PetscErrorCode DSNormalize_NHEP(DS ds,DSMatType mat,PetscInt col)
{
PetscErrorCode ierr;
PetscInt i,i0,i1;
PetscBLASInt ld,n,one = 1;
PetscScalar *A = ds->mat[DS_MAT_A],norm,*x;
#if !defined(PETSC_USE_COMPLEX)
PetscScalar norm0;
#endif
PetscFunctionBegin;
switch (mat) {
case DS_MAT_X:
case DS_MAT_Y:
case DS_MAT_Q:
/* Supported matrices */
break;
case DS_MAT_U:
case DS_MAT_VT:
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
break;
default:
SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
}
ierr = PetscBLASIntCast(ds->n,&n);CHKERRQ(ierr);
ierr = PetscBLASIntCast(ds->ld,&ld);CHKERRQ(ierr);
ierr = DSGetArray(ds,mat,&x);CHKERRQ(ierr);
if (col < 0) {
i0 = 0; i1 = ds->n;
} else if (col>0 && A[ds->ld*(col-1)+col] != 0.0) {
i0 = col-1; i1 = col+1;
} else {
i0 = col; i1 = col+1;
}
for (i=i0;i<i1;i++) {
#if !defined(PETSC_USE_COMPLEX)
if (i<n-1 && A[ds->ld*i+i+1] != 0.0) {
norm = BLASnrm2_(&n,&x[ld*i],&one);
norm0 = BLASnrm2_(&n,&x[ld*(i+1)],&one);
norm = 1.0/SlepcAbsEigenvalue(norm,norm0);
PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*i],&one));
PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*(i+1)],&one));
i++;
} else
#endif
{
norm = BLASnrm2_(&n,&x[ld*i],&one);
norm = 1.0/norm;
PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*i],&one));
}
}
PetscFunctionReturn(0);
}
static PetscErrorCode MatScaleUserImpl_SeqAIJ(Mat inA,PetscScalar alpha)
{
Mat_SeqAIJ *a = (Mat_SeqAIJ*)inA->data;
PetscScalar oalpha = alpha;
PetscBLASInt one = 1,bnz;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = PetscBLASIntCast(a->nz,&bnz);CHKERRQ(ierr);
BLASscal_(&bnz,&oalpha,a->a,&one);
PetscFunctionReturn(0);
}
PetscErrorCode MatScale_MPIDense(Mat inA,PetscScalar alpha)
{
Mat_MPIDense *A = (Mat_MPIDense*)inA->data;
Mat_SeqDense *a = (Mat_SeqDense*)A->A->data;
PetscScalar oalpha = alpha;
PetscErrorCode ierr;
PetscBLASInt one = 1,nz = PetscBLASIntCast(inA->rmap->n*inA->cmap->N);
PetscFunctionBegin;
BLASscal_(&nz,&oalpha,a->v,&one);
ierr = PetscLogFlops(nz);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode DSFunction_EXP_NHEP_PADE(DS ds)
{
#if defined(PETSC_MISSING_LAPACK_GESV) || defined(SLEPC_MISSING_LAPACK_LANGE)
PetscFunctionBegin;
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GESV/LANGE - Lapack routines are unavailable");
#else
PetscErrorCode ierr;
PetscBLASInt n,ld,ld2,*ipiv,info,inc=1;
PetscInt j,k,odd;
const PetscInt p=MAX_PADE;
PetscReal c[MAX_PADE+1],s;
PetscScalar scale,mone=-1.0,one=1.0,two=2.0,zero=0.0;
PetscScalar *A,*A2,*Q,*P,*W,*aux;
PetscFunctionBegin;
ierr = PetscBLASIntCast(ds->n,&n);CHKERRQ(ierr);
ierr = PetscBLASIntCast(ds->ld,&ld);CHKERRQ(ierr);
ld2 = ld*ld;
ierr = DSAllocateWork_Private(ds,0,ld,ld);CHKERRQ(ierr);
ipiv = ds->iwork;
if (!ds->mat[DS_MAT_W]) { ierr = DSAllocateMat_Private(ds,DS_MAT_W);CHKERRQ(ierr); }
if (!ds->mat[DS_MAT_Z]) { ierr = DSAllocateMat_Private(ds,DS_MAT_Z);CHKERRQ(ierr); }
A = ds->mat[DS_MAT_A];
A2 = ds->mat[DS_MAT_Z];
Q = ds->mat[DS_MAT_Q];
P = ds->mat[DS_MAT_F];
W = ds->mat[DS_MAT_W];
/* Pade' coefficients */
c[0] = 1.0;
for (k=1;k<=p;k++) {
