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OpenBLAS/lapack-netlib/SRC/sgedmdq.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 int logical;
typedef short int shortlogical;
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++ */
#define F2C_proc_par_types 1
#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)
*/
/* -- 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_n1 = -1;
/* Subroutine */ int sgedmdq_(char *jobs, char *jobz, char *jobr, char *jobq,
char *jobt, char *jobf, integer *whtsvd, integer *m, integer *n, real
*f, integer *ldf, real *x, integer *ldx, real *y, integer *ldy,
integer *nrnk, real *tol, integer *k, real *reig, real *imeig, real *
z__, integer *ldz, real *res, real *b, integer *ldb, real *v, integer
*ldv, real *s, integer *lds, real *work, integer *lwork, integer *
iwork, integer *liwork, integer *info)
{
/* System generated locals */
integer f_dim1, f_offset, x_dim1, x_offset, y_dim1, y_offset, z_dim1,
z_offset, b_dim1, b_offset, v_dim1, v_offset, s_dim1, s_offset,
i__1, i__2;
/* Local variables */
real zero;
integer info1;
extern logical lsame_(char *, char *);
char jobvl[1];
integer minmn;
logical wantq;
integer mlwqr, olwqr;
logical wntex;
extern /* Subroutine */ int sgedmd_(char *, char *, char *, char *,
integer *, integer *, integer *, real *, integer *, real *,
integer *, integer *, real *, integer *, real *, real *, real *,
integer *, real *, real *, integer *, real *, integer *, real *,
integer *, real *, integer *, integer *, integer *, integer *), xerbla_(char *, integer *);
integer mlwdmd, olwdmd;
extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *);
logical sccolx, sccoly;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), slaset_(char *, integer *,
integer *, real *, real *, real *, integer *);
integer iminwr;
logical wntvec, wntvcf;
integer mlwgqr;
logical wntref;
integer mlwork, olwgqr, olwork;
real rdummy[2];
integer mlwmqr, olwmqr;
logical lquery, wntres, wnttrf, wntvcq;
extern /* Subroutine */ int sorgqr_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *, integer *), sormqr_(char
*, char *, integer *, integer *, integer *, real *, integer *,
real *, real *, integer *, real *, integer *, integer *);
real one;
/* March 2023 */
/* ..... */
/* USE iso_fortran_env */
/* INTEGER, PARAMETER :: WP = real32 */
/* ..... */
/* Scalar arguments */
/* Array arguments */
/* ..... */
/* Purpose */
/* ======= */
/* SGEDMDQ computes the Dynamic Mode Decomposition (DMD) for */
/* a pair of data snapshot matrices, using a QR factorization */
/* based compression of the data. For the input matrices */
/* X and Y such that Y = A*X with an unaccessible matrix */
/* A, SGEDMDQ computes a certain number of Ritz pairs of A using */
/* the standard Rayleigh-Ritz extraction from a subspace of */
/* range(X) that is determined using the leading left singular */
/* vectors of X. Optionally, SGEDMDQ returns the residuals */
/* of the computed Ritz pairs, the information needed for */
/* a refinement of the Ritz vectors, or the eigenvectors of */
/* the Exact DMD. */
/* For further details see the references listed */
/* below. For more details of the implementation see [3]. */
/* References */
/* ========== */
/* [1] P. Schmid: Dynamic mode decomposition of numerical */
/* and experimental data, */
/* Journal of Fluid Mechanics 656, 5-28, 2010. */
/* [2] Z. Drmac, I. Mezic, R. Mohr: Data driven modal */
/* decompositions: analysis and enhancements, */
/* SIAM J. on Sci. Comp. 40 (4), A2253-A2285, 2018. */
/* [3] Z. Drmac: A LAPACK implementation of the Dynamic */
/* Mode Decomposition I. Technical report. AIMDyn Inc. */
/* and LAPACK Working Note 298. */
