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OpenBLAS/lapack-netlib/SRC/dlansf.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 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++ */
#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<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
}
}
pCf(z) = zdotc;
}
#else
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
#endif
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
}
}
pCd(z) = zdotc;
}
#else
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
#endif
static inline void cdotu_(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<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
}
}
pCf(z) = zdotc;
}
#else
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i]) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
#endif
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
}
}
pCd(z) = zdotc;
}
#else
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i]) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
#endif
/* -- 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 DLANSF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the ele
ment of largest absolute value of a symmetric matrix in RFP format. */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DLANSF + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlansf.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlansf.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlansf.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* DOUBLE PRECISION FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK ) */
/* CHARACTER NORM, TRANSR, UPLO */
/* INTEGER N */
/* DOUBLE PRECISION A( 0: * ), WORK( 0: * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLANSF returns the value of the one norm, or the Frobenius norm, or */
/* > the infinity norm, or the element of largest absolute value of a */
/* > real symmetric matrix A in RFP format. */
/* > \endverbatim */
/* > */
/* > \return DLANSF */
/* > \verbatim */
/* > */
/* > DLANSF = ( f2cmax(abs(A(i,j))), NORM = 'M' or 'm' */
/* > ( */
/* > ( norm1(A), NORM = '1', 'O' or 'o' */
/* > ( */
/* > ( normI(A), NORM = 'I' or 'i' */
/* > ( */
/* > ( normF(A), NORM = 'F', 'f', 'E' or 'e' */
/* > */
/* > where norm1 denotes the one norm of a matrix (maximum column sum), */
/* > normI denotes the infinity norm of a matrix (maximum row sum) and */
/* > normF denotes the Frobenius norm of a matrix (square root of sum of */
/* > squares). Note that f2cmax(abs(A(i,j))) is not a matrix norm. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] NORM */
/* > \verbatim */
/* > NORM is CHARACTER*1 */
/* > Specifies the value to be returned in DLANSF as described */
/* > above. */
/* > \endverbatim */
/* > */
/* > \param[in] TRANSR */
/* > \verbatim */
/* > TRANSR is CHARACTER*1 */
/* > Specifies whether the RFP format of A is normal or */
/* > transposed format. */
/* > = 'N': RFP format is Normal; */
/* > = 'T': RFP format is Transpose. */
/* > \endverbatim */
/* > */
/* > \param[in] UPLO */
/* > \verbatim */
/* > UPLO is CHARACTER*1 */
/* > On entry, UPLO specifies whether the RFP matrix A came from */
/* > an upper or lower triangular matrix as follows: */
/* > = 'U': RFP A came from an upper triangular matrix; */
/* > = 'L': RFP A came from a lower triangular matrix. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrix A. N >= 0. When N = 0, DLANSF is */
