/*
--------------------------------------------------
copy the first column of mtxA into the vector H0[]
created -- 98may30, cca
--------------------------------------------------
*/
static int
copyIntoVec1 (
A2 *mtxA,
double H0[],
int msglvl,
FILE *msgFile
) {
double ival, rval ;
double *colA ;
int ii, inc1, irow, jj, lastrow, ncolA, nrowA ;
/*
----------------------------------
copy the column of A into a vector
and find the last nonzero element
----------------------------------
*/
nrowA = mtxA->n1 ;
ncolA = mtxA->n2 ;
inc1 = mtxA->inc1 ;
lastrow = -1 ;
colA = A2_column(mtxA, 0) ;
if ( A2_IS_REAL(mtxA) ) {
for ( irow = ii = jj = 0 ;
irow < nrowA ;
irow++, ii += inc1, jj++ ) {
rval = colA[ii] ;
if ( rval != 0.0 ) {
H0[jj] = rval ;
lastrow = irow ;
}
}
} else if ( A2_IS_COMPLEX(mtxA) ) {
for ( irow = ii = jj = 0 ;
irow < nrowA ;
irow++, ii += 2*inc1, jj += 2 ) {
rval = colA[ii] ; ival = colA[ii+1] ;
if ( rval != 0.0 || ival != 0.0 ) {
H0[jj] = rval ; H0[jj+1] = ival ;
lastrow = irow ;
}
}
}
return(lastrow) ; }
/*
----------------------------------------------
sort the rows of the matrix in ascending order
of the rowids[] vector. on return, rowids is
in asending order. return value is the number
of row swaps made.
created -- 98apr15, cca
----------------------------------------------
*/
int
A2_sortRowsUp (
A2 *mtx,
int nrow,
int rowids[]
) {
int ii, minrow, minrowid, nswap, target ;
/*
---------------
check the input
---------------
*/
if ( mtx == NULL || mtx->n1 < nrow || nrow < 0 || rowids == NULL ) {
fprintf(stderr, "\n fatal error in A2_sortRowsUp(%p,%d,%p)"
"\n bad input\n", mtx, nrow, rowids) ;
if ( mtx != NULL ) {
A2_writeStats(mtx, stderr) ;
}
exit(-1) ;
}
if ( ! (A2_IS_REAL(mtx) || A2_IS_COMPLEX(mtx)) ) {
fprintf(stderr, "\n fatal error in A2_sortRowsUp(%p,%d,%p)"
"\n bad type %d, must be SPOOLES_REAL or SPOOLES_COMPLEX\n",
mtx, nrow, rowids, mtx->type) ;
exit(-1) ;
}
nswap = 0 ;
if ( mtx->inc1 == 1 ) {
double *dvtmp ;
int jcol, ncol ;
int *ivtmp ;
/*
---------------------------------------------------
matrix is stored by columns, so permute each column
---------------------------------------------------
*/
ivtmp = IVinit(nrow, -1) ;
if ( A2_IS_REAL(mtx) ) {
dvtmp = DVinit(nrow, 0.0) ;
} else if ( A2_IS_COMPLEX(mtx) ) {
dvtmp = DVinit(2*nrow, 0.0) ;
}
IVramp(nrow, ivtmp, 0, 1) ;
IV2qsortUp(nrow, rowids, ivtmp) ;
ncol = mtx->n2 ;
for ( jcol = 0 ; jcol < ncol ; jcol++ ) {
if ( A2_IS_REAL(mtx) ) {
DVcopy(nrow, dvtmp, A2_column(mtx, jcol)) ;
DVgather(nrow, A2_column(mtx, jcol), dvtmp, ivtmp) ;
} else if ( A2_IS_COMPLEX(mtx) ) {
ZVcopy(nrow, dvtmp, A2_column(mtx, jcol)) ;
ZVgather(nrow, A2_column(mtx, jcol), dvtmp, ivtmp) ;
}
}
IVfree(ivtmp) ;
DVfree(dvtmp) ;
} else {
/*
----------------------------------------
use a simple insertion sort to swap rows
----------------------------------------
*/
for ( target = 0 ; target < nrow ; target++ ) {
minrow = target ;
minrowid = rowids[target] ;
for ( ii = target + 1 ; ii < nrow ; ii++ ) {
if ( minrowid > rowids[ii] ) {
minrow = ii ;
minrowid = rowids[ii] ;
}
}
if ( minrow != target ) {
rowids[minrow] = rowids[target] ;
rowids[target] = minrowid ;
A2_swapRows(mtx, target, minrow) ;
nswap++ ;
}
}
}
return(nswap) ; }
/*
-----------------------------------------------------------
A contains the following data from the A = QR factorization
A(1:ncolA,1:ncolA) = R
A(j+1:nrowA,j) is v_j, the j-th householder vector,
where v_j[j] = 1.0
we compute Y = Q^T X when A is real
and Y = Q^H X when A is complex
NOTE: A, Y and X must be column major.
