OpenBLAS/lapack-netlib/SRC/sgbcon.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;

/* > \brief \b SGBCON */

/*  =========== DOCUMENTATION =========== */

/* Online html documentation available at */
/*            http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */
/* > Download SGBCON + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgbcon.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgbcon.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgbcon.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

/*  Definition: */
/*  =========== */

/*       SUBROUTINE SGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, */
/*                          WORK, IWORK, INFO ) */

/*       CHARACTER          NORM */
/*       INTEGER            INFO, KL, KU, LDAB, N */
/*       REAL               ANORM, RCOND */
/*       INTEGER            IPIV( * ), IWORK( * ) */
/*       REAL               AB( LDAB, * ), WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGBCON estimates the reciprocal of the condition number of a real */
/* > general band matrix A, in either the 1-norm or the infinity-norm, */
/* > using the LU factorization computed by SGBTRF. */
/* > */
/* > An estimate is obtained for norm(inv(A)), and the reciprocal of the */
/* > condition number is computed as */
/* >    RCOND = 1 / ( norm(A) * norm(inv(A)) ). */
/* > \endverbatim */

/*  Arguments: */
/*  ========== */

/* > \param[in] NORM */
/* > \verbatim */
/* >          NORM is CHARACTER*1 */
/* >          Specifies whether the 1-norm condition number or the */
/* >          infinity-norm condition number is required: */
/* >          = '1' or 'O':  1-norm; */
/* >          = 'I':         Infinity-norm. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the matrix A.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] KL */
/* > \verbatim */
/* >          KL is INTEGER */
/* >          The number of subdiagonals within the band of A.  KL >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] KU */
/* > \verbatim */
/* >          KU is INTEGER */
/* >          The number of superdiagonals within the band of A.  KU >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] AB */
/* > \verbatim */
/* >          AB is REAL array, dimension (LDAB,N) */
/* >          Details of the LU factorization of the band matrix A, as */
/* >          computed by SGBTRF.  U is stored as an upper triangular band */
/* >          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and */
/* >          the multipliers used during the factorization are stored in */
/* >          rows KL+KU+2 to 2*KL+KU+1. */
/* > \endverbatim */
/* > */
/* > \param[in] LDAB */
/* > \verbatim */
/* >          LDAB is INTEGER */
/* >          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1. */
/* > \endverbatim */
/* > */
/* > \param[in] IPIV */
/* > \verbatim */
/* >          IPIV is INTEGER array, dimension (N) */
/* >          The pivot indices; for 1 <= i <= N, row i of the matrix was */
/* >          interchanged with row IPIV(i). */
/* > \endverbatim */
/* > */
/* > \param[in] ANORM */
/* > \verbatim */
/* >          ANORM is REAL */
/* >          If NORM = '1' or 'O', the 1-norm of the original matrix A. */
/* >          If NORM = 'I', the infinity-norm of the original matrix A. */
/* > \endverbatim */
/* > */
/* > \param[out] RCOND */
/* > \verbatim */
/* >          RCOND is REAL */
/* >          The reciprocal of the condition number of the matrix A, */
/* >          computed as RCOND = 1/(norm(A) * norm(inv(A))). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is REAL array, dimension (3*N) */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* >          IWORK is INTEGER array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is INTEGER */
/* >          = 0:  successful exit */
/* >          < 0: if INFO = -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 realGBcomputational */

/*  ===================================================================== */
/* Subroutine */ void sgbcon_(char *norm, integer *n, integer *kl, integer *ku,
	 real *ab, integer *ldab, integer *ipiv, real *anorm, real *rcond, 
	real *work, integer *iwork, integer *info)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, i__1, i__2, i__3;
    real r__1;

