|
- #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]/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 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 ZLANHF 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 Hermitian matrix in RFP format. */
-
- /* =========== DOCUMENTATION =========== */
-
- /* Online html documentation available at */
- /* http://www.netlib.org/lapack/explore-html/ */
-
- /* > \htmlonly */
- /* > Download ZLANHF + dependencies */
- /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlanhf.
- f"> */
- /* > [TGZ]</a> */
- /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlanhf.
- f"> */
- /* > [ZIP]</a> */
- /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlanhf.
- f"> */
- /* > [TXT]</a> */
- /* > \endhtmlonly */
-
- /* Definition: */
- /* =========== */
-
- /* DOUBLE PRECISION FUNCTION ZLANHF( NORM, TRANSR, UPLO, N, A, WORK ) */
-
- /* CHARACTER NORM, TRANSR, UPLO */
- /* INTEGER N */
- /* DOUBLE PRECISION WORK( 0: * ) */
- /* COMPLEX*16 A( 0: * ) */
-
-
- /* > \par Purpose: */
- /* ============= */
- /* > */
- /* > \verbatim */
- /* > */
- /* > ZLANHF returns the value of the one norm, or the Frobenius norm, or */
- /* > the infinity norm, or the element of largest absolute value of a */
- /* > complex Hermitian matrix A in RFP format. */
- /* > \endverbatim */
- /* > */
- /* > \return ZLANHF */
- /* > \verbatim */
- /* > */
- /* > ZLANHF = ( 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 */
- /* > Specifies the value to be returned in ZLANHF as described */
- /* > above. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] TRANSR */
- /* > \verbatim */
- /* > TRANSR is CHARACTER */
- /* > Specifies whether the RFP format of A is normal or */
- /* > conjugate-transposed format. */
- /* > = 'N': RFP format is Normal */
- /* > = 'C': RFP format is Conjugate-transposed */
- /* > \endverbatim */
- /* > */
- /* > \param[in] UPLO */
- /* > \verbatim */
- /* > UPLO is CHARACTER */
- /* > On entry, UPLO specifies whether the RFP matrix A came from */
- /* > an upper or lower triangular matrix as follows: */
- /* > */
- /* > UPLO = 'U' or 'u' RFP A came from an upper triangular */
- /* > matrix */
- /* > */
- /* > UPLO = 'L' or '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, ZLANHF is */
- /* > set to zero. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] A */
- /* > \verbatim */
- /* > A is COMPLEX*16 array, dimension ( N*(N+1)/2 ); */
- /* > On entry, the matrix A in RFP Format. */
- /* > RFP Format is described by TRANSR, UPLO and N as follows: */
- /* > If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even; */
- /* > K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If */
- /* > TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A */
- /* > as defined when TRANSR = 'N'. The contents of RFP A are */
- /* > defined by UPLO as follows: If UPLO = 'U' the RFP A */
- /* > contains the ( N*(N+1)/2 ) elements of upper packed A */
- /* > either in normal or conjugate-transpose Format. If */
- /* > UPLO = 'L' the RFP A contains the ( N*(N+1) /2 ) elements */
- /* > of lower packed A either in normal or conjugate-transpose */
- /* > Format. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When */
- /* > TRANSR is 'N' the LDA is N+1 when N is even and is N when */
- /* > is odd. See the Note below for more details. */
- /* > Unchanged on exit. */
- /* > \endverbatim */
- /* > */
- /* > \param[out] WORK */
- /* > \verbatim */
- /* > WORK is DOUBLE PRECISION array, dimension (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 complex16OTHERcomputational */
