > A = L*D*L**T computed by ZSYTRF. */ /* > \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 triangular, form is A = U*D*U**T; */ /* > = 'L': Lower triangular, form is A = L*D*L**T. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix A. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] NRHS */ /* > \verbatim */ /* > NRHS is INTEGER */ /* > The number of right hand sides, i.e., the number of columns */ /* > of the matrix B. NRHS >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] A */ /* > \verbatim */ /* > A is COMPLEX*16 array, dimension (LDA,N) */ /* > The block diagonal matrix D and the multipliers used to */ /* > obtain the factor U or L as computed by ZSYTRF. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in] IPIV */ /* > \verbatim */ /* > IPIV is INTEGER array, dimension (N) */ /* > Details of the interchanges and the block structure of D */ /* > as determined by ZSYTRF. */ /* > \endverbatim */ /* > */ /* > \param[in,out] B */ /* > \verbatim */ /* > B is COMPLEX*16 array, dimension (LDB,NRHS) */ /* > On entry, the right hand side matrix B. */ /* > On exit, the solution matrix X. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if INFO = -i, the i-th argument had an illegal value */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup complex16SYcomputational */ /* ===================================================================== */ /* Subroutine */ int zsytrs_(char *uplo, integer *n, integer *nrhs, doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *b, integer *ldb, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2; doublecomplex z__1, z__2, z__3; /* Local variables */ doublecomplex akm1k; integer j, k; extern logical lsame_(char *, char *); doublecomplex denom; extern /* Subroutine */ int zscal_(integer *, doublecomplex *, doublecomplex *, integer *), zgemv_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *); logical upper; extern /* Subroutine */ int zgeru_(integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *); doublecomplex ak, bk; integer kp; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); doublecomplex akm1, bkm1; /* -- LAPACK computational routine (version 3.7.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* December 2016 */ /* ===================================================================== */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --ipiv; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*nrhs < 0) { *info = -3; } else if (*lda < f2cmax(1,*n)) { *info = -5; } else if (*ldb < f2cmax(1,*n)) { *info = -8; } if (*info != 0) { i__1 = -(*info); xerbla_("ZSYTRS", &i__1, (ftnlen)6); return 0; } /* Quick return if possible */ if (*n == 0 || *nrhs == 0) { return 0; } if (upper) { /* Solve A*X = B, where A = U*D*U**T. */ /* First solve U*D*X = B, overwriting B with X. */ /* K is the main loop index, decreasing from N to 1 in steps of */ /* 1 or 2, depending on the size of the diagonal blocks. */ k = *n; L10: /* If K < 1, exit from loop. */ if (k < 1) { goto L30; } if (ipiv[k] > 0) { /* 1 x 1 diagonal block */ /* Interchange rows K and IPIV(K). */ kp = ipiv[k]; if (kp != k) { zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb); } /* Multiply by inv(U(K)), where U(K) is the transformation */ /* stored in column K of A. */ i__1 = k - 1; z__1.r = -1., z__1.i = 0.; zgeru_(&i__1, nrhs, &z__1, &a[k * a_dim1 + 1], &c__1, &b[k + b_dim1], ldb, &b[b_dim1 + 1], ldb); /* Multiply by the inverse of the diagonal block. */ z_div(&z__1, &c_b1, &a[k + k * a_dim1]); zscal_(nrhs, &z__1, &b[k + b_dim1], ldb); --k; } else { /* 2 x 2 diagonal block */ /* Interchange rows K-1 and -IPIV(K). */ kp = -ipiv[k]; if (kp != k - 1) { zswap_(nrhs, &b[k - 1 + b_dim1], ldb, &b[kp + b_dim1], ldb); } /* Multiply by inv(U(K)), where U(K) is the transformation */ /* stored in columns K-1 and K of A. */ i__1 = k - 2; z__1.r = -1., z__1.i = 0.; zgeru_(&i__1, nrhs, &z__1, &a[k * a_dim1 + 1], &c__1, &b[k + b_dim1], ldb, &b[b_dim1 + 1], ldb); i__1 = k - 2; z__1.r = -1., z__1.i = 0.; zgeru_(&i__1, nrhs, &z__1, &a[(k - 1) * a_dim1 + 1], &c__1, &b[k - 1 + b_dim1], ldb, &b[b_dim1 + 1], ldb); /* Multiply by the inverse of the diagonal block. */ i__1 = k - 1 + k * a_dim1; akm1k.r = a[i__1].r, akm1k.i = a[i__1].i; z_div(&z__1, &a[k - 1 + (k - 1) * a_dim1], &akm1k); akm1.r = z__1.r, akm1.i = z__1.i; z_div(&z__1, &a[k + k * a_dim1], &akm1k); ak.r = z__1.r, ak.i = z__1.i; z__2.r = akm1.r * ak.r - akm1.i * ak.i, z__2.i = akm1.r * ak.i + akm1.i * ak.r; z__1.r = z__2.r - 1., z__1.i = z__2.i + 0.; denom.r = z__1.r, denom.i = z__1.i; i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { z_div(&z__1, &b[k - 1 + j * b_dim1], &akm1k); bkm1.r = z__1.r, bkm1.i = z__1.i; z_div(&z__1, &b[k + j * b_dim1], &akm1k); bk.r = z__1.r, bk.i = z__1.i; i__2 = k - 1 + j * b_dim1; z__3.r = ak.r * bkm1.r - ak.i * bkm1.i, z__3.i = ak.r * bkm1.i + ak.i * bkm1.r; z__2.r = z__3.r - bk.r, z__2.i = z__3.i - bk.i; z_div(&z__1, &z__2, &denom); b[i__2].r = z__1.r, b[i__2].i = z__1.i; i__2 = k + j * b_dim1; z__3.r = akm1.r * bk.r - akm1.i * bk.i, z__3.i = akm1.r * bk.i + akm1.i * bk.r; z__2.r = z__3.r - bkm1.r, z__2.i = z__3.i - bkm1.i; z_div(&z__1, &z__2, &denom); b[i__2].r = z__1.r, b[i__2].i = z__1.i; /* L20: */ } k += -2; } goto L10; L30: /* Next solve U**T *X = B, overwriting B with X. */ /* K is the main loop index, increasing from 1 to N in steps of */ /* 1 or 2, depending on the size of the diagonal blocks. */ k = 1; L40: /* If K > N, exit from loop. */ if (k > *n) { goto L50; } if (ipiv[k] > 0) { /* 1 x 1 diagonal block */ /* Multiply by inv(U**T(K)), where U(K) is the transformation */ /* stored in column K of A. */ i__1 = k - 1; z__1.r = -1., z__1.i = 0.; zgemv_("Transpose", &i__1, nrhs, &z__1, &b[b_offset], ldb, &a[k * a_dim1 + 1], &c__1, &c_b1, &b[k + b_dim1], ldb) ; /* Interchange rows K and IPIV(K). */ kp = ipiv[k]; if (kp != k) { zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb); } ++k; } else { /* 2 x 2 diagonal block */ /* Multiply by inv(U**T(K+1)), where U(K+1) is the transformation */ /* stored in columns K and K+1 of A. */ i__1 = k - 1; z__1.r = -1., z__1.i = 0.; zgemv_("Transpose", &i__1, nrhs, &z__1, &b[b_offset], ldb, &a[k * a_dim1 + 1], &c__1, &c_b1, &b[k + b_dim1], ldb) ; i__1 = k - 1; z__1.r = -1., z__1.i = 0.; zgemv_("Transpose", &i__1, nrhs, &z__1, &b[b_offset], ldb, &a[(k + 1) * a_dim1 + 1], &c__1, &c_b1, &b[k + 1 + b_dim1], ldb); /* Interchange rows K and -IPIV(K). */ kp = -ipiv[k]; if (kp != k) { zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb); } k += 2; } goto L40; L50: ; } else { /* Solve A*X = B, where A = L*D*L**T. */ /* First solve L*D*X = B, overwriting B with X. */ /* K is the main loop index, increasing from 1 to N in steps of */ /* 1 or 2, depending on the size of the diagonal blocks. */ k = 1; L60: /* If K > N, exit from loop. */ if (k > *n) { goto L80; } if (ipiv[k] > 0) { /* 1 x 1 diagonal block */ /* Interchange rows K and IPIV(K). */ kp = ipiv[k]; if (kp != k) { zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb); } /* Multiply by inv(L(K)), where