c[k] = c[k-1]*(p+1-k)/(k*(2*p+1-k));
}
/* Scaling */
s = LAPACKlange_("I",&n,&n,A,&ld,ds->rwork);
if (s>0.5) {
s = PetscMax(0,(int)(PetscLogReal(s)/PetscLogReal(2.0)) + 2);
scale = PetscPowReal(2.0,(-1)*s);
PetscStackCallBLAS("BLASscal",BLASscal_(&ld2,&scale,A,&inc));
}
/* Horner evaluation */
PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,A,&ld,A,&ld,&zero,A2,&ld));
ierr = PetscMemzero(Q,ld*ld*sizeof(PetscScalar));CHKERRQ(ierr);
ierr = PetscMemzero(P,ld*ld*sizeof(PetscScalar));CHKERRQ(ierr);
for (j=0;j<n;j++) {
Q[j+j*ld] = c[p];
P[j+j*ld] = c[p-1];
}
odd = 1;
for (k=p-1;k>0;k--) {
if (odd==1) {
PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,Q,&ld,A2,&ld,&zero,W,&ld));
aux = Q;
Q = W;
W = aux;
for (j=0;j<n;j++)
Q[j+j*ld] = Q[j+j*ld] + c[k-1];
} else {
PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,P,&ld,A2,&ld,&zero,W,&ld));
aux = P;
P = W;
W = aux;
for (j=0;j<n;j++)
P[j+j*ld] = P[j+j*ld] + c[k-1];
}
odd = 1-odd;
}
if (odd==1) {
PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,Q,&ld,A,&ld,&zero,W,&ld));
aux = Q;
Q = W;
W = aux;
PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&ld2,&mone,P,&inc,Q,&inc));
PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&n,&n,Q,&ld,ipiv,P,&ld,&info));
PetscStackCallBLAS("BLASscal",BLASscal_(&ld2,&two,P,&inc));
for (j=0;j<n;j++)
P[j+j*ld] = P[j+j*ld] + 1.0;
PetscStackCallBLAS("BLASscal",BLASscal_(&ld2,&mone,P,&inc));
} else {
PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,P,&ld,A,&ld,&zero,W,&ld));
aux = P;
P = W;
W = aux;
PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&ld2,&mone,P,&inc,Q,&inc));
PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&n,&n,Q,&ld,ipiv,P,&ld,&info));
PetscStackCallBLAS("BLASscal",BLASscal_(&ld2,&two,P,&inc));
for (j=0;j<n;j++)
P[j+j*ld] = P[j+j*ld] + 1.0;
}
for (k=1;k<=s;k++) {
PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&n,&n,&one,P,&ld,P,&ld,&zero,W,&ld));
ierr = PetscMemcpy(P,W,ld2*sizeof(PetscScalar));CHKERRQ(ierr);
}
if (P!=ds->mat[DS_MAT_F]) {
ierr = PetscMemcpy(ds->mat[DS_MAT_F],P,ld2*sizeof(PetscScalar));CHKERRQ(ierr);
}
PetscFunctionReturn(0);
#endif
}
PetscErrorCode DSVectors_NHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
{
#if defined(SLEPC_MISSING_LAPACK_TREVC)
PetscFunctionBegin;
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TREVC - Lapack routine is unavailable");
#else
PetscErrorCode ierr;
PetscInt i;
PetscBLASInt mm=1,mout,info,ld,n,inc = 1;
PetscScalar tmp,done=1.0,zero=0.0;
PetscReal norm;
PetscBool iscomplex = PETSC_FALSE;
PetscBLASInt *select;
PetscScalar *A = ds->mat[DS_MAT_A];
PetscScalar *Q = ds->mat[DS_MAT_Q];
PetscScalar *X = ds->mat[left?DS_MAT_Y:DS_MAT_X];
PetscScalar *Y;
PetscFunctionBegin;
ierr = PetscBLASIntCast(ds->n,&n);CHKERRQ(ierr);
ierr = PetscBLASIntCast(ds->ld,&ld);CHKERRQ(ierr);
ierr = DSAllocateWork_Private(ds,0,0,ld);CHKERRQ(ierr);
select = ds->iwork;
for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;
/* Compute k-th eigenvector Y of A */
Y = X+(*k)*ld;
select[*k] = (PetscBLASInt)PETSC_TRUE;
#if !defined(PETSC_USE_COMPLEX)