-
- /* > \par Further Details: */
- /* ===================== */
- /* > */
- /* > \verbatim */
- /* > */
- /* > We first consider Standard Packed 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 */
- /* > conjugate-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 */
- /* > conjugate-transpose of the last three columns of AP lower. */
- /* > To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate- */
- /* > 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 next consider Standard Packed 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 */
- /* > conjugate-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 */
- /* > conjugate-transpose of the last two columns of AP lower. */
- /* > To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate- */
- /* > 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 zlanhf_(char *norm, char *transr, char *uplo, integer *n,
- doublecomplex *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 zlassq_(integer *, doublecomplex *, 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 = (d__1 = a[0].r, abs(d__1));
- 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='C' or 'c' and 1 otherwise */
-
- ifm = 1;
- if (lsame_(transr, "C")) {
- 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 & n = k + k - 1 */
- if (ifm == 1) {
- /* A is n by k */
- if (ilu == 1) {
- /* uplo ='L' */
- j = 0;
- /* -> L(0,0) */
- i__1 = j + j * lda;
- temp = (d__1 = a[i__1].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__1 = *n - 1;
- for (i__ = 1; i__ <= i__1; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- i__1 = k - 1;
- for (j = 1; j <= i__1; ++j) {
- i__2 = j - 2;
- for (i__ = 0; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- i__ = j - 1;
- /* L(k+j,k+j) */
- i__2 = i__ + j * lda;
- temp = (d__1 = a[i__2].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__ = j;
- /* -> L(j,j) */
- i__2 = i__ + j * lda;
- temp = (d__1 = a[i__2].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__2 = *n - 1;
- for (i__ = j + 1; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- }
- } else {
- /* uplo = 'U' */
- i__1 = k - 2;
- for (j = 0; j <= i__1; ++j) {
- i__2 = k + j - 2;
- for (i__ = 0; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- i__ = k + j - 1;
- /* -> U(i,i) */
- i__2 = i__ + j * lda;
- temp = (d__1 = a[i__2].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- ++i__;
- /* =k+j; i -> U(j,j) */
- i__2 = i__ + j * lda;
- temp = (d__1 = a[i__2].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__2 = *n - 1;
- for (i__ = k + j + 1; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- }
- i__1 = *n - 2;
- for (i__ = 0; i__ <= i__1; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- /* j=k-1 */
- }
- /* i=n-1 -> U(n-1,n-1) */
- i__1 = i__ + j * lda;
- temp = (d__1 = a[i__1].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- } else {
- /* xpose case; A is k by n */
- if (ilu == 1) {
- /* uplo ='L' */
- i__1 = k - 2;
- for (j = 0; j <= i__1; ++j) {
- i__2 = j - 1;
- for (i__ = 0; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- i__ = j;
- /* L(i,i) */
- i__2 = i__ + j * lda;
- temp = (d__1 = a[i__2].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__ = j + 1;
- /* L(j+k,j+k) */
- i__2 = i__ + j * lda;
- temp = (d__1 = a[i__2].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__2 = k - 1;
- for (i__ = j + 2; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- }
- j = k - 1;
- i__1 = k - 2;
- for (i__ = 0; i__ <= i__1; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- i__ = k - 1;
- /* -> L(i,i) is at A(i,j) */
- i__1 = i__ + j * lda;
- temp = (d__1 = a[i__1].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__1 = *n - 1;
- for (j = k; j <= i__1; ++j) {
- i__2 = k - 1;
- for (i__ = 0; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- }
- } else {
- /* uplo = 'U' */
- i__1 = k - 2;
- for (j = 0; j <= i__1; ++j) {
- i__2 = k - 1;
- for (i__ = 0; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- }
- j = k - 1;
- /* -> U(j,j) is at A(0,j) */
- i__1 = j * lda;
- temp = (d__1 = a[i__1].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__1 = k - 1;
- for (i__ = 1; i__ <= i__1; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- i__1 = *n - 1;
- for (j = k; j <= i__1; ++j) {
- i__2 = j - k - 1;
- for (i__ = 0; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- i__ = j - k;
- /* -> U(i,i) at A(i,j) */
- i__2 = i__ + j * lda;
- temp = (d__1 = a[i__2].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__ = j - k + 1;
- /* U(j,j) */
- i__2 = i__ + j * lda;
- temp = (d__1 = a[i__2].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__2 = k - 1;
- for (i__ = j - k + 2; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- }
- }
- }
- } else {
- /* n is even & k = n/2 */
- if (ifm == 1) {
- /* A is n+1 by k */
- if (ilu == 1) {
- /* uplo ='L' */
- j = 0;
- /* -> L(k,k) & j=1 -> L(0,0) */
- i__1 = j + j * lda;
- temp = (d__1 = a[i__1].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__1 = j + 1 + j * lda;
- temp = (d__1 = a[i__1].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__1 = *n;
- for (i__ = 2; i__ <= i__1; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- i__1 = k - 1;
- for (j = 1; j <= i__1; ++j) {
- i__2 = j - 1;
- for (i__ = 0; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- i__ = j;
- /* L(k+j,k+j) */
- i__2 = i__ + j * lda;
- temp = (d__1 = a[i__2].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__ = j + 1;
- /* -> L(j,j) */
- i__2 = i__ + j * lda;
- temp = (d__1 = a[i__2].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__2 = *n;
- for (i__ = j + 2; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- }
- } else {
- /* uplo = 'U' */
- i__1 = k - 2;
- for (j = 0; j <= i__1; ++j) {
- i__2 = k + j - 1;
- for (i__ = 0; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- i__ = k + j;
- /* -> U(i,i) */
- i__2 = i__ + j * lda;
- temp = (d__1 = a[i__2].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- ++i__;
- /* =k+j+1; i -> U(j,j) */
- i__2 = i__ + j * lda;
- temp = (d__1 = a[i__2].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__2 = *n;
- for (i__ = k + j + 2; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- }
- i__1 = *n - 2;
- for (i__ = 0; i__ <= i__1; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- /* j=k-1 */
- }
- /* i=n-1 -> U(n-1,n-1) */
- i__1 = i__ + j * lda;
- temp = (d__1 = a[i__1].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__ = *n;
- /* -> U(k-1,k-1) */
- i__1 = i__ + j * lda;
- temp = (d__1 = a[i__1].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- } else {
- /* xpose case; A is k by n+1 */
- if (ilu == 1) {
- /* uplo ='L' */
- j = 0;
- /* -> L(k,k) at A(0,0) */
- i__1 = j + j * lda;
- temp = (d__1 = a[i__1].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__1 = k - 1;
- for (i__ = 1; i__ <= i__1; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- i__1 = k - 1;
- for (j = 1; j <= i__1; ++j) {
- i__2 = j - 2;
- for (i__ = 0; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- i__ = j - 1;
- /* L(i,i) */
- i__2 = i__ + j * lda;
- temp = (d__1 = a[i__2].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__ = j;
