#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 SLARFB applies a block reflector or its transpose to a general rectangular matrix. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SLARFB + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, */ /* T, LDT, C, LDC, WORK, LDWORK ) */ /* CHARACTER DIRECT, SIDE, STOREV, TRANS */ /* INTEGER K, LDC, LDT, LDV, LDWORK, M, N */ /* REAL C( LDC, * ), T( LDT, * ), V( LDV, * ), */ /* $ WORK( LDWORK, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SLARFB applies a real block reflector H or its transpose H**T to a */ /* > real m by n matrix C, from either the left or the right. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] SIDE */ /* > \verbatim */ /* > SIDE is CHARACTER*1 */ /* > = 'L': apply H or H**T from the Left */ /* > = 'R': apply H or H**T from the Right */ /* > \endverbatim */ /* > */ /* > \param[in] TRANS */ /* > \verbatim */ /* > TRANS is CHARACTER*1 */ /* > = 'N': apply H (No transpose) */ /* > = 'T': apply H**T (Transpose) */ /* > \endverbatim */ /* > */ /* > \param[in] DIRECT */ /* > \verbatim */ /* > DIRECT is CHARACTER*1 */ /* > Indicates how H is formed from a product of elementary */ /* > reflectors */ /* > = 'F': H = H(1) H(2) . . . H(k) (Forward) */ /* > = 'B': H = H(k) . . . H(2) H(1) (Backward) */ /* > \endverbatim */ /* > */ /* > \param[in] STOREV */ /* > \verbatim */ /* > STOREV is CHARACTER*1 */ /* > Indicates how the vectors which define the elementary */ /* > reflectors are stored: */ /* > = 'C': Columnwise */ /* > = 'R': Rowwise */ /* > \endverbatim */ /* > */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of rows of the matrix C. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The number of columns of the matrix C. */ /* > \endverbatim */ /* > */ /* > \param[in] K */ /* > \verbatim */ /* > K is INTEGER */ /* > The order of the matrix T (= the number of elementary */ /* > reflectors whose product defines the block reflector). */ /* > If SIDE = 'L', M >= K >= 0; */ /* > if SIDE = 'R', N >= K >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] V */ /* > \verbatim */ /* > V is REAL array, dimension */ /* > (LDV,K) if STOREV = 'C' */ /* > (LDV,M) if STOREV = 'R' and SIDE = 'L' */ /* > (LDV,N) if STOREV = 'R' and SIDE = 'R' */ /* > The matrix V. See Further Details. */ /* > \endverbatim */ /* > */ /* > \param[in] LDV */ /* > \verbatim */ /* > LDV is INTEGER */ /* > The leading dimension of the array V. */ /* > If STOREV = 'C' and SIDE = 'L', LDV >= f2cmax(1,M); */ /* > if STOREV = 'C' and SIDE = 'R', LDV >= f2cmax(1,N); */ /* > if STOREV = 'R', LDV >= K. */ /* > \endverbatim */ /* > */ /* > \param[in] T */ /* > \verbatim */ /* > T is REAL array, dimension (LDT,K) */ /* > The triangular k by k matrix T in the representation of the */ /* > block reflector. */ /* > \endverbatim */ /* > */ /* > \param[in] LDT */ /* > \verbatim */ /* > LDT is INTEGER */ /* > The leading dimension of the array T. LDT >= K. */ /* > \endverbatim */ /* > */ /* > \param[in,out] C */ /* > \verbatim */ /* > C is REAL array, dimension (LDC,N) */ /* > On entry, the m by n matrix C. */ /* > On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T. */ /* > \endverbatim */ /* > */ /* > \param[in] LDC */ /* > \verbatim */ /* > LDC is INTEGER */ /* > The leading dimension of the array C. LDC >= f2cmax(1,M). */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is REAL array, dimension (LDWORK,K) */ /* > \endverbatim */ /* > */ /* > \param[in] LDWORK */ /* > \verbatim */ /* > LDWORK is INTEGER */ /* > The leading dimension of the array WORK. */ /* > If SIDE = 'L', LDWORK >= f2cmax(1,N); */ /* > if SIDE = 'R', LDWORK >= f2cmax(1,M). */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date June 2013 */ /* > \ingroup realOTHERauxiliary */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > The shape of the matrix V and the storage of the vectors which define */ /* > the H(i) is best illustrated by the following example with n = 5 and */ /* > k = 3. The elements equal to 1 are not stored; the corresponding */ /* > array elements are modified but restored on exit. The rest of the */ /* > array is not used. */ /* > */ /* > DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */ /* > */ /* > V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */ /* > ( v1 1 ) ( 1 v2 v2 v2 ) */ /* > ( v1 v2 1 ) ( 1 v3 v3 ) */ /* > ( v1 v2 v3 ) */ /* > ( v1 v2 v3 ) */ /* > */ /* > DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */ /* > */ /* > V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */ /* > ( v1 v2 v3 ) ( v2 v2 v2 1 ) */ /* > ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */ /* > ( 1 v3 ) */ /* > ( 1 ) */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int slarfb_(char *side, char *trans, char *direct, char * storev, integer *m, integer *n, integer *k, real *v, integer *ldv, real *t, integer *ldt, real *c__, integer *ldc, real *work, integer * ldwork) { /* System generated locals */ integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1, work_offset, i__1, i__2; /* Local variables */ integer i__, j; extern logical lsame_(char *, char *); extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *), scopy_(integer *, real *, integer *, real *, integer *), strmm_(char *, char *, char *, char *, integer *, integer *, real *, real *, integer *, real *, integer *); char transt[1]; /* -- 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..-- */ /* June 2013 */ /* ===================================================================== */ /* Quick return if possible */ /* Parameter adjustments */ v_dim1 = *ldv; v_offset = 1 + v_dim1 * 1; v -= v_offset; t_dim1 = *ldt; t_offset = 1 + t_dim1 * 1; t -= t_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1 * 1; c__ -= c_offset; work_dim1 = *ldwork; work_offset = 1 + work_dim1 * 1; work -= work_offset; /* Function Body */ if (*m <= 0 || *n <= 0) { return 0; } if (lsame_(trans, "N")) { *(unsigned char *)transt = 'T'; } else { *(unsigned char *)transt = 'N'; } if (lsame_(storev, "C")) { if (lsame_(direct, "F")) { /* Let V = ( V1 ) (first K rows) */ /* ( V2 ) */ /* where V1 is unit lower triangular. */ if (lsame_(side, "L")) { /* Form H * C or H**T * C where C = ( C1 ) */ /* ( C2 ) */ /* W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK) */ /* W := C1**T */ i__1 = *k; for (j = 1; j <= i__1; ++j) { scopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); /* L10: */ } /* W := W * V1 */ strmm_("Right", "Lower", "No transpose", "Unit", n, k, &c_b14, &v[v_offset], ldv, &work[work_offset], ldwork); if (*m > *k) { /* W := W + C2**T * V2 */ i__1 = *m - *k; sgemm_("Transpose", "No transpose", n, k, &i__1, &c_b14, & c__[*k + 1 + c_dim1], ldc, &v[*k + 1 + v_dim1], ldv, &c_b14, &work[work_offset], ldwork); } /* W := W * T**T or W * T */ strmm_("Right", "Upper", transt, "Non-unit", n, k, &c_b14, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - V * W**T */ if (*m > *k) { /* C2 := C2 - V2 * W**T */ i__1 = *m - *k; sgemm_("No transpose", "Transpose", &i__1, n, k, &c_b25, & v[*k + 1 + v_dim1], ldv, &work[work_offset], ldwork, &c_b14, &c__[*k + 1 + c_dim1], ldc); } /* W := W * V1**T */ strmm_("Right", "Lower", "Transpose", "Unit", n, k, &c_b14, & v[v_offset], ldv, &work[work_offset], ldwork); /* C1 := C1 - W**T */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1]; /* L20: */ } /* L30: */ } } else if (lsame_(side, "R")) { /* Form C * H or C * H**T where C = ( C1 C2 ) */ /* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */ /* W := C1 */ i__1 = *k; for (j = 1; j <= i__1; ++j) { scopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * work_dim1 + 1], &c__1); /* L40: */ } /* W := W * V1 */ strmm_("Right", "Lower", "No transpose", "Unit", m, k, &c_b14, &v[v_offset], ldv, &work[work_offset], ldwork); if (*n > *k) { /* W := W + C2 * V2 */ i__1 = *n - *k; sgemm_("No transpose", "No transpose", m, k, &i__1, & c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + 1 + v_dim1], ldv, &c_b14, &work[work_offset], ldwork); } /* W := W * T or W * T**T */ strmm_("Right", "Upper", trans, "Non-unit", m, k, &c_b14, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - W * V**T */ if (*n > *k) { /* C2 := C2 - W * V2**T */ i__1 = *n - *k; sgemm_("No transpose", "Transpose", m, &i__1, k, &c_b25, & work[work_offset], ldwork, &v[*k + 1 + v_dim1], ldv, &c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc); } /* W := W * V1**T */ strmm_("Right", "Lower", "Transpose", "Unit", m, k, &c_b14, & v[v_offset], ldv, &work[work_offset], ldwork); /* C1 := C1 - W */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1]; /* L50: */ } /* L60: */ } } } else { /* Let V = ( V1 ) */ /* ( V2 ) (last K rows) */ /* where V2 is unit upper triangular. */ if (lsame_(side, "L")) { /* Form H * C or H**T * C where C = ( C1 ) */ /* ( C2 ) */ /* W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK) */ /* W := C2**T */ i__1 = *k; for (j = 1; j <= i__1; ++j) { scopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); /* L70: */ } /* W := W * V2 */ strmm_("Right", "Upper", "No transpose", "Unit", n, k, &c_b14, &v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], ldwork); if (*m > *k) { /* W := W + C1**T * V1 */ i__1 = *m - *k; sgemm_("Transpose", "No transpose", n, k, &i__1, &c_b14, & c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & work[work_offset], ldwork); } /* W := W * T**T or W * T */ strmm_("Right", "Lower", transt, "Non-unit", n, k, &c_b14, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - V * W**T */ if (*m > *k) { /* C1 := C1 - V1 * W**T */ i__1 = *m - *k; sgemm_("No transpose", "Transpose", &i__1, n, k, &c_b25, & v[v_offset], ldv, &work[work_offset], ldwork, & c_b14, &c__[c_offset], ldc) ; } /* W := W * V2**T */ strmm_("Right", "Upper", "Transpose", "Unit", n, k, &c_b14, & v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], ldwork); /* C2 := C2 - W**T */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { c__[*m - *k + j + i__ * c_dim1] -= work[i__ + j * work_dim1]; /* L80: */ } /* L90: */ } } else if (lsame_(side, "R")) { /* Form C * H or C * H' where C = ( C1 C2 ) */ /* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */ /* W := C2 */ i__1 = *k; for (j = 1; j <= i__1; ++j) { scopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ j * work_dim1 + 1], &c__1); /* L100: */ } /* W := W * V2 */ strmm_("Right", "Upper", "No transpose", "Unit", m, k, &c_b14, &v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], ldwork); if (*n > *k) { /* W := W + C1 * V1 */ i__1 = *n - *k; sgemm_("No transpose", "No transpose", m, k, &i__1, & c_b14, &c__[c_offset], ldc, &v[v_offset], ldv, & c_b14, &work[work_offset], ldwork); } /* W := W * T or W * T**T */ strmm_("Right", "Lower", trans, "Non-unit", m, k, &c_b14, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - W * V**T */ if (*n > *k) { /* C1 := C1 - W * V1**T */ i__1 = *n - *k; sgemm_("No transpose", "Transpose", m, &i__1, k, &c_b25, & work[work_offset], ldwork, &v[v_offset], ldv, & c_b14, &c__[c_offset], ldc) ; } /* W := W * V2**T */ strmm_("Right", "Upper", "Transpose", "Unit", m, k, &c_b14, & v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], ldwork); /* C2 := C2 - W */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + (*n - *k + j) * c_dim1] -= work[i__ + j * work_dim1]; /* L110: */ } /* L120: */ } } } } else if (lsame_(storev, "R")) { if (lsame_(direct, "F")) { /* Let V = ( V1 V2 ) (V1: first K columns) */ /* where V1 is unit upper triangular. */ if (lsame_(side, "L")) { /* Form H * C or H**T * C where C = ( C1 ) */ /* ( C2 ) */ /* W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK) */ /* W := C1**T */ i__1 = *k; for (j = 1; j <= i__1; ++j) { scopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); /* L130: */ } /* W := W * V1**T */ strmm_("Right", "Upper", "Transpose", "Unit", n, k, &c_b14, & v[v_offset], ldv, &work[work_offset], ldwork); if (*m > *k) { /* W := W + C2**T * V2**T */ i__1 = *m - *k; sgemm_("Transpose", "Transpose", n, k, &i__1, &c_b14, & c__[*k + 1 + c_dim1], ldc, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b14, &work[work_offset], ldwork); } /* W := W * T**T or W * T */ strmm_("Right", "Upper", transt, "Non-unit", n, k, &c_b14, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - V**T * W**T */ if (*m > *k) { /* C2 := C2 - V2**T * W**T */ i__1 = *m - *k; sgemm_("Transpose", "Transpose", &i__1, n, k, &c_b25, &v[( *k + 1) * v_dim1 + 1], ldv, &work[work_offset], ldwork, &c_b14, &c__[*k + 1 + c_dim1], ldc); } /* W := W * V1 */ strmm_("Right", "Upper", "No