#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 DLASYF_AA */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download DLASYF_AA + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE DLASYF_AA( UPLO, J1, M, NB, A, LDA, IPIV, */ /* H, LDH, WORK ) */ /* CHARACTER UPLO */ /* INTEGER J1, M, NB, LDA, LDH */ /* INTEGER IPIV( * ) */ /* DOUBLE PRECISION A( LDA, * ), H( LDH, * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > DLATRF_AA factorizes a panel of a real symmetric matrix A using */ /* > the Aasen's algorithm. The panel consists of a set of NB rows of A */ /* > when UPLO is U, or a set of NB columns when UPLO is L. */ /* > */ /* > In order to factorize the panel, the Aasen's algorithm requires the */ /* > last row, or column, of the previous panel. The first row, or column, */ /* > of A is set to be the first row, or column, of an identity matrix, */ /* > which is used to factorize the first panel. */ /* > */ /* > The resulting J-th row of U, or J-th column of L, is stored in the */ /* > (J-1)-th row, or column, of A (without the unit diagonals), while */ /* > the diagonal and subdiagonal of A are overwritten by those of T. */ /* > */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] UPLO */ /* > \verbatim */ /* > UPLO is CHARACTER*1 */ /* > = 'U': Upper triangle of A is stored; */ /* > = 'L': Lower triangle of A is stored. */ /* > \endverbatim */ /* > */ /* > \param[in] J1 */ /* > \verbatim */ /* > J1 is INTEGER */ /* > The location of the first row, or column, of the panel */ /* > within the submatrix of A, passed to this routine, e.g., */ /* > when called by DSYTRF_AA, for the first panel, J1 is 1, */ /* > while for the remaining panels, J1 is 2. */ /* > \endverbatim */ /* > */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The dimension of the submatrix. M >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] NB */ /* > \verbatim */ /* > NB is INTEGER */ /* > The dimension of the panel to be facotorized. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is DOUBLE PRECISION array, dimension (LDA,M) for */ /* > the first panel, while dimension (LDA,M+1) for the */ /* > remaining panels. */ /* > */ /* > On entry, A contains the last row, or column, of */ /* > the previous panel, and the trailing submatrix of A */ /* > to be factorized, except for the first panel, only */ /* > the panel is passed. */ /* > */ /* > On exit, the leading panel is factorized. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */ /* > \endverbatim */ /* > */ /* > \param[out] IPIV */ /* > \verbatim */ /* > IPIV is INTEGER array, dimension (M) */ /* > Details of the row and column interchanges, */ /* > the row and column k were interchanged with the row and */ /* > column IPIV(k). */ /* > \endverbatim */ /* > */ /* > \param[in,out] H */ /* > \verbatim */ /* > H is DOUBLE PRECISION workspace, dimension (LDH,NB). */ /* > */ /* > \endverbatim */ /* > */ /* > \param[in] LDH */ /* > \verbatim */ /* > LDH is INTEGER */ /* > The