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OpenBLAS/lapack-netlib/SRC/sgglse.c

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#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;
static real c_b31 = -1.f;
static real c_b33 = 1.f;
/* > \brief <b> SGGLSE solves overdetermined or underdetermined systems for OTHER matrices</b> */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SGGLSE + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgglse.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgglse.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgglse.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK, */
/* INFO ) */
/* INTEGER INFO, LDA, LDB, LWORK, M, N, P */
/* REAL A( LDA, * ), B( LDB, * ), C( * ), D( * ), */
/* $ WORK( * ), X( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGGLSE solves the linear equality-constrained least squares (LSE) */
/* > problem: */
/* > */
/* > minimize || c - A*x ||_2 subject to B*x = d */
/* > */
/* > where A is an M-by-N matrix, B is a P-by-N matrix, c is a given */
/* > M-vector, and d is a given P-vector. It is assumed that */
/* > P <= N <= M+P, and */
/* > */
/* > rank(B) = P and rank( (A) ) = N. */
/* > ( (B) ) */
/* > */
/* > These conditions ensure that the LSE problem has a unique solution, */
/* > which is obtained using a generalized RQ factorization of the */
/* > matrices (B, A) given by */
/* > */
/* > B = (0 R)*Q, A = Z*T*Q. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] M */
/* > \verbatim */
/* > M is INTEGER */
/* > The number of rows of the matrix A. M >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The number of columns of the matrices A and B. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] P */
/* > \verbatim */
/* > P is INTEGER */
/* > The number of rows of the matrix B. 0 <= P <= N <= M+P. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* > A is REAL array, dimension (LDA,N) */
/* > On entry, the M-by-N matrix A. */
/* > On exit, the elements on and above the diagonal of the array */
/* > contain the f2cmin(M,N)-by-N upper trapezoidal matrix T. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
/* > \endverbatim */
/* > */
/* > \param[in,out] B */
/* > \verbatim */
/* > B is REAL array, dimension (LDB,N) */
/* > On entry, the P-by-N matrix B. */
/* > On exit, the upper triangle of the subarray B(1:P,N-P+1:N) */
/* > contains the P-by-P upper triangular matrix R. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* > LDB is INTEGER */
/* > The leading dimension of the array B. LDB >= f2cmax(1,P). */
/* > \endverbatim */
/* > */
/* > \param[in,out] C */
/* > \verbatim */
/* > C is REAL array, dimension (M) */
/* > On entry, C contains the right hand side vector for the */
/* > least squares part of the LSE problem. */
/* > On exit, the residual sum of squares for the solution */
/* > is given by the sum of squares of elements N-P+1 to M of */
/* > vector C. */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* > D is REAL array, dimension (P) */
/* > On entry, D contains the right hand side vector for the */
/* > constrained equation. */
/* > On exit, D is destroyed. */
/* > \endverbatim */
/* > */
/* > \param[out] X */
/* > \verbatim */
/* > X is REAL array, dimension (N) */
/* > On exit, X is the solution of the LSE problem. */
/* > \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,M+N+P). */
/* > For optimum performance LWORK >= P+f2cmin(M,N)+f2cmax(M,N)*NB, */
/* > where NB is an upper bound for the optimal blocksizes for */
/* > SGEQRF, SGERQF, SORMQR and 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 INFO = -i, the i-th argument had an illegal value. */
/* > = 1: the upper triangular factor R associated with B in the */
/* > generalized RQ factorization of the pair (B, A) is */
/* > singular, so that rank(B) < P; the least squares */
/* > solution could not be computed. */
/* > = 2: the (N-P) by (N-P) part of the upper trapezoidal factor */
/* > T associated with A in the generalized RQ factorization */
/* > of the pair (B, A) is singular, so that */
/* > rank( (A) ) < N; the least squares solution could not */
/* > ( (B) ) */
/* > be computed. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date December 2016 */
/* > \ingroup realOTHERsolve */
/* ===================================================================== */
/* Subroutine */ void sgglse_(integer *m, integer *n, integer *p, real *a,