if ((*k)<n-1 && A[(*k)+1+(*k)*ld]!=0.0) iscomplex = PETSC_TRUE;
mm = iscomplex? 2: 1;
if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
ierr = DSAllocateWork_Private(ds,3*ld,0,0);CHKERRQ(ierr);
PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(left?"L":"R","S",select,&n,A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,&info));
#else
ierr = DSAllocateWork_Private(ds,2*ld,ld,0);CHKERRQ(ierr);
PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(left?"L":"R","S",select,&n,A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,ds->rwork,&info));
#endif
if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xTREVC %d",info);
if (mout != mm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Inconsistent arguments");
/* accumulate and normalize eigenvectors */
if (ds->state>=DS_STATE_CONDENSED) {
ierr = PetscMemcpy(ds->work,Y,mout*ld*sizeof(PetscScalar));CHKERRQ(ierr);
PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&done,Q,&ld,ds->work,&inc,&zero,Y,&inc));
#if !defined(PETSC_USE_COMPLEX)
if (iscomplex) PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&done,Q,&ld,ds->work+ld,&inc,&zero,Y+ld,&inc));
#endif
norm = BLASnrm2_(&n,Y,&inc);
#if !defined(PETSC_USE_COMPLEX)
if (iscomplex) {
tmp = BLASnrm2_(&n,Y+ld,&inc);
norm = SlepcAbsEigenvalue(norm,tmp);
}
#endif
tmp = 1.0 / norm;
PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Y,&inc));
#if !defined(PETSC_USE_COMPLEX)
if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Y+ld,&inc));
#endif
}
/* set output arguments */
if (iscomplex) (*k)++;
if (rnorm) {
if (iscomplex) *rnorm = SlepcAbsEigenvalue(Y[n-1],Y[n-1+ld]);
else *rnorm = PetscAbsScalar(Y[n-1]);
}
PetscFunctionReturn(0);
#endif
}
static PetscErrorCode estsv(PetscInt n, PetscReal *r, PetscInt ldr, PetscReal *svmin, PetscReal *z)
{
PetscBLASInt blas1=1, blasn=n, blasnmi, blasj, blasldr = ldr;
PetscInt i,j;
PetscReal e,temp,w,wm,ynorm,znorm,s,sm;
PetscFunctionBegin;
for (i=0;i<n;i++) {
z[i]=0.0;
}
e = PetscAbs(r[0]);
if (e == 0.0) {
*svmin = 0.0;
z[0] = 1.0;
} else {
/* Solve R'*y = e */
for (i=0;i<n;i++) {
/* Scale y. The scaling factor (0.01) reduces the number of scalings */
if (z[i] >= 0.0) e =-PetscAbs(e);
else e = PetscAbs(e);
if (PetscAbs(e - z[i]) > PetscAbs(r[i + ldr*i])) {
temp = PetscMin(0.01,PetscAbs(r[i + ldr*i]))/PetscAbs(e-z[i]);
PetscStackCallBLAS("BLASscal",BLASscal_(&blasn, &temp, z, &blas1));
e = temp*e;
}
/* Determine the two possible choices of y[i] */
if (r[i + ldr*i] == 0.0) {
w = wm = 1.0;
} else {
w = (e - z[i]) / r[i + ldr*i];
wm = - (e + z[i]) / r[i + ldr*i];
}
/* Chose y[i] based on the predicted value of y[j] for j>i */
s = PetscAbs(e - z[i]);
sm = PetscAbs(e + z[i]);
for (j=i+1;j<n;j++) {
sm += PetscAbs(z[j] + wm * r[i + ldr*j]);
}
if (i < n-1) {
blasnmi = n-i-1;
PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasnmi, &w, &r[i + ldr*(i+1)], &blasldr, &z[i+1], &blas1));
s += BLASasum_(&blasnmi, &z[i+1], &blas1);
}
if (s < sm) {
temp = wm - w;
w = wm;
if (i < n-1) {
PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasnmi, &temp, &r[i + ldr*(i+1)], &blasldr, &z[i+1], &blas1));
}
}
z[i] = w;
}
ynorm = BLASnrm2_(&blasn, z, &blas1);
/* Solve R*z = y */
for (j=n-1; j>=0; j--) {
/* Scale z */
if (PetscAbs(z[j]) > PetscAbs(r[j + ldr*j])) {
temp = PetscMin(0.01, PetscAbs(r[j + ldr*j] / z[j]));
PetscStackCallBLAS("BLASscal",BLASscal_(&blasn, &temp, z, &blas1));
ynorm *=temp;
}
if (r[j + ldr*j] == 0) {
z[j] = 1.0;
} else {
z[j] = z[j] / r[j + ldr*j];
}
temp = -z[j];
blasj=j;
PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasj,&temp,&r[0+ldr*j],&blas1,z,&blas1));
}
/* Compute svmin and normalize z */
znorm = 1.0 / BLASnrm2_(&blasn, z, &blas1);
*svmin = ynorm*znorm;
PetscStackCallBLAS("BLASscal",BLASscal_(&blasn, &znorm, z, &blas1));
}
PetscFunctionReturn(0);
}
/*
c ***********
c
c Subroutine dgqt
c
c Given an n by n symmetric matrix A, an n-vector b, and a
c positive number delta, this subroutine determines a vector
c x which approximately minimizes the quadratic function
c
c f(x) = (1/2)*x'*A*x + b'*x
c
c subject to the Euclidean norm constraint
c
c norm(x) <= delta.
c
c This subroutine computes an approximation x and a Lagrange
c multiplier par such that either par is zero and
c
c norm(x) <= (1+rtol)*delta,
c
c or par is positive and
c
c abs(norm(x) - delta) <= rtol*delta.
c
c If xsol is the solution to the problem, the approximation x
c satisfies
c
c f(x) <= ((1 - rtol)**2)*f(xsol)
c
c The subroutine statement is
c
c subroutine dgqt(n,a,lda,b,delta,rtol,atol,itmax,
c par,f,x,info,z,wa1,wa2)
c
c where
c
c n is an integer variable.
c On entry n is the order of A.
c On exit n is unchanged.
c
c a is a double precision array of dimension (lda,n).
c On entry the full upper triangle of a must contain the
c full upper triangle of the symmetric matrix A.
c On exit the array contains the matrix A.
c
c lda is an integer variable.
c On entry lda is the leading dimension of the array a.
c On exit lda is unchanged.
c
c b is an double precision array of dimension n.
c On entry b specifies the linear term in the quadratic.
c On exit b is unchanged.
c
c delta is a double precision variable.
c On entry delta is a bound on the Euclidean norm of x.
c On exit delta is unchanged.
c
c rtol is a double precision variable.
c On entry rtol is the relative accuracy desired in the
c solution. Convergence occurs if
c
c f(x) <= ((1 - rtol)**2)*f(xsol)
c
c On exit rtol is unchanged.
c
c atol is a double precision variable.
c On entry atol is the absolute accuracy desired in the
c solution. Convergence occurs when
c
c norm(x) <= (1 + rtol)*delta
c
c max(-f(x),-f(xsol)) <= atol
c
c On exit atol is unchanged.
c
c itmax is an integer variable.
c On entry itmax specifies the maximum number of iterations.
c On exit itmax is unchanged.
c
c par is a double precision variable.
c On entry par is an initial estimate of the Lagrange
c multiplier for the constraint norm(x) <= delta.
c On exit par contains the final estimate of the multiplier.
c
c f is a double precision variable.
c On entry f need not be specified.
c On exit f is set to f(x) at the output x.