/* [4] J. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. */
/* Brunton, N. Kutz: On Dynamic Mode Decomposition: */
/* Theory and Applications, Journal of Computational */
/* Dynamics 1(2), 391 -421, 2014. */
/* Developed and supported by: */
/* =========================== */
/* Developed and coded by Zlatko Drmac, Faculty of Science, */
/* University of Zagreb; drmac@math.hr */
/* In cooperation with */
/* AIMdyn Inc., Santa Barbara, CA. */
/* and supported by */
/* - DARPA SBIR project "Koopman Operator-Based Forecasting */
/* for Nonstationary Processes from Near-Term, Limited */
/* Observational Data" Contract No: W31P4Q-21-C-0007 */
/* - DARPA PAI project "Physics-Informed Machine Learning */
/* Methodologies" Contract No: HR0011-18-9-0033 */
/* - DARPA MoDyL project "A Data-Driven, Operator-Theoretic */
/* Framework for Space-Time Analysis of Process Dynamics" */
/* Contract No: HR0011-16-C-0116 */
/* Any opinions, findings and conclusions or recommendations */
/* expressed in this material are those of the author and */
/* do not necessarily reflect the views of the DARPA SBIR */
/* Program Office. */
/* ============================================================ */
/* Distribution Statement A: */
/* Approved for Public Release, Distribution Unlimited. */
/* Cleared by DARPA on September 29, 2022 */
/* ============================================================ */
/* ...................................................................... */
/* Arguments */
/* ========= */
/* JOBS (input) CHARACTER*1 */
/* Determines whether the initial data snapshots are scaled */
/* by a diagonal matrix. The data snapshots are the columns */
/* of F. The leading N-1 columns of F are denoted X and the */
/* trailing N-1 columns are denoted Y. */
/* 'S' :: The data snapshots matrices X and Y are multiplied */
/* with a diagonal matrix D so that X*D has unit */
/* nonzero columns (in the Euclidean 2-norm) */
/* 'C' :: The snapshots are scaled as with the 'S' option. */
/* If it is found that an i-th column of X is zero */
/* vector and the corresponding i-th column of Y is */
/* non-zero, then the i-th column of Y is set to */
/* zero and a warning flag is raised. */
/* 'Y' :: The data snapshots matrices X and Y are multiplied */
/* by a diagonal matrix D so that Y*D has unit */
/* nonzero columns (in the Euclidean 2-norm) */
/* 'N' :: No data scaling. */
/* ..... */
/* JOBZ (input) CHARACTER*1 */
/* Determines whether the eigenvectors (Koopman modes) will */
/* be computed. */
/* 'V' :: The eigenvectors (Koopman modes) will be computed */
/* and returned in the matrix Z. */
/* See the description of Z. */
/* 'F' :: The eigenvectors (Koopman modes) will be returned */
/* in factored form as the product Z*V, where Z */
/* is orthonormal and V contains the eigenvectors */
/* of the corresponding Rayleigh quotient. */
/* See the descriptions of F, V, Z. */
/* 'Q' :: The eigenvectors (Koopman modes) will be returned */
/* in factored form as the product Q*Z, where Z */
/* contains the eigenvectors of the compression of the */
/* underlying discretized operator onto the span of */
/* the data snapshots. See the descriptions of F, V, Z. */
/* Q is from the initial QR factorization. */
/* 'N' :: The eigenvectors are not computed. */
/* ..... */
/* JOBR (input) CHARACTER*1 */
/* Determines whether to compute the residuals. */
/* 'R' :: The residuals for the computed eigenpairs will */
/* be computed and stored in the array RES. */
/* See the description of RES. */
/* For this option to be legal, JOBZ must be 'V'. */
/* 'N' :: The residuals are not computed. */
/* ..... */
/* JOBQ (input) CHARACTER*1 */
/* Specifies whether to explicitly compute and return the */