NOTE: Y and X can be the same object,
in which case X is overwritten with Y
created -- 98dec10, cca
-----------------------------------------------------------
*/
void
A2_applyQT (
A2 *Y,
A2 *A,
A2 *X,
DV *workDV,
int msglvl,
FILE *msgFile
) {
double *betas ;
int irowA, jcolA, jcolX, ncolA, ncolX, nrowA ;
/*
---------------
check the input
---------------
*/
if ( A == NULL ) {
fprintf(stderr, "\n fatal error in A2_applyQT()"
"\n A is NULL\n") ;
exit(-1) ;
}
if ( X == NULL ) {
fprintf(stderr, "\n fatal error in A2_applyQT()"
"\n X is NULL\n") ;
exit(-1) ;
}
if ( workDV == NULL ) {
fprintf(stderr, "\n fatal error in A2_applyQT()"
"\n workDV is NULL\n") ;
exit(-1) ;
}
if ( msglvl > 0 && msgFile == NULL ) {
fprintf(stderr, "\n fatal error in A2_applyQT()"
"\n msglvl > 0 and msgFile is NULL\n") ;
exit(-1) ;
}
nrowA = A2_nrow(A) ;
ncolA = A2_ncol(A) ;
ncolX = A2_ncol(X) ;
if ( nrowA <= 0 ) {
fprintf(stderr, "\n fatal error in A2_applyQT()"
"\n nrowA = %d\n", nrowA) ;
exit(-1) ;
}
if ( ncolA <= 0 ) {
fprintf(stderr, "\n fatal error in A2_applyQT()"
"\n ncolA = %d\n", nrowA) ;
exit(-1) ;
}
if ( nrowA != A2_nrow(X) ) {
fprintf(stderr, "\n fatal error in A2_applyQT()"
"\n nrowA = %d, nrowX = %d\n", nrowA, A2_nrow(X)) ;
exit(-1) ;
}
switch ( A->type ) {
case SPOOLES_REAL :
case SPOOLES_COMPLEX :
break ;
default :
fprintf(stderr, "\n fatal error in A2_applyQT()"
"\n invalid type for A\n") ;
exit(-1) ;
}
if ( A->type != X->type ) {
fprintf(stderr, "\n fatal error in A2_applyQT()"
"\n A->type = %d, X->type = %d\n", A->type, X->type) ;
exit(-1) ;
}
if ( A2_inc1(A) != 1 ) {
fprintf(stderr, "\n fatal error in A2_applyQT()"
"\n A->inc1 = %d \n", A2_inc1(A)) ;
exit(-1) ;
}
if ( A2_inc1(X) != 1 ) {
fprintf(stderr, "\n fatal error in A2_applyQT()"
"\n X->inc1 = %d, \n", A2_inc1(X)) ;
exit(-1) ;
}
/*
--------------------------------------------------
compute the beta values, beta_j = 2./(V_j^H * V_j)
--------------------------------------------------
*/
DV_setSize(workDV, ncolA) ;
betas = DV_entries(workDV) ;
if ( A2_IS_REAL(A) ) {
int irowA, jcolA ;
double sum ;
double *colA ;
for ( jcolA = 0 ; jcolA < ncolA ; jcolA++ ) {
sum = 1.0 ;
colA = A2_column(A, jcolA) ;
for ( irowA = jcolA + 1 ; irowA < nrowA ; irowA++ ) {
sum += colA[irowA] * colA[irowA] ;
}
betas[jcolA] = 2./sum ;
}
} else {
double ival, rval, sum ;
double *colA ;
for ( jcolA = 0 ; jcolA < ncolA ; jcolA++ ) {
sum = 1.0 ;
colA = A2_column(A, jcolA) ;
for ( irowA = jcolA + 1 ; irowA < nrowA ; irowA++ ) {
rval = colA[2*irowA] ; ival = colA[2*irowA+1] ;
sum += rval*rval + ival*ival ;
}
betas[jcolA] = 2./sum ;
}
}
/*
------------------------------------------
loop over the number of columns in X and Y
------------------------------------------
*/
for ( jcolX = 0 ; jcolX < ncolX ; jcolX++ ) {
double *V, *colX, *colY ;
int jcolV ;
if ( msglvl > 2 ) {
fprintf(msgFile, "\n\n %% jcolX = %d", jcolX) ;
fflush(msgFile) ;
}
/*
-------------------------------
copy X(:,jcolX) into Y(:,jcolX)
-------------------------------
*/
colY = A2_column(Y, jcolX) ;
colX = A2_column(X, jcolX) ;
if ( A2_IS_REAL(A) ) {
DVcopy(nrowA, colY, colX) ;
} else {
DVcopy(2*nrowA, colY, colX) ;
}
for ( jcolV = 0 ; jcolV < ncolA ; jcolV++ ) {
double beta ;
if ( msglvl > 2 ) {
fprintf(msgFile, "\n %% jcolV = %d", jcolV) ;
fflush(msgFile) ;
}
/*
------------------------------------------------------------
update colY = (I - beta_jcolV * V_jcolV * V_jcolV^T)colY
= colY - beta_jcolV * V_jcolV * V_jcolV^T * colY
= colY - (beta_jcolV * V_jcolV^T * Y) * V_jcolV
------------------------------------------------------------
*/
V = A2_column(A, jcolV) ;
beta = betas[jcolV] ;
if ( msglvl > 2 ) {
fprintf(msgFile, "\n %% beta = %12.4e", beta) ;
fflush(msgFile) ;
}
if ( A2_IS_REAL(A) ) {
double fac, sum = colY[jcolV] ;
int irow ;
for ( irow = jcolV + 1 ; irow < nrowA ; irow++ ) {
if ( msglvl > 2 ) {
fprintf(msgFile,
"\n %% V[%d] = %12.4e, X[%d] = %12.4e",
irow, V[irow], irow, colY[irow]) ;
fflush(msgFile) ;
}
sum += V[irow] * colY[irow] ;
}
if ( msglvl > 2 ) {
fprintf(msgFile, "\n %% sum = %12.4e", sum) ;
fflush(msgFile) ;
}
fac = beta * sum ;
if ( msglvl > 2 ) {
fprintf(msgFile, "\n %% fac = %12.4e", fac) ;
fflush(msgFile) ;
}
colY[jcolV] -= fac ;
for ( irow = jcolV + 1 ; irow < nrowA ; irow++ ) {
colY[irow] -= fac * V[irow] ;
}
} else {
double rfac, ifac,
rsum = colY[2*jcolV], isum = colY[2*jcolV+1] ;
int irow ;
for ( irow = jcolV + 1 ; irow < nrowA ; irow++ ) {
double Vi, Vr, Yi, Yr ;
Vr = V[2*irow] ; Vi = V[2*irow+1] ;
Yr = colY[2*irow] ; Yi = colY[2*irow+1] ;
rsum += Vr*Yr + Vi*Yi ;
isum += Vr*Yi - Vi*Yr ;
}
rfac = beta * rsum ;
ifac = beta * isum ;
colY[2*jcolV] -= rfac ;
colY[2*jcolV+1] -= ifac ;
for ( irow = jcolV + 1 ; irow < nrowA ; irow++ ) {
double Vi, Vr ;
Vr = V[2*irow] ; Vi = V[2*irow+1] ;
colY[2*irow] -= rfac*Vr - ifac*Vi ;
colY[2*irow+1] -= rfac*Vi + ifac*Vr ;
}
}
}
}
return ; }
/*
-----------------------------------------------------------
A contains the following data from the A = QR factorization
A(1:ncolA,1:ncolA) = R
A(j+1:nrowA,j) is v_j, the j-th householder vector,
where v_j[j] = 1.0
NOTE: A and Q must be column major
created -- 98dec10, cca
-----------------------------------------------------------
*/
void
A2_computeQ (
A2 *Q,
A2 *A,
DV *workDV,
int msglvl,
FILE *msgFile
) {
double *betas ;
int irowA, jcolA, ncolA, nrowA ;
/*
---------------
check the input
---------------
*/
if ( Q == NULL ) {
fprintf(stderr, "\n fatal error in A2_computeQ()"
"\n Q is NULL\n") ;
exit(-1) ;
}
if ( A == NULL ) {
fprintf(stderr, "\n fatal error in A2_computeQ()"
"\n A is NULL\n") ;
exit(-1) ;
}
if ( workDV == NULL ) {
fprintf(stderr, "\n fatal error in A2_computeQ()"
"\n workDV is NULL\n") ;
exit(-1) ;
}
if ( msglvl > 0 && msgFile == NULL ) {
fprintf(stderr, "\n fatal error in A2_computeQ()"
"\n msglvl > 0 and msgFile is NULL\n") ;
exit(-1) ;
}
nrowA = A2_nrow(A) ;
ncolA = A2_ncol(A) ;
if ( nrowA <= 0 ) {
fprintf(stderr, "\n fatal error in A2_computeQ()"
"\n nrowA = %d\n", nrowA) ;
exit(-1) ;
}
if ( ncolA <= 0 ) {
fprintf(stderr, "\n fatal error in A2_computeQ()"
"\n ncolA = %d\n", nrowA) ;
exit(-1) ;
}
if ( nrowA != A2_nrow(Q) ) {
fprintf(stderr, "\n fatal error in A2_computeQ()"
"\n nrowA = %d, nrowQ = %d\n", nrowA, A2_nrow(Q)) ;
exit(-1) ;
}
if ( ncolA != A2_ncol(Q) ) {
fprintf(stderr, "\n fatal error in A2_computeQ()"
"\n ncolA = %d, ncolQ = %d\n", ncolA, A2_ncol(Q)) ;
exit(-1) ;
}
switch ( A->type ) {
case SPOOLES_REAL :
case SPOOLES_COMPLEX :
break ;
default :
fprintf(stderr, "\n fatal error in A2_computeQ()"
"\n invalid type for A\n") ;
exit(-1) ;
}
if ( A->type != Q->type ) {
fprintf(stderr, "\n fatal error in A2_computeQ()"
"\n A->type = %d, Q->type = %d\n", A->type, Q->type) ;
exit(-1) ;
}
if ( A2_inc1(A) != 1 ) {
fprintf(stderr, "\n fatal error in A2_computeQ()"
"\n A->inc1 = %d \n", A2_inc1(A)) ;
exit(-1) ;
}
if ( A2_inc1(Q) != 1 ) {
fprintf(stderr, "\n fatal error in A2_computeQ()"
"\n Q->inc1 = %d, \n", A2_inc1(Q)) ;
exit(-1) ;
}
/*
--------------------------------------------------
compute the beta values, beta_j = 2./(V_j^H * V_j)
--------------------------------------------------
*/
DV_setSize(workDV, ncolA) ;
betas = DV_entries(workDV) ;
if ( A2_IS_REAL(A) ) {
int irowA, jcolA ;
double sum ;
double *colA ;
for ( jcolA = 0 ; jcolA < ncolA ; jcolA++ ) {
sum = 1.0 ;
colA = A2_column(A, jcolA) ;
for ( irowA = jcolA + 1 ; irowA < nrowA ; irowA++ ) {
sum += colA[irowA] * colA[irowA] ;
}
betas[jcolA] = 2./sum ;
}
} else {
double ival, rval, sum ;
double *colA ;
for ( jcolA = 0 ; jcolA < ncolA ; jcolA++ ) {
sum = 1.0 ;
colA = A2_column(A, jcolA) ;
for ( irowA = jcolA + 1 ; irowA < nrowA ; irowA++ ) {
rval = colA[2*irowA] ; ival = colA[2*irowA+1] ;
sum += rval*rval + ival*ival ;
}
betas[jcolA] = 2./sum ;
}
}
/*
-------------------------------------------
loop over the number of householder vectors
-------------------------------------------
*/
for ( jcolA = 0 ; jcolA < ncolA ; jcolA++ ) {
double *V, *X ;
int jcolV ;
if ( msglvl > 2 ) {
fprintf(msgFile, "\n\n %% jcolA = %d", jcolA) ;
fflush(msgFile) ;
}
/*
------------------
set X[] to e_jcolA
------------------
*/
X = A2_column(Q, jcolA) ;
if ( A2_IS_REAL(Q) ) {
DVzero(nrowA, X) ;
X[jcolA] = 1.0 ;
} else {
DVzero(2*nrowA, X) ;
X[2*jcolA] = 1.0 ;
}
for ( jcolV = jcolA ; jcolV >= 0 ; jcolV-- ) {
double beta ;
if ( msglvl > 2 ) {
fprintf(msgFile, "\n %% jcolV = %d", jcolV) ;
fflush(msgFile) ;
}
/*
-----------------------------------------------------
update X = (I - beta_jcolV * V_jcolV * V_jcolV^T)X
= X - beta_jcolV * V_jcolV * V_jcolV^T * X
= X - (beta_jcolV * V_jcolV^T * X) * V_jcolV
-----------------------------------------------------
*/
V = A2_column(A, jcolV) ;
beta = betas[jcolV] ;
if ( msglvl > 2 ) {
fprintf(msgFile, "\n %% beta = %12.4e", beta) ;
fflush(msgFile) ;
}
if ( A2_IS_REAL(Q) ) {
double fac, sum = X[jcolV] ;
int irow ;
for ( irow = jcolV + 1 ; irow < nrowA ; irow++ ) {
if ( msglvl > 2 ) {
fprintf(msgFile,
"\n %% V[%d] = %12.4e, X[%d] = %12.4e",
irow, V[irow], irow, X[irow]) ;
fflush(msgFile) ;
}
sum += V[irow] * X[irow] ;
}
if ( msglvl > 2 ) {
fprintf(msgFile, "\n %% sum = %12.4e", sum) ;
fflush(msgFile) ;
}
fac = beta * sum ;
if ( msglvl > 2 ) {
fprintf(msgFile, "\n %% fac = %12.4e", fac) ;
fflush(msgFile) ;
}
X[jcolV] -= fac ;
for ( irow = jcolV + 1 ; irow < nrowA ; irow++ ) {
X[irow] -= fac * V[irow] ;
}
} else {
double rfac, ifac, rsum = X[2*jcolV], isum = X[2*jcolV+1] ;
int irow ;
for ( irow = jcolV + 1 ; irow < nrowA ; irow++ ) {
double Vi, Vr, Xi, Xr ;
Vr = V[2*irow] ; Vi = V[2*irow+1] ;
Xr = X[2*irow] ; Xi = X[2*irow+1] ;
rsum += Vr*Xr + Vi*Xi ;
isum += Vr*Xi - Vi*Xr ;
}
rfac = beta * rsum ;
ifac = beta * isum ;
X[2*jcolV] -= rfac ;
X[2*jcolV+1] -= ifac ;
for ( irow = jcolV + 1 ; irow < nrowA ; irow++ ) {
double Vi, Vr ;
Vr = V[2*irow] ; Vi = V[2*irow+1] ;
X[2*irow] -= rfac*Vr - ifac*Vi ;
X[2*irow+1] -= rfac*Vi + ifac*Vr ;
}
}
}
}
return ; }
/*
---------------------------------
compute A := A - H0 * beta0 * W0
created -- 98may30, cca
---------------------------------
*/
static double
updateA1 (
A2 *mtxA,
double H0[],
double beta0,
double W0[],
int msglvl,
FILE *msgFile
) {
double nops ;
int inc1, inc2, ncolA, nrowA ;
if ( msglvl > 5 ) {
fprintf(msgFile, "\n %% inside updateA1, nrow %d, ncol %d",
mtxA->n1, mtxA->n2) ;
}
nrowA = mtxA->n1 ;
ncolA = mtxA->n2 ;
inc1 = mtxA->inc1 ;
inc2 = mtxA->inc2 ;
nops = 0.0 ;
if ( A2_IS_REAL(mtxA) ) {
int irow, jcol ;
if ( inc1 == 1 ) {
double alpha[3] ;
double *colA0, *colA1, *colA2 ;
/*
-----------------------------------------
A is column major
compute A(:,jcol) -= beta * W0(jcol) * H0
-----------------------------------------
*/
for ( jcol = 0 ; jcol < ncolA - 2 ; jcol += 3 ) {
colA0 = A2_column(mtxA, jcol) ;
colA1 = A2_column(mtxA, jcol+1) ;
colA2 = A2_column(mtxA, jcol+2) ;
alpha[0] = -beta0 * W0[jcol] ;
alpha[1] = -beta0 * W0[jcol+1] ;
alpha[2] = -beta0 * W0[jcol+2] ;
DVaxpy31(nrowA, colA0, colA1, colA2, alpha, H0) ;
nops += 6*nrowA ;
}
if ( jcol == ncolA - 2 ) {
colA0 = A2_column(mtxA, jcol) ;
colA1 = A2_column(mtxA, jcol+1) ;
alpha[0] = -beta0 * W0[jcol] ;
alpha[1] = -beta0 * W0[jcol+1] ;
DVaxpy21(nrowA, colA0, colA1, alpha, H0) ;
nops += 4*nrowA ;
} else if ( jcol == ncolA - 1 ) {
colA0 = A2_column(mtxA, jcol) ;
alpha[0] = -beta0 * W0[jcol] ;
DVaxpy11(nrowA, colA0, alpha, H0) ;
nops += 2*nrowA ;
}
} else {
double alpha[3] ;
double *rowA0, *rowA1, *rowA2 ;
/*
-----------------------------------------
A is row major
compute A(irow,:) -= H0[irow]*beta0*W0(:)
-----------------------------------------
*/
for ( irow = 0 ; irow < nrowA - 2 ; irow += 3 ) {
rowA0 = A2_row(mtxA, irow) ;
rowA1 = A2_row(mtxA, irow+1) ;
rowA2 = A2_row(mtxA, irow+2) ;
alpha[0] = -beta0 * H0[irow] ;
alpha[1] = -beta0 * H0[irow+1] ;
alpha[2] = -beta0 * H0[irow+2] ;
DVaxpy31(ncolA, rowA0, rowA1, rowA2, alpha, W0) ;
nops += 6*ncolA + 3 ;
}
if ( irow == nrowA - 2 ) {
rowA0 = A2_row(mtxA, irow) ;
rowA1 = A2_row(mtxA, irow+1) ;
alpha[0] = -beta0 * H0[irow] ;
alpha[1] = -beta0 * H0[irow+1] ;
DVaxpy21(ncolA, rowA0, rowA1, alpha, W0) ;
nops += 4*ncolA + 2 ;
} else if ( irow == nrowA - 1 ) {
rowA0 = A2_row(mtxA, irow) ;
alpha[0] = -beta0 * H0[irow] ;
DVaxpy11(ncolA, rowA0, alpha, W0) ;
nops += 2*ncolA + 1 ;
}
}
} else if ( A2_IS_COMPLEX(mtxA) ) {
int irow, jcol ;
if ( inc1 == 1 ) {
double alpha[6] ;
double *colA0, *colA1, *colA2 ;
/*
-----------------------------------------
A is column major
compute A(:,jcol) -= beta * W0(jcol) * H0
-----------------------------------------
*/
for ( jcol = 0 ; jcol < ncolA - 2 ; jcol += 3 ) {
colA0 = A2_column(mtxA, jcol) ;
colA1 = A2_column(mtxA, jcol+1) ;
colA2 = A2_column(mtxA, jcol+2) ;
alpha[0] = -beta0 * W0[2*jcol] ;
alpha[1] = -beta0 * W0[2*jcol+1] ;
alpha[2] = -beta0 * W0[2*(jcol+1)] ;
alpha[3] = -beta0 * W0[2*(jcol+1)+1] ;
alpha[4] = -beta0 * W0[2*(jcol+2)] ;
alpha[5] = -beta0 * W0[2*(jcol+2)+1] ;
ZVaxpy31(nrowA, colA0, colA1, colA2, alpha, H0) ;
nops += 24*nrowA ;
}
if ( jcol == ncolA - 2 ) {
colA0 = A2_column(mtxA, jcol) ;
colA1 = A2_column(mtxA, jcol+1) ;
alpha[0] = -beta0 * W0[2*jcol] ;
alpha[1] = -beta0 * W0[2*jcol+1] ;
alpha[2] = -beta0 * W0[2*(jcol+1)] ;
alpha[3] = -beta0 * W0[2*(jcol+1)+1] ;
ZVaxpy21(nrowA, colA0, colA1, alpha, H0) ;
nops += 16*nrowA ;
} else if ( jcol == ncolA - 1 ) {
colA0 = A2_column(mtxA, jcol) ;
alpha[0] = -beta0 * W0[2*jcol] ;
alpha[1] = -beta0 * W0[2*jcol+1] ;
ZVaxpy11(nrowA, colA0, alpha, H0) ;
nops += 8*nrowA ;
}
} else {
double alpha[6] ;
double *rowA0, *rowA1, *rowA2 ;
/*
-----------------------------------------
A is row major
compute A(irow,:) -= H0[irow]*beta0*W0(:)
-----------------------------------------
*/
for ( irow = 0 ; irow < nrowA - 2 ; irow += 3 ) {
rowA0 = A2_row(mtxA, irow) ;
rowA1 = A2_row(mtxA, irow+1) ;
rowA2 = A2_row(mtxA, irow+2) ;
alpha[0] = -beta0 * H0[2*irow] ;
alpha[1] = -beta0 * H0[2*irow+1] ;
alpha[2] = -beta0 * H0[2*(irow+1)] ;
alpha[3] = -beta0 * H0[2*(irow+1)+1] ;
alpha[4] = -beta0 * H0[2*(irow+2)] ;
alpha[5] = -beta0 * H0[2*(irow+2)+1] ;
ZVaxpy31(ncolA, rowA0, rowA1, rowA2, alpha, W0) ;
nops += 24*ncolA + 12 ;
}
if( irow == nrowA - 2 ) {
rowA0 = A2_row(mtxA, irow) ;
rowA1 = A2_row(mtxA, irow+1) ;
alpha[0] = -beta0 * H0[2*irow] ;
alpha[1] = -beta0 * H0[2*irow+1] ;
alpha[2] = -beta0 * H0[2*(irow+1)] ;
alpha[3] = -beta0 * H0[2*(irow+1)+1] ;
ZVaxpy21(ncolA, rowA0, rowA1, alpha, W0) ;
nops += 16*ncolA + 8 ;
} else if( irow == nrowA - 1 ) {
rowA0 = A2_row(mtxA, irow) ;
alpha[0] = -beta0 * H0[2*irow] ;
alpha[1] = -beta0 * H0[2*irow+1] ;
ZVaxpy11(ncolA, rowA0, alpha, W0) ;
nops += 8*ncolA + 4 ;
}
}
}
return(nops) ; }
/*
-----------------------
compute W0 = v^H * A
created -- 98may30, cca
-----------------------
*/
static double
computeW1 (
A2 *mtxA,
double H0[],
double W0[],
int msglvl,
FILE *msgFile
) {
double nops ;
int inc1, inc2, ncolA, nrowA ;
if ( msglvl > 5 ) {
fprintf(msgFile, "\n %% inside computeW1, nrow %d, ncol %d",
mtxA->n1, mtxA->n2) ;
}
nrowA = mtxA->n1 ;
ncolA = mtxA->n2 ;
inc1 = mtxA->inc1 ;
inc2 = mtxA->inc2 ;
if ( inc1 != 1 && inc2 != 1 ) {
fprintf(stderr, "\n error in computeW1"
"\n inc1 = %d, inc2 = %d\n", inc1, inc2) ;
exit(-1) ;
}
nops = 0.0 ;
if ( A2_IS_REAL(mtxA) ) {
int irow, jcol ;
if ( inc1 == 1 ) {
double sums[3] ;
double *colA0, *colA1, *colA2 ;
/*
----------------------------
A is column major,
compute W(j) = H0^T * A(*,j)
----------------------------
*/
for ( jcol = 0 ; jcol < ncolA - 2 ; jcol += 3 ) {
colA0 = A2_column(mtxA, jcol) ;
colA1 = A2_column(mtxA, jcol+1) ;
colA2 = A2_column(mtxA, jcol+2) ;
DVdot13(nrowA, H0, colA0, colA1, colA2, sums) ;
W0[jcol] = sums[0] ;
W0[jcol+1] = sums[1] ;
W0[jcol+2] = sums[2] ;
nops += 6*nrowA ;
}
if ( jcol == ncolA - 2 ) {
colA0 = A2_column(mtxA, jcol) ;
colA1 = A2_column(mtxA, jcol+1) ;
DVdot12(nrowA, H0, colA0, colA1, sums) ;
W0[jcol] = sums[0] ;
W0[jcol+1] = sums[1] ;
nops += 4*nrowA ;
} else if ( jcol == ncolA - 1 ) {
colA0 = A2_column(mtxA, jcol) ;
DVdot11(nrowA, H0, colA0, sums) ;
W0[jcol] = sums[0] ;
nops += 2*nrowA ;
}
} else {
double alpha[3] ;
double *rowA0, *rowA1, *rowA2 ;
/*
-------------------------------
A is row major
compute W := W + H0(j) * A(j,*)
-------------------------------
*/
DVzero(ncolA, W0) ;
for ( irow = 0 ; irow < nrowA - 2 ; irow += 3 ) {
rowA0 = A2_row(mtxA, irow) ;
rowA1 = A2_row(mtxA, irow+1) ;
rowA2 = A2_row(mtxA, irow+2) ;
alpha[0] = H0[irow] ;
alpha[1] = H0[irow+1] ;
alpha[2] = H0[irow+2] ;
DVaxpy13(ncolA, W0, alpha, rowA0, rowA1, rowA2) ;
nops += 6*ncolA ;
}
if ( irow == nrowA - 2 ) {
rowA0 = A2_row(mtxA, irow) ;
rowA1 = A2_row(mtxA, irow+1) ;
alpha[0] = H0[irow] ;
alpha[1] = H0[irow+1] ;
DVaxpy12(ncolA, W0, alpha, rowA0, rowA1) ;
nops += 4*ncolA ;
} else if ( irow == nrowA - 1 ) {
rowA0 = A2_row(mtxA, irow) ;
alpha[0] = H0[irow] ;
DVaxpy11(ncolA, W0, alpha, rowA0) ;
nops += 2*ncolA ;
}
}
} else if ( A2_IS_COMPLEX(mtxA) ) {
int irow, jcol ;
if ( inc1 == 1 ) {
double sums[6] ;
double *colA0, *colA1, *colA2 ;
/*
----------------------------
A is column major
compute W(j) = H0^H * A(*,j)
----------------------------
*/
for ( jcol = 0 ; jcol < ncolA - 2 ; jcol += 3 ) {
colA0 = A2_column(mtxA, jcol) ;
colA1 = A2_column(mtxA, jcol+1) ;
colA2 = A2_column(mtxA, jcol+2) ;
ZVdotC13(nrowA, H0, colA0, colA1, colA2, sums) ;
W0[2*jcol] = sums[0] ; W0[2*jcol+1] = sums[1] ;
W0[2*(jcol+1)] = sums[2] ; W0[2*(jcol+1)+1] = sums[3] ;
W0[2*(jcol+2)] = sums[4] ; W0[2*(jcol+2)+1] = sums[5] ;
nops += 24*nrowA ;
}
if ( jcol == ncolA - 2 ) {
colA0 = A2_column(mtxA, jcol) ;
colA1 = A2_column(mtxA, jcol+1) ;
ZVdotC12(nrowA, H0, colA0, colA1, sums) ;
W0[2*jcol] = sums[0] ; W0[2*jcol+1] = sums[1] ;
W0[2*(jcol+1)] = sums[2] ; W0[2*(jcol+1)+1] = sums[3] ;
nops += 16*nrowA ;
} else if ( jcol == ncolA - 1 ) {
colA0 = A2_column(mtxA, jcol) ;
ZVdotC11(nrowA, H0, colA0, sums) ;
W0[2*jcol] = sums[0] ; W0[2*jcol+1] = sums[1] ;
nops += 8*nrowA ;
}
} else {
double alpha[6] ;
double *rowA0, *rowA1, *rowA2 ;
/*
---------------------------------
A is row major
compute W := W + H0(j)^H * A(j,*)
---------------------------------
*/
DVzero(2*ncolA, W0) ;
for ( irow = 0 ; irow < nrowA - 2 ; irow += 3 ) {
rowA0 = A2_row(mtxA, irow) ;
rowA1 = A2_row(mtxA, irow+1) ;
rowA2 = A2_row(mtxA, irow+2) ;
alpha[0] = H0[2*irow] ; alpha[1] = -H0[2*irow+1] ;
alpha[2] = H0[2*(irow+1)] ; alpha[3] = -H0[2*(irow+1)+1] ;
alpha[4] = H0[2*(irow+2)] ; alpha[5] = -H0[2*(irow+2)+1] ;
ZVaxpy13(ncolA, W0, alpha, rowA0, rowA1, rowA2) ;
nops += 24*ncolA ;
}
if ( irow == nrowA - 2 ) {
rowA0 = A2_row(mtxA, irow) ;
rowA1 = A2_row(mtxA, irow+1) ;
alpha[0] = H0[2*irow] ; alpha[1] = -H0[2*irow+1] ;
alpha[2] = H0[2*(irow+1)] ; alpha[3] = -H0[2*(irow+1)+1] ;
ZVaxpy12(ncolA, W0, alpha, rowA0, rowA1) ;
nops += 16*ncolA ;
} else if ( irow == nrowA - 1 ) {
rowA0 = A2_row(mtxA, irow) ;
alpha[0] = H0[2*irow] ; alpha[1] = -H0[2*irow+1] ;
ZVaxpy11(ncolA, W0, alpha, rowA0) ;
nops += 8*ncolA ;
}
}
}
return(nops) ; }
/*
--------------------------------------------------------------
purpose -- compute A = QR, where Q is a product of householder
vectors, (I - beta_j v_j v_j^T). on return, v_j is
found in the lower triangle of A, v_j(j) = 1.0.