c
c x is a double precision array of dimension n.
c On entry x need not be specified.
c On exit x is set to the final estimate of the solution.
c
c info is an integer variable.
c On entry info need not be specified.
c On exit info is set as follows:
c
c info = 1 The function value f(x) has the relative
c accuracy specified by rtol.
c
c info = 2 The function value f(x) has the absolute
c accuracy specified by atol.
c
c info = 3 Rounding errors prevent further progress.
c On exit x is the best available approximation.
c
c info = 4 Failure to converge after itmax iterations.
c On exit x is the best available approximation.
c
c z is a double precision work array of dimension n.
c
c wa1 is a double precision work array of dimension n.
c
c wa2 is a double precision work array of dimension n.
c
c Subprograms called
c
c MINPACK-2 ...... destsv
c
c LAPACK ......... dpotrf
c
c Level 1 BLAS ... daxpy, dcopy, ddot, dnrm2, dscal
c
c Level 2 BLAS ... dtrmv, dtrsv
c
c MINPACK-2 Project. October 1993.
c Argonne National Laboratory and University of Minnesota.
c Brett M. Averick, Richard Carter, and Jorge J. More'
c
c ***********
*/
PetscErrorCode gqt(PetscInt n, PetscReal *a, PetscInt lda, PetscReal *b,
PetscReal delta, PetscReal rtol, PetscReal atol,
PetscInt itmax, PetscReal *retpar, PetscReal *retf,
PetscReal *x, PetscInt *retinfo, PetscInt *retits,
PetscReal *z, PetscReal *wa1, PetscReal *wa2)
{
PetscErrorCode ierr;
PetscReal f=0.0,p001=0.001,p5=0.5,minusone=-1,delta2=delta*delta;
PetscInt iter, j, rednc,info;
PetscBLASInt indef;
PetscBLASInt blas1=1, blasn=n, iblas, blaslda = lda,blasldap1=lda+1,blasinfo;
PetscReal alpha, anorm, bnorm, parc, parf, parl, pars, par=*retpar,paru, prod, rxnorm, rznorm=0.0, temp, xnorm;
PetscFunctionBegin;
parf = 0.0;
xnorm = 0.0;
rxnorm = 0.0;
rednc = 0;
for (j=0; j<n; j++) {
x[j] = 0.0;
z[j] = 0.0;
}
/* Copy the diagonal and save A in its lower triangle */
PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,a,&blasldap1, wa1, &blas1));
for (j=0;j<n-1;j++) {
iblas = n - j - 1;
PetscStackCallBLAS("BLAScopy",BLAScopy_(&iblas,&a[j + lda*(j+1)], &blaslda, &a[j+1 + lda*j], &blas1));
}
/* Calculate the l1-norm of A, the Gershgorin row sums, and the
l2-norm of b */
anorm = 0.0;
for (j=0;j<n;j++) {
wa2[j] = BLASasum_(&blasn, &a[0 + lda*j], &blas1);
CHKMEMQ;
anorm = PetscMax(anorm,wa2[j]);
}
for (j=0;j<n;j++) {
wa2[j] = wa2[j] - PetscAbs(wa1[j]);
}
bnorm = BLASnrm2_(&blasn,b,&blas1);
CHKMEMQ;
/* Calculate a lower bound, pars, for the domain of the problem.