/* > set to zero. */
/* > \endverbatim */
/* > */
/* > \param[in] A */
/* > \verbatim */
/* > A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ); */
/* > On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') */
/* > part of the symmetric matrix A stored in RFP format. See the */
/* > "Notes" below for more details. */
/* > Unchanged on exit. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), */
/* > where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, */
/* > WORK is not referenced. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date December 2016 */
/* > \ingroup doubleOTHERcomputational */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > We first consider Rectangular Full Packed (RFP) Format when N is */
/* > even. We give an example where N = 6. */
/* > */
/* > AP is Upper AP is Lower */
/* > */
/* > 00 01 02 03 04 05 00 */
/* > 11 12 13 14 15 10 11 */
/* > 22 23 24 25 20 21 22 */
/* > 33 34 35 30 31 32 33 */
/* > 44 45 40 41 42 43 44 */
/* > 55 50 51 52 53 54 55 */
/* > */
/* > */
/* > Let TRANSR = 'N'. RFP holds AP as follows: */
/* > For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last */
/* > three columns of AP upper. The lower triangle A(4:6,0:2) consists of */
/* > the transpose of the first three columns of AP upper. */
/* > For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first */
/* > three columns of AP lower. The upper triangle A(0:2,0:2) consists of */
/* > the transpose of the last three columns of AP lower. */
/* > This covers the case N even and TRANSR = 'N'. */
/* > */
/* > RFP A RFP A */
/* > */
/* > 03 04 05 33 43 53 */
/* > 13 14 15 00 44 54 */
/* > 23 24 25 10 11 55 */
/* > 33 34 35 20 21 22 */
/* > 00 44 45 30 31 32 */
/* > 01 11 55 40 41 42 */
/* > 02 12 22 50 51 52 */
/* > */
/* > Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */
/* > transpose of RFP A above. One therefore gets: */
/* > */
/* > */
/* > RFP A RFP A */
/* > */
/* > 03 13 23 33 00 01 02 33 00 10 20 30 40 50 */
/* > 04 14 24 34 44 11 12 43 44 11 21 31 41 51 */
/* > 05 15 25 35 45 55 22 53 54 55 22 32 42 52 */
/* > */
/* > */
/* > We then consider Rectangular Full Packed (RFP) Format when N is */
/* > odd. We give an example where N = 5. */
/* > */
/* > AP is Upper AP is Lower */
/* > */
/* > 00 01 02 03 04 00 */
/* > 11 12 13 14 10 11 */
/* > 22 23 24 20 21 22 */
/* > 33 34 30 31 32 33 */
/* > 44 40 41 42 43 44 */
/* > */
/* > */
/* > Let TRANSR = 'N'. RFP holds AP as follows: */
/* > For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last */
/* > three columns of AP upper. The lower triangle A(3:4,0:1) consists of */
/* > the transpose of the first two columns of AP upper. */
/* > For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first */
/* > three columns of AP lower. The upper triangle A(0:1,1:2) consists of */
/* > the transpose of the last two columns of AP lower. */
/* > This covers the case N odd and TRANSR = 'N'. */
/* > */
/* > RFP A RFP A */
/* > */
/* > 02 03 04 00 33 43 */
/* > 12 13 14 10 11 44 */
/* > 22 23 24 20 21 22 */
/* > 00 33 34 30 31 32 */
/* > 01 11 44 40 41 42 */
/* > */
/* > Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */
/* > transpose of RFP A above. One therefore gets: */
/* > */
/* > RFP A RFP A */
/* > */
/* > 02 12 22 00 01 00 10 20 30 40 50 */
/* > 03 13 23 33 11 33 11 21 31 41 51 */
/* > 04 14 24 34 44 43 44 22 32 42 52 */