/* orthogonal matrix from the QR factorization. */
/* 'Q' :: The matrix Q of the QR factorization of the data */
/* snapshot matrix is computed and stored in the */
/* array F. See the description of F. */
/* 'N' :: The matrix Q is not explicitly computed. */
/* ..... */
/* JOBT (input) CHARACTER*1 */
/* Specifies whether to return the upper triangular factor */
/* from the QR factorization. */
/* 'R' :: The matrix R of the QR factorization of the data */
/* snapshot matrix F is returned in the array Y. */
/* See the description of Y and Further details. */
/* 'N' :: The matrix R is not returned. */
/* ..... */
/* JOBF (input) CHARACTER*1 */
/* Specifies whether to store information needed for post- */
/* processing (e.g. computing refined Ritz vectors) */
/* 'R' :: The matrix needed for the refinement of the Ritz */
/* vectors is computed and stored in the array B. */
/* See the description of B. */
/* 'E' :: The unscaled eigenvectors of the Exact DMD are */
/* computed and returned in the array B. See the */
/* description of B. */
/* 'N' :: No eigenvector refinement data is computed. */
/* To be useful on exit, this option needs JOBQ='Q'. */
/* ..... */
/* WHTSVD (input) INTEGER, WHSTVD in { 1, 2, 3, 4 } */
/* Allows for a selection of the SVD algorithm from the */
/* LAPACK library. */
/* 1 :: SGESVD (the QR SVD algorithm) */
/* 2 :: SGESDD (the Divide and Conquer algorithm; if enough */
/* workspace available, this is the fastest option) */
/* 3 :: SGESVDQ (the preconditioned QR SVD ; this and 4 */
/* are the most accurate options) */
/* 4 :: SGEJSV (the preconditioned Jacobi SVD; this and 3 */
/* are the most accurate options) */
/* For the four methods above, a significant difference in */
/* the accuracy of small singular values is possible if */
/* the snapshots vary in norm so that X is severely */
/* ill-conditioned. If small (smaller than EPS*||X||) */
/* singular values are of interest and JOBS=='N', then */
/* the options (3, 4) give the most accurate results, where */
/* the option 4 is slightly better and with stronger */
/* theoretical background. */
/* If JOBS=='S', i.e. the columns of X will be normalized, */
/* then all methods give nearly equally accurate results. */
/* ..... */
/* M (input) INTEGER, M >= 0 */
/* The state space dimension (the number of rows of F) */
/* ..... */
/* N (input) INTEGER, 0 <= N <= M */
/* The number of data snapshots from a single trajectory, */
/* taken at equidistant discrete times. This is the */
/* number of columns of F. */
/* ..... */
/* F (input/output) REAL(KIND=WP) M-by-N array */
/* > On entry, */
/* the columns of F are the sequence of data snapshots */
/* from a single trajectory, taken at equidistant discrete */
/* times. It is assumed that the column norms of F are */
/* in the range of the normalized floating point numbers. */
/* < On exit, */
/* If JOBQ == 'Q', the array F contains the orthogonal */
/* matrix/factor of the QR factorization of the initial */
/* data snapshots matrix F. See the description of JOBQ. */
/* If JOBQ == 'N', the entries in F strictly below the main */
/* diagonal contain, column-wise, the information on the */
/* Householder vectors, as returned by SGEQRF. The */
/* remaining information to restore the orthogonal matrix */
/* of the initial QR factorization is stored in WORK(1:N). */
/* See the description of WORK. */
/* ..... */
/* LDF (input) INTEGER, LDF >= M */
/* The leading dimension of the array F. */
/* ..... */
/* X (workspace/output) REAL(KIND=WP) MIN(M,N)-by-(N-1) array */
/* X is used as workspace to hold representations of the */
/* leading N-1 snapshots in the orthonormal basis computed */
/* in the QR factorization of F. */