Also calculate an upper bound, paru, and a lower bound, parl,
for the Lagrange multiplier. */
pars = parl = paru = -anorm;
for (j=0;j<n;j++) {
pars = PetscMax(pars, -wa1[j]);
parl = PetscMax(parl, wa1[j] + wa2[j]);
paru = PetscMax(paru, -wa1[j] + wa2[j]);
}
parl = PetscMax(bnorm/delta - parl,pars);
parl = PetscMax(0.0,parl);
paru = PetscMax(0.0, bnorm/delta + paru);
/* If the input par lies outside of the interval (parl, paru),
set par to the closer endpoint. */
par = PetscMax(par,parl);
par = PetscMin(par,paru);
/* Special case: parl == paru */
paru = PetscMax(paru, (1.0 + rtol)*parl);
/* Beginning of an iteration */
info = 0;
for (iter=1;iter<=itmax;iter++) {
/* Safeguard par */
if (par <= pars && paru > 0) {
par = PetscMax(p001, PetscSqrtScalar(parl/paru)) * paru;
}
/* Copy the lower triangle of A into its upper triangle and
compute A + par*I */
for (j=0;j<n-1;j++) {
iblas = n - j - 1;
PetscStackCallBLAS("BLAScopy",BLAScopy_(&iblas,&a[j+1 + j*lda], &blas1,&a[j + (j+1)*lda], &blaslda));
}
for (j=0;j<n;j++) {
a[j + j*lda] = wa1[j] + par;
}
/* Attempt the Cholesky factorization of A without referencing
the lower triangular part. */
PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("U",&blasn,a,&blaslda,&indef));
/* Case 1: A + par*I is pos. def. */
if (indef == 0) {
/* Compute an approximate solution x and save the
last value of par with A + par*I pos. def. */
parf = par;
PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn, b, &blas1, wa2, &blas1));
PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&blasn,&blas1,a,&blaslda,wa2,&blasn,&blasinfo));
rxnorm = BLASnrm2_(&blasn, wa2, &blas1);
PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","N","N",&blasn,&blas1,a,&blaslda,wa2,&blasn,&blasinfo));
PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn, wa2, &blas1, x, &blas1));
PetscStackCallBLAS("BLASscal",BLASscal_(&blasn, &minusone, x, &blas1));
xnorm = BLASnrm2_(&blasn, x, &blas1);
CHKMEMQ;
/* Test for convergence */
if (PetscAbs(xnorm - delta) <= rtol*delta ||
(par == 0 && xnorm <= (1.0+rtol)*delta)) {
info = 1;
}
/* Compute a direction of negative curvature and use this
information to improve pars. */
iblas=blasn*blasn;
ierr = estsv(n,a,lda,&rznorm,z);CHKERRQ(ierr);
CHKMEMQ;
pars = PetscMax(pars, par-rznorm*rznorm);
/* Compute a negative curvature solution of the form
x + alpha*z, where norm(x+alpha*z)==delta */
rednc = 0;
if (xnorm < delta) {
/* Compute alpha */
prod = BLASdot_(&blasn, z, &blas1, x, &blas1) / delta;
temp = (delta - xnorm)*((delta + xnorm)/delta);
alpha = temp/(PetscAbs(prod) + PetscSqrtScalar(prod*prod + temp/delta));
if (prod >= 0) alpha = PetscAbs(alpha);
else alpha =-PetscAbs(alpha);
/* Test to decide if the negative curvature step
produces a larger reduction than with z=0 */
rznorm = PetscAbs(alpha) * rznorm;
if ((rznorm*rznorm + par*xnorm*xnorm)/(delta2) <= par) {
rednc = 1;
}
/* Test for convergence */
if (p5 * rznorm*rznorm / delta2 <= rtol*(1.0-p5*rtol)*(par + rxnorm*rxnorm/delta2)) {
info = 1;
} else if (info == 0 && (p5*(par + rxnorm*rxnorm/delta2) <= atol/delta2)) {
info = 2;
}
}
/* Compute the Newton correction parc to par. */
if (xnorm == 0) {
parc = -par;
} else {
PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn, x, &blas1, wa2, &blas1));
temp = 1.0/xnorm;
PetscStackCallBLAS("BLASscal",BLASscal_(&blasn, &temp, wa2, &blas1));
PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&blasn, &blas1, a, &blaslda, wa2, &blasn, &blasinfo));