/* > \endverbatim */
/* ===================================================================== */
doublereal dlansf_(char *norm, char *transr, char *uplo, integer *n,
doublereal *a, doublereal *work)
{
/* System generated locals */
integer i__1, i__2;
doublereal ret_val, d__1;
/* Local variables */
doublereal temp;
integer i__, j, k, l;
doublereal s, scale;
extern logical lsame_(char *, char *);
doublereal value;
integer n1;
doublereal aa;
extern logical disnan_(doublereal *);
extern /* Subroutine */ void dlassq_(integer *, doublereal *, integer *,
doublereal *, doublereal *);
integer lda, ifm, noe, ilu;
/* -- 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 */
/* ===================================================================== */
if (*n == 0) {
ret_val = 0.;
return ret_val;
} else if (*n == 1) {
ret_val = abs(a[0]);
return ret_val;
}
/* set noe = 1 if n is odd. if n is even set noe=0 */
noe = 1;
if (*n % 2 == 0) {
noe = 0;
}
/* set ifm = 0 when form='T or 't' and 1 otherwise */
ifm = 1;
if (lsame_(transr, "T")) {
ifm = 0;
}
/* set ilu = 0 when uplo='U or 'u' and 1 otherwise */
ilu = 1;
if (lsame_(uplo, "U")) {
ilu = 0;
}
/* set lda = (n+1)/2 when ifm = 0 */
/* set lda = n when ifm = 1 and noe = 1 */
/* set lda = n+1 when ifm = 1 and noe = 0 */
if (ifm == 1) {
if (noe == 1) {
lda = *n;
} else {
/* noe=0 */
lda = *n + 1;
}
} else {
/* ifm=0 */
lda = (*n + 1) / 2;
}
if (lsame_(norm, "M")) {
/* Find f2cmax(abs(A(i,j))). */
k = (*n + 1) / 2;
value = 0.;
if (noe == 1) {
/* n is odd */
if (ifm == 1) {
/* A is n by k */
i__1 = k - 1;
for (j = 0; j <= i__1; ++j) {
i__2 = *n - 1;
for (i__ = 0; i__ <= i__2; ++i__) {
temp = (d__1 = a[i__ + j * lda], abs(d__1));
if (value < temp || disnan_(&temp)) {
value = temp;
}
}
}
} else {
/* xpose case; A is k by n */
i__1 = *n - 1;
for (j = 0; j <= i__1; ++j) {
i__2 = k - 1;
for (i__ = 0; i__ <= i__2; ++i__) {
temp = (d__1 = a[i__ + j * lda], abs(d__1));
if (value < temp || disnan_(&temp)) {
value = temp;
}
}
}
}
} else {
/* n is even */
if (ifm == 1) {
/* A is n+1 by k */
i__1 = k - 1;
for (j = 0; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 0; i__ <= i__2; ++i__) {
temp = (d__1 = a[i__ + j * lda], abs(d__1));
if (value < temp || disnan_(&temp)) {
value = temp;
}
}
}
} else {
/* xpose case; A is k by n+1 */
i__1 = *n;
for (j = 0; j <= i__1; ++j) {
i__2 = k - 1;
for (i__ = 0; i__ <= i__2; ++i__) {
temp = (d__1 = a[i__ + j * lda], abs(d__1));
if (value < temp || disnan_(&temp)) {
value = temp;
}
}
}
}
}
} else if (lsame_(norm, "I") || lsame_(norm, "O") || *(unsigned char *)norm == '1') {
/* Find normI(A) ( = norm1(A), since A is symmetric). */
if (ifm == 1) {
k = *n / 2;
if (noe == 1) {
/* n is odd */
if (ilu == 0) {
i__1 = k - 1;
for (i__ = 0; i__ <= i__1; ++i__) {
work[i__] = 0.;
}
i__1 = k;
for (j = 0; j <= i__1; ++j) {
s = 0.;
i__2 = k + j - 1;
for (i__ = 0; i__ <= i__2; ++i__) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* -> A(i,j+k) */
s += aa;
work[i__] += aa;
}
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* -> A(j+k,j+k) */
work[j + k] = s + aa;
if (i__ == k + k) {
goto L10;
}
++i__;
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* -> A(j,j) */
work[j] += aa;
s = 0.;
i__2 = k - 1;
for (l = j + 1; l <= i__2; ++l) {
++i__;
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* -> A(l,j) */
s += aa;
work[l] += aa;
}
work[j] += s;
}
L10:
