/
block_matrix.c
1670 lines (1527 loc) · 44.8 KB
/
block_matrix.c
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/*
assemble matrices for the block inversion routine
all matrices are stored FORTRAN style
$Id: block_matrix.c,v 1.16 2004/10/05 01:09:46 becker Exp $
*/
#include "interact.h"
#include "blockinvert.h"
/*
assemble the matrices which change with the fault coupling
factors: F, GF, E, K2, and K
some input: G, D, I
the funny memory handling was added to track down a memory leak problem
*/
void assemble_block_fltdep_matrices(COMP_PRECISION **f,
COMP_PRECISION **gf,
COMP_PRECISION **e,
COMP_PRECISION **k2mat,
COMP_PRECISION *g,
COMP_PRECISION *d,
COMP_PRECISION *imat,
int m,int n,int nflt,int nrb,
int nrgp,int nrsp,int nsnf,
COMP_PRECISION *xtry,
struct bflt *fault,
struct bck *block,
my_boolean invert_for_ld,
my_boolean invert_for_cfac)
{
int pdim,tsize;
static int gf_size=0;
/*
assemble F which relates the block motion parameters
to differences in fault location velocities,
ie. global slip. dimensions: (dim*nflt, nbase*nrb)
F uses the globally-projected fault coordinates
we are passing the locking factor vector, it is a [nflt] and has
potentially different coupling factors for each fault, normally
should be all unity. if we are inverting for both cfacs and lds,
the vector also holds the locking depths, hence we have to shift
this vector gets only reference if invert_for_cfac is set
*/
assemble_block_f(f,fault,nflt,nrb,block,
(xtry+n+((invert_for_ld)?(nflt):(0))),
invert_for_cfac);
#ifdef BLOCK_SPHERICAL
pdim = 3;
#else
pdim = BLOCK_DIM;
#endif
//
//
// calculate GF = G(nslip*nflt,dim*nflt) *
// F(block_dim*nflt,nbase*nrb)
//
// dimensions: (nslip*nflt, nbase*nblock)
//
/* allocate space for GF */
tsize = nsnf *n;
if(gf_size != tsize){
my_vecrealloc(gf,tsize,"assemble_block_fltdep_matrices: gf");
gf_size = tsize;
}
calc_AB_ftn(g,nsnf,BLOCK_DIM*nflt,*f,n,*gf);
//
// calculate E=D(pdim*nrgp,nslip*nflt).GF(nslip*nflt, nbase*nrb)
// dimensions: E(pdim*nrgp, n = nbase*nrb)
//
/* allocate space for E */
tsize = pdim * nrgp *n;
my_vecrealloc(e,tsize,"assemble_block_fltdep_matrices: e");
calc_AB_ftn(d,pdim * nrgp, nsnf, *gf, n, *e);
if(nrsp){
//
// assemble K2(nrsp*6,nbase*nrb) = I G F
//
/* allocate space for K2 */
tsize = nrsp * 6 * n;
my_vecrealloc(k2mat,tsize,"assemble_block_fltdep_matrices: k2");
calc_AB_ftn(imat,6*nrsp, nsnf, *gf, n, *k2mat);
}
}
/*
assemble A matrix that links block motion parameters, b, to
velocities at the nrp velocity observational points
b is NBASE * nrb (nrb: nr of blocks)
A is DIM * nrp x NBASE * nrb
DIM is either BLOCK_DIM or 3 (for spherical)
gpx[nrp*BLOCK_DIM] are the projected
locations of the observational points
bcode[nrp*BLOCK_DIM] the block code of each point
block[nrb].fixed the no-rigid motion flag
assemble A matrix in FORTRAN style (for solvers)
A is only dependent on the block geometry, not the faults
if single_block is >= 0, will assume that all points belong
to single_block.