- /* L(j+k,j+k) */
- i__2 = i__ + j * lda;
- temp = (d__1 = a[i__2].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__2 = k - 1;
- for (i__ = j + 1; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- }
- j = k;
- i__1 = k - 2;
- for (i__ = 0; i__ <= i__1; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- i__ = k - 1;
- /* -> L(i,i) is at A(i,j) */
- i__1 = i__ + j * lda;
- temp = (d__1 = a[i__1].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__1 = *n;
- for (j = k + 1; j <= i__1; ++j) {
- i__2 = k - 1;
- for (i__ = 0; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- }
- } else {
- /* uplo = 'U' */
- i__1 = k - 1;
- for (j = 0; j <= i__1; ++j) {
- i__2 = k - 1;
- for (i__ = 0; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- }
- j = k;
- /* -> U(j,j) is at A(0,j) */
- i__1 = j * lda;
- temp = (d__1 = a[i__1].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__1 = k - 1;
- for (i__ = 1; i__ <= i__1; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- i__1 = *n - 1;
- for (j = k + 1; j <= i__1; ++j) {
- i__2 = j - k - 2;
- for (i__ = 0; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- i__ = j - k - 1;
- /* -> U(i,i) at A(i,j) */
- i__2 = i__ + j * lda;
- temp = (d__1 = a[i__2].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__ = j - k;
- /* U(j,j) */
- i__2 = i__ + j * lda;
- temp = (d__1 = a[i__2].r, abs(d__1));
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- i__2 = k - 1;
- for (i__ = j - k + 1; i__ <= i__2; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- }
- j = *n;
- i__1 = k - 2;
- for (i__ = 0; i__ <= i__1; ++i__) {
- temp = z_abs(&a[i__ + j * lda]);
- if (value < temp || disnan_(&temp)) {
- value = temp;
- }
- }
- i__ = k - 1;
- /* U(k,k) at A(i,j) */
- i__1 = i__ + j * lda;
- temp = (d__1 = a[i__1].r, 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 Hermitian). */
-
- if (ifm == 1) {
- /* A is 'N' */
- k = *n / 2;
- if (noe == 1) {
- /* n is odd & A is n by (n+1)/2 */
- if (ilu == 0) {
- /* uplo = 'U' */
- 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 = z_abs(&a[i__ + j * lda]);
- /* -> A(i,j+k) */
- s += aa;
- work[i__] += aa;
- }
- i__2 = i__ + j * lda;
- aa = (d__1 = a[i__2].r, abs(d__1));
- /* -> A(j+k,j+k) */
- work[j + k] = s + aa;
- if (i__ == k + k) {
- goto L10;
- }
- ++i__;
- i__2 = i__ + j * lda;
- aa = (d__1 = a[i__2].r, 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 = z_abs(&a[i__ + j * lda]);
- /* -> 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 & uplo = 'L' */
- ++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 = z_abs(&a[i__ + j * lda]);
- /* -> A(j+k,i+k) */
- s += aa;
- work[i__ + k] += aa;
- }
- if (j > 0) {
- i__1 = i__ + j * lda;
- aa = (d__1 = a[i__1].r, abs(d__1));
- /* -> A(j+k,j+k) */
- s += aa;
- work[i__ + k] += s;
- /* i=j */
- ++i__;
- }
- i__1 = i__ + j * lda;
- aa = (d__1 = a[i__1].r, 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 = z_abs(&a[i__ + j * lda]);
- /* -> 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 & A is n+1 by k = n/2 */
- if (ilu == 0) {
- /* uplo = 'U' */
- 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 = z_abs(&a[i__ + j * lda]);
- /* -> A(i,j+k) */
- s += aa;
- work[i__] += aa;
- }
- i__2 = i__ + j * lda;
- aa = (d__1 = a[i__2].r, abs(d__1));
- /* -> A(j+k,j+k) */
- work[j + k] = s + aa;
- ++i__;
- i__2 = i__ + j * lda;
- aa = (d__1 = a[i__2].r, 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 = z_abs(&a[i__ + j * lda]);
- /* -> 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 & uplo = 'L' */