value = work[0];
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
temp = work[i__];
if (value < temp || disnan_(&temp)) {
value = temp;
}
}
} else {
/* ilu = 1 */
++k;
/* k=(n+1)/2 for n odd and ilu=1 */
i__1 = *n - 1;
for (i__ = k; i__ <= i__1; ++i__) {
work[i__] = 0.;
}
for (j = k - 1; j >= 0; --j) {
s = 0.;
i__1 = j - 2;
for (i__ = 0; i__ <= i__1; ++i__) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* -> A(j+k,i+k) */
s += aa;
work[i__ + k] += aa;
}
if (j > 0) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* -> A(j+k,j+k) */
s += aa;
work[i__ + k] += s;
/* i=j */
++i__;
}
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* -> A(j,j) */
work[j] = aa;
s = 0.;
i__1 = *n - 1;
for (l = j + 1; l <= i__1; ++l) {
++i__;
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* -> A(l,j) */
s += aa;
work[l] += aa;
}
work[j] += s;
}
value = work[0];
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
temp = work[i__];
if (value < temp || disnan_(&temp)) {
value = temp;
}
}
}
} else {
/* n is even */
if (ilu == 0) {
i__1 = k - 1;
for (i__ = 0; i__ <= i__1; ++i__) {
work[i__] = 0.;
}
i__1 = k - 1;
for (j = 0; j <= i__1; ++j) {
s = 0.;
i__2 = k + j - 1;
for (i__ = 0; i__ <= i__2; ++i__) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* -> A(i,j+k) */
s += aa;
work[i__] += aa;
}
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* -> A(j+k,j+k) */
work[j + k] = s + aa;
++i__;
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* -> A(j,j) */
work[j] += aa;
s = 0.;
i__2 = k - 1;
for (l = j + 1; l <= i__2; ++l) {
++i__;
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* -> A(l,j) */
s += aa;
work[l] += aa;
}
work[j] += s;
}
value = work[0];
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
temp = work[i__];
if (value < temp || disnan_(&temp)) {
value = temp;
}
}
} else {
/* ilu = 1 */
i__1 = *n - 1;
for (i__ = k; i__ <= i__1; ++i__) {
work[i__] = 0.;
}
for (j = k - 1; j >= 0; --j) {
s = 0.;
i__1 = j - 1;
for (i__ = 0; i__ <= i__1; ++i__) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* -> A(j+k,i+k) */
s += aa;
work[i__ + k] += aa;
}
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* -> A(j+k,j+k) */
s += aa;
work[i__ + k] += s;
/* i=j */
++i__;
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* -> A(j,j) */
work[j] = aa;
s = 0.;
i__1 = *n - 1;
for (l = j + 1; l <= i__1; ++l) {
++i__;
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* -> A(l,j) */
s += aa;
work[l] += aa;
}
work[j] += s;
}
value = work[0];
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
temp = work[i__];
if (value < temp || disnan_(&temp)) {
value = temp;
}
}
}
}
} else {
/* ifm=0 */
k = *n / 2;
if (noe == 1) {
/* n is odd */
if (ilu == 0) {
n1 = k;
/* n/2 */
++k;
/* k is the row size and lda */
i__1 = *n - 1;
for (i__ = n1; i__ <= i__1; ++i__) {
work[i__] = 0.;
}
i__1 = n1 - 1;
for (j = 0; j <= i__1; ++j) {
s = 0.;
i__2 = k - 1;
for (i__ = 0; i__ <= i__2; ++i__) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(j,n1+i) */
work[i__ + n1] += aa;
s += aa;
}
work[j] = s;
}
/* j=n1=k-1 is special */
s = (d__1 = a[j * lda], abs(d__1));
/* A(k-1,k-1) */
i__1 = k - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(k-1,i+n1) */
work[i__ + n1] += aa;
s += aa;
}
work[j] += s;
i__1 = *n - 1;
for (j = k; j <= i__1; ++j) {
s = 0.;
i__2 = j - k - 1;
for (i__ = 0; i__ <= i__2; ++i__) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(i,j-k) */