*/
void assemble_block_a(COMP_PRECISION **a,COMP_PRECISION *gpx,
int *bcode, int nrp,int nrb,struct bck *block,
int single_block,struct bmd *mod)
{
int i,j,k,icol,n,m,offset,*loc_bcode,inode,pdim,irow;
/*
normally, we will use the fixed flag for blocks whose rotation
is set to zero. however, if we are only looking for one block's
rotation, we will set it to FALSE (else all zero entries in A)
*/
my_boolean use_fixed_block_flag = TRUE;
#ifdef SUPER_DEBUG
static my_boolean pinit = FALSE;
#endif
if((BLOCK_NBASE != 3)||(BLOCK_DIM != 2)){
fprintf(stderr,"assemble_block_a: dim: %i or nbase: %i not implemented\n",
BLOCK_DIM,BLOCK_NBASE);
exit(-1);
}
/*
number of rows of A
*/
#ifdef BLOCK_SPHERICAL
pdim = 3; /* x,y,z cartesian components */
#else
pdim = BLOCK_DIM; /* only x and y in projected frame */
#endif
m = pdim * nrp;
/*
generate a copy of the boundary code vector, but make it only nrp
long. (bcode is nrp * BLOCK_DIM)
*/
my_ivecalloc(&loc_bcode,nrp,"assmble_block_a: loc_bcode");
if(single_block >= 0){
if(block[single_block].fixed){
fprintf(stderr,"assmble_block_a: WARNING: assuming all points belong to block %i\n",
single_block+1);
fprintf(stderr,"assmble_block_a: WARNING: disregarding block fixedness for all blocks (nbase: %i)\n",
BLOCK_NBASE);
use_fixed_block_flag = FALSE;
}
for(i=0;i < nrp;i++) /* all points are in single_block */
loc_bcode[i] = single_block;
}else{
/* original */
for(i=0;i < nrp;i++)
loc_bcode[i] = bcode[i*BLOCK_DIM];
}
/*
number of columns of A
*/
n = BLOCK_NBASE * nrb;
/*
re-allocate A array
*/
my_vecrealloc(a,n*m,"assemble_block_a: a");
if((BLOCK_DIM != 2)||(BLOCK_NBASE != 3)){
fprintf(stderr,"assemble_block_a: not prepared for dim != 2 or block_base != 3\n");
exit(-1);
}
#ifdef BLOCK_SPHERICAL
if(!mod->pbase_init) /* init basis vectors */
init_gps_pbase(mod);
#endif
for(k=0;k < nrb;k++){ /* block loop */
for(j=0;j < BLOCK_NBASE;j++){
icol = k * BLOCK_NBASE + j; /* column counter
0 ... n-1 */
offset = icol * m;
for(i=inode=irow=0;i < m;i++){/*
row counter, loops through
all data points and pdim dimensions
*/
if(loc_bcode[inode] == k){
/*
point i is in block k
*/
/*
rigid body translation and rotation part
*/
if((!block[loc_bcode[inode]].fixed)||
(!use_fixed_block_flag)){ /* this block is not fixed with
respect to rigid body
motions and we are using the
fixed block flags
*/
#ifdef BLOCK_SPHERICAL
/*
spherical setup:
| 0 r_z -r_y |
A' w = | -r_z 0 r_x | w = v
| r_y -r_x 0 |
where r_x, r_y, r_z are the cartesian coordinates and the
solution vector will be omega_x, omega_y, omega_z
NOTE THAT THIS ASSIGNMENT WORKS COLUMN BY COLUMN!
*/
if(j == 0){ /* first sub-col */
if(irow == 0) /* 0 */
*(*a+offset+i)= 0.0;
else if(irow == 1)
*(*a+offset+i)= -mod->gcx[inode*3+INT_Z]; /* -r_z */
else
*(*a+offset+i)= mod->gcx[inode*3+INT_Y]; /* r_y */
}else if(j == 1){ /* second sub-col */
if(irow == 0)
*(*a+offset+i)= mod->gcx[inode*3+INT_Z]; /* r_z */
else if(irow == 1)
*(*a+offset+i)= 0.0; /* 0 */
else
*(*a+offset+i)= -mod->gcx[inode*3+INT_X]; /* -r_x */
}else{ /* third sub-col */
if(irow == 0)
*(*a+offset+i)= -mod->gcx[inode*3+INT_Y]; /* -r_y */
else if(irow == 1)
*(*a+offset+i)= mod->gcx[inode*3+INT_X]; /* r_x */
else
*(*a+offset+i)= 0.0; /* 0 */
}
#else
/*
cartesian setup:
| -x_y 1 0 |
| x_x 0 1 |
where x_x, x_y are the mercator projected coordinates
and the solution vector will be omega, v_x, v_y
*/
if(j == 0){ /* first sub-col: omega */
if(irow==0)
*(*a+offset+i)= -gpx[inode*BLOCK_DIM+INT_Y]; /* - x_data_y */
else
*(*a+offset+i)= gpx[inode*BLOCK_DIM+INT_X]; /* x_data_x */
}else if(j == 1){ /* second sub-col: vx_0 */
if(irow==0)
*(*a+offset+i)=1.0;
else
*(*a+offset+i)=0.0;
}else{ /* third sub-col: vy_0 */
if(irow==0)
*(*a+offset+i)=0.0;
else
*(*a+offset+i)=1.0;
}
#endif
}else{
/*
block is fixed with respect to rigid body motions, SVD
should find the minimum norm solution that corresponds
to vx_0,vy_0,omega = 0 for this point
*/
*(*a+offset+i)=0.0;
}
}else{
/*
point is not in block
*/
*(*a+offset+i)=0.0;
}
irow++;/* row counter */
if(irow == pdim){ /* increment node counter */
irow=0;
inode++;
}
}
}
}
free(loc_bcode);
#ifdef SUPER_DEBUG
if(!pinit){
print_matrix_ftrn_file(*a,m,n,"a.dat",FALSE);
pinit=TRUE;
}
#endif
}
/*
assemble the D matrix that links fault-local slip,
\hat{vec{u}}, and global displacement rates
(velocities), \vec{v}
C is the coseismic displacement part as in
v = R - C
D has dimensions DIM * nrp times nr_of_slip_dir * nrf
C = \vec{v} = D \hat\vec{u}
DIM is either BLOCK_DIM or 3 (for spherical)
D will be assembled in FORTRAN convention
*/
void assemble_block_d(COMP_PRECISION **d,struct bflt *fault,
int nflt,int nrp,int nslip,
struct bmd *mod)
{
int i,j,k,m,n,irow,icol,offset,idir,tsize;
static int d_size=0;
#ifdef SUPER_DEBUG
static my_boolean pinit=FALSE;
#endif
#ifdef BLOCK_SPHERICAL
COMP_PRECISION xp[3];
m = 3 * nrp;
if(!mod->cvel_init) /* initialize cartesian GPS velocities */
init_cart_gps_velsig(mod,FALSE);
#else
int l;
m = BLOCK_DIM * nrp;
#endif
n = nslip * nflt; /* nslip is nr of types of slip */
/* allocate space for D */
tsize = n * m;
if(d_size != tsize){
my_vecrealloc(d,tsize,"assemble_block_d: d");
d_size = tsize;
}
#ifdef BLOCK_SPHERICAL
xp[INT_R] = 0.0;
#endif
for(i=0;i < nflt;i++){ /* i: fault loop */
if((!fault[i].vertical)&&(nslip < 2)){
fprintf(stderr,"assemble_block_d: fault %i has dip %g but nslip: %i\n",
i+1,fault[i].dip,nslip);
exit(-1);
}
for(j=0;j < nslip;j++){
/* j: fault slip direction loop */
/* fault slip directions have been sorted:
strike, dip, normal in read_bflt
if j=0: strike direction
j=1: normal or dip direction, depending on the fault
being vertical or not
*/
icol = nslip * i + j;
offset = icol * m;
idir = block_slip_direction(j,(fault+i));
for(k=0;k < nrp;k++){ /* k: loop through observational points */
#ifdef BLOCK_SPHERICAL
// convert polar, rotated displacements to cartesian
xp[INT_THETA]= -(fault+i)->v[k].vc[idir][INT_Y];
xp[INT_PHI] = (fault+i)->v[k].vc[idir][INT_X];
irow = k * 3;
pv2cv(xp,(*d + offset + irow),(mod->pbase + k*9));
#else
for(l=0;l < BLOCK_DIM;l++){ /* l: global directions */
irow = k * BLOCK_DIM + l;
*(*d + offset + irow) = (fault+i)->v[k].vc[idir][l];
}
#endif
}
}
}
#ifdef SUPER_DEBUG
if(!pinit){
print_matrix_ftrn_file(*d,m,n,"d.dat",FALSE);
pinit=TRUE;
}
#endif
}
/*
assemble the I matrix that links fault-local slip, \hat{vec{u}},
and global stresses
I has dimensions 6 * nrp x nr_of_slip_dir * nrf
I will be assembled in FORTRAN convention
*/
void assemble_block_i(COMP_PRECISION **imat,struct bflt *fault,
int nflt,int nrp,int nslip)
{
int i,j,k,l,m,n,irow,icol,offset,idir,tsize;
static int i_size=0;
#ifdef DEBUG
static my_boolean pinit=FALSE;
#endif
m = 6 * nrp;
n = nslip * nflt; /* nslip is nr of types of slip */
/*
realloc space for I
*/
tsize = n * m;
if(i_size != tsize){
my_vecrealloc(imat,tsize,"assemble_block_i: I");
i_size = tsize;
}
for(i=0;i < nflt;i++){ /* i: fault loop */
if((!fault[i].vertical)&&(nslip < 2)){
fprintf(stderr,"assemble_block_i: fault %i has dip %g but nslip: %i\n",
i+1,fault[i].dip,nslip);
exit(-1);
}
for(j=0;j < nslip;j++){ /* j: fault slip direction loop */
icol = nslip * i + j;
offset = icol * m;
idir = block_slip_direction(j,(fault+i));
for(k=irow=0;k < nrp;k++,irow += 6){/* k: loop through observational points */
for(l=0;l < 6;l++) /* l: stress components */
*(*imat + offset + irow + l) =
(fault+i)->s[k].sc[idir][l];
}
}
}
#ifdef DEBUG
if(!pinit){
print_matrix_ftrn_file(*imat,m,n,"i.dat",FALSE);
pinit=TRUE;
}
#endif
}
/*
assemble the G matrix that links global slip, \vec{u}, in a
cartesian lon/lat system to fault-local strike, normal (and dip)
components,\hat{\vec{u}}
G has dimensions
nslip * nrf times BLOCK_DIM * nrf
\hat{u} = G . u
G will be assembled in FORTRAN convention
G depends on the fault geometry orientation, but not the
locking depth
*/
void assemble_block_g(COMP_PRECISION **g,struct bflt *fault,
int nflt, int nslip)
{
int i,j,k,l,m,n,idir,irow,icol,offset,tsize;
static int g_size=0;
#ifdef SUPER_DEBUG
static my_boolean pinit=FALSE;
#endif
m = nslip * nflt; /* nslip is nr of types of slip */
n = BLOCK_DIM * nflt;
if(BLOCK_DIM != 2){
fprintf(stderr,"assemble_block_g should be adpted for DIM != 2\n");
exit(-1);
}
/*
realloc space for G
*/
tsize = n * m;
if(g_size != tsize){
my_vecrealloc(g,tsize,"assemble_block_g: g");
g_size = tsize;
}
for(i=0;i < nflt;i++){ /* i: fault loop */
for(j=0;j < BLOCK_DIM;j++){ /* j: global direction loop */
icol = BLOCK_DIM * i + j;
offset = icol * m;
for(k=0;k < nflt;k++) /* k: second (row) fault loop */
for(l=0;l < nslip;l++){/* l: slip directions */
irow = k * nslip + l;
if(i == k){ /*
this matrix corresponds to t
the unity vectors in
strike and normal/dip
direction and is zero else
*/
idir = block_slip_direction(l,(fault+i));
*(*g + offset + irow) = (fault+i)->evec[idir*3+j];
}else{
*(*g + offset + irow) = 0.0;
}
}
}
}
#ifdef SUPER_DEBUG
if(!pinit){
print_matrix_ftrn_file(*g,m,n,"g.dat",FALSE);
pinit++;
}
#endif
}
/*
assemble F matrix that links block motion parameters, b, to
global velocity differences (v_left - v_right) at the
fault midpoints, interpreted as slip, in a global, lon/lat
cartesian system
b is NBASE * nrb (nrb: nr of blocks)
F is DIM * nflt x NBASE * nrb
assemble F matrix in FORTRAN style (for solvers)
block[nrb].fixed is TRUE if the block is fixed with respect to
rigid body motions
cfac[nflt] is a coupling factor vector (different from the
constant factor we have for each fault during input), that should
normally be initialized to all unity
cfac only gets referenced if invert_for_cfac is set
for a spherical calculation, we determine F from
B . S
where S links the rotation vectors to cartesian velocities
and B rotates those into the lon/lat system
*/
void assemble_block_f(COMP_PRECISION **f,struct bflt *fault,
int nflt,int nrb, struct bck *block,
COMP_PRECISION *cfac,
my_boolean invert_for_cfac)
{
int i,j,k,l,icol,irow,n,m,offset,pdim,mf,tsize;
COMP_PRECISION fac,loc_cfac;
#ifdef BLOCK_SPHERICAL
COMP_PRECISION *b, *s;
#endif
#ifdef SUPER_DEBUG
static my_boolean written=FALSE;
#endif
#ifdef DEBUG
static my_boolean warned=FALSE;
if(invert_for_cfac)
if(!warned){
for(i=0;i<nflt;i++){
if(fabs(cfac[i]-1.0) > EPS_COMP_PREC){
fprintf(stderr,"assemble_block_f: WARNING: at least one coupling factor != 1.0\n");
warned = TRUE;
break;
}
}
}
#endif
if((BLOCK_NBASE != 3)||(BLOCK_DIM!=2)){
fprintf(stderr,"assemble_block_f: dim: %i or nbase: %i not implemented\n",
BLOCK_DIM,BLOCK_NBASE);
exit(-1);
}
/*
nr of columns
*/
n = BLOCK_NBASE * nrb;
#ifdef BLOCK_SPHERICAL
pdim = 3;
/*
nr of rows of S
*/
m = pdim * nflt;
/* nr of rows of F */
mf = BLOCK_DIM * nflt;
/*
allocate space for S
*/
my_vecalloc(&s,n*m,"assemble_block_f: s");
#else
pdim = BLOCK_DIM;
m = BLOCK_DIM * nflt;
mf = m;
tsize = mf * n;
/* allocate space for F */
my_vecrealloc(f,tsize,"assemble_block_f: f");
#endif
for(k=0;k < nrb;k++){ /* loop through blocks */
for(j=0;j < BLOCK_NBASE;j++){ /* loop through base functions */
icol = k * BLOCK_NBASE + j; /* column counter */
offset = icol * m;
for(i=0;i < nflt;i++){ /* loop through faults */
loc_cfac = (invert_for_cfac)?(cfac[i]):(1.0);
if(block[k].fixed) /* block is fixed */
fac = 0.0;
else{ /* block has rigid body motion */
if(fault[i].block[0] == k) /* left border of fault
in block*/
fac = loc_cfac; /* normally unity */
else if(fault[i].block[1] == k) /* right border */
fac = -loc_cfac; /* normally -unity */
else
fac = 0.0; /* zero else */
}
for(l=0;l < pdim;l++){ /* loop through global directions */
irow = pdim * i + l;
if(fac != 0.0){
#ifdef BLOCK_SPHERICAL
/*
assemble S
| 0 r_z -r_y |
| -r_z 0 r_x | w = v
| r_y -r_x 0 |
NOTE THAT THIS ASSIGMENT WORKS COLUMN BY COLUMN
*/
if(j == 0){ /* first sub-col */