integer *lda, real *b, integer *ldb, real *c__, real *d__, real *x,
real *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
/* Local variables */
integer lopt;
extern /* Subroutine */ void 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 *),
strmv_(char *, char *, char *, integer *, real *, integer *, real
*, integer *);
integer nb, mn, nr;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ void sggrqf_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *, real *, real *, integer *
, integer *);
integer lwkmin, nb1, nb2, nb3, nb4, lwkopt;
logical lquery;
extern /* Subroutine */ void sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *), sormrq_(char *, char *,
integer *, integer *, integer *, real *, integer *, real *, real *
, integer *, real *, integer *, integer *);
extern int strtrs_(char *, char *, char *, integer *, integer *, real *,
integer *, real *, integer *, integer *);
/* -- LAPACK driver 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;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--c__;
--d__;
--x;
--work;
/* Function Body */
*info = 0;
mn = f2cmin(*m,*n);
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*p < 0 || *p > *n || *p < *n - *m) {
*info = -3;
} else if (*lda < f2cmax(1,*m)) {
*info = -5;
} else if (*ldb < f2cmax(1,*p)) {
*info = -7;
}
/* Calculate workspace */
if (*info == 0) {
if (*n == 0) {
lwkmin = 1;
lwkopt = 1;
} else {
nb1 = ilaenv_(&c__1, "SGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6,
(ftnlen)1);
nb2 = ilaenv_(&c__1, "SGERQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6,
(ftnlen)1);
nb3 = ilaenv_(&c__1, "SORMQR", " ", m, n, p, &c_n1, (ftnlen)6, (
ftnlen)1);
nb4 = ilaenv_(&c__1, "SORMRQ", " ", m, n, p, &c_n1, (ftnlen)6, (
ftnlen)1);
/* Computing MAX */
i__1 = f2cmax(nb1,nb2), i__1 = f2cmax(i__1,nb3);
nb = f2cmax(i__1,nb4);
lwkmin = *m + *n + *p;
lwkopt = *p + mn + f2cmax(*m,*n) * nb;
}
work[1] = (real) lwkopt;
if (*lwork < lwkmin && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGGLSE", &i__1, (ftnlen)6);
return;
} else if (lquery) {
return;
}
/* Quick return if possible */
if (*n == 0) {
return;
}
/* Compute the GRQ factorization of matrices B and A: */
/* B*Q**T = ( 0 T12 ) P Z**T*A*Q**T = ( R11 R12 ) N-P */
/* N-P P ( 0 R22 ) M+P-N */
/* N-P P */
/* where T12 and R11 are upper triangular, and Q and Z are */
/* orthogonal. */
i__1 = *lwork - *p - mn;
sggrqf_(p, m, n, &b[b_offset], ldb, &work[1], &a[a_offset], lda, &work[*p
+ 1], &work[*p + mn + 1], &i__1, info);
lopt = work[*p + mn + 1];
/* Update c = Z**T *c = ( c1 ) N-P */
/* ( c2 ) M+P-N */
i__1 = f2cmax(1,*m);
i__2 = *lwork - *p - mn;
sormqr_("Left", "Transpose", m, &c__1, &mn, &a[a_offset], lda, &work[*p +
1], &c__[1], &i__1, &work[*p + mn + 1], &i__2, info);
/* Computing MAX */
i__1 = lopt, i__2 = (integer) work[*p + mn + 1];
lopt = f2cmax(i__1,i__2);
/* Solve T12*x2 = d for x2 */
if (*p > 0) {
strtrs_("Upper", "No transpose", "Non-unit", p, &c__1, &b[(*n - *p +
1) * b_dim1 + 1], ldb, &d__[1], p, info);
if (*info > 0) {
*info = 1;
return;
}
/* Put the solution in X */
scopy_(p, &d__[1], &c__1, &x[*n - *p + 1], &c__1);
/* Update c1 */
i__1 = *n - *p;
sgemv_("No transpose", &i__1, p, &c_b31, &a[(*n - *p + 1) * a_dim1 +
1], lda, &d__[1], &c__1, &c_b33, &c__[1], &c__1);
}
/* Solve R11*x1 = c1 for x1 */
if (*n > *p) {
i__1 = *n - *p;
i__2 = *n - *p;
strtrs_("Upper", "No transpose", "Non-unit", &i__1, &c__1, &a[
a_offset], lda, &c__[1], &i__2, info);
if (*info > 0) {
*info = 2;
return;
}
/* Put the solutions in X */
i__1 = *n - *p;
scopy_(&i__1, &c__[1], &c__1, &x[1], &c__1);
}
/* Compute the residual vector: */
if (*m < *n) {
nr = *m + *p - *n;
if (nr > 0) {
i__1 = *n - *m;
sgemv_("No transpose", &nr, &i__1, &c_b31, &a[*n - *p + 1 + (*m +
1) * a_dim1], lda, &d__[nr + 1], &c__1, &c_b33, &c__[*n -
*p + 1], &c__1);
}
} else {
nr = *p;
}
if (nr > 0) {
strmv_("Upper", "No transpose", "Non unit", &nr, &a[*n - *p + 1 + (*n
- *p + 1) * a_dim1], lda, &d__[1], &c__1);
saxpy_(&nr, &c_b31, &d__[1], &c__1, &c__[*n - *p + 1], &c__1);
}
/* Backward transformation x = Q**T*x */
i__1 = *lwork - *p - mn;
sormrq_("Left", "Transpose", n, &c__1, p, &b[b_offset], ldb, &work[1], &x[
1], n, &work[*p + mn + 1], &i__1, info);
/* Computing MAX */
i__1 = lopt, i__2 = (integer) work[*p + mn + 1];
work[1] = (real) (*p + mn + f2cmax(i__1,i__2));
return;
/* End of SGGLSE */
} /* sgglse_ */
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