    /* Local variables */
    integer kase;
    extern real sdot_(integer *, real *, integer *, real *, integer *);
    integer kase1, j;
    real t, scale;
    extern logical lsame_(char *, char *);
    integer isave[3];
    logical lnoti;
    extern /* Subroutine */ void srscl_(integer *, real *, real *, integer *), 
	    saxpy_(integer *, real *, real *, integer *, real *, integer *), 
	    slacn2_(integer *, real *, real *, integer *, real *, integer *, 
	    integer *);
    integer kd, lm, jp, ix;
    extern real slamch_(char *);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    extern integer isamax_(integer *, real *, integer *);
    real ainvnm;
    extern /* Subroutine */ void slatbs_(char *, char *, char *, char *, 
	    integer *, integer *, real *, integer *, real *, real *, real *, 
	    integer *);
    logical onenrm;
    char normin[1];
    real smlnum;


/*  -- 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 */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1 * 1;
    ab -= ab_offset;
    --ipiv;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;
    onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O");
    if (! onenrm && ! lsame_(norm, "I")) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*kl < 0) {
	*info = -3;
    } else if (*ku < 0) {
	*info = -4;
    } else if (*ldab < (*kl << 1) + *ku + 1) {
	*info = -6;
    } else if (*anorm < 0.f) {
	*info = -8;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SGBCON", &i__1, (ftnlen)6);
	return;
    }

/*     Quick return if possible */

    *rcond = 0.f;
    if (*n == 0) {
	*rcond = 1.f;
	return;
    } else if (*anorm == 0.f) {
	return;
    }

    smlnum = slamch_("Safe minimum");

/*     Estimate the norm of inv(A). */

    ainvnm = 0.f;
    *(unsigned char *)normin = 'N';
    if (onenrm) {
	kase1 = 1;
    } else {
	kase1 = 2;
    }
    kd = *kl + *ku + 1;
    lnoti = *kl > 0;
    kase = 0;
L10:
    slacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave);
    if (kase != 0) {
	if (kase == kase1) {

/*           Multiply by inv(L). */

	    if (lnoti) {
		i__1 = *n - 1;
		for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
		    i__2 = *kl, i__3 = *n - j;
		    lm = f2cmin(i__2,i__3);
		    jp = ipiv[j];
		    t = work[jp];
		    if (jp != j) {
			work[jp] = work[j];
			work[j] = t;
		    }
		    r__1 = -t;
		    saxpy_(&lm, &r__1, &ab[kd + 1 + j * ab_dim1], &c__1, &
			    work[j + 1], &c__1);
/* L20: */
		}
	    }

/*           Multiply by inv(U). */

	    i__1 = *kl + *ku;
	    slatbs_("Upper", "No transpose", "Non-unit", normin, n, &i__1, &
		    ab[ab_offset], ldab, &work[1], &scale, &work[(*n << 1) + 
		    1], info);
	} else {

/*           Multiply by inv(U**T). */

	    i__1 = *kl + *ku;
	    slatbs_("Upper", "Transpose", "Non-unit", normin, n, &i__1, &ab[
		    ab_offset], ldab, &work[1], &scale, &work[(*n << 1) + 1], 
		    info);

/*           Multiply by inv(L**T). */

	    if (lnoti) {
		for (j = *n - 1; j >= 1; --j) {
/* Computing MIN */
		    i__1 = *kl, i__2 = *n - j;
		    lm = f2cmin(i__1,i__2);
		    work[j] -= sdot_(&lm, &ab[kd + 1 + j * ab_dim1], &c__1, &
			    work[j + 1], &c__1);
		    jp = ipiv[j];
		    if (jp != j) {
			t = work[jp];
			work[jp] = work[j];
			work[j] = t;
		    }
/* L30: */
		}
	    }
	}

/*        Divide X by 1/SCALE if doing so will not cause overflow. */

	*(unsigned char *)normin = 'Y';
	if (scale != 1.f) {
	    ix = isamax_(n, &work[1], &c__1);
	    if (scale < (r__1 = work[ix], abs(r__1)) * smlnum || scale == 0.f)
		     {
		goto L40;
	    }
	    srscl_(n, &scale, &work[1], &c__1);
	}
	goto L10;
    }

/*     Compute the estimate of the reciprocal condition number. */

    if (ainvnm != 0.f) {
	*rcond = 1.f / ainvnm / *anorm;
    }

L40:
    return;

/*     End of SGBCON */

} /* sgbcon_ */