/* On exit, the leading K columns of X contain the leading */
/* K left singular vectors of the above described content */
/* of X. To lift them to the space of the left singular */
/* vectors U(:,1:K)of the input data, pre-multiply with the */
/* Q factor from the initial QR factorization. */
/* See the descriptions of F, K, V and Z. */
/* ..... */
/* LDX (input) INTEGER, LDX >= N */
/* The leading dimension of the array X */
/* ..... */
/* Y (workspace/output) REAL(KIND=WP) MIN(M,N)-by-(N-1) array */
/* Y is used as workspace to hold representations of the */
/* trailing N-1 snapshots in the orthonormal basis computed */
/* in the QR factorization of F. */
/* On exit, */
/* If JOBT == 'R', Y contains the MIN(M,N)-by-N upper */
/* triangular factor from the QR factorization of the data */
/* snapshot matrix F. */
/* ..... */
/* LDY (input) INTEGER , LDY >= N */
/* The leading dimension of the array Y */
/* ..... */
/* NRNK (input) INTEGER */
/* Determines the mode how to compute the numerical rank, */
/* i.e. how to truncate small singular values of the input */
/* matrix X. On input, if */
/* NRNK = -1 :: i-th singular value sigma(i) is truncated */
/* if sigma(i) <= TOL*sigma(1) */
/* This option is recommended. */
/* NRNK = -2 :: i-th singular value sigma(i) is truncated */
/* if sigma(i) <= TOL*sigma(i-1) */
/* This option is included for R&D purposes. */
/* It requires highly accurate SVD, which */
/* may not be feasible. */
/* The numerical rank can be enforced by using positive */
/* value of NRNK as follows: */
/* 0 < NRNK <= N-1 :: at most NRNK largest singular values */
/* will be used. If the number of the computed nonzero */
/* singular values is less than NRNK, then only those */
/* nonzero values will be used and the actually used */
/* dimension is less than NRNK. The actual number of */
/* the nonzero singular values is returned in the variable */
/* K. See the description of K. */
/* ..... */
/* TOL (input) REAL(KIND=WP), 0 <= TOL < 1 */
/* The tolerance for truncating small singular values. */
/* See the description of NRNK. */
/* ..... */
/* K (output) INTEGER, 0 <= K <= N */
/* The dimension of the SVD/POD basis for the leading N-1 */
/* data snapshots (columns of F) and the number of the */
/* computed Ritz pairs. The value of K is determined */
/* according to the rule set by the parameters NRNK and */
/* TOL. See the descriptions of NRNK and TOL. */
/* ..... */
/* REIG (output) REAL(KIND=WP) (N-1)-by-1 array */
/* The leading K (K<=N) entries of REIG contain */
/* the real parts of the computed eigenvalues */
/* REIG(1:K) + sqrt(-1)*IMEIG(1:K). */
/* See the descriptions of K, IMEIG, Z. */
/* ..... */
/* IMEIG (output) REAL(KIND=WP) (N-1)-by-1 array */
/* The leading K (K<N) entries of REIG contain */
/* the imaginary parts of the computed eigenvalues */
/* REIG(1:K) + sqrt(-1)*IMEIG(1:K). */
/* The eigenvalues are determined as follows: */
/* If IMEIG(i) == 0, then the corresponding eigenvalue is */
/* real, LAMBDA(i) = REIG(i). */
/* If IMEIG(i)>0, then the corresponding complex */
/* conjugate pair of eigenvalues reads */
/* LAMBDA(i) = REIG(i) + sqrt(-1)*IMAG(i) */
/* LAMBDA(i+1) = REIG(i) - sqrt(-1)*IMAG(i) */
/* That is, complex conjugate pairs have consecutive */
/* indices (i,i+1), with the positive imaginary part */
/* listed first. */
/* See the descriptions of K, REIG, Z. */
/* ..... */
/* Z (workspace/output) REAL(KIND=WP) M-by-(N-1) array */
/* If JOBZ =='V' then */
/* Z contains real Ritz vectors as follows: */
/* If IMEIG(i)=0, then Z(:,i) is an eigenvector of */
/* the i-th Ritz value. */
/* If IMEIG(i) > 0 (and IMEIG(i+1) < 0) then */
/* [Z(:,i) Z(:,i+1)] span an invariant subspace and */