transpose", "Unit", n, k, &c_b14, &v[v_offset], ldv, &work[work_offset], ldwork); /* C1 := C1 - W**T */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1]; /* L140: */ } /* L150: */ } } else if (lsame_(side, "R")) { /* Form C * H or C * H**T where C = ( C1 C2 ) */ /* W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK) */ /* W := C1 */ i__1 = *k; for (j = 1; j <= i__1; ++j) { scopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * work_dim1 + 1], &c__1); /* L160: */ } /* W := W * V1**T */ strmm_("Right", "Upper", "Transpose", "Unit", m, k, &c_b14, & v[v_offset], ldv, &work[work_offset], ldwork); if (*n > *k) { /* W := W + C2 * V2**T */ i__1 = *n - *k; sgemm_("No transpose", "Transpose", m, k, &i__1, &c_b14, & c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b14, &work[work_offset], ldwork); } /* W := W * T or W * T**T */ strmm_("Right", "Upper", trans, "Non-unit", m, k, &c_b14, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - W * V */ if (*n > *k) { /* C2 := C2 - W * V2 */ i__1 = *n - *k; sgemm_("No transpose", "No transpose", m, &i__1, k, & c_b25, &work[work_offset], ldwork, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc); } /* W := W * V1 */ strmm_("Right", "Upper", "No transpose", "Unit", m, k, &c_b14, &v[v_offset], ldv, &work[work_offset], ldwork); /* C1 := C1 - W */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1]; /* L170: */ } /* L180: */ } } } else { /* Let V = ( V1 V2 ) (V2: last K columns) */ /* where V2 is unit lower triangular. */ if (lsame_(side, "L")) { /* Form H * C or H**T * C where C = ( C1 ) */ /* ( C2 ) */ /* W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK) */ /* W := C2**T */ i__1 = *k; for (j = 1; j <= i__1; ++j) { scopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); /* L190: */ } /* W := W * V2**T */ strmm_("Right", "Lower", "Transpose", "Unit", n, k, &c_b14, & v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[work_offset] , ldwork); if (*m > *k) { /* W := W + C1**T * V1**T */ i__1 = *m - *k; sgemm_("Transpose", "Transpose", n, k, &i__1, &c_b14, & c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & work[work_offset], ldwork); } /* W := W * T**T or W * T */ strmm_("Right", "Lower", transt, "Non-unit", n, k, &c_b14, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - V**T * W**T */ if (*m > *k) { /* C1 := C1 - V1**T * W**T */ i__1 = *m - *k; sgemm_("Transpose", "Transpose", &i__1, n, k, &c_b25, &v[ v_offset], ldv, &work[work_offset], ldwork, & c_b14, &c__[c_offset], ldc); } /* W := W * V2 */ strmm_("Right", "Lower", "No transpose", "Unit", n, k, &c_b14, &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[ work_offset], ldwork); /* C2 := C2 - W**T */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { c__[*m - *k + j + i__ * c_dim1] -= work[i__ + j * work_dim1]; /* L200: */ } /* L210: */ } } else if (lsame_(side, "R")) { /* Form C * H or C * H**T where C = ( C1 C2 ) */ /* W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK) */ /* W := C2 */ i__1 = *k; for (j = 1; j <= i__1; ++j) { scopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ j * work_dim1 + 1], &c__1); /* L220: */ } /* W := W * V2**T */ strmm_("Right", "Lower", "Transpose", "Unit", m, k, &c_b14, & v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[work_offset] , ldwork); if (*n > *k) { /* W := W + C1 * V1**T */ i__1 = *n - *k; sgemm_("No transpose", "Transpose", m, k, &i__1, &c_b14, & c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & work[work_offset], ldwork); } /* W := W * T or W * T**T */ strmm_("Right", "Lower", trans, "Non-unit", m, k, &c_b14, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - W * V */ if (*n > *k) { /* C1 := C1 - W * V1 */ i__1 = *n - *k; sgemm_("No transpose", "No transpose", m, &i__1, k, & c_b25, &work[work_offset], ldwork, &v[v_offset], ldv, &c_b14, &c__[c_offset], ldc); } /* W := W * V2 */ strmm_("Right", "Lower", "No transpose", "Unit", m, k, &c_b14, &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[ work_offset], ldwork); /* C1 := C1 - W */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + (*n - *k + j) * c_dim1] -= work[i__ + j * work_dim1]; /* L230: */ } /* L240: */ } } } } return 0; /* End of SLARFB */ } /* slarfb_ */