return value -- # of floating point operations
created -- 98may25, cca
--------------------------------------------------------------
*/
double
A2_QRreduce (
A2 *mtxA,
DV *workDV,
int msglvl,
FILE *msgFile
) {
A2 tempA ;
double nops ;
double beta0 ;
double *colA, *H0, *W0 ;
int inc1, inc2, jcol, lastrow, length, ncolA, nrowA, nstep ;
/*
---------------
check the input
---------------
*/
if ( mtxA == NULL || workDV == NULL
|| (msglvl > 0 && msgFile == NULL) ) {
fprintf(stderr, "\n fatal error in A2_QRreduce()"
"\n bad input\n") ;
exit(-1) ;
}
if ( ! (A2_IS_REAL(mtxA) || A2_IS_COMPLEX(mtxA)) ) {
fprintf(stderr, "\n fatal error in A2_QRreduce()"
"\n matrix must be real or complex\n") ;
exit(-1) ;
}
nrowA = A2_nrow(mtxA) ;
ncolA = A2_ncol(mtxA) ;
inc1 = A2_inc1(mtxA) ;
inc2 = A2_inc2(mtxA) ;
if ( A2_IS_REAL(mtxA) ) {
DV_setSize(workDV, nrowA + ncolA) ;
H0 = DV_entries(workDV) ;
W0 = H0 + nrowA ;
} else if ( A2_IS_COMPLEX(mtxA) ) {
DV_setSize(workDV, 2*(nrowA + ncolA)) ;
H0 = DV_entries(workDV) ;
W0 = H0 + 2*nrowA ;
}
/*
-------------------------------------------------
determine the number of steps = min(ncolA, nrowA)
-------------------------------------------------
*/
nstep = (ncolA <= nrowA) ? ncolA : nrowA ;
/*
-------------------
loop over the steps
-------------------
*/
nops = 0.0 ;
for ( jcol = 0 ; jcol < nstep ; jcol++ ) {
if ( msglvl > 3 ) {
fprintf(msgFile, "\n %% jcol = %d", jcol) ;
}
/*
----------------------------------
copy the column of A into a vector
and find the last nonzero element
----------------------------------
*/
A2_subA2(&tempA, mtxA, jcol, nrowA-1, jcol, ncolA-1) ;
length = 1 + copyIntoVec1(&tempA, H0, msglvl, msgFile) ;
lastrow = jcol + length - 1 ;
if ( msglvl > 5 ) {
fprintf(msgFile,
"\n %% return from copyIntoVec1, length = %d, lastrow = %d",
length, lastrow) ;
}
/*
------------------------------
compute the Householder vector
and place into the column of A
------------------------------
*/
colA = A2_column(mtxA, jcol) ;
if ( A2_IS_REAL(mtxA) ) {
nops += getHouseholderVector1(SPOOLES_REAL, length, H0,
&beta0, msglvl, msgFile) ;
A2_subA2(&tempA, mtxA, jcol, lastrow, jcol, jcol) ;
A2_setColumn(&tempA, H0, 0) ;
H0[0] = 1.0 ;
} else if ( A2_IS_COMPLEX(mtxA) ) {
nops += getHouseholderVector1(SPOOLES_COMPLEX, length, H0,
&beta0, msglvl, msgFile) ;
A2_subA2(&tempA, mtxA, jcol, lastrow, jcol, jcol) ;
A2_setColumn(&tempA, H0, 0) ;
H0[0] = 1.0 ; H0[1] = 0.0 ;
}
if ( msglvl > 5 && jcol == 0 ) {
fprintf(msgFile, "\n %% beta0 = %12.4e;", beta0) ;
}
if ( beta0 != 0.0 && jcol + 1 < ncolA ) {
A2_subA2(&tempA, mtxA, jcol, lastrow, jcol+1, ncolA-1) ;
/*
------------------------------------------------
compute w = v^T * A(jcol:lastrow,jcol+1:nrowA-1)
------------------------------------------------
*/
if ( msglvl > 3 ) {
fprintf(msgFile, "\n %% compute w") ;
}
nops += computeW1(&tempA, H0, W0, msglvl, msgFile) ;
/*
-------------------------------------------------
update A(jcol:lastrow,jcol+1:nrowA-1) -= beta*v*w
-------------------------------------------------
*/
if ( msglvl > 3 ) {
fprintf(msgFile, "\n %% update A") ;
}
nops += updateA1(&tempA, H0, beta0, W0, msglvl, msgFile) ;
}
}
return(nops) ; }