if(l == 0)
*(s+offset+irow)= 0.0; /* 0 */
else if(l == 1)
*(s+offset+irow)= -fault[i].xc[INT_Z] * fac; /* -r_z */
else
*(s+offset+irow)= fault[i].xc[INT_Y] * fac; /* r_y */
}else if(j == 1){ /* second sub-col */
if(l == 0)
*(s+offset+irow)= fault[i].xc[INT_Z] * fac; /* r_z */
else if(l == 1)
*(s+offset+irow)= 0.0; /* 0 */
else
*(s+offset+irow)= -fault[i].xc[INT_X]* fac; /* -r_x */
}else{ /* third sub-col */
if(l == 0)
*(s+offset+irow)= -fault[i].xc[INT_Y] * fac; /* -r_y */
else if(l == 1)
*(s+offset+irow)= fault[i].xc[INT_X] * fac; /* r_x */
else
*(s+offset+irow)= 0.0; /* 0 */
}
#else
/* rotation and translation part */
if(j == 0) /* first sub-col: omega */
if(l==0) /* those are, like in assemble_block_a
the projected coordinates of the
fault midpoint (with respect to
the genral, not local projection)
*/
*(*f+offset+irow)= -fault[i].px[INT_Y] * fac;
else
*(*f+offset+irow)= fault[i].px[INT_X] * fac;
else if(j == 1) /* second sub-col: vx_0 */
if(l==0)
*(*f+offset+irow) = fac; /* 1 or -1 */
else
*(*f+offset+irow) = 0.0;
else /* third sub-col: vy_0 */
if(l==0)
*(*f+offset+irow) = 0.0;
else
*(*f+offset+irow) = fac; /* 1 or -1 */
#endif
}else{
#ifdef BLOCK_SPHERICAL
*(s+offset+irow) = 0.0;
#else
*(*f+offset+irow) = 0.0;
#endif
}
}
}
}
}
#ifdef BLOCK_SPHERICAL
/*
assemble B which is mf rows by m columns and links the cartesian
system relative velocities to polar (lon/lat) displacements
*/
tsize = mf * m;
/* allocate space for B */
my_vecalloc(&b,tsize,"assemble_block_f: b");
/* have to initialize with zeros */
for(i=0;i < tsize;i++)
b[i] = 0.0;
/* PS: don't use calloc to allow memory debugging */
for(k=0;k < nflt;k++){ /* column flt loop */
for(j=0;j < pdim;j++){ /* column dimension loop */
icol = k * pdim + j;
offset = icol * mf;
/* assign only one row, i=k, the rest of B is zeroes */
for(l=0;l < BLOCK_DIM;l++){ /* row dimension loop */
irow = BLOCK_DIM * k + l;
if(l==0)// lon or phi direction
*(b+offset+irow) = fault[k].pbase[INT_PHI*3 +j];
else// lat or -theta direction
*(b+offset+irow) = -fault[k].pbase[INT_THETA*3+j];
}
}
}
#ifdef SUPER_DEBUG
if(!written){
print_matrix_ftrn_file(s,m,n,"s.dat",FALSE);
print_matrix_ftrn_file(b,mf,m,"b.dat",FALSE);
/* `written' gets set to true later */
}
#endif /* end debug if */
/*
obtain F from B.S
*/
/* allocate space for F */
tsize = n * mf;
my_vecrealloc(f,tsize,"assemble_block_f: f");
calc_AB_ftn(b,mf,m,s,n,*f);
#ifdef MEM_ALLOC_DEBUG
fprintf(stderr,"assemble_block_f: freeing b and s\n");
#endif /* end mem alloc if */
free(b);free(s);
#endif /* end block_spherical part if */
#ifdef SUPER_DEBUG
if(!written){
print_matrix_ftrn_file(*f,mf,n,"f.dat",FALSE);
written=TRUE;
}
#endif
}
/*
assemble the complete K(m=nrgp+nrsp+nfdamp+nxdamp,
n=nbase*nbl) matrix
-----n-----
( A - E ) E = D.G.F and K2=I.G.F (m1 = nrgp*2/3 rows)
( - K2 ) (m2 = nrsp*6 rows)
( g G.F ) if damping of slip is activated (m3 = nfdamp rows)
( aI ) if damping of x sol. is activated (m4 = nxdamp(0/n), I being the
unity matrix)
m1 = nrgp * BLOCK_DIM or nrgp * 3 (for spherical);