temp = BLASnrm2_(&blasn, wa2, &blas1);
parc = (xnorm - delta)/(delta*temp*temp);
}
/* update parl or paru */
if (xnorm > delta) {
parl = PetscMax(parl, par);
} else if (xnorm < delta) {
paru = PetscMin(paru, par);
}
} else {
/* Case 2: A + par*I is not pos. def. */
/* Use the rank information from the Cholesky
decomposition to update par. */
if (indef > 1) {
/* Restore column indef to A + par*I. */
iblas = indef - 1;
PetscStackCallBLAS("BLAScopy",BLAScopy_(&iblas,&a[indef-1 + 0*lda],&blaslda,&a[0 + (indef-1)*lda],&blas1));
a[indef-1 + (indef-1)*lda] = wa1[indef-1] + par;
/* compute parc. */
PetscStackCallBLAS("BLAScopy",BLAScopy_(&iblas,&a[0 + (indef-1)*lda], &blas1, wa2, &blas1));
PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&iblas,&blas1,a,&blaslda,wa2,&blasn,&blasinfo));
PetscStackCallBLAS("BLAScopy",BLAScopy_(&iblas,wa2,&blas1,&a[0 + (indef-1)*lda],&blas1));
temp = BLASnrm2_(&iblas,&a[0 + (indef-1)*lda],&blas1);
CHKMEMQ;
a[indef-1 + (indef-1)*lda] -= temp*temp;
PetscStackCallBLAS("LAPACKtrtr",LAPACKtrtrs_("U","N","N",&iblas,&blas1,a,&blaslda,wa2,&blasn,&blasinfo));
}
wa2[indef-1] = -1.0;
iblas = indef;
temp = BLASnrm2_(&iblas,wa2,&blas1);
parc = - a[indef-1 + (indef-1)*lda]/(temp*temp);
pars = PetscMax(pars,par+parc);
/* If necessary, increase paru slightly.
This is needed because in some exceptional situations
paru is the optimal value of par. */
paru = PetscMax(paru, (1.0+rtol)*pars);
}
/* Use pars to update parl */
parl = PetscMax(parl,pars);
/* Test for converged. */
if (info == 0) {
if (iter == itmax) info=4;
if (paru <= (1.0+p5*rtol)*pars) info=3;
if (paru == 0.0) info = 2;
}
/* If exiting, store the best approximation and restore
the upper triangle of A. */
if (info != 0) {
/* Compute the best current estimates for x and f. */
par = parf;
f = -p5 * (rxnorm*rxnorm + par*xnorm*xnorm);
if (rednc) {
f = -p5 * (rxnorm*rxnorm + par*delta*delta - rznorm*rznorm);
PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn, &alpha, z, &blas1, x, &blas1));
}
/* Restore the upper triangle of A */
for (j = 0; j<n; j++) {
iblas = n - j - 1;
PetscStackCallBLAS("BLAScopy",BLAScopy_(&iblas,&a[j+1 + j*lda],&blas1, &a[j + (j+1)*lda],&blaslda));
}
iblas = lda+1;
PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,wa1,&blas1,a,&iblas));
break;
}
par = PetscMax(parl,par+parc);
}
*retpar = par;
*retf = f;
*retinfo = info;
*retits = iter;
CHKMEMQ;
PetscFunctionReturn(0);
}
PetscErrorCode KSPAGMRESRoddec(KSP ksp, PetscInt nvec)
{
KSP_AGMRES *agmres = (KSP_AGMRES*) ksp->data;
MPI_Comm comm;
PetscScalar *Qloc = agmres->Qloc;
PetscScalar *sgn = agmres->sgn;
PetscScalar *tloc = agmres->tloc;
PetscErrorCode ierr;
PetscReal *wbufptr = agmres->wbufptr;
PetscMPIInt rank = agmres->rank;
PetscMPIInt First = agmres->First;
PetscMPIInt Last = agmres->Last;
PetscBLASInt nloc,pas,len;
PetscInt d, i, j, k;
PetscInt pos,tag;
PetscReal c, s, rho, Ajj, val, tt, old;
PetscScalar *col;
MPI_Status status;
PetscBLASInt N = MAXKSPSIZE + 1;
PetscFunctionBegin;
ierr = PetscObjectGetComm((PetscObject)ksp,&comm);CHKERRQ(ierr);
tag = 0x666;
ierr = PetscLogEventBegin(KSP_AGMRESRoddec,ksp,0,0,0);CHKERRQ(ierr);
ierr = PetscMemzero(agmres->Rloc, N*N*sizeof(PetscScalar));CHKERRQ(ierr);
/* check input arguments */
if (nvec < 1) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE, "The number of input vectors shoud be positive");
ierr = VecGetLocalSize(VEC_V(0), &nloc);CHKERRQ(ierr);
if (nