/* nag_dggrqf (f08zfc) Example Program.
*
* Copyright 2017 Numerical Algorithms Group.
*
* Mark 26.1, 2017.
*/

#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagf07.h>
#include <nagf08.h>
#include <nagf16.h>

int main(void)
{
/* Scalars */
double alpha, beta, rnorm;
Integer i, j, m, n, p, pda, pdb, pdc, pdd, pdx;
Integer y1rows, y2rows, y3rows;
Integer exit_status = 0;

/* Arrays */
double *a = 0, *b = 0, *c = 0, *d = 0, *taua = 0, *taub = 0, *x = 0;

/* Nag Types */
NagError fail;
Nag_OrderType order;

#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J-1)*pda + I - 1]
#define B(I, J) b[(J-1)*pdb + I - 1]
order = Nag_ColMajor;
#else
#define A(I, J) a[(I-1)*pda + J - 1]
#define B(I, J) b[(I-1)*pdb + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_dggrqf (f08zfc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &m, &n, &p);
if (n < 0 || m < 0 || p < 0) {
printf("Invalid n, m or p\n");
exit_status = 1;
goto END;
}

#ifdef NAG_COLUMN_MAJOR
pda = m;
pdb = p;
pdc = m;
pdd = p;
pdx = n;
#else
pda = n;
pdb = n;
pdc = 1;
pdd = 1;
pdx = 1;
#endif

/* Allocate memory */
if (!(a = NAG_ALLOC(m * n, double)) ||
!(b = NAG_ALLOC(p * n, double)) ||
!(c = NAG_ALLOC(m, double)) ||
!(d = NAG_ALLOC(p, double)) ||
!(taua = NAG_ALLOC(MIN(m, n), double)) ||
!(taub = NAG_ALLOC(MIN(n, p), double)) || !(x = NAG_ALLOC(n, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Read A, B, c and d from data file for the problem
* min{||c-Ax||_2, x in R^n and B x = d}.
*/
for (i = 1; i <= m; ++i)
for (j = 1; j <= n; ++j)
scanf("%lf", &A(i, j));
scanf("%*[^\n]");
for (i = 1; i <= p; ++i)
for (j = 1; j <= n; ++j)
scanf("%lf", &B(i, j));
scanf("%*[^\n]");
for (i = 0; i < m; ++i)
scanf("%lf", &c[i]);
scanf("%*[^\n]");
for (i = 0; i < p; ++i)
scanf("%lf", &d[i]);
scanf("%*[^\n]");

/* First compute the generalized RQ factorization of (B,A) as
* B = (0 R12)*Q,   A = Z*(T11 T12 T13)*Q = T*Q.
*                        ( 0  T22 T23)
* where R12, T11 and T22 are upper triangular,
* using  nag_dggrqf (f08zfc).
*/
nag_dggrqf(order, p, m, n, b, pdb, taub, a, pda, taua, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dggrqf (f08zfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Now, trans(z)*(c-Ax) = trans(z)*c - T*Q*x, and
* let f = (f1) = trans(z) * (c1) => minimize ||f - T*Q*x||
*         (f2)              (c2)
* Compute f using  nag_dormqr (f08agc), storing result in c
*/
nag_dormqr(order, Nag_LeftSide, Nag_Trans, m, 1, MIN(m, n), a, pda, taua,
c, pdc, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dormqr (f08agc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Putting Q*x = (y1), B * x = d becomes (0 R12) (y1) = d;
*               (w )                            (w )
* => R12 * w = d.
* Solve for w using nag_dtrtrs (f07tec), storing result in d;
* R12 is (p by p) triangular submatrix starting at B(1,n-p+1).
*/
nag_dtrtrs(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, p, 1,
&B(1, n - p + 1), pdb, d, pdd, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dtrtrs (f07tec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* The problem now reduces to finding the minimum norm of
* g = (g1) = (f1) - T11*y1 - (T12 T13)*w
*     (g2)   (f2)          - (T22 T23)*w.
* Form c1 = f1 - (T12 T13)*w using  nag_dgemv (f16pac).
*/
alpha = -1.0;
beta = 1.0;
y1rows = n - p;
nag_dgemv(order, Nag_NoTrans, y1rows, p, alpha, &A(1, n - p + 1), pda, d, 1,
beta, c, 1, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dgemv (f16pac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* => now (g1) = c - T11*y1 and ||g1|| = 0 when T11 * y1 = c1.
* Solve this for y1 using nag_dtrtrs (f07tec) storing result in c1.
*/
nag_dtrtrs(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, y1rows, 1, a,
pda, c, pdc, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dtrtrs (f07tec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* So now Q*x = (y1) is stored in (c1), which is now copied to x.
*              (w )              (d )
*/
for (i = 0; i < y1rows; ++i)
x[i] = c[i];
for (i = y1rows; i < n; ++i)
x[i] = d[i - y1rows];

/* Compute x by applying transpose of Q using nag_dormrq (f08ckc). */
nag_dormrq(order, Nag_LeftSide, Nag_Trans, n, 1, p, b, pdb, taub, x, pdx,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dormrq (f08ckc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* It remains to minimize  ||g2||, g2 = f2 - (T22 T23)*w.
* Putting w = (y2), gives g2 = f2 - T22*y2 - T23*y3
*             (y3)
* [y2 stored in d1, first y2rows of d; y3 stored in d2, next n-m rows of d.]
*
* First form T22*y2 using  nag_dtrmv (f16pfc) where y2 is held in d.
*/
y2rows = MIN(m, n) - y1rows;
alpha = 1.0;
nag_dtrmv(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, y2rows, alpha,
&A(n - p + 1, n - p + 1), pda, d, 1, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dtrmv (f16pfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Then, f2 - T22*y2 (c2 = c2 - d) */
for (i = 0; i < y2rows; ++i)
c[y1rows + i] -= d[i];
y2rows = m - y1rows;
if (m < n) {
y3rows = n - m;
/* Then g2 = f2 - T22*y2 - T23*y3 (c2 = c2 - T23*d2) */
alpha = -1.0;
beta = 1.0;
nag_dgemv(order, Nag_NoTrans, y2rows, y3rows, alpha, &A(n - p + 1, m + 1),
pda, &d[y2rows], 1, beta, &c[y1rows], 1, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dgemv (f16pac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
}

/* Compute ||g|| = ||g2|| = norm(f2 - T22*y2 - T23*y3)
* using nag_dge_norm (f16rac).
*/
nag_dge_norm(Nag_ColMajor, Nag_FrobeniusNorm, y2rows, 1, &c[y1rows], y2rows,
&rnorm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dge_norm (f16rac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Print least squares solution x */
printf("Constrained least squares solution\n");
for (i = 0; i < n; ++i)
printf(" %10.4f%s", x[i], i % 7 == 6 ? "\n" : "");

/* Print the square root of the residual sum of squares */
printf("\nSquare root of the residual sum of squares\n");
printf("%11.2e\n", rnorm);

END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(c);
NAG_FREE(d);
NAG_FREE(taua);
NAG_FREE(taub);
NAG_FREE(x);

return exit_status;
}