m2 = nrsp * 6;
m3 = nsnf or nflt rows. if nsnf, full G.F matrix, if nflt only
normal motion parts
m4 = 0 or n depending on nxdamp
on input, can be m1, m1+m2, or m1+m2+m3
*/
void assemble_block_k(COMP_PRECISION **kmat, int m,int m1,
int m2,int n, int nrgp, int nrsp, int nflt,
COMP_PRECISION *a, COMP_PRECISION *e,
COMP_PRECISION *k2mat,my_boolean rigid,
my_boolean damp_nslip,COMP_PRECISION *gf,
struct bflt *fault, int nsnf,int nslip,
int nfdamp, int nxdamp,
COMP_PRECISION xdamp)
{
int i,j,k,nm,o1,offset,offset2,m1m2,icount,kcount,tsize;
static int k_size=0;
nm = n * m;
m1m2 = m1 + m2;
if(m1m2 + nfdamp + nxdamp != m){
fprintf(stderr,"assemble_block_k: logic error: m: %i m1: %i m2: %i nfdamp: %i nxdamp: %i\n",
m,m1,m2,nfdamp,nxdamp);
exit(-1);
}
tsize = nm;
if(k_size != tsize){
// reallocate K matrix
my_vecrealloc(kmat,tsize,"assemble_block_k: kmat");
k_size = tsize;
}
//
for(i=0;i < tsize;i++) /* initialize K with zeroes */
*(*kmat+i) = 0.0;
//
// check the damping assignment numbers
//
if(damp_nslip){ /* damping part */
if(rigid){
fprintf(stderr,"assemble_block_k: logic error: both normal damping and rigid flag set\n");
exit(-1);
}
if(nsnf <= 0){
fprintf(stderr,"assemble_block_k: error with m1: %i m2: %i m: %i nsnf: %i\n",
m1,m2,m,nsnf);
exit(-1);
}
/* prepare j-loop in case of damping:
if nfdamp is nflt and nslip=2, use every other (normal)
component.
*/
switch(nslip){
case 1:
if(nfdamp != nflt){
fprintf(stderr,"assemble_block_k: error: nslip: %i nflt: %i nfdamp: %i\n",
nslip,nflt,nfdamp);
exit(-1);
}
break;
case 2:
if((nfdamp != nflt)&&(nfdamp != nsnf)){
fprintf(stderr,"assemble_block_k: error: nslip: %i nflt: %i nfdamp: %i\n",
nslip,nflt,nfdamp);
exit(-1);
}
break;
default:
fprintf(stderr,"assemble_block_k: error: nslip: %i\n",
nslip);
exit(-1);
break;
}
}else{
/*
no slip damping
*/
if(nfdamp != 0){
fprintf(stderr,"assemble_block_k: logic error: no damping set, but nfdamp %i\n",
nfdamp);
exit(-1);
}
}
#ifdef BLOCK_SPHERICAL
if(m1 != 3 * nrgp){
fprintf(stderr,"assemble_block_k: error: m1: %i nrgp: %i pdim: %i (spherical)\n",
m1,nrgp,3);
exit(-1);
}
#else
if(m1 != BLOCK_DIM * nrgp){
fprintf(stderr,"assemble_block_k: error: m1: %i nrgp: %i pdim: %i\n",
m1,nrgp,BLOCK_DIM);
exit(-1);
}
#endif
if((!rigid)&&(nflt)){
for(j=o1=0;j < n;j++,o1+=m){ /* j-loop through solution
parameters, columns of K */
//
// actually subtract interseismic deformation part
/* A - E part */
//
offset2 = o1; /* start off at first row */
/* this is the increment */
offset = j * m1; /* A and E are nrgp*pdim by n */
for(i=0;i < m1;i++){ /* i loop through GPS data rows */
*(*kmat + offset2 + i) = a[offset + i] - e[offset + i];
}
offset2 += m1; /* shift offset to end of GPS row */
/*
if there are stress observations, add the stress part, K2
*/
if(m2){
offset = j * m2; /* K2 is nrsp * 6 by n */
for(i=0;i < m2;i++){ /* -K2 = - I.G.F lower part,
loop through stress rows
*/
*(*kmat + offset2 + i) = -k2mat[offset + i];
}
/* shift to end of stress rows */
offset2 += m2;
}
if(damp_nslip){
/* damping of slip motion part */
offset = j * nsnf; /* nfdamp may be nflt or
nflt*nslip=nsnf however, G.F is
nsnf by n */
for(i=icount=kcount=0;i < nflt;i++){ /* fault loop */
for(k=0;k < nslip;k++){ /* slip direction loop */
/* only those fault slip motions with damping
have entries other than zero */
if(fault[i].use_damp[k]){
*(*kmat+ offset2 + icount) =
fault[i].sdamp[k] * gf[offset + kcount];
icount++; /* increases only with damped
directions */
}
kcount++; /* increases with all possibble
slip directions 0...nfns-1*/
}
}
if((icount != nfdamp)||(kcount != nsnf)){
fprintf(stderr,"assemble_block_k: assembly error: icount: %i m3: %i kcount: %i nsnf: %i\n",
icount,nfdamp,kcount,nsnf);
exit(-1);
}
/* shift offset to end of slip damping */
offset2 += nfdamp;
} /* end slip damping loop */
if(nxdamp){
/*
solution vector damping toward rigid solution,
only the diagonal elements are unity * damping factor,
else leave at zero
*/
*(*kmat + offset2 + j) = xdamp ;
}
} /* end j-loop through the columns of K */
/* end non-rigid computation */
}else{
/*
only rigid computation
*/
if(nfdamp || m2){
fprintf(stderr,"assemble_block_k: logic error: rigid, but m2: %i and nfdamp: %i\n",
m2,nfdamp);
exit(-1);
}
for(j=o1=0;j < n;j++,o1 += m){
/* the upper part of K = A */
offset2 = o1;
offset = j * m1;
for(i=0;i < m1;i++)
*(*kmat + offset2 + i) = a[offset + i];
offset2 += m1; /* shift to end of GPS */
/*
damping of solution vector toward rigid solution,
diagonal elements are 1 * xdamp
*/
if(nxdamp){
*(*kmat + offset2 + j) = xdamp;
}
}
fprintf(stderr,"assemble_block_k: WARNING: rigid calculation: no interseismic deformation\n");
}
}
/*
given a fault structure with initialized interaction coefficients,
and a fault slip vector slip[nslip*nflt] obtained by multiplying
G.F.x (calc_Ax_ftn(gf,nsnf,n,xsol,fslip)) calculate the stress
matrix in short (6) vector storage format at point ipnt
the effect of the stress should be taken negative like
the velocity field which is block motion - effect of locking
*/
void assemble_stress_matrix(COMP_PRECISION *sloc,int ipnt,
struct bflt *fault,
COMP_PRECISION *fslip,int nflt,
int nslip)
{
int i,j,k,offset,idir;
for(i=0;i<6;i++)
sloc[i] = 0.0; /* only upper right half */
for(j=0;j < nflt;j++) /* loop through faults */
for(i = 0;i < nslip;i++){ /* add all slip modes */
offset = j * nslip + i; /* stress contributions */
idir = block_slip_direction(i,(fault+j));
for(k=0;k < 6;k++)
sloc[k] -= (fault+j)->s[ipnt].sc[idir][k] *
fslip[offset];
}
}
/*
calculate the fit vector component jrow where jrow runs from
0 .. m, the number of velocity components (DIM * # GPS obs.)
if jrow == -1, will produce the whole solution (fit) vector
if assemble_k is false, the routine simply performs the
multiplication of row jrow of K with xsol[n] to return
the y[jrow] prediction, assuming that kmat has been assembled
already
if assemble_k is true, then K will be reassembled. for this to
work, a, d, and g will have to be precomputed and allocated,
kmat only has to be allocated
further input is nrb, the block[] array, nsnf