- 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 = z_abs(&a[i__ + j * lda]);
- /* -> A(j+k,i+k) */
- s += aa;
- work[i__ + k] += aa;
- }
- i__1 = i__ + j * lda;
- aa = (d__1 = a[i__1].r, abs(d__1));
- /* -> A(j+k,j+k) */
- s += aa;
- work[i__ + k] += s;
- /* i=j */
- ++i__;
- i__1 = i__ + j * lda;
- aa = (d__1 = a[i__1].r, 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 = z_abs(&a[i__ + j * lda]);
- /* -> 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 & A is (n+1)/2 by n */
- if (ilu == 0) {
- /* uplo = 'U' */
- 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 = z_abs(&a[i__ + j * lda]);
- /* A(j,n1+i) */
- work[i__ + n1] += aa;
- s += aa;
- }
- work[j] = s;
- }
- /* j=n1=k-1 is special */
- i__1 = j * lda;
- s = (d__1 = a[i__1].r, abs(d__1));
- /* A(k-1,k-1) */
- i__1 = k - 1;
- for (i__ = 1; i__ <= i__1; ++i__) {
- aa = z_abs(&a[i__ + j * lda]);
- /* 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 = z_abs(&a[i__ + j * lda]);
- /* A(i,j-k) */
- work[i__] += aa;
- s += aa;
- }
- /* i=j-k */
- i__2 = i__ + j * lda;
- aa = (d__1 = a[i__2].r, abs(d__1));
- /* A(j-k,j-k) */
- s += aa;
- work[j - k] += s;
- ++i__;
- i__2 = i__ + j * lda;
- s = (d__1 = a[i__2].r, abs(d__1));
- /* A(j,j) */
- i__2 = *n - 1;
- for (l = j + 1; l <= i__2; ++l) {
- ++i__;
- aa = z_abs(&a[i__ + j * lda]);
- /* 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 & uplo = 'L' */
- ++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 = z_abs(&a[i__ + j * lda]);
- /* A(j,i) */
- work[i__] += aa;
- s += aa;
- }
- i__2 = i__ + j * lda;
- aa = (d__1 = a[i__2].r, 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) */
- i__2 = i__ + j * lda;
- aa = (d__1 = a[i__2].r, abs(d__1));
- s = aa;
- i__2 = *n - 1;
- for (l = k + j + 1; l <= i__2; ++l) {
- ++i__;
- aa = z_abs(&a[i__ + j * lda]);
- /* 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 = z_abs(&a[i__ + j * lda]);
- /* A(k,i) */
- work[i__] += aa;
- s += aa;
- }
- /* i=k-1 */
- i__1 = i__ + j * lda;
- aa = (d__1 = a[i__1].r, 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 = z_abs(&a[i__ + j * lda]);
- /* 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 & A is k=n/2 by n+1 */
- if (ilu == 0) {
- /* uplo = 'U' */
- 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 = z_abs(&a[i__ + j * lda]);
- /* A(j,i+k) */
- work[i__ + k] += aa;
- s += aa;
- }
- work[j] = s;
- }
- /* j=k */
- i__1 = j * lda;
- aa = (d__1 = a[i__1].r, abs(d__1));
- /* A(k,k) */
- s = aa;
- i__1 = k - 1;
- for (i__ = 1; i__ <= i__1; ++i__) {
- aa = z_abs(&a[i__ + j * lda]);
- /* 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 = z_abs(&a[i__ + j * lda]);
- /* A(i,j-k-1) */
- work[i__] += aa;
- s += aa;
- }
- /* i=j-1-k */
- i__2 = i__ + j * lda;
- aa = (d__1 = a[i__2].r, abs(d__1));
- /* A(j-k-1,j-k-1) */
- s += aa;
- work[j - k - 1] += s;
- ++i__;
- i__2 = i__ + j * lda;
- aa = (d__1 = a[i__2].r, abs(d__1));
- /* A(j,j) */
- s = aa;
- i__2 = *n - 1;
- for (l = j + 1; l <= i__2; ++l) {
- ++i__;
- aa = z_abs(&a[i__ + j * lda]);
- /* 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 = z_abs(&a[i__ + j * lda]);
- /* A(i,k-1) */
- work[i__] += aa;
- s += aa;
- }
- /* i=k-1 */
- i__1 = i__ + j * lda;
- aa = (d__1 = a[i__1].r, 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 & uplo = 'L' */
- 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 = (d__1 = a[0].r, abs(d__1));
- /* A(k,k) */
- i__1 = k - 1;
- for (i__ = 1; i__ <= i__1; ++i__) {
- aa = z_abs(&a[i__]);
- /* 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 = z_abs(&a[i__ + j * lda]);
- /* A(j-1,i) */
- work[i__] += aa;
- s += aa;
