592 lines
18 KiB
C
592 lines
18 KiB
C
#include <math.h>
|
|
#include <stdlib.h>
|
|
#include <string.h>
|
|
#include <stdio.h>
|
|
#include <complex.h>
|
|
#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]/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 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;
|
|
|
|
/* > \brief \b SGGRQF */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download SGGRQF + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sggrqf.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sggrqf.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sggrqf.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE SGGRQF( M, P, N, A, LDA, TAUA, B, LDB, TAUB, WORK, */
|
|
/* LWORK, INFO ) */
|
|
|
|
/* INTEGER INFO, LDA, LDB, LWORK, M, N, P */
|
|
/* REAL A( LDA, * ), B( LDB, * ), TAUA( * ), TAUB( * ), */
|
|
/* $ WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > SGGRQF computes a generalized RQ factorization of an M-by-N matrix A */
|
|
/* > and a P-by-N matrix B: */
|
|
/* > */
|
|
/* > A = R*Q, B = Z*T*Q, */
|
|
/* > */
|
|
/* > where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal */
|
|
/* > matrix, and R and T assume one of the forms: */
|
|
/* > */
|
|
/* > if M <= N, R = ( 0 R12 ) M, or if M > N, R = ( R11 ) M-N, */
|
|
/* > N-M M ( R21 ) N */
|
|
/* > N */
|
|
/* > */
|
|
/* > where R12 or R21 is upper triangular, and */
|
|
/* > */
|
|
/* > if P >= N, T = ( T11 ) N , or if P < N, T = ( T11 T12 ) P, */
|
|
/* > ( 0 ) P-N P N-P */
|
|
/* > N */
|
|
/* > */
|
|
/* > where T11 is upper triangular. */
|
|
/* > */
|
|
/* > In particular, if B is square and nonsingular, the GRQ factorization */
|
|
/* > of A and B implicitly gives the RQ factorization of A*inv(B): */
|
|
/* > */
|
|
/* > A*inv(B) = (R*inv(T))*Z**T */
|
|
/* > */
|
|
/* > where inv(B) denotes the inverse of the matrix B, and Z**T denotes the */
|
|
/* > transpose of the matrix Z. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of rows of the matrix A. M >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] P */
|
|
/* > \verbatim */
|
|
/* > P is INTEGER */
|
|
/* > The number of rows of the matrix B. P >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of columns of the matrices A and B. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is REAL array, dimension (LDA,N) */
|
|
/* > On entry, the M-by-N matrix A. */
|
|
/* > On exit, if M <= N, the upper triangle of the subarray */
|
|
/* > A(1:M,N-M+1:N) contains the M-by-M upper triangular matrix R; */
|
|
/* > if M > N, the elements on and above the (M-N)-th subdiagonal */
|
|
/* > contain the M-by-N upper trapezoidal matrix R; the remaining */
|
|
/* > elements, with the array TAUA, represent the orthogonal */
|
|
/* > matrix Q as a product of elementary reflectors (see Further */
|
|
/* > Details). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] TAUA */
|
|
/* > \verbatim */
|
|
/* > TAUA is REAL array, dimension (f2cmin(M,N)) */
|
|
/* > The scalar factors of the elementary reflectors which */
|
|
/* > represent the orthogonal matrix Q (see Further Details). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] B */
|
|
/* > \verbatim */
|
|
/* > B is REAL array, dimension (LDB,N) */
|
|
/* > On entry, the P-by-N matrix B. */
|
|
/* > On exit, the elements on and above the diagonal of the array */
|
|
/* > contain the f2cmin(P,N)-by-N upper trapezoidal matrix T (T is */
|
|
/* > upper triangular if P >= N); the elements below the diagonal, */
|
|
/* > with the array TAUB, represent the orthogonal matrix Z as a */
|
|
/* > product of elementary reflectors (see Further Details). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of the array B. LDB >= f2cmax(1,P). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] TAUB */
|
|
/* > \verbatim */
|
|
/* > TAUB is REAL array, dimension (f2cmin(P,N)) */
|
|
/* > The scalar factors of the elementary reflectors which */
|
|
/* > represent the orthogonal matrix Z (see Further Details). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is REAL array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. LWORK >= f2cmax(1,N,M,P). */
|
|
/* > For optimum performance LWORK >= f2cmax(N,M,P)*f2cmax(NB1,NB2,NB3), */
|
|
/* > where NB1 is the optimal blocksize for the RQ factorization */
|
|
/* > of an M-by-N matrix, NB2 is the optimal blocksize for the */
|
|
/* > QR factorization of a P-by-N matrix, and NB3 is the optimal */
|
|
/* > blocksize for a call of SORMRQ. */
|
|