work[i__] += aa;
s += aa;
}
/* i=j-k */
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(j-k,j-k) */
s += aa;
work[j - k] += s;
++i__;
s = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(j,j) */
i__2 = *n - 1;
for (l = j + 1; l <= i__2; ++l) {
++i__;
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(j,l) */
work[l] += aa;
s += aa;
}
work[j] += s;
}
value = work[0];
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
temp = work[i__];
if (value < temp || disnan_(&temp)) {
value = temp;
}
}
} else {
/* ilu=1 */
++k;
/* k=(n+1)/2 for n odd and ilu=1 */
i__1 = *n - 1;
for (i__ = k; i__ <= i__1; ++i__) {
work[i__] = 0.;
}
i__1 = k - 2;
for (j = 0; j <= i__1; ++j) {
/* process */
s = 0.;
i__2 = j - 1;
for (i__ = 0; i__ <= i__2; ++i__) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(j,i) */
work[i__] += aa;
s += aa;
}
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* i=j so process of A(j,j) */
s += aa;
work[j] = s;
/* is initialised here */
++i__;
/* i=j process A(j+k,j+k) */
aa = (d__1 = a[i__ + j * lda], abs(d__1));
s = aa;
i__2 = *n - 1;
for (l = k + j + 1; l <= i__2; ++l) {
++i__;
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(l,k+j) */
s += aa;
work[l] += aa;
}
work[k + j] += s;
}
/* j=k-1 is special :process col A(k-1,0:k-1) */
s = 0.;
i__1 = k - 2;
for (i__ = 0; i__ <= i__1; ++i__) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(k,i) */
work[i__] += aa;
s += aa;
}
/* i=k-1 */
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(k-1,k-1) */
s += aa;
work[i__] = s;
/* done with col j=k+1 */
i__1 = *n - 1;
for (j = k; j <= i__1; ++j) {
/* process col j of A = A(j,0:k-1) */
s = 0.;
i__2 = k - 1;
for (i__ = 0; i__ <= i__2; ++i__) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(j,i) */
work[i__] += aa;
s += aa;
}
work[j] += s;
}
value = work[0];
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
temp = work[i__];
if (value < temp || disnan_(&temp)) {
value = temp;
}
}
}
} else {
/* n is even */
if (ilu == 0) {
i__1 = *n - 1;
for (i__ = k; i__ <= i__1; ++i__) {
work[i__] = 0.;
}
i__1 = k - 1;
for (j = 0; j <= i__1; ++j) {
s = 0.;
i__2 = k - 1;
for (i__ = 0; i__ <= i__2; ++i__) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(j,i+k) */
work[i__ + k] += aa;
s += aa;
}
work[j] = s;
}
/* j=k */
aa = (d__1 = a[j * lda], abs(d__1));
/* A(k,k) */
s = aa;
i__1 = k - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(k,k+i) */
work[i__ + k] += aa;
s += aa;
}
work[j] += s;
i__1 = *n - 1;
for (j = k + 1; j <= i__1; ++j) {
s = 0.;
i__2 = j - 2 - k;
for (i__ = 0; i__ <= i__2; ++i__) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(i,j-k-1) */
work[i__] += aa;
s += aa;
}
/* i=j-1-k */
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(j-k-1,j-k-1) */
s += aa;
work[j - k - 1] += s;
++i__;
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(j,j) */
s = aa;
i__2 = *n - 1;
for (l = j + 1; l <= i__2; ++l) {
++i__;
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(j,l) */
work[l] += aa;
s += aa;
}
work[j] += s;
}
/* j=n */
s = 0.;
i__1 = k - 2;
for (i__ = 0; i__ <= i__1; ++i__) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(i,k-1) */
work[i__] += aa;
s += aa;
}
/* i=k-1 */
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(k-1,k-1) */
s += aa;
work[i__] += s;
value = work[0];
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
temp = work[i__];