leading dimension of the workspace H. LDH >= f2cmax(1,M). */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is DOUBLE PRECISION workspace, dimension (M). */ /* > \endverbatim */ /* > */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date November 2017 */ /* > \ingroup doubleSYcomputational */ /* ===================================================================== */ /* Subroutine */ int dlasyf_aa_(char *uplo, integer *j1, integer *m, integer *nb, doublereal *a, integer *lda, integer *ipiv, doublereal *h__, integer *ldh, doublereal *work) { /* System generated locals */ integer a_dim1, a_offset, h_dim1, h_offset, i__1; /* Local variables */ integer j, k; doublereal alpha; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); extern logical lsame_(char *, char *); extern /* Subroutine */ int dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *), dcopy_(integer *, doublereal *, integer *, doublereal *, integer *), dswap_(integer *, doublereal *, integer *, doublereal *, integer *), daxpy_( integer *, doublereal *, doublereal *, integer *, doublereal *, integer *); integer i1, k1, i2, mj; extern integer idamax_(integer *, doublereal *, integer *); extern /* Subroutine */ int dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *); doublereal piv; /* -- LAPACK computational routine (version 3.8.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* November 2017 */ /* ===================================================================== */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --ipiv; h_dim1 = *ldh; h_offset = 1 + h_dim1 * 1; h__ -= h_offset; --work; /* Function Body */ j = 1; /* K1 is the first column of the panel to be factorized */ /* i.e., K1 is 2 for the first block column, and 1 for the rest of the blocks */ k1 = 2 - *j1 + 1; if (lsame_(uplo, "U")) { /* ..................................................... */ /* Factorize A as U**T*D*U using the upper triangle of A */ /* ..................................................... */ L10: if (j > f2cmin(*m,*nb)) { goto L20; } /* K is the column to be factorized */ /* when being called from DSYTRF_AA, */ /* > for the first block column, J1 is 1, hence J1+J-1 is J, */ /* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1, */ k = *j1 + j - 1; if (j == *m) { /* Only need to compute T(J, J) */ mj = 1; } else { mj = *m - j + 1; } /* H(J:M, J) := A(J, J:M) - H(J:M, 1:(J-1)) * L(J1:(J-1), J), */ /* where H(J:M, J) has been initialized to be A(J, J:M) */ if (k > 2) { /* K is the column to be factorized */ /* > for the first block column, K is J, skipping the first two */ /* columns */ /* > for the rest of the columns, K is J+1, skipping only the */ /* first column */ i__1 = j - k1; dgemv_("No transpose", &mj, &i__1, &c_b6, &h__[j + k1 * h_dim1], ldh, &a[j * a_dim1 + 1], &c__1, &c_b8, &h__[j + j * h_dim1], &c__1); } /* Copy H(i:M, i) into WORK */ dcopy_(&mj, &h__[j + j * h_dim1], &c__1, &work[1], &c__1); if (j > k1) { /* Compute WORK := WORK - L(J-1, J:M) * T(J-1,J), */ /* where A(J-1, J) stores T(J-1, J) and A(J-2, J:M) stores U(J-1, J:M) */ alpha = -a[k - 1 + j * a_dim1]; daxpy_(&mj, &alpha, &a[k - 2 + j * a_dim1], lda, &work[1], &c__1); } /* Set A(J, J) = T(J, J) */ a[k + j * a_dim1] = work[1]; if (j < *m) { /* Compute WORK(2:M) = T(J, J) L(J, (J+1):M) */ /* where A(J, J) stores T(J, J) and A(J-1, (J+1):M) stores U(J, (J+1):M) */ if (k > 1) { alpha = -a[k + j * a_dim1]; i__1 = *m - j; daxpy_(&i__1, &alpha, &a[k - 1 + (j + 1) * a_dim1], lda, & work[2], &c__1); } /* Find f2cmax(|WORK(2:M)|) */ i__1 = *m - j; i2 = idamax_(&i__1, &work[2], &c__1) + 1; piv = work[i2]; /* Apply symmetric pivot */ if (i2 != 2 && piv != 0.) { /* Swap WORK(I1) and WORK(I2) */ i1 = 2; work[i2] = work[i1]; work[i1] = piv; /* Swap A(I1, I1+1:M) with A(I1+1:M, I2) */ i1 = i1 + j - 1; i2 = i2 + j - 1; i__1 = i2 - i1 - 1; dswap_(&i__1, &a[*j1 + i1 - 1 + (i1 + 1) * a_dim1], lda, &a[* j1 + i1 + i2 * a_dim1], &c__1); /* Swap A(I1, I2+1:M) with A(I2, I2+1:M) */ if (i2 < *m) { i__1 = *m - i2; dswap_(&i__1, &a[*j1 + i1 - 1 + (i2 + 1) * a_dim1], lda, & a[*j1 + i2 - 1 + (i2 + 1) * a_dim1], lda); } /* Swap A(I1, I1) with A(I2,I2) */ piv = a[i1 + *j1 - 1 + i1 * a_dim1]; a[*j1 + i1 - 1 + i1 * a_dim1] = a[*j1 + i2 - 1 + i2 * a_dim1]; a[*j1 + i2 - 1 + i2 * a_dim1] = piv; /* Swap H(I1, 1:J1) with H(I2, 1:J1) */ i__1 = i1 - 1; dswap_(&i__1, &h__[i1 + h_dim1], ldh, &h__[i2 + h_dim1], ldh); ipiv[i1] = i2; if (i1 > k1 - 1) { /* Swap L(1:I1-1, I1) with L(1:I1-1, I2), */ /* skipping the first column */ i__1 = i1 - k1 + 1; dswap_(&i__1, &a[i1 * a_dim1 + 1], &c__1, &a[i2 * a_dim1 + 1], &c__1); } } else { ipiv[j + 1] = j + 1; } /* Set A(J, J+1) = T(J, J+1) */ a[k + (j + 1) * a_dim1] = work[2]; if (j < *nb) { /* Copy A(J+1:M, J+1) into H(J:M, J), */ i__1 = *m - j; dcopy_(&i__1, &a[k + 1 + (j + 1) * a_dim1], lda, &h__[j + 1 + (j + 1) * h_dim1], &c__1); } /* Compute L(J+2, J+1) = WORK( 3:M ) / T(J, J+1), */ /* where A(J, J+1) = T(J, J+1) and A(J+2:M, J) = L(J+2:M, J+1) */ if (j < *m - 1) { if (a[k + (j + 1) * a_dim1] != 0.) { alpha = 1. / a[k + (j + 1) * a_dim1]; i__1 = *m - j - 1; dcopy_(&i__1, &work[3], &c__1, &a[k + (j + 2) * a_dim1], lda); i__1 = *m - j - 1; dscal_(&i__1, &alpha, &a[k + (j + 2) * a_dim1], lda); } else { i__1 = *m - j - 1; dlaset_("Full", &c__1, &i__1, &c_b22, &c_b22, &a[k + (j + 2) * a_dim1], lda); } } } ++j; goto L10; L20: ; } else { /* ..................................................... */ /* Factorize A as L*D*L**T using the lower triangle of A */ /* ..................................................... */ L30: if (j > f2cmin(*m,*nb)) { goto L40; } /* K is the column to be factorized */ /* when being called from DSYTRF_AA, */ /* > for the first block column, J1 is 1, hence J1+J-1 is J, */ /* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1, */ k = *j1 + j - 1; if (j == *m) { /* Only need to compute T(J, J) */ mj = 1; } else { mj = *m - j + 1; } /* H(J:M, J) := A(J:M, J) - H(J:M, 1:(J-1)) * L(J, J1:(J-1))^T, */ /* where H(J:M, J) has been initialized to be A(J:M, J) */ if (k > 2) { /* K is the column to be factorized */ /* > for the first block column, K is J, skipping the first two */ /* columns */ /* > for the rest of the columns, K is J+1, skipping only the */ /* first column */ i__1 = j - k1; dgemv_("No transpose", &mj, &i__1, &c_b6, &h__[j + k1 * h_dim1], ldh, &a[j + a_dim1], lda, &c_b8, &h__[j + j * h_dim1], & c__1); } /* Copy H(J:M, J) into WORK */ dcopy_(&mj, &h__[j + j * h_dim1], &c__1, &work[1], &c__1); if (j > k1) { /* Compute WORK := WORK - L(J:M, J-1) * T(J-1,J), */ /* where A(J-1, J) = T(J-1, J) and A(J, J-2) = L(J, J-1) */ alpha = -a[j + (k - 1) * a_dim1]; daxpy_(&mj, &alpha, &a[j + (k - 2) * a_dim1], &c__1, &work[1], & c__1); } /* Set A(J, J) = T(J, J) */ a[j + k * a_dim1] = work[1]; if (j < *m) { /* Compute WORK(2:M) = T(J, J) L((J+1):M, J) */ /* where A(J, J) = T(J, J) and A((J+1):M, J-1) = L((J+1):M, J) */ if (k > 1) { alpha = -a[j + k * a_dim1]; i__1 = *m - j; daxpy_(&i__1, &alpha, &a[j + 1 + (k - 1) * a_dim1], &c__1, & work[2], &c__1); } /* Find f2cmax(|WORK(2:M)|) */ i__1 = *m - j; i2 = idamax_(&i__1, &work[2], &c__1) + 1; piv = work[i2]; /* Apply symmetric pivot */ if (i2 != 2 && piv != 0.) { /* Swap WORK(I1) and WORK(I2) */ i1 = 2; work[i2] = work[i1]; work[i1] = piv; /* Swap A(I1+1:M, I1) with A(I2, I1+1:M) */ i1 = i1 + j - 1; i2 = i2 + j - 1; i__1 = i2 - i1 - 1; dswap_(&i__1, &a[i1 + 1 + (*j1 + i1 - 1) * a_dim1], &c__1, &a[ i2 + (*j1 + i1) * a_dim1], lda); /* Swap A(I2+1:M, I1) with A(I2+1:M, I2) */ if (i2 < *m) { i__1 = *m - i2; dswap_(&i__1, &a[i2 + 1 + (*j1 + i1 - 1) * a_dim1], &c__1, &a[i2 + 1 + (*j1 + i2 - 1) * a_dim1], &c__1); } /* Swap A(I1, I1) with A(I2, I2) */ piv = a[i1 + (*j1 + i1 - 1) * a_dim1]; a[i1 + (*j1 + i1 - 1) * a_dim1] = a[i2 + (*j1 + i2 - 1) * a_dim1]; a[i2 + (*j1 + i2 - 1) * a_dim1] = piv; /* Swap H(I1, I1:J1) with H(I2, I2:J1) */ i__1 = i1 - 1; dswap_(&i__1, &h__[i1 + h_dim1], ldh, &h__[i2 + h_dim1], ldh); ipiv[i1] = i2; if (i1 > k1 - 1) { /* Swap L(1:I1-1, I1) with L(1:I1-1, I2), */ /* skipping the first column */ i__1 = i1 - k1 + 1; dswap_(&i__1, &a[i1 + a_dim1], lda, &a[i2 + a_dim1], lda); } } else { ipiv[j + 1] = j + 1; } /* Set A(J+1, J) = T(J+1, J) */ a[j + 1 + k * a_dim1] = work[2]; if (j < *nb) { /* Copy A(J+1:M, J+1) into H(J+1:M, J), */ i__1 = *m - j; dcopy_(&i__1, &a[j + 1 + (k + 1) * a_dim1], &c__1, &h__[j + 1 + (j + 1) * h_dim1], &c__1); } /* Compute L(J+2, J+1) = WORK( 3:M ) / T(J, J+1), */ /* where A(J, J+1) = T(J, J+1) and A(J+2:M, J) = L(J+2:M, J+1) */ if (j < *m - 1) { if (a[j + 1 + k * a_dim1] != 0.) { alpha = 1. / a[j + 1 + k * a_dim1]; i__1 = *m - j - 1; dcopy_(&i__1, &work[3], &c__1, &a[j + 2 + k * a_dim1], & c__1); i__1 = *m - j - 1; dscal_(&i__1, &alpha, &a[j + 2 + k * a_dim1], &c__1); } else { i__1 = *m - j - 1; dlaset_("Full", &i__1, &c__1, &c_b22, &c_b22, &a[j + 2 + k * a_dim1], lda); } } } ++j; goto L30; L40: ; } return 0; /* End of DLASYF_AA */ } /* dlasyf_aa__ */