L(K) is the transformation */ /* stored in column K of A. */ if (k < *n) { i__1 = *n - k; z__1.r = -1., z__1.i = 0.; zgeru_(&i__1, nrhs, &z__1, &a[k + 1 + k * a_dim1], &c__1, &b[ k + b_dim1], ldb, &b[k + 1 + b_dim1], ldb); } /* Multiply by the inverse of the diagonal block. */ z_div(&z__1, &c_b1, &a[k + k * a_dim1]); zscal_(nrhs, &z__1, &b[k + b_dim1], ldb); ++k; } else { /* 2 x 2 diagonal block */ /* Interchange rows K+1 and -IPIV(K). */ kp = -ipiv[k]; if (kp != k + 1) { zswap_(nrhs, &b[k + 1 + b_dim1], ldb, &b[kp + b_dim1], ldb); } /* Multiply by inv(L(K)), where L(K) is the transformation */ /* stored in columns K and K+1 of A. */ if (k < *n - 1) { i__1 = *n - k - 1; z__1.r = -1., z__1.i = 0.; zgeru_(&i__1, nrhs, &z__1, &a[k + 2 + k * a_dim1], &c__1, &b[ k + b_dim1], ldb, &b[k + 2 + b_dim1], ldb); i__1 = *n - k - 1; z__1.r = -1., z__1.i = 0.; zgeru_(&i__1, nrhs, &z__1, &a[k + 2 + (k + 1) * a_dim1], & c__1, &b[k + 1 + b_dim1], ldb, &b[k + 2 + b_dim1], ldb); } /* Multiply by the inverse of the diagonal block. */ i__1 = k + 1 + k * a_dim1; akm1k.r = a[i__1].r, akm1k.i = a[i__1].i; z_div(&z__1, &a[k + k * a_dim1], &akm1k); akm1.r = z__1.r, akm1.i = z__1.i; z_div(&z__1, &a[k + 1 + (k + 1) * a_dim1], &akm1k); ak.r = z__1.r, ak.i = z__1.i; z__2.r = akm1.r * ak.r - akm1.i * ak.i, z__2.i = akm1.r * ak.i + akm1.i * ak.r; z__1.r = z__2.r - 1., z__1.i = z__2.i + 0.; denom.r = z__1.r, denom.i = z__1.i; i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { z_div(&z__1, &b[k + j * b_dim1], &akm1k); bkm1.r = z__1.r, bkm1.i = z__1.i; z_div(&z__1, &b[k + 1 + j * b_dim1], &akm1k); bk.r = z__1.r, bk.i = z__1.i; i__2 = k + j * b_dim1; z__3.r = ak.r * bkm1.r - ak.i * bkm1.i, z__3.i = ak.r * bkm1.i + ak.i * bkm1.r; z__2.r = z__3.r - bk.r, z__2.i = z__3.i - bk.i; z_div(&z__1, &z__2, &denom); b[i__2].r = z__1.r, b[i__2].i = z__1.i; i__2 = k + 1 + j * b_dim1; z__3.r = akm1.r * bk.r - akm1.i * bk.i, z__3.i = akm1.r * bk.i + akm1.i * bk.r; z__2.r = z__3.r - bkm1.r, z__2.i = z__3.i - bkm1.i; z_div(&z__1, &z__2, &denom); b[i__2].r = z__1.r, b[i__2].i = z__1.i; /* L70: */ } k += 2; } goto L60; L80: /* Next solve L**T *X = B, overwriting B with X. */ /* K is the main loop index, decreasing from N to 1 in steps of */ /* 1 or 2, depending on the size of the diagonal blocks. */ k = *n; L90: /* If K < 1, exit from loop. */ if (k < 1) { goto L100; } if (ipiv[k] > 0) { /* 1 x 1 diagonal block */ /* Multiply by inv(L**T(K)), where L(K) is the transformation */ /* stored in column K of A. */ if (k < *n) { i__1 = *n - k; z__1.r = -1., z__1.i = 0.; zgemv_("Transpose", &i__1, nrhs, &z__1, &b[k + 1 + b_dim1], ldb, &a[k + 1 + k * a_dim1], &c__1, &c_b1, &b[k + b_dim1], ldb); } /* Interchange rows K and IPIV(K). */ kp = ipiv[k]; if (kp != k) { zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb); } --k; } else { /* 2 x 2 diagonal block */ /* Multiply by inv(L**T(K-1)), where L(K-1) is the transformation */ /* stored in columns K-1 and K of A. */ if (k < *n) { i__1 = *n - k; z__1.r = -1., z__1.i = 0.; zgemv_("Transpose", &i__1, nrhs, &z__1, &b[k + 1 + b_dim1], ldb, &a[k + 1 + k * a_dim1], &c__1, &c_b1, &b[k + b_dim1], ldb); i__1 = *n - k; z__1.r = -1., z__1.i = 0.; zgemv_("Transpose", &i__1, nrhs, &z__1, &b[k + 1 + b_dim1], ldb, &a[k + 1 + (k - 1) * a_dim1], &c__1, &c_b1, &b[k - 1 + b_dim1], ldb); } /* Interchange rows K and -IPIV(K). */ kp = -ipiv[k]; if (kp != k) { zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb); } k += -2; } goto L90; L100: ; } return 0; /* End of ZSYTRS */ } /* zsytrs_ */