/* the Ritz values extracted from this subspace are */
/* REIG(i) + sqrt(-1)*IMEIG(i) and */
/* REIG(i) - sqrt(-1)*IMEIG(i). */
/* The corresponding eigenvectors are */
/* Z(:,i) + sqrt(-1)*Z(:,i+1) and */
/* Z(:,i) - sqrt(-1)*Z(:,i+1), respectively. */
/* If JOBZ == 'F', then the above descriptions hold for */
/* the columns of Z*V, where the columns of V are the */
/* eigenvectors of the K-by-K Rayleigh quotient, and Z is */
/* orthonormal. The columns of V are similarly structured: */
/* If IMEIG(i) == 0 then Z*V(:,i) is an eigenvector, and if */
/* IMEIG(i) > 0 then Z*V(:,i)+sqrt(-1)*Z*V(:,i+1) and */
/* Z*V(:,i)-sqrt(-1)*Z*V(:,i+1) */
/* are the eigenvectors of LAMBDA(i), LAMBDA(i+1). */
/* See the descriptions of REIG, IMEIG, X and V. */
/* ..... */
/* LDZ (input) INTEGER , LDZ >= M */
/* The leading dimension of the array Z. */
/* ..... */
/* RES (output) REAL(KIND=WP) (N-1)-by-1 array */
/* RES(1:K) contains the residuals for the K computed */
/* Ritz pairs. */
/* If LAMBDA(i) is real, then */
/* RES(i) = || A * Z(:,i) - LAMBDA(i)*Z(:,i))||_2. */
/* If [LAMBDA(i), LAMBDA(i+1)] is a complex conjugate pair */
/* then */
/* RES(i)=RES(i+1) = || A * Z(:,i:i+1) - Z(:,i:i+1) *B||_F */
/* where B = [ real(LAMBDA(i)) imag(LAMBDA(i)) ] */
/* [-imag(LAMBDA(i)) real(LAMBDA(i)) ]. */
/* It holds that */
/* RES(i) = || A*ZC(:,i) - LAMBDA(i) *ZC(:,i) ||_2 */
/* RES(i+1) = || A*ZC(:,i+1) - LAMBDA(i+1)*ZC(:,i+1) ||_2 */
/* where ZC(:,i) = Z(:,i) + sqrt(-1)*Z(:,i+1) */
/* ZC(:,i+1) = Z(:,i) - sqrt(-1)*Z(:,i+1) */
/* See the description of Z. */
/* ..... */
/* B (output) REAL(KIND=WP) MIN(M,N)-by-(N-1) array. */
/* IF JOBF =='R', B(1:N,1:K) contains A*U(:,1:K), and can */
/* be used for computing the refined vectors; see further */
/* details in the provided references. */
/* If JOBF == 'E', B(1:N,1;K) contains */
/* A*U(:,1:K)*W(1:K,1:K), which are the vectors from the */
/* Exact DMD, up to scaling by the inverse eigenvalues. */
/* In both cases, the content of B can be lifted to the */
/* original dimension of the input data by pre-multiplying */
/* with the Q factor from the initial QR factorization. */
/* Here A denotes a compression of the underlying operator. */
/* See the descriptions of F and X. */
/* If JOBF =='N', then B is not referenced. */
/* ..... */
/* LDB (input) INTEGER, LDB >= MIN(M,N) */
/* The leading dimension of the array B. */
/* ..... */
/* V (workspace/output) REAL(KIND=WP) (N-1)-by-(N-1) array */
/* On exit, V(1:K,1:K) contains the K eigenvectors of */
/* the Rayleigh quotient. The eigenvectors of a complex */
/* conjugate pair of eigenvalues are returned in real form */
/* as explained in the description of Z. The Ritz vectors */
/* (returned in Z) are the product of X and V; see */
/* the descriptions of X and Z. */
/* ..... */
/* LDV (input) INTEGER, LDV >= N-1 */
/* The leading dimension of the array V. */
/* ..... */
/* S (output) REAL(KIND=WP) (N-1)-by-(N-1) array */
/* The array S(1:K,1:K) is used for the matrix Rayleigh */
/* quotient. This content is overwritten during */
/* the eigenvalue decomposition by SGEEV. */
/* See the description of K. */
/* ..... */
/* LDS (input) INTEGER, LDS >= N-1 */
/* The leading dimension of the array S. */
/* ..... */
/* WORK (workspace/output) REAL(KIND=WP) LWORK-by-1 array */
/* On exit, */
/* WORK(1:MIN(M,N)) contains the scalar factors of the */
/* elementary reflectors as returned by SGEQRF of the */
/* M-by-N input matrix F. */
/* WORK(MIN(M,N)+1:MIN(M,N)+N-1) contains the singular values of */
/* the input submatrix F(1:M,1:N-1). */
/* If the call to SGEDMDQ is only workspace query, then */
/* WORK(1) contains the minimal workspace length and */
/* WORK(2) is the optimal workspace length. Hence, the */
/* length of work is at least 2. */
/* See the description of LWORK. */
/* ..... */
/* LWORK (input) INTEGER */
/* The minimal length of the workspace vector WORK. */
/* LWORK is calculated as follows: */
/* Let MLWQR = N (minimal workspace for SGEQRF[M,N]) */
/* MLWDMD = minimal workspace for SGEDMD (see the */
/* description of LWORK in SGEDMD) for */
/* snapshots of dimensions MIN(M,N)-by-(N-1) */
/* MLWMQR = N (minimal workspace for */
/* SORMQR['L','N',M,N,N]) */
/* MLWGQR = N (minimal workspace for SORGQR[M,N,N]) */
/* Then */
/* LWORK = MAX(N+MLWQR, N+MLWDMD) */
/* is updated as follows: */
/* if JOBZ == 'V' or JOBZ == 'F' THEN */
/* LWORK = MAX( LWORK,MIN(M,N)+N-1 +MLWMQR ) */
/* if JOBQ == 'Q' THEN */
/* LWORK = MAX( LWORK,MIN(M,N)+N-1+MLWGQR) */
/* If on entry LWORK = -1, then a workspace query is */
/* assumed and the procedure only computes the minimal */
/* and the optimal workspace lengths for both WORK and */
/* IWORK. See the descriptions of WORK and IWORK. */
/* ..... */
/* IWORK (workspace/output) INTEGER LIWORK-by-1 array */
/* Workspace that is required only if WHTSVD equals */
/* 2 , 3 or 4. (See the description of WHTSVD). */
/* If on entry LWORK =-1 or LIWORK=-1, then the */
/* minimal length of IWORK is computed and returned in */
/* IWORK(1). See the description of LIWORK. */
/* ..... */
/* LIWORK (input) INTEGER */
/* The minimal length of the workspace vector IWORK. */
/* If WHTSVD == 1, then only IWORK(1) is used; LIWORK >=1 */
/* Let M1=MIN(M,N), N1=N-1. Then */
/* If WHTSVD == 2, then LIWORK >= MAX(1,8*MIN(M1,N1)) */
/* If WHTSVD == 3, then LIWORK >= MAX(1,M1+N1-1) */
/* If WHTSVD == 4, then LIWORK >= MAX(3,M1+3*N1) */
/* If on entry LIWORK = -1, then a worskpace query is */
/* assumed and the procedure only computes the minimal */
/* and the optimal workspace lengths for both WORK and */
/* IWORK. See the descriptions of WORK and IWORK. */
/* ..... */
/* INFO (output) INTEGER */
/* -i < 0 :: On entry, the i-th argument had an */
/* illegal value */
/* = 0 :: Successful return. */
/* = 1 :: Void input. Quick exit (M=0 or N=0). */
/* = 2 :: The SVD computation of X did not converge. */
/* Suggestion: Check the input data and/or */
/* repeat with different WHTSVD. */
/* = 3 :: The computation of the eigenvalues did not */
/* converge. */
/* = 4 :: If data scaling was requested on input and */
/* the procedure found inconsistency in the data */
/* such that for some column index i, */
/* X(:,i) = 0 but Y(:,i) /= 0, then Y(:,i) is set */
/* to zero if JOBS=='C'. The computation proceeds */
/* with original or modified data and warning */
/* flag is set with INFO=4. */
/* ............................................................. */
/* ............................................................. */
/* Parameters */
/* ~~~~~~~~~~ */
/* Local scalars */
/* ~~~~~~~~~~~~~ */
/* Local array */
/* ~~~~~~~~~~~ */
/* External functions (BLAS and LAPACK) */
/* ~~~~~~~~~~~~~~~~~ */
/* External subroutines (BLAS and LAPACK) */
/* ~~~~~~~~~~~~~~~~~~~~ */
/* External subroutines */
/* ~~~~~~~~~~~~~~~~~~~~ */
/* Intrinsic functions */
/* ~~~~~~~~~~~~~~~~~~~ */
/* Parameter adjustments */
f_dim1 = *ldf;
f_offset = 1 + f_dim1 * 1;
f -= f_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1 * 1;
x -= x_offset;
y_dim1 = *ldy;
y_offset = 1 + y_dim1 * 1;
y -= y_offset;
--reig;
--imeig;
z_dim1 = *ldz;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
--res;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
v_dim1 = *ldv;
v_offset = 1 + v_dim1 * 1;
v -= v_offset;
s_dim1 = *lds;
s_offset = 1 + s_dim1 * 1;
s -= s_offset;
--work;
--iwork;
/* Function Body */