- }
- i__2 = i__ + j * lda;
- aa = (d__1 = a[i__2].r, 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) */
- i__2 = i__ + j * lda;
- aa = (d__1 = a[i__2].r, abs(d__1));
- s = aa;
- i__2 = *n - 1;
- for (l = k + j + 1; l <= i__2; ++l) {
- ++i__;
- aa = z_abs(&a[i__ + j * lda]);
- /* 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 = z_abs(&a[i__ + j * lda]);
- /* A(k,i) */
- work[i__] += aa;
- s += aa;
- }
-
- /* i=k-1 */
- i__1 = i__ + j * lda;
- aa = (d__1 = a[i__1].r, 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 = z_abs(&a[i__ + j * lda]);
- /* 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 & A is n by k */
- if (ilu == 0) {
- /* A is upper */
- i__1 = k - 3;
- for (j = 0; j <= i__1; ++j) {
- i__2 = k - j - 2;
- zlassq_(&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;
- zlassq_(&i__2, &a[j * lda], &c__1, &scale, &s);
- /* trap U at A(0,0) */
- }
- s += s;
- /* double s for the off diagonal elements */
- l = k - 1;
- /* -> U(k,k) at A(k-1,0) */
- i__1 = k - 2;
- for (i__ = 0; i__ <= i__1; ++i__) {
- i__2 = l;
- aa = a[i__2].r;
- /* U(k+i,k+i) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- i__2 = l + 1;
- aa = a[i__2].r;
- /* U(i,i) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- l = l + lda + 1;
- }
- i__1 = l;
- aa = a[i__1].r;
- /* U(n-1,n-1) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- } else {
- /* ilu=1 & A is lower */
- i__1 = k - 1;
- for (j = 0; j <= i__1; ++j) {
- i__2 = *n - j - 1;
- zlassq_(&i__2, &a[j + 1 + j * lda], &c__1, &scale, &s)
- ;
- /* trap L at A(0,0) */
- }
- i__1 = k - 2;
- for (j = 1; j <= i__1; ++j) {
- zlassq_(&j, &a[(j + 1) * lda], &c__1, &scale, &s);
- /* U at A(0,1) */
- }
- s += s;
- /* double s for the off diagonal elements */
- aa = a[0].r;
- /* L(0,0) at A(0,0) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- l = lda;
- /* -> L(k,k) at A(0,1) */
- i__1 = k - 1;
- for (i__ = 1; i__ <= i__1; ++i__) {
- i__2 = l;
- aa = a[i__2].r;
- /* L(k-1+i,k-1+i) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- i__2 = l + 1;
- aa = a[i__2].r;
- /* L(i,i) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- l = l + lda + 1;
- }
- }
- } else {
- /* A is xpose & A is k by n */
- if (ilu == 0) {
- /* A**H is upper */
- i__1 = k - 2;
- for (j = 1; j <= i__1; ++j) {
- zlassq_(&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) {
- zlassq_(&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;
- zlassq_(&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 */
- l = k * lda - lda;
- /* -> U(k-1,k-1) at A(0,k-1) */
- i__1 = l;
- aa = a[i__1].r;
- /* U(k-1,k-1) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- l += lda;
- /* -> U(0,0) at A(0,k) */
- i__1 = *n - 1;
- for (j = k; j <= i__1; ++j) {
- i__2 = l;
- aa = a[i__2].r;
- /* -> U(j-k,j-k) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- i__2 = l + 1;
- aa = a[i__2].r;
- /* -> U(j,j) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- l = l + lda + 1;
- }
- } else {
- /* A**H is lower */
- i__1 = k - 1;
- for (j = 1; j <= i__1; ++j) {
- zlassq_(&j, &a[j * lda], &c__1, &scale, &s);
- /* U at A(0,0) */
- }
- i__1 = *n - 1;
- for (j = k; j <= i__1; ++j) {
- zlassq_(&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;
- zlassq_(&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 */
- l = 0;
- /* -> L(0,0) at A(0,0) */
- i__1 = k - 2;
- for (i__ = 0; i__ <= i__1; ++i__) {
- i__2 = l;
- aa = a[i__2].r;
- /* L(i,i) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- i__2 = l + 1;
- aa = a[i__2].r;
- /* L(k+i,k+i) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- l = l + lda + 1;
