#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 blasint logical; 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 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);} #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) /* -- translated by f2c (version 20000121). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ /* Table of constant values */ static integer c__1 = 1; static integer c_n1 = -1; static integer c__3 = 3; static integer c__2 = 2; /* Subroutine */ int sgeqp3rk_(integer *m, integer *n, integer *nrhs, integer *kmax, real *abstol, real *reltol, real *a, integer *lda, integer *k, real *maxc2nrmk, real *relmaxc2nrmk, integer *jpiv, real *tau, real * work, integer *lwork, integer *iwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; real r__1, r__2; /* Local variables */ real maxc2nrm; extern /* Subroutine */ int slaqp2rk_(integer *, integer *, integer *, integer *, integer *, real *, real *, integer *, real *, real *, integer *, integer *, real *, real *, integer *, real *, real *, real *, real *, integer *), slaqp3rk_(integer *, integer *, integer *, integer *, integer *, real *, real *, integer *, real * , real *, integer *, logical *, integer *, real *, real *, integer *, real *, real *, real *, real *, real *, integer *, integer *, integer *); logical done; integer jmax; extern real snrm2_(integer *, real *, integer *); integer j, jmaxc2nrm, jmaxb, nbmin, iinfo, n_sub__, minmn; real myhugeval; integer jb, nb, kf, nx; extern real slamch_(char *); real safmin; extern /* Subroutine */ int xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen), isamax_(integer *, real *, integer *); extern logical sisnan_(real *); integer kp1, lwkopt; logical lquery; integer jbf; real eps; integer iws, ioffset; /* -- LAPACK computational routine -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* ===================================================================== */ /* Test input arguments */ /* ==================== */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --jpiv; --tau; --work; --iwork; /* Function Body */ *info = 0; lquery = *lwork == -1; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*nrhs < 0) { *info = -3; } else if (*kmax < 0) { *info = -4; } else if (sisnan_(abstol)) { *info = -5; } else if (sisnan_(reltol)) { *info = -6; } else if (*lda < f2cmax(1,*m)) { *info = -8; } /* If the input parameters M, N, NRHS, KMAX, LDA are valid: */ /* a) Test the input workspace size LWORK for the minimum */ /* size requirement IWS. */ /* b) Determine the optimal block size NB and optimal */ /* workspace size LWKOPT to be returned in WORK(1) */ /* in case of (1) LWORK < IWS, (2) LQUERY = .TRUE., */ /* (3) when routine exits. */ /* Here, IWS is the miminum workspace required for unblocked */ /* code. */ if (*info == 0) { minmn = f2cmin(*m,*n); if (minmn == 0) { iws = 1; lwkopt = 1; } else { /* Minimal workspace size in case of using only unblocked */ /* BLAS 2 code in SLAQP2RK. */ /* 1) SGEQP3RK and SLAQP2RK: 2*N to store full and partial */ /* column 2-norms. */ /* 2) SLAQP2RK: N+NRHS-1 to use in WORK array that is used */ /* in SLARF subroutine inside SLAQP2RK to apply an */ /* elementary reflector from the left. */ /* TOTAL_WORK_SIZE = 3*N + NRHS - 1 */ iws = *n * 3 + *nrhs - 1; /* Assign to NB optimal block size. */ nb = ilaenv_(&c__1, "SGEQP3RK", " ", m, n, &c_n1, &c_n1, (ftnlen) 8, (ftnlen)1); /* A formula for the optimal workspace size in case of using */ /* both unblocked BLAS 2 in SLAQP2RK and blocked BLAS 3 code */ /* in SLAQP3RK. */ /* 1) SGEQP3RK, SLAQP2RK, SLAQP3RK: 2*N to store full and */ /* partial column 2-norms. */ /* 2) SLAQP2RK: N+NRHS-1 to use in WORK array that is used */ /* in SLARF subroutine to apply an elementary reflector */ /* from the left. */ /* 3) SLAQP3RK: NB*(N+NRHS) to use in the work array F that */ /* is used to apply a block reflector from */ /* the left. */ /* 4) SLAQP3RK: NB to use in the auxilixary array AUX. */ /* Sizes (2) and ((3) + (4)) should intersect, therefore */ /* TOTAL_WORK_SIZE = 2*N + NB*( N+NRHS+1 ), given NBMIN=2. */ lwkopt = (*n << 1) + nb * (*n + *nrhs + 1); } work[1] = (real) lwkopt; if (*lwork < iws && ! lquery) { *info = -15; } } /* NOTE: The optimal workspace size is returned in WORK(1), if */ /* the input parameters M, N, NRHS, KMAX, LDA are valid. */ if (*info != 0) { i__1 = -(*info); xerbla_("SGEQP3RK", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible for M=0 or N=0. */ if (minmn == 0) { *k = 0; *maxc2nrmk = 0.f; *relmaxc2nrmk = 0.f; work[1] = (real) lwkopt; return 0; } /* ================================================================== */ /* Initialize column pivot array JPIV. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { jpiv[j] = j; } /* ================================================================== */ /* Initialize storage for partial and exact column 2-norms. */ /* a) The elements WORK(1:N) are used to store partial column */ /* 2-norms of the matrix A, and may decrease in each computation */ /* step; initialize to the values of complete columns 2-norms. */ /* b) The elements WORK(N+1:2*N) are used to store complete column */ /* 2-norms of the matrix A, they are not changed during the */ /* computation; initialize the values of complete columns 2-norms. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { work[j] = snrm2_(m, &a[j * a_dim1 + 1], &c__1); work[*n + j] = work[j]; } /* ================================================================== */ /* Compute the pivot column index and the maximum column 2-norm */ /* for the whole original matrix stored in A(1:M,1:N). */ kp1 = isamax_(n, &work[1], &c__1); maxc2nrm = work[kp1]; /* ==================================================================. */ if (sisnan_(&maxc2nrm)) { /* Check if the matrix A contains NaN, set INFO parameter */ /* to the column number where the first NaN is found and return */ /* from the routine. */ *k = 0; *info = kp1; /* Set MAXC2NRMK and RELMAXC2NRMK to NaN. */ *maxc2nrmk = maxc2nrm; *relmaxc2nrmk = maxc2nrm; /* Array TAU is not set and contains undefined elements. */ work[1] = (real) lwkopt; return 0; } /* =================================================================== */ if (maxc2nrm == 0.f) { /* Check is the matrix A is a zero matrix, set array TAU and */ /* return from the routine. */ *k = 0; *maxc2nrmk = 0.f; *relmaxc2nrmk = 0.f; i__1 = minmn; for (j = 1; j <= i__1; ++j) { tau[j] = 0.f; } work[1] = (real) lwkopt; return 0; } /* =================================================================== */ myhugeval = slamch_("Overflow"); if (maxc2nrm > myhugeval) { /* Check if the matrix A contains +Inf or -Inf, set INFO parameter */ /* to the column number, where the first +/-Inf is found plus N, */ /* and continue the computation. */ *info = *n + kp1; } /* ================================================================== */ /* Quick return if possible for the case when the first */ /* stopping criterion is satisfied, i.e. KMAX = 0. */ if (*kmax == 0) { *k = 0; *maxc2nrmk = maxc2nrm; *relmaxc2nrmk = 1.f; i__1 = minmn; for (j = 1; j <= i__1; ++j) { tau[j] = 0.f; } work[1] = (real) lwkopt; return 0; } /* ================================================================== */ eps = slamch_("Epsilon"); /* Adjust ABSTOL */ if (*abstol >= 0.f) { safmin = slamch_("Safe minimum"); /* Computing MAX */ r__1 = *abstol, r__2 = safmin * 2.f; *abstol = f2cmax(r__1,r__2); } /* Adjust RELTOL */ if (*reltol >= 0.f) { *reltol = f2cmax(*reltol,eps); } /* =================================================================== */ /* JMAX is the maximum index of the column to be factorized, */ /* which is also limited by the first stopping criterion KMAX. */ jmax = f2cmin(*kmax,minmn); /* =================================================================== */ /* Quick return if possible for the case when the second or third */ /* stopping criterion for the whole original matrix is satified, */ /* i.e. MAXC2NRM <= ABSTOL or RELMAXC2NRM <= RELTOL */ /* (which is ONE <= RELTOL). */ if (maxc2nrm <= *abstol || 1.f <= *reltol) { *k = 0; *maxc2nrmk = maxc2nrm; *relmaxc2nrmk = 1.f; i__1 = minmn; for (j = 1; j <= i__1; ++j) { tau[j] = 0.f; } work[1] = (real) lwkopt; return 0; } /* ================================================================== */ /* Factorize columns */ /* ================================================================== */ /* Determine the block size. */ nbmin = 2; nx = 0; if (nb > 1 && nb < minmn) { /* Determine when to cross over from blocked to unblocked code. */ /* (for N less than NX, unblocked code should be used). */ /* Computing MAX */ i__1 = 0, i__2 = ilaenv_(&c__3, "SGEQP3RK", " ", m, n, &c_n1, &c_n1, ( ftnlen)8, (ftnlen)1); nx = f2cmax(i__1,i__2); if (nx < minmn) { /* Determine if workspace is large enough for blocked code. */ if (*lwork < lwkopt) { /* Not enough workspace to use optimal block size that */ /* is currently stored in NB. */ /* Reduce NB and determine the minimum value of NB. */ nb = (*lwork - (*n << 1)) / (*n + 1); /* Computing MAX */ i__1 = 2, i__2 = ilaenv_(&c__2, "SGEQP3RK", " ", m, n, &c_n1, &c_n1, (ftnlen)8, (ftnlen)1); nbmin = f2cmax(i__1,i__2); } } } /* ================================================================== */ /* DONE is the boolean flag to rerpresent the case when the */ /* factorization completed in the block factorization routine, */ /* before the end of the block. */ done = FALSE_; /* J is the column index. */ j = 1; /* (1) Use blocked code initially. */ /* JMAXB is the maximum column index of the block, when the */ /* blocked code is used, is also limited by the first stopping */ /* criterion KMAX. */ /* Computing MIN */ i__1 = *kmax, i__2 = minmn - nx; jmaxb = f2cmin(i__1,i__2); if (nb >= nbmin && nb < jmax && jmaxb > 0) { /* Loop over the column blocks of the matrix A(1:M,1:JMAXB). Here: */ /* J is the column index of a column block; */ /* JB is the column block size to pass to block factorization */ /* routine in a loop step; */ /* JBF is the number of columns that were actually factorized */ /* that was returned by the block factorization routine */ /* in a loop step, JBF <= JB; */ /* N_SUB is the number of columns in the submatrix; */ /* IOFFSET is the number of rows that should not be factorized. */ while(j <= jmaxb) { /* Computing MIN */ i__1 = nb, i__2 = jmaxb - j + 1; jb = f2cmin(i__1,i__2); n_sub__ = *n - j + 1; ioffset = j - 1; /* Factorize JB columns among the columns A(J:N). */ i__1 = *n + *nrhs - j + 1; slaqp3rk_(m, &n_sub__, nrhs, &ioffset, &jb, abstol, reltol, &kp1, &maxc2nrm, &a[j * a_dim1 + 1], lda, &done, &jbf, maxc2nrmk, relmaxc2nrmk, &jpiv[j], &tau[j], &work[j], & work[*n + j], &work[(*n << 1) + 1], &work[(*n << 1) + jb + 1], &i__1, &iwork[1], &iinfo); /* Set INFO on the first occurence of Inf. */ if (iinfo > n_sub__ && *info == 0) { *info = (ioffset << 1) + iinfo; } if (done) { /* Either the submatrix is zero before the end of the */ /* column block, or ABSTOL or RELTOL criterion is */ /* satisfied before the end of the column block, we can */ /* return from the routine. Perform the following before */ /* returning: */ /* a) Set the number of factorized columns K, */ /* K = IOFFSET + JBF from the last call of blocked */ /* routine. */ /* NOTE: 1) MAXC2NRMK and RELMAXC2NRMK are returned */ /* by the block factorization routine; */ /* 2) The remaining TAUs are set to ZERO by the */ /* block factorization routine. */ *k = ioffset + jbf; /* Set INFO on the first occurrence of NaN, NaN takes */ /* prcedence over Inf. */ if (iinfo <= n_sub__ && iinfo > 0) { *info = ioffset + iinfo; } /* Return from the routine. */ work[1] = (real) lwkopt; return 0; } j += jbf; } } /* Use unblocked code to factor the last or only block. */ /* J = JMAX+1 means we factorized the maximum possible number of */ /* columns, that is in ELSE clause we need to compute */ /* the MAXC2NORM and RELMAXC2NORM to return after we processed */ /* the blocks. */ if (j <= jmax) { /* N_SUB is the number of columns in the submatrix; */ /* IOFFSET is the number of rows that should not be factorized. */ n_sub__ = *n - j + 1; ioffset = j - 1; i__1 = jmax - j + 1; slaqp2rk_(m, &n_sub__, nrhs, &ioffset, &i__1, abstol, reltol, &kp1, & maxc2nrm, &a[j * a_dim1 + 1], lda, &kf, maxc2nrmk, relmaxc2nrmk, &jpiv[j], &tau[j], &work[j], &work[*n + j], & work[(*n << 1) + 1], &iinfo); /* ABSTOL or RELTOL criterion is satisfied when the number of */ /* the factorized columns KF is smaller then the number */ /* of columns JMAX-J+1 supplied to be factorized by the */ /* unblocked routine, we can return from */ /* the routine. Perform the following before returning: */ /* a) Set the number of factorized columns K, */ /* b) MAXC2NRMK and RELMAXC2NRMK are returned by the */ /* unblocked factorization routine above. */ *k = j - 1 + kf; /* Set INFO on the first exception occurence. */ /* Set INFO on the first exception occurence of Inf or NaN, */ /* (NaN takes precedence over Inf). */ if (iinfo > n_sub__ && *info == 0) { *info = (ioffset << 1) + iinfo; } else if (iinfo <= n_sub__ && iinfo > 0) { *info = ioffset + iinfo; } } else { /* Compute the return values for blocked code. */ /* Set the number of factorized columns if the unblocked routine */ /* was not called. */ *k = jmax; /* If there exits a residual matrix after the blocked code: */ /* 1) compute the values of MAXC2NRMK, RELMAXC2NRMK of the */ /* residual matrix, otherwise set them to ZERO; */ /* 2) Set TAU(K+1:MINMN) to ZERO. */ if (*k < minmn) { i__1 = *n - *k; jmaxc2nrm = *k + isamax_(&i__1, &work[*k + 1], &c__1); *maxc2nrmk = work[jmaxc2nrm]; if (*k == 0) { *relmaxc2nrmk = 1.f; } else { *relmaxc2nrmk = *maxc2nrmk / maxc2nrm; } i__1 = minmn; for (j = *k + 1; j <= i__1; ++j) { tau[j] = 0.f; } } /* END IF( J.LE.JMAX ) THEN */ } work[1] = (real) lwkopt; return 0; /* End of SGEQP3RK */ } /* sgeqp3rk_ */