one = 1.f;
zero = 0.f;
/* .......................................................... */
/* Test the input arguments */
wntres = lsame_(jobr, "R");
sccolx = lsame_(jobs, "S") || lsame_(jobs, "C");
sccoly = lsame_(jobs, "Y");
wntvec = lsame_(jobz, "V");
wntvcf = lsame_(jobz, "F");
wntvcq = lsame_(jobz, "Q");
wntref = lsame_(jobf, "R");
wntex = lsame_(jobf, "E");
wantq = lsame_(jobq, "Q");
wnttrf = lsame_(jobt, "R");
minmn = f2cmin(*m,*n);
*info = 0;
lquery = *lwork == -1 || *liwork == -1;
if (! (sccolx || sccoly || lsame_(jobs, "N"))) {
*info = -1;
} else if (! (wntvec || wntvcf || wntvcq || lsame_(jobz, "N"))) {
*info = -2;
} else if (! (wntres || lsame_(jobr, "N")) ||
wntres && lsame_(jobz, "N")) {
*info = -3;
} else if (! (wantq || lsame_(jobq, "N"))) {
*info = -4;
} else if (! (wnttrf || lsame_(jobt, "N"))) {
*info = -5;
} else if (! (wntref || wntex || lsame_(jobf, "N")))
{
*info = -6;
} else if (! (*whtsvd == 1 || *whtsvd == 2 || *whtsvd == 3 || *whtsvd ==
4)) {
*info = -7;
} else if (*m < 0) {
*info = -8;
} else if (*n < 0 || *n > *m + 1) {
*info = -9;
} else if (*ldf < *m) {
*info = -11;
} else if (*ldx < minmn) {
*info = -13;
} else if (*ldy < minmn) {
*info = -15;
} else if (! (*nrnk == -2 || *nrnk == -1 || *nrnk >= 1 && *nrnk <= *n)) {
*info = -16;
} else if (*tol < zero || *tol >= one) {
*info = -17;
} else if (*ldz < *m) {
*info = -22;
} else if ((wntref || wntex) && *ldb < minmn) {
*info = -25;
} else if (*ldv < *n - 1) {
*info = -27;
} else if (*lds < *n - 1) {
*info = -29;
}
if (wntvec || wntvcf) {
*(unsigned char *)jobvl = 'V';
} else {
*(unsigned char *)jobvl = 'N';
}
if (*info == 0) {
/* Compute the minimal and the optimal workspace */
/* requirements. Simulate running the code and */
/* determine minimal and optimal sizes of the */
/* workspace at any moment of the run. */
if (*n == 0 || *n == 1) {
/* All output except K is void. INFO=1 signals */
/* the void input. In case of a workspace query, */
/* the minimal workspace lengths are returned. */
if (lquery) {
iwork[1] = 1;
work[1] = 2.f;
work[2] = 2.f;
} else {
*k = 0;
}
*info = 1;
return 0;
}
mlwqr = f2cmax(1,*n);
/* Minimal workspace length for SGEQRF. */
mlwork = f2cmin(*m,*n) + mlwqr;
if (lquery) {
sgeqrf_(m, n, &f[f_offset], ldf, &work[1], rdummy, &c_n1, &info1);
olwqr = (integer) rdummy[0];
olwork = f2cmin(*m,*n) + olwqr;
}
i__1 = *n - 1;
sgedmd_(jobs, jobvl, jobr, jobf, whtsvd, &minmn, &i__1, &x[x_offset],
ldx, &y[y_offset], ldy, nrnk, tol, k, &reig[1], &imeig[1], &
z__[z_offset], ldz, &res[1], &b[b_offset], ldb, &v[v_offset],
ldv, &s[s_offset], lds, &work[1], &c_n1, &iwork[1], liwork, &
info1);
mlwdmd = (integer) work[1];
/* Computing MAX */
i__1 = mlwork, i__2 = minmn + mlwdmd;
mlwork = f2cmax(i__1,i__2);
iminwr = iwork[1];
if (lquery) {
olwdmd = (integer) work[2];
/* Computing MAX */
i__1 = olwork, i__2 = minmn + olwdmd;
olwork = f2cmax(i__1,i__2);
}
if (wntvec || wntvcf) {
mlwmqr = f2cmax(1,*n);
/* Computing MAX */
i__1 = mlwork, i__2 = minmn + *n - 1 + mlwmqr;
mlwork = f2cmax(i__1,i__2);
if (lquery) {
sormqr_("L", "N", m, n, &minmn, &f[f_offset], ldf, &work[1], &
z__[z_offset], ldz, &work[1], &c_n1, &info1);
olwmqr = (integer) work[1];
/* Computing MAX */
i__1 = olwork, i__2 = minmn + *n - 1 + olwmqr;
olwork = f2cmax(i__1,i__2);
}
}
if (wantq) {
mlwgqr = *n;
/* Computing MAX */
i__1 = mlwork, i__2 = minmn + *n - 1 + mlwgqr;
mlwork = f2cmax(i__1,i__2);
if (lquery) {
sorgqr_(m, &minmn, &minmn, &f[f_offset], ldf, &work[1], &work[
1], &c_n1, &info1);
olwgqr = (integer) work[1];
/* Computing MAX */
i__1 = olwork, i__2 = minmn + *n - 1 + olwgqr;
olwork = f2cmax(i__1,i__2);
}
}
iminwr = f2cmax(1,iminwr);
mlwork = f2cmax(2,mlwork);
if (*lwork < mlwork && ! lquery) {