- }
- /* L-> k-1 + (k-1)*lda or L(k-1,k-1) at A(k-1,k-1) */
- i__1 = l;
- aa = a[i__1].r;
- /* L(k-1,k-1) at A(k-1,k-1) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- }
- }
- } 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;
- zlassq_(&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;
- zlassq_(&i__2, &a[j * lda], &c__1, &scale, &s);
- /* trap U at A(0,0) */
- }
- s += s;
- /* double s for the off diagonal elements */
- l = k;
- /* -> U(k,k) at A(k,0) */
- i__1 = k - 1;
- for (i__ = 0; i__ <= i__1; ++i__) {
- i__2 = l;
- aa = a[i__2].r;
- /* U(k+i,k+i) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- i__2 = l + 1;
- aa = a[i__2].r;
- /* U(i,i) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- l = l + lda + 1;
- }
- } else {
- /* ilu=1 & A is lower */
- i__1 = k - 1;
- for (j = 0; j <= i__1; ++j) {
- i__2 = *n - j - 1;
- zlassq_(&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) {
- zlassq_(&j, &a[j * lda], &c__1, &scale, &s);
- /* U at A(0,0) */
- }
- s += s;
- /* double s for the off diagonal elements */
- l = 0;
- /* -> L(k,k) at A(0,0) */
- i__1 = k - 1;
- for (i__ = 0; i__ <= i__1; ++i__) {
- i__2 = l;
- aa = a[i__2].r;
- /* L(k-1+i,k-1+i) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- i__2 = l + 1;
- aa = a[i__2].r;
- /* L(i,i) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- l = l + lda + 1;
- }
- }
- } else {
- /* A is xpose */
- if (ilu == 0) {
- /* A**H is upper */
- i__1 = k - 1;
- for (j = 1; j <= i__1; ++j) {
- zlassq_(&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) {
- zlassq_(&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;
- zlassq_(&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 */
- l = k * lda;
- /* -> U(k,k) at A(0,k) */
- i__1 = l;
- aa = a[i__1].r;
- /* U(k,k) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- l += lda;
- /* -> U(0,0) at A(0,k+1) */
- i__1 = *n - 1;
- for (j = k + 1; j <= i__1; ++j) {
- i__2 = l;
- aa = a[i__2].r;
- /* -> U(j-k-1,j-k-1) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- i__2 = l + 1;
- aa = a[i__2].r;
- /* -> U(j,j) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- l = l + lda + 1;
- }
- /* L=k-1+n*lda */
- /* -> U(k-1,k-1) at A(k-1,n) */
- i__1 = l;
- aa = a[i__1].r;
- /* U(k,k) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- } else {
- /* A**H is lower */
- i__1 = k - 1;
- for (j = 1; j <= i__1; ++j) {
- zlassq_(&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) {
- zlassq_(&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;
- zlassq_(&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 */
- l = 0;
- /* -> L(k,k) at A(0,0) */
- i__1 = l;
- aa = a[i__1].r;
- /* L(k,k) at A(0,0) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- l = lda;
- /* -> L(0,0) at A(0,1) */
- i__1 = k - 2;
- for (i__ = 0; i__ <= i__1; ++i__) {
- i__2 = l;
- aa = a[i__2].r;
- /* L(i,i) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- i__2 = l + 1;
- aa = a[i__2].r;
- /* L(k+i+1,k+i+1) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- l = l + lda + 1;
- }
- /* L-> k - 1 + k*lda or L(k-1,k-1) at A(k-1,k) */
- i__1 = l;
- aa = a[i__1].r;
- /* L(k-1,k-1) at A(k-1,k) */
- if (aa != 0.) {
- if (scale < aa) {
- /* Computing 2nd power */
- d__1 = scale / aa;
- s = s * (d__1 * d__1) + 1.;
- scale = aa;
- } else {
- /* Computing 2nd power */
- d__1 = aa / scale;
- s += d__1 * d__1;
- }
- }
- }
- }
- }
- value = scale * sqrt(s);
- }
-
- ret_val = value;
- return ret_val;
-
- /* End of ZLANHF */
-
- } /* zlanhf_ */
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