/* > */
|
|
/* > If LWORK = -1, then a workspace query is assumed; the routine */
|
|
/* > only calculates the optimal size of the WORK array, returns */
|
|
/* > this value as the first entry of the WORK array, and no error */
|
|
/* > message related to LWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INF0= -i, the i-th argument had an illegal value. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup realOTHERcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > The matrix Q is represented as a product of elementary reflectors */
|
|
/* > */
|
|
/* > Q = H(1) H(2) . . . H(k), where k = f2cmin(m,n). */
|
|
/* > */
|
|
/* > Each H(i) has the form */
|
|
/* > */
|
|
/* > H(i) = I - taua * v * v**T */
|
|
/* > */
|
|
/* > where taua is a real scalar, and v is a real vector with */
|
|
/* > v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in */
|
|
/* > A(m-k+i,1:n-k+i-1), and taua in TAUA(i). */
|
|
/* > To form Q explicitly, use LAPACK subroutine SORGRQ. */
|
|
/* > To use Q to update another matrix, use LAPACK subroutine SORMRQ. */
|
|
/* > */
|
|
/* > The matrix Z is represented as a product of elementary reflectors */
|
|
/* > */
|
|
/* > Z = H(1) H(2) . . . H(k), where k = f2cmin(p,n). */
|
|
/* > */
|
|
/* > Each H(i) has the form */
|
|
/* > */
|
|
/* > H(i) = I - taub * v * v**T */
|
|
/* > */
|
|
/* > where taub is a real scalar, and v is a real vector with */
|
|
/* > v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i), */
|
|
/* > and taub in TAUB(i). */
|
|
/* > To form Z explicitly, use LAPACK subroutine SORGQR. */
|
|
/* > To use Z to update another matrix, use LAPACK subroutine SORMQR. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void sggrqf_(integer *m, integer *p, integer *n, real *a,
|
|
integer *lda, real *taua, real *b, integer *ldb, real *taub, real *
|
|
work, integer *lwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
|
|
|
|
/* Local variables */
|
|
integer lopt, nb;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
extern /* Subroutine */ void sgeqrf_(integer *, integer *, real *, integer
|
|
*, real *, real *, integer *, integer *), sgerqf_(integer *,
|
|
integer *, real *, integer *, real *, real *, integer *, integer *
|
|
);
|
|
integer nb1, nb2, nb3, lwkopt;
|
|
logical lquery;
|
|
extern /* Subroutine */ void sormrq_(char *, char *, integer *, integer *,
|
|
integer *, real *, integer *, real *, real *, integer *, real *,
|
|
integer *, integer *);
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
--taua;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
--taub;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
nb1 = ilaenv_(&c__1, "SGERQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (
|
|
ftnlen)1);
|
|
nb2 = ilaenv_(&c__1, "SGEQRF", " ", p, n, &c_n1, &c_n1, (ftnlen)6, (
|
|
ftnlen)1);
|
|
nb3 = ilaenv_(&c__1, "SORMRQ", " ", m, n, p, &c_n1, (ftnlen)6, (ftnlen)1);
|
|
/* Computing MAX */
|
|
i__1 = f2cmax(nb1,nb2);
|
|
nb = f2cmax(i__1,nb3);
|
|
/* Computing MAX */
|
|
i__1 = f2cmax(*n,*m);
|
|
lwkopt = f2cmax(i__1,*p) * nb;
|
|
work[1] = (real) lwkopt;
|
|
lquery = *lwork == -1;
|
|
if (*m < 0) {
|
|
*info = -1;
|
|
} else if (*p < 0) {
|
|
*info = -2;
|
|
} else if (*n < 0) {
|
|
*info = -3;
|
|
} else if (*lda < f2cmax(1,*m)) {
|
|
*info = -5;
|
|
} else if (*ldb < f2cmax(1,*p)) {
|
|
*info = -8;
|
|
} else /* if(complicated condition) */ {
|
|
/* Computing MAX */
|
|
i__1 = f2cmax(1,*m), i__1 = f2cmax(i__1,*p);
|
|
if (*lwork < f2cmax(i__1,*n) && ! lquery) {
|
|
*info = -11;
|
|
}
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("SGGRQF", &i__1, (ftnlen)6);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* RQ factorization of M-by-N matrix A: A = R*Q */
|
|
|
|
sgerqf_(m, n, &a[a_offset], lda, &taua[1], &work[1], lwork, info);
|
|
lopt = work[1];
|
|
|
|
/* Update B := B*Q**T */
|
|
|
|
i__1 = f2cmin(*m,*n);
|
|
/* Computing MAX */
|
|
i__2 = 1, i__3 = *m - *n + 1;
|
|
sormrq_("Right", "Transpose", p, n, &i__1, &a[f2cmax(i__2,i__3) + a_dim1],
|
|
lda, &taua[1], &b[b_offset], ldb, &work[1], lwork, info);
|
|
/* Computing MAX */
|
|
i__1 = lopt, i__2 = (integer) work[1];
|
|
lopt = f2cmax(i__1,i__2);
|
|
|
|
/* QR factorization of P-by-N matrix B: B = Z*T */
|
|
|
|
sgeqrf_(p, n, &b[b_offset], ldb, &taub[1], &work[1], lwork, info);
|
|
/* Computing MAX */
|
|
i__1 = lopt, i__2 = (integer) work[1];
|
|
work[1] = (real) f2cmax(i__1,i__2);
|
|
|
|
return;
|
|
|
|
/* End of SGGRQF */
|
|
|
|
} /* sggrqf_ */
|
|
|