*info = -31;
}
if (*liwork < iminwr && ! lquery) {
*info = -33;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGEDMDQ", &i__1);
return 0;
} else if (lquery) {
/* Return minimal and optimal workspace sizes */
iwork[1] = iminwr;
work[1] = (real) mlwork;
work[2] = (real) olwork;
return 0;
}
/* ..... */
/* Initial QR factorization that is used to represent the */
/* snapshots as elements of lower dimensional subspace. */
/* For large scale computation with M >>N , at this place */
/* one can use an out of core QRF. */
i__1 = *lwork - minmn;
sgeqrf_(m, n, &f[f_offset], ldf, &work[1], &work[minmn + 1], &i__1, &
info1);
/* Define X and Y as the snapshots representations in the */
/* orthogonal basis computed in the QR factorization. */
/* X corresponds to the leading N-1 and Y to the trailing */
/* N-1 snapshots. */
i__1 = *n - 1;
slaset_("L", &minmn, &i__1, &zero, &zero, &x[x_offset], ldx);
i__1 = *n - 1;
slacpy_("U", &minmn, &i__1, &f[f_offset], ldf, &x[x_offset], ldx);
i__1 = *n - 1;
slacpy_("A", &minmn, &i__1, &f[(f_dim1 << 1) + 1], ldf, &y[y_offset], ldy);
if (*m >= 3) {
i__1 = minmn - 2;
i__2 = *n - 2;
slaset_("L", &i__1, &i__2, &zero, &zero, &y[y_dim1 + 3], ldy);
}
/* Compute the DMD of the projected snapshot pairs (X,Y) */
i__1 = *n - 1;
i__2 = *lwork - minmn;
sgedmd_(jobs, jobvl, jobr, jobf, whtsvd, &minmn, &i__1, &x[x_offset], ldx,
&y[y_offset], ldy, nrnk, tol, k, &reig[1], &imeig[1], &z__[
z_offset], ldz, &res[1], &b[b_offset], ldb, &v[v_offset], ldv, &s[
s_offset], lds, &work[minmn + 1], &i__2, &iwork[1], liwork, &
info1);
if (info1 == 2 || info1 == 3) {
/* Return with error code. */
*info = info1;
return 0;
} else {
*info = info1;
}
/* The Ritz vectors (Koopman modes) can be explicitly */
/* formed or returned in factored form. */
if (wntvec) {
/* Compute the eigenvectors explicitly. */
if (*m > minmn) {
i__1 = *m - minmn;
slaset_("A", &i__1, k, &zero, &zero, &z__[minmn + 1 + z_dim1],
ldz);
}
i__1 = *lwork - (minmn + *n - 1);
sormqr_("L", "N", m, k, &minmn, &f[f_offset], ldf, &work[1], &z__[
z_offset], ldz, &work[minmn + *n], &i__1, &info1);
} else if (wntvcf) {
/* Return the Ritz vectors (eigenvectors) in factored */
/* form Z*V, where Z contains orthonormal matrix (the */
/* product of Q from the initial QR factorization and */
/* the SVD/POD_basis returned by SGEDMD in X) and the */
/* second factor (the eigenvectors of the Rayleigh */
/* quotient) is in the array V, as returned by SGEDMD. */
slacpy_("A", n, k, &x[x_offset], ldx, &z__[z_offset], ldz);
if (*m > *n) {
i__1 = *m - *n;
slaset_("A", &i__1, k, &zero, &zero, &z__[*n + 1 + z_dim1], ldz);
}
i__1 = *lwork - (minmn + *n - 1);
sormqr_("L", "N", m, k, &minmn, &f[f_offset], ldf, &work[1], &z__[
z_offset], ldz, &work[minmn + *n], &i__1, &info1);
}
/* Some optional output variables: */
/* The upper triangular factor in the initial QR */
/* factorization is optionally returned in the array Y. */
/* This is useful if this call to SGEDMDQ is to be */
/* followed by a streaming DMD that is implemented in a */
/* QR compressed form. */
if (wnttrf) {
/* Return the upper triangular R in Y */
slaset_("A", &minmn, n, &zero, &zero, &y[y_offset], ldy);
slacpy_("U", &minmn, n, &f[f_offset], ldf, &y[y_offset], ldy);
}
/* The orthonormal/orthogonal factor in the initial QR */
/* factorization is optionally returned in the array F. */
/* Same as with the triangular factor above, this is */
/* useful in a streaming DMD. */
if (wantq) {
/* Q overwrites F */
i__1 = *lwork - (minmn + *n - 1);
sorgqr_(m, &minmn, &minmn, &f[f_offset], ldf, &work[1], &work[minmn +
*n], &i__1, &info1);
}
return 0;
} /* sgedmdq_ */
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