if (value < temp || disnan_(&temp)) {
value = temp;
}
}
} else {
/* ilu=1 */
i__1 = *n - 1;
for (i__ = k; i__ <= i__1; ++i__) {
work[i__] = 0.;
}
/* j=0 is special :process col A(k:n-1,k) */
s = abs(a[0]);
/* A(k,k) */
i__1 = k - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
aa = (d__1 = a[i__], abs(d__1));
/* A(k+i,k) */
work[i__ + k] += aa;
s += aa;
}
work[k] += s;
i__1 = k - 1;
for (j = 1; j <= i__1; ++j) {
/* process */
s = 0.;
i__2 = j - 2;
for (i__ = 0; i__ <= i__2; ++i__) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(j-1,i) */
work[i__] += aa;
s += aa;
}
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* i=j-1 so process of A(j-1,j-1) */
s += aa;
work[j - 1] = s;
/* is initialised here */
++i__;
/* i=j process A(j+k,j+k) */
aa = (d__1 = a[i__ + j * lda], abs(d__1));
s = aa;
i__2 = *n - 1;
for (l = k + j + 1; l <= i__2; ++l) {
++i__;
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(l,k+j) */
s += aa;
work[l] += aa;
}
work[k + j] += s;
}
/* j=k is special :process col A(k,0:k-1) */
s = 0.;
i__1 = k - 2;
for (i__ = 0; i__ <= i__1; ++i__) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(k,i) */
work[i__] += aa;
s += aa;
}
/* i=k-1 */
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(k-1,k-1) */
s += aa;
work[i__] = s;
/* done with col j=k+1 */
i__1 = *n;
for (j = k + 1; j <= i__1; ++j) {
/* process col j-1 of A = A(j-1,0:k-1) */
s = 0.;
i__2 = k - 1;
for (i__ = 0; i__ <= i__2; ++i__) {
aa = (d__1 = a[i__ + j * lda], abs(d__1));
/* A(j-1,i) */
work[i__] += aa;
s += aa;
}
work[j - 1] += s;
}
value = work[0];
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
temp = work[i__];
if (value < temp || disnan_(&temp)) {
value = temp;
}
}
}
}
}
} else if (lsame_(norm, "F") || lsame_(norm, "E")) {
/* Find normF(A). */
k = (*n + 1) / 2;
scale = 0.;
s = 1.;
if (noe == 1) {
/* n is odd */
if (ifm == 1) {
/* A is normal */
if (ilu == 0) {
/* A is upper */
i__1 = k - 3;
for (j = 0; j <= i__1; ++j) {
i__2 = k - j - 2;
dlassq_(&i__2, &a[k + j + 1 + j * lda], &c__1, &scale,
&s);
/* L at A(k,0) */
}
i__1 = k - 1;
for (j = 0; j <= i__1; ++j) {
i__2 = k + j - 1;
dlassq_(&i__2, &a[j * lda], &c__1, &scale, &s);
/* trap U at A(0,0) */
}
s += s;
/* double s for the off diagonal elements */
i__1 = k - 1;
i__2 = lda + 1;
dlassq_(&i__1, &a[k], &i__2, &scale, &s);
/* tri L at A(k,0) */
i__1 = lda + 1;
dlassq_(&k, &a[k - 1], &i__1, &scale, &s);
/* tri U at A(k-1,0) */
} else {
/* ilu=1 & A is lower */
i__1 = k - 1;
for (j = 0; j <= i__1; ++j) {
i__2 = *n - j - 1;
dlassq_(&i__2, &a[j + 1 + j * lda], &c__1, &scale, &s)
;
/* trap L at A(0,0) */
}
i__1 = k - 2;
for (j = 0; j <= i__1; ++j) {
dlassq_(&j, &a[(j + 1) * lda], &c__1, &scale, &s);
/* U at A(0,1) */
}
s += s;
/* double s for the off diagonal elements */
i__1 = lda + 1;
dlassq_(&k, a, &i__1, &scale, &s);
/* tri L at A(0,0) */
i__1 = k - 1;
i__2 = lda + 1;
dlassq_(&i__1, &a[lda], &i__2, &scale, &s);
/* tri U at A(0,1) */
}
} else {
/* A is xpose */
if (ilu == 0) {
/* A**T is upper */
i__1 = k - 2;
for (j = 1; j <= i__1; ++j) {
dlassq_(&j, &a[(k + j) * lda], &c__1, &scale, &s);
/* U at A(0,k) */
}
i__1 = k - 2;
for (j = 0; j <= i__1; ++j) {
dlassq_(&k, &a[j * lda], &c__1, &scale, &s);
/* k by k-1 rect. at A(0,0) */
}
i__1 = k - 2;
for (j = 0; j <= i__1; ++j) {
i__2 = k - j - 1;
dlassq_(&i__2, &a[j + 1 + (j + k - 1) * lda], &c__1, &
scale, &s);
/* L at A(0,k-1) */
}
