#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 STGSY2 solves the generalized Sylvester equation (unblocked algorithm). */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download STGSY2 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE STGSY2( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, */ /* LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL, */ /* IWORK, PQ, INFO ) */ /* CHARACTER TRANS */ /* INTEGER IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF, M, N, */ /* $ PQ */ /* REAL RDSCAL, RDSUM, SCALE */ /* INTEGER IWORK( * ) */ /* REAL A( LDA, * ), B( LDB, * ), C( LDC, * ), */ /* $ D( LDD, * ), E( LDE, * ), F( LDF, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > STGSY2 solves the generalized Sylvester equation: */ /* > */ /* > A * R - L * B = scale * C (1) */ /* > D * R - L * E = scale * F, */ /* > */ /* > using Level 1 and 2 BLAS. where R and L are unknown M-by-N matrices, */ /* > (A, D), (B, E) and (C, F) are given matrix pairs of size M-by-M, */ /* > N-by-N and M-by-N, respectively, with real entries. (A, D) and (B, E) */ /* > must be in generalized Schur canonical form, i.e. A, B are upper */ /* > quasi triangular and D, E are upper triangular. The solution (R, L) */ /* > overwrites (C, F). 0 <= SCALE <= 1 is an output scaling factor */ /* > chosen to avoid overflow. */ /* > */ /* > In matrix notation solving equation (1) corresponds to solve */ /* > Z*x = scale*b, where Z is defined as */ /* > */ /* > Z = [ kron(In, A) -kron(B**T, Im) ] (2) */ /* > [ kron(In, D) -kron(E**T, Im) ], */ /* > */ /* > Ik is the identity matrix of size k and X**T is the transpose of X. */ /* > kron(X, Y) is the Kronecker product between the matrices X and Y. */ /* > In the process of solving (1), we solve a number of such systems */ /* > where Dim(In), Dim(In) = 1 or 2. */ /* > */ /* > If TRANS = 'T', solve the transposed system Z**T*y = scale*b for y, */ /* > which is equivalent to solve for R and L in */ /* > */ /* > A**T * R + D**T * L = scale * C (3) */ /* > R * B**T + L * E**T = scale * -F */ /* > */ /* > This case is used to compute an estimate of Dif[(A, D), (B, E)] = */ /* > sigma_min(Z) using reverse communication with SLACON. */ /* > */ /* > STGSY2 also (IJOB >= 1) contributes to the computation in STGSYL */ /* > of an upper bound on the separation between to matrix pairs. Then */ /* > the input (A, D), (B, E) are sub-pencils of the matrix pair in */ /* > STGSYL. See STGSYL for details. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] TRANS */ /* > \verbatim */ /* > TRANS is CHARACTER*1 */ /* > = 'N': solve the generalized Sylvester equation (1). */ /* > = 'T': solve the 'transposed' system (3). */ /* > \endverbatim */ /* > */ /* > \param[in] IJOB */ /* > \verbatim */ /* > IJOB is INTEGER */ /* > Specifies what kind of functionality to be performed. */ /* > = 0: solve (1) only. */ /* > = 1: A contribution from this subsystem to a Frobenius */ /* > norm-based estimate of the separation between two matrix */ /* > pairs is computed. (look ahead strategy is used). */ /* > = 2: A contribution from this subsystem to a Frobenius */ /* > norm-based estimate of the separation between two matrix */ /* > pairs is computed. (SGECON on sub-systems is used.) */ /* > Not referenced if TRANS = 'T'. */ /* > \endverbatim */ /* > */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > On entry, M specifies the order of A and D, and the row */ /* > dimension of C, F, R and L. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > On entry, N specifies the order of B and E, and the column */ /* > dimension of C, F, R and L. */ /* > \endverbatim */ /* > */ /* > \param[in] A */ /* > \verbatim */ /* > A is REAL array, dimension (LDA, M) */ /* > On entry, A contains an upper quasi triangular matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the matrix A. LDA >= f2cmax(1, M). */ /* > \endverbatim */ /* > */ /* > \param[in] B */ /* > \verbatim */ /* > B is REAL array, dimension (LDB, N) */ /* > On entry, B contains an upper quasi triangular matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of the matrix B. LDB >= f2cmax(1, N). */ /* > \endverbatim */ /* > */ /* > \param[in,out] C */ /* > \verbatim */ /* > C is REAL array, dimension (LDC, N) */ /* > On entry, C contains the right-hand-side of the first matrix */ /* > equation in (1). */ /* > On exit, if IJOB = 0, C has been overwritten by the */ /* > solution R. */ /* > \endverbatim */ /* > */ /* > \param[in] LDC */ /* > \verbatim */ /* > LDC is INTEGER */ /* > The leading dimension of the matrix C. LDC >= f2cmax(1, M). */ /* > \endverbatim */ /* > */ /* > \param[in] D */ /* > \verbatim */ /* > D is REAL array, dimension (LDD, M) */ /* > On entry, D contains an upper triangular matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] LDD */ /* > \verbatim */ /* > LDD is INTEGER */ /* > The leading dimension of the matrix D. LDD >= f2cmax(1, M). */ /* > \endverbatim */ /* > */ /* > \param[in] E */ /* > \verbatim */ /* > E is REAL array, dimension (LDE, N) */ /* > On entry, E contains an upper triangular matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] LDE */ /* > \verbatim */ /* > LDE is INTEGER */ /* > The leading dimension of the matrix E. LDE >= f2cmax(1, N). */ /* > \endverbatim */ /* > */ /* > \param[in,out] F */ /* > \verbatim */ /* > F is REAL array, dimension (LDF, N) */ /* > On entry, F contains the right-hand-side of the second matrix */ /* > equation in (1). */ /* > On exit, if IJOB = 0, F has been overwritten by the */ /* > solution L. */ /* > \endverbatim */ /* > */ /* > \param[in] LDF */ /* > \verbatim */ /* > LDF is INTEGER */ /* > The leading dimension of the matrix F. LDF >= f2cmax(1, M). */ /* > \endverbatim */ /* > */ /* > \param[out] SCALE */ /* > \verbatim */ /* > SCALE is REAL */ /* > On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions */ /* > R and L (C and F on entry) will hold the solutions to a */ /* > slightly perturbed system but the input matrices A, B, D and */ /* > E have not been changed. If SCALE = 0, R and L will hold the */ /* > solutions to the homogeneous system with C = F = 0. Normally, */ /* > SCALE = 1. */ /* > \endverbatim */ /* > */ /* > \param[in,out] RDSUM */ /* > \verbatim */ /* > RDSUM is REAL */ /* > On entry, the sum of squares of computed contributions to */ /* > the Dif-estimate under computation by STGSYL, where the */ /* > scaling factor RDSCAL (see below) has been factored out. */ /* > On exit, the corresponding sum of squares updated with the */ /* > contributions from the current sub-system. */ /* > If TRANS = 'T' RDSUM is not touched. */ /* > NOTE: RDSUM only makes sense when STGSY2 is called by STGSYL. */ /* > \endverbatim */ /* > */ /* > \param[in,out] RDSCAL */ /* > \verbatim */ /* > RDSCAL is REAL */ /* > On entry, scaling factor used to prevent overflow in RDSUM. */ /* > On exit, RDSCAL is updated w.r.t. the current contributions */ /* > in RDSUM. */ /* > If TRANS = 'T', RDSCAL is not touched. */ /* > NOTE: RDSCAL only makes sense when STGSY2 is called by */ /* > STGSYL. */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (M+N+2) */ /* > \endverbatim */ /* > */ /* > \param[out] PQ */ /* > \verbatim */ /* > PQ is INTEGER */ /* > On exit, the number of subsystems (of size 2-by-2, 4-by-4 and */ /* > 8-by-8) solved by this routine. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > On exit, if INFO is set to */ /* > =0: Successful exit */ /* > <0: If INFO = -i, the i-th argument had an illegal value. */ /* > >0: The matrix pairs (A, D) and (B, E) have common or very */ /* > close eigenvalues. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup realSYauxiliary */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */ /* > Umea University, S-901 87 Umea, Sweden. */ /* ===================================================================== */ /* Subroutine */ int stgsy2_(char *trans, integer *ijob, integer *m, integer * n, real *a, integer *lda, real *b, integer *ldb, real *c__, integer * ldc, real *d__, integer *ldd, real *e, integer *lde, real *f, integer *ldf, real *scale, real *rdsum, real *rdscal, integer *iwork, integer *pq, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, d_dim1, d_offset, e_dim1, e_offset, f_dim1, f_offset, i__1, i__2, i__3; /* Local variables */ extern /* Subroutine */ int sger_(integer *, integer *, real *, real *, integer *, real *, integer *, real *, integer *); integer ierr, zdim, ipiv[8], jpiv[8], i__, j, k, p, q; real alpha, z__[64] /* was [8][8] */; extern logical lsame_(char *, char *); extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *), sgemm_(char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *), sgemv_(char *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *), scopy_(integer *, real *, integer *, real *, integer *), saxpy_(integer *, real *, real *, integer *, real *, integer *), sgesc2_(integer *, real *, integer *, real *, integer *, integer * , real *), sgetc2_(integer *, real *, integer *, integer *, integer *, integer *); integer ie, je, mb, nb, ii, jj, is, js; real scaloc; extern /* Subroutine */ int slatdf_(integer *, integer *, real *, integer *, real *, real *, real *, integer *, integer *), xerbla_(char *, integer *, ftnlen), slaset_(char *, integer *, integer *, real *, real *, real *, integer *); logical notran; real rhs[8]; integer isp1, jsp1; /* -- LAPACK auxiliary 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 */ /* ===================================================================== */ /* Replaced various illegal calls to SCOPY by calls to SLASET. */ /* Sven Hammarling, 27/5/02. */ /* Decode and test input parameters */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1 * 1; c__ -= c_offset; d_dim1 = *ldd; d_offset = 1 + d_dim1 * 1; d__ -= d_offset; e_dim1 = *lde; e_offset = 1 + e_dim1 * 1; e -= e_offset; f_dim1 = *ldf; f_offset = 1 + f_dim1 * 1; f -= f_offset; --iwork; /* Function Body */ *info = 0; ierr = 0; notran = lsame_(trans, "N"); if (! notran && ! lsame_(trans, "T")) { *info = -1; } else if (notran) { if (*ijob < 0 || *ijob > 2) { *info = -2; } } if (*info == 0) { if (*m <= 0) { *info = -3; } else if (*n <= 0) { *info = -4; } else if (*lda < f2cmax(1,*m)) { *info = -6; } else if (*ldb < f2cmax(1,*n)) { *info = -8; } else if (*ldc < f2cmax(1,*m)) { *info = -10; } else if (*ldd < f2cmax(1,*m)) { *info = -12; } else if (*lde < f2cmax(1,*n)) { *info = -14; } else if (*ldf < f2cmax(1,*m)) { *info = -16; } } if (*info != 0) { i__1 = -(*info); xerbla_("STGSY2", &i__1, (ftnlen)6); return 0; } /* Determine block structure of A */ *pq = 0; p = 0; i__ = 1; L10: if (i__ > *m) { goto L20; } ++p; iwork[p] = i__; if (i__ == *m) { goto L20; } if (a[i__ + 1 + i__ * a_dim1] != 0.f) { i__ += 2; } else { ++i__; } goto L10; L20: iwork[p + 1] = *m + 1; /* Determine block structure of B */ q = p + 1; j = 1; L30: if (j > *n) { goto L40; } ++q; iwork[q] = j; if (j == *n) { goto L40; } if (b[j + 1 + j * b_dim1] != 0.f) { j += 2; } else { ++j; } goto L30; L40: iwork[q + 1] = *n + 1; *pq = p * (q - p - 1); if (notran) { /* Solve (I, J) - subsystem */ /* A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J) */ /* D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J) */ /* for I = P, P - 1, ..., 1; J = 1, 2, ..., Q */ *scale = 1.f; scaloc = 1.f; i__1 = q; for (j = p + 2; j <= i__1; ++j) { js = iwork[j]; jsp1 = js + 1; je = iwork[j + 1] - 1; nb = je - js + 1; for (i__ = p; i__ >= 1; --i__) { is = iwork[i__]; isp1 = is + 1; ie = iwork[i__ + 1] - 1; mb = ie - is + 1; zdim = mb * nb << 1; if (mb == 1 && nb == 1) { /* Build a 2-by-2 system Z * x = RHS */ z__[0] = a[is + is * a_dim1]; z__[1] = d__[is + is * d_dim1]; z__[8] = -b[js + js * b_dim1]; z__[9] = -e[js + js * e_dim1]; /* Set up right hand side(s) */ rhs[0] = c__[is + js * c_dim1]; rhs[1] = f[is + js * f_dim1]; /* Solve Z * x = RHS */ sgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } if (*ijob == 0) { sgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.f) { i__2 = *n; for (k = 1; k <= i__2; ++k) { sscal_(m, &scaloc, &c__[k * c_dim1 + 1], & c__1); sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1); /* L50: */ } *scale *= scaloc; } } else { slatdf_(ijob, &zdim, z__, &c__8, rhs, rdsum, rdscal, ipiv, jpiv); } /* Unpack solution vector(s) */ c__[is + js * c_dim1] = rhs[0]; f[is + js * f_dim1] = rhs[1]; /* Substitute R(I, J) and L(I, J) into remaining */ /* equation. */ if (i__ > 1) { alpha = -rhs[0]; i__2 = is - 1; saxpy_(&i__2, &alpha, &a[is * a_dim1 + 1], &c__1, & c__[js * c_dim1 + 1], &c__1); i__2 = is - 1; saxpy_(&i__2, &alpha, &d__[is * d_dim1 + 1], &c__1, & f[js * f_dim1 + 1], &c__1); } if (j < q) { i__2 = *n - je; saxpy_(&i__2, &rhs[1], &b[js + (je + 1) * b_dim1], ldb, &c__[is + (je + 1) * c_dim1], ldc); i__2 = *n - je; saxpy_(&i__2, &rhs[1], &e[js + (je + 1) * e_dim1], lde, &f[is + (je + 1) * f_dim1], ldf); } } else if (mb == 1 && nb == 2) { /* Build a 4-by-4 system Z * x = RHS */ z__[0] = a[is + is * a_dim1]; z__[1] = 0.f; z__[2] = d__[is + is * d_dim1]; z__[3] = 0.f; z__[8] = 0.f; z__[9] = a[is + is * a_dim1]; z__[10] = 0.f; z__[11] = d__[is + is * d_dim1]; z__[16] = -b[js + js * b_dim1]; z__[17] = -b[js + jsp1 * b_dim1]; z__[18] = -e[js + js * e_dim1]; z__[19] = -e[js + jsp1 * e_dim1]; z__[24] = -b[jsp1 + js * b_dim1]; z__[25] = -b[jsp1 + jsp1 * b_dim1]; z__[26] = 0.f; z__[27] = -e[jsp1 + jsp1 * e_dim1]; /* Set up right hand side(s) */ rhs[0] = c__[is + js * c_dim1]; rhs[1] = c__[is + jsp1 * c_dim1]; rhs[2] = f[is + js * f_dim1]; rhs[3] = f[is + jsp1 * f_dim1]; /* Solve Z * x = RHS */ sgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } if (*ijob == 0) { sgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.f) { i__2 = *n; for (k = 1; k <= i__2; ++k) { sscal_(m, &scaloc, &c__[k * c_dim1 + 1], & c__1); sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1); /* L60: */ } *scale *= scaloc; } } else { slatdf_(ijob, &zdim, z__, &c__8, rhs, rdsum, rdscal, ipiv, jpiv); } /* Unpack solution vector(s) */ c__[is + js * c_dim1] = rhs[0]; c__[is + jsp1 * c_dim1] = rhs[1]; f[is + js * f_dim1] = rhs[2]; f[is + jsp1 * f_dim1] = rhs[3]; /* Substitute R(I, J) and L(I, J) into remaining */ /* equation. */ if (i__ > 1) { i__2 = is - 1; sger_(&i__2, &nb, &c_b27, &a[is * a_dim1 + 1], &c__1, rhs, &c__1, &c__[js * c_dim1 + 1], ldc); i__2 = is - 1; sger_(&i__2, &nb, &c_b27, &d__[is * d_dim1 + 1], & c__1, rhs, &c__1, &f[js * f_dim1 + 1], ldf); } if (j < q) { i__2 = *n - je; saxpy_(&i__2, &rhs[2], &b[js + (je + 1) * b_dim1], ldb, &c__[is + (je + 1) * c_dim1], ldc); i__2 = *n - je; saxpy_(&i__2, &rhs[2], &e[js + (je + 1) * e_dim1], lde, &f[is + (je + 1) * f_dim1], ldf); i__2 = *n - je; saxpy_(&i__2, &rhs[3], &b[jsp1 + (je + 1) * b_dim1], ldb, &c__[is + (je + 1) * c_dim1], ldc); i__2 = *n - je; saxpy_(&i__2, &rhs[3], &e[jsp1 + (je + 1) * e_dim1], lde, &f[is + (je + 1) * f_dim1], ldf); } } else if (mb == 2 && nb == 1) { /* Build a 4-by-4 system Z * x = RHS */ z__[0] = a[is + is * a_dim1]; z__[1] = a[isp1 + is * a_dim1]; z__[2] = d__[is + is * d_dim1]; z__[3] = 0.f; z__[8] = a[is + isp1 * a_dim1]; z__[9] = a[isp1 + isp1 * a_dim1]; z__[10] = d__[is + isp1 * d_dim1]; z__[11] = d__[isp1 + isp1 * d_dim1]; z__[16] = -b[js + js * b_dim1]; z__[17] = 0.f; z__[18] = -e[js + js * e_dim1]; z__[19] = 0.f; z__[24] = 0.f; z__[25] = -b[js + js * b_dim1]; z__[26] = 0.f; z__[27] = -e[js + js * e_dim1]; /* Set up right hand side(s) */ rhs[0] = c__[is + js * c_dim1]; rhs[1] = c__[isp1 + js * c_dim1]; rhs[2] = f[is + js * f_dim1]; rhs[3] = f[isp1 + js * f_dim1]; /* Solve Z * x = RHS */ sgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } if (*ijob == 0) { sgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.f) { i__2 = *n; for (k = 1; k <= i__2; ++k) { sscal_(m, &scaloc, &c__[k * c_dim1 + 1], & c__1); sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1); /* L70: */ } *scale *= scaloc; } } else { slatdf_(ijob, &zdim, z__, &c__8, rhs, rdsum, rdscal, ipiv, jpiv); } /* Unpack solution vector(s) */ c__[is + js * c_dim1] = rhs[0]; c__[isp1 + js * c_dim1] = rhs[1]; f[is + js * f_dim1] = rhs[2]; f[isp1 + js * f_dim1] = rhs[3]; /* Substitute R(I, J) and L(I, J) into remaining */ /* equation. */ if (i__ > 1) { i__2 = is - 1; sgemv_("N", &i__2, &mb, &c_b27, &a[is * a_dim1 + 1], lda, rhs, &c__1, &c_b42, &c__[js * c_dim1 + 1] , &c__1); i__2 = is - 1; sgemv_("N", &i__2, &mb, &c_b27, &d__[is * d_dim1 + 1], ldd, rhs, &c__1, &c_b42, &f[js * f_dim1 + 1], &c__1); } if (j < q) { i__2 = *n - je; sger_(&mb, &i__2, &c_b42, &rhs[2], &c__1, &b[js + (je + 1) * b_dim1], ldb, &c__[is + (je + 1) * c_dim1], ldc); i__2 = *n - je; sger_(&mb, &i__2, &c_b42, &rhs[2], &c__1, &e[js + (je + 1) * e_dim1], lde, &f[is + (je + 1) * f_dim1], ldf); } } else if (mb == 2 && nb == 2) { /* Build an 8-by-8 system Z * x = RHS */ slaset_("F", &c__8, &c__8, &c_b56, &c_b56, z__, &c__8); z__[0] = a[is + is * a_dim1]; z__[1] = a[isp1 + is * a_dim1]; z__[4] = d__[is + is * d_dim1]; z__[8] = a[is + isp1 * a_dim1]; z__[9] = a[isp1 + isp1 * a_dim1]; z__[12] = d__[is + isp1 * d_dim1]; z__[13] = d__[isp1 + isp1 * d_dim1]; z__[18] = a[is + is * a_dim1]; z__[19] = a[isp1 + is * a_dim1]; z__[22] = d__[is + is * d_dim1]; z__[26] = a[is + isp1 * a_dim1]; z__[27] = a[isp1 + isp1 * a_dim1]; z__[30] = d__[is + isp1 * d_dim1]; z__[31] = d__[isp1 + isp1 * d_dim1]; z__[32] = -b[js + js * b_dim1]; z__[34] = -b[js + jsp1 * b_dim1]; z__[36] = -e[js + js * e_dim1]; z__[38] = -e[js + jsp1 * e_dim1]; z__[41] = -b[js + js * b_dim1]; z__[43] = -b[js + jsp1 * b_dim1]; z__[45] = -e[js + js * e_dim1]; z__[47] = -e[js + jsp1 * e_dim1]; z__[48] = -b[jsp1 + js * b_dim1]; z__[50] = -b[jsp1 + jsp1 * b_dim1]; z__[54] = -e[jsp1 + jsp1 * e_dim1]; z__[57] = -b[jsp1 + js * b_dim1]; z__[59] = -b[jsp1 + jsp1 * b_dim1]; z__[63] = -e[jsp1 + jsp1 * e_dim1]; /* Set up right hand side(s) */ k = 1; ii = mb * nb + 1; i__2 = nb - 1; for (jj = 0; jj <= i__2; ++jj) { scopy_(&mb, &c__[is + (js + jj) * c_dim1], &c__1, & rhs[k - 1], &c__1); scopy_(&mb, &f[is + (js + jj) * f_dim1], &c__1, &rhs[ ii - 1], &c__1); k += mb; ii += mb; /* L80: */ } /* Solve Z * x = RHS */ sgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } if (*ijob == 0) { sgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.f) { i__2 = *n; for (k = 1; k <= i__2; ++k) { sscal_(m, &scaloc, &c__[k * c_dim1 + 1], & c__1); sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1); /* L90: */ } *scale *= scaloc; } } else { slatdf_(ijob, &zdim, z__, &c__8, rhs, rdsum, rdscal, ipiv, jpiv); } /* Unpack solution vector(s) */ k = 1; ii = mb * nb + 1; i__2 = nb - 1; for (jj = 0; jj <= i__2; ++jj) { scopy_(&mb, &rhs[k - 1], &c__1, &c__[is + (js + jj) * c_dim1], &c__1); scopy_(&mb, &rhs[ii - 1], &c__1, &f[is + (js + jj) * f_dim1], &c__1); k += mb; ii += mb; /* L100: */ } /* Substitute R(I, J) and L(I, J) into remaining */ /* equation. */ if (i__ > 1) { i__2 = is - 1; sgemm_("N", "N", &i__2, &nb, &mb, &c_b27, &a[is * a_dim1 + 1], lda, rhs, &mb, &c_b42, &c__[js * c_dim1 + 1], ldc); i__2 = is - 1; sgemm_("N", "N", &i__2, &nb, &mb, &c_b27, &d__[is * d_dim1 + 1], ldd, rhs, &mb, &c_b42, &f[js * f_dim1 + 1], ldf); } if (j < q) { k = mb * nb + 1; i__2 = *n - je; sgemm_("N", "N", &mb, &i__2, &nb, &c_b42, &rhs[k - 1], &mb, &b[js + (je + 1) * b_dim1], ldb, &c_b42, &c__[is + (je + 1) * c_dim1], ldc); i__2 = *n - je; sgemm_("N", "N", &mb, &i__2, &nb, &c_b42, &rhs[k - 1], &mb, &e[js + (je + 1) * e_dim1], lde, &c_b42, &f[is + (je + 1) * f_dim1], ldf); } } /* L110: */ } /* L120: */ } } else { /* Solve (I, J) - subsystem */ /* A(I, I)**T * R(I, J) + D(I, I)**T * L(J, J) = C(I, J) */ /* R(I, I) * B(J, J) + L(I, J) * E(J, J) = -F(I, J) */ /* for I = 1, 2, ..., P, J = Q, Q - 1, ..., 1 */ *scale = 1.f; scaloc = 1.f; i__1 = p; for (i__ = 1; i__ <= i__1; ++i__) { is = iwork[i__]; isp1 = is + 1; ie = iwork[i__ + 1] - 1; mb = ie - is + 1; i__2 = p + 2; for (j = q; j >= i__2; --j) { js = iwork[j]; jsp1 = js + 1; je = iwork[j + 1] - 1; nb = je - js + 1; zdim = mb * nb << 1; if (mb == 1 && nb == 1) { /* Build a 2-by-2 system Z**T * x = RHS */ z__[0] = a[is + is * a_dim1]; z__[1] = -b[js + js * b_dim1]; z__[8] = d__[is + is * d_dim1]; z__[9] = -e[js + js * e_dim1]; /* Set up right hand side(s) */ rhs[0] = c__[is + js * c_dim1]; rhs[1] = f[is + js * f_dim1]; /* Solve Z**T * x = RHS */ sgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } sgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.f) { i__3 = *n; for (k = 1; k <= i__3; ++k) { sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1); sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1); /* L130: */ } *scale *= scaloc; } /* Unpack solution vector(s) */ c__[is + js * c_dim1] = rhs[0]; f[is + js * f_dim1] = rhs[1]; /* Substitute R(I, J) and L(I, J) into remaining */ /* equation. */ if (j > p + 2) { alpha = rhs[0]; i__3 = js - 1; saxpy_(&i__3, &alpha, &b[js * b_dim1 + 1], &c__1, &f[ is + f_dim1], ldf); alpha = rhs[1]; i__3 = js - 1; saxpy_(&i__3, &alpha, &e[js * e_dim1 + 1], &c__1, &f[ is + f_dim1], ldf); } if (i__ < p) { alpha = -rhs[0]; i__3 = *m - ie; saxpy_(&i__3, &alpha, &a[is + (ie + 1) * a_dim1], lda, &c__[ie + 1 + js * c_dim1], &c__1); alpha = -rhs[1]; i__3 = *m - ie; saxpy_(&i__3, &alpha, &d__[is + (ie + 1) * d_dim1], ldd, &c__[ie + 1 + js * c_dim1], &c__1); } } else if (mb == 1 && nb == 2) { /* Build a 4-by-4 system Z**T * x = RHS */ z__[0] = a[is + is * a_dim1]; z__[1] = 0.f; z__[2] = -b[js + js * b_dim1]; z__[3] = -b[jsp1 + js * b_dim1]; z__[8] = 0.f; z__[9] = a[is + is * a_dim1]; z__[10] = -b[js + jsp1 * b_dim1]; z__[11] = -b[jsp1 + jsp1 * b_dim1]; z__[16] = d__[is + is * d_dim1]; z__[17] = 0.f; z__[18] = -e[js + js * e_dim1]; z__[19] = 0.f; z__[24] = 0.f; z__[25] = d__[is + is * d_dim1]; z__[26] = -e[js + jsp1 * e_dim1]; z__[27] = -e[jsp1 + jsp1 * e_dim1]; /* Set up right hand side(s) */ rhs[0] = c__[is + js * c_dim1]; rhs[1] = c__[is + jsp1 * c_dim1]; rhs[2] = f[is + js * f_dim1]; rhs[3] = f[is + jsp1 * f_dim1]; /* Solve Z**T * x = RHS */ sgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } sgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.f) { i__3 = *n; for (k = 1; k <= i__3; ++k) { sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1); sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1); /* L140: */ } *scale *= scaloc; } /* Unpack solution vector(s) */ c__[is + js * c_dim1] = rhs[0]; c__[is + jsp1 * c_dim1] = rhs[1]; f[is + js * f_dim1] = rhs[2]; f[is + jsp1 * f_dim1] = rhs[3]; /* Substitute R(I, J) and L(I, J) into remaining */ /* equation. */ if (j > p + 2) { i__3 = js - 1; saxpy_(&i__3, rhs, &b[js * b_dim1 + 1], &c__1, &f[is + f_dim1], ldf); i__3 = js - 1; saxpy_(&i__3, &rhs[1], &b[jsp1 * b_dim1 + 1], &c__1, & f[is + f_dim1], ldf); i__3 = js - 1; saxpy_(&i__3, &rhs[2], &e[js * e_dim1 + 1], &c__1, &f[ is + f_dim1], ldf); i__3 = js - 1; saxpy_(&i__3, &rhs[3], &e[jsp1 * e_dim1 + 1], &c__1, & f[is + f_dim1], ldf); } if (i__ < p) { i__3 = *m - ie; sger_(&i__3, &nb, &c_b27, &a[is + (ie + 1) * a_dim1], lda, rhs, &c__1, &c__[ie + 1 + js * c_dim1], ldc); i__3 = *m - ie; sger_(&i__3, &nb, &c_b27, &d__[is + (ie + 1) * d_dim1] , ldd, &rhs[2], &c__1, &c__[ie + 1 + js * c_dim1], ldc); } } else if (mb == 2 && nb == 1) { /* Build a 4-by-4 system Z**T * x = RHS */ z__[0] = a[is + is * a_dim1]; z__[1] = a[is + isp1 * a_dim1]; z__[2] = -b[js + js * b_dim1]; z__[3] = 0.f; z__[8] = a[isp1 + is * a_dim1]; z__[9] = a[isp1 + isp1 * a_dim1]; z__[10] = 0.f; z__[11] = -b[js + js * b_dim1]; z__[16] = d__[is + is * d_dim1]; z__[17] = d__[is + isp1 * d_dim1]; z__[18] = -e[js + js * e_dim1]; z__[19] = 0.f; z__[24] = 0.f; z__[25] = d__[isp1 + isp1 * d_dim1]; z__[26] = 0.f; z__[27] = -e[js + js * e_dim1]; /* Set up right hand side(s) */ rhs[0] = c__[is + js * c_dim1]; rhs[1] = c__[isp1 + js * c_dim1]; rhs[2] = f[is + js * f_dim1]; rhs[3] = f[isp1 + js * f_dim1]; /* Solve Z**T * x = RHS */ sgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } sgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.f) { i__3 = *n; for (k = 1; k <= i__3; ++k) { sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1); sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1); /* L150: */ } *scale *= scaloc; } /* Unpack solution vector(s) */ c__[is + js * c_dim1] = rhs[0]; c__[isp1 + js * c_dim1] = rhs[1]; f[is + js * f_dim1] = rhs[2]; f[isp1 + js * f_dim1] = rhs[3]; /* Substitute R(I, J) and L(I, J) into remaining */ /* equation. */ if (j > p + 2) { i__3 = js - 1; sger_(&mb, &i__3, &c_b42, rhs, &c__1, &b[js * b_dim1 + 1], &c__1, &f[is + f_dim1], ldf); i__3 = js - 1; sger_(&mb, &i__3, &c_b42, &rhs[2], &c__1, &e[js * e_dim1 + 1], &c__1, &f[is + f_dim1], ldf); } if (i__ < p) { i__3 = *m - ie; sgemv_("T", &mb, &i__3, &c_b27, &a[is + (ie + 1) * a_dim1], lda, rhs, &c__1, &c_b42, &c__[ie + 1 + js * c_dim1], &c__1); i__3 = *m - ie; sgemv_("T", &mb, &i__3, &c_b27, &d__[is + (ie + 1) * d_dim1], ldd, &rhs[2], &c__1, &c_b42, &c__[ie + 1 + js * c_dim1], &c__1); } } else if (mb == 2 && nb == 2) { /* Build an 8-by-8 system Z**T * x = RHS */ slaset_("F", &c__8, &c__8, &c_b56, &c_b56, z__, &c__8); z__[0] = a[is + is * a_dim1]; z__[1] = a[is + isp1 * a_dim1]; z__[4] = -b[js + js * b_dim1]; z__[6] = -b[jsp1 + js * b_dim1]; z__[8] = a[isp1 + is * a_dim1]; z__[9] = a[isp1 + isp1 * a_dim1]; z__[13] = -b[js + js * b_dim1]; z__[15] = -b[jsp1 + js * b_dim1]; z__[18] = a[is + is * a_dim1]; z__[19] = a[is + isp1 * a_dim1]; z__[20] = -b[js + jsp1 * b_dim1]; z__[22] = -b[jsp1 + jsp1 * b_dim1]; z__[26] = a[isp1 + is * a_dim1]; z__[27] = a[isp1 + isp1 * a_dim1]; z__[29] = -b[js + jsp1 * b_dim1]; z__[31] = -b[jsp1 + jsp1 * b_dim1]; z__[32] = d__[is + is * d_dim1]; z__[33] = d__[is + isp1 * d_dim1]; z__[36] = -e[js + js * e_dim1]; z__[41] = d__[isp1 + isp1 * d_dim1]; z__[45] = -e[js + js * e_dim1]; z__[50] = d__[is + is * d_dim1]; z__[51] = d__[is + isp1 * d_dim1]; z__[52] = -e[js + jsp1 * e_dim1]; z__[54] = -e[jsp1 + jsp1 * e_dim1]; z__[59] = d__[isp1 + isp1 * d_dim1]; z__[61] = -e[js + jsp1 * e_dim1]; z__[63] = -e[jsp1 + jsp1 * e_dim1]; /* Set up right hand side(s) */ k = 1; ii = mb * nb + 1; i__3 = nb - 1; for (jj = 0; jj <= i__3; ++jj) { scopy_(&mb, &c__[is + (js + jj) * c_dim1], &c__1, & rhs[k - 1], &c__1); scopy_(&mb, &f[is + (js + jj) * f_dim1], &c__1, &rhs[ ii - 1], &c__1); k += mb; ii += mb; /* L160: */ } /* Solve Z**T * x = RHS */ sgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } sgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.f) { i__3 = *n; for (k = 1; k <= i__3; ++k) { sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1); sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1); /* L170: */ } *scale *= scaloc; } /* Unpack solution vector(s) */ k = 1; ii = mb * nb + 1; i__3 = nb - 1; for (jj = 0; jj <= i__3; ++jj) { scopy_(&mb, &rhs[k - 1], &c__1, &c__[is + (js + jj) * c_dim1], &c__1); scopy_(&mb, &rhs[ii - 1], &c__1, &f[is + (js + jj) * f_dim1], &c__1); k += mb; ii += mb; /* L180: */ } /* Substitute R(I, J) and L(I, J) into remaining */ /* equation. */ if (j > p + 2) { i__3 = js - 1; sgemm_("N", "T", &mb, &i__3, &nb, &c_b42, &c__[is + js * c_dim1], ldc, &b[js * b_dim1 + 1], ldb, & c_b42, &f[is + f_dim1], ldf); i__3 = js - 1; sgemm_("N", "T", &mb, &i__3, &nb, &c_b42, &f[is + js * f_dim1], ldf, &e[js * e_dim1 + 1], lde, & c_b42, &f[is + f_dim1], ldf); } if (i__ < p) { i__3 = *m - ie; sgemm_("T", "N", &i__3, &nb, &mb, &c_b27, &a[is + (ie + 1) * a_dim1], lda, &c__[is + js * c_dim1], ldc, &c_b42, &c__[ie + 1 + js * c_dim1], ldc); i__3 = *m - ie; sgemm_("T", "N", &i__3, &nb, &mb, &c_b27, &d__[is + ( ie + 1) * d_dim1], ldd, &f[is + js * f_dim1], ldf, &c_b42, &c__[ie + 1 + js * c_dim1], ldc); } } /* L190: */ } /* L200: */ } } return 0; /* End of STGSY2 */ } /* stgsy2_ */