s += s;
/* double s for the off diagonal elements */
i__1 = k - 1;
i__2 = lda + 1;
dlassq_(&i__1, &a[k * lda], &i__2, &scale, &s);
/* tri U at A(0,k) */
i__1 = lda + 1;
dlassq_(&k, &a[(k - 1) * lda], &i__1, &scale, &s);
/* tri L at A(0,k-1) */
} else {
/* A**T is lower */
i__1 = k - 1;
for (j = 1; j <= i__1; ++j) {
dlassq_(&j, &a[j * lda], &c__1, &scale, &s);
/* U at A(0,0) */
}
i__1 = *n - 1;
for (j = k; j <= i__1; ++j) {
dlassq_(&k, &a[j * lda], &c__1, &scale, &s);
/* k by k-1 rect. at A(0,k) */
}
i__1 = k - 3;
for (j = 0; j <= i__1; ++j) {
i__2 = k - j - 2;
dlassq_(&i__2, &a[j + 2 + j * lda], &c__1, &scale, &s)
;
/* L at A(1,0) */
}
s += s;
/* double s for the off diagonal elements */
i__1 = lda + 1;
dlassq_(&k, a, &i__1, &scale, &s);
/* tri U at A(0,0) */
i__1 = k - 1;
i__2 = lda + 1;
dlassq_(&i__1, &a[1], &i__2, &scale, &s);
/* tri L at A(1,0) */
}
}
} else {
/* n is even */
if (ifm == 1) {
/* A is normal */
if (ilu == 0) {
/* A is upper */
i__1 = k - 2;
for (j = 0; j <= i__1; ++j) {
i__2 = k - j - 1;
dlassq_(&i__2, &a[k + j + 2 + j * lda], &c__1, &scale,
&s);
/* L at A(k+1,0) */
}
i__1 = k - 1;
for (j = 0; j <= i__1; ++j) {
i__2 = k + j;
dlassq_(&i__2, &a[j * lda], &c__1, &scale, &s);
/* trap U at A(0,0) */
}
s += s;
/* double s for the off diagonal elements */
i__1 = lda + 1;
dlassq_(&k, &a[k + 1], &i__1, &scale, &s);
/* tri L at A(k+1,0) */
i__1 = lda + 1;
dlassq_(&k, &a[k], &i__1, &scale, &s);
/* tri U at A(k,0) */
} else {
/* ilu=1 & A is lower */
i__1 = k - 1;
for (j = 0; j <= i__1; ++j) {
i__2 = *n - j - 1;
dlassq_(&i__2, &a[j + 2 + j * lda], &c__1, &scale, &s)
;
/* trap L at A(1,0) */
}
i__1 = k - 1;
for (j = 1; j <= i__1; ++j) {
dlassq_(&j, &a[j * lda], &c__1, &scale, &s);
/* U at A(0,0) */
}
s += s;
/* double s for the off diagonal elements */
i__1 = lda + 1;
dlassq_(&k, &a[1], &i__1, &scale, &s);
/* tri L at A(1,0) */
i__1 = lda + 1;
dlassq_(&k, a, &i__1, &scale, &s);
/* tri U at A(0,0) */
}
} else {
/* A is xpose */
if (ilu == 0) {
/* A**T is upper */
i__1 = k - 1;
for (j = 1; j <= i__1; ++j) {
dlassq_(&j, &a[(k + 1 + j) * lda], &c__1, &scale, &s);
/* U at A(0,k+1) */
}
i__1 = k - 1;
for (j = 0; j <= i__1; ++j) {
dlassq_(&k, &a[j * lda], &c__1, &scale, &s);
/* k by k rect. at A(0,0) */
}
i__1 = k - 2;
for (j = 0; j <= i__1; ++j) {
i__2 = k - j - 1;
dlassq_(&i__2, &a[j + 1 + (j + k) * lda], &c__1, &
scale, &s);
/* L at A(0,k) */
}
s += s;
/* double s for the off diagonal elements */
i__1 = lda + 1;
dlassq_(&k, &a[(k + 1) * lda], &i__1, &scale, &s);
/* tri U at A(0,k+1) */
i__1 = lda + 1;
dlassq_(&k, &a[k * lda], &i__1, &scale, &s);
/* tri L at A(0,k) */
} else {
/* A**T is lower */
i__1 = k - 1;
for (j = 1; j <= i__1; ++j) {
dlassq_(&j, &a[(j + 1) * lda], &c__1, &scale, &s);
/* U at A(0,1) */
}
i__1 = *n;
for (j = k + 1; j <= i__1; ++j) {
dlassq_(&k, &a[j * lda], &c__1, &scale, &s);
/* k by k rect. at A(0,k+1) */
}
i__1 = k - 2;
for (j = 0; j <= i__1; ++j) {
i__2 = k - j - 1;
dlassq_(&i__2, &a[j + 1 + j * lda], &c__1, &scale, &s)
;
/* L at A(0,0) */
}
s += s;
/* double s for the off diagonal elements */
i__1 = lda + 1;
dlassq_(&k, &a[lda], &i__1, &scale, &s);
/* tri L at A(0,1) */
i__1 = lda + 1;
dlassq_(&k, a, &i__1, &scale, &s);
/* tri U at A(0,0) */
}
}
}
value = scale * sqrt(s);
}
ret_val = value;
return ret_val;
/* End of DLANSF */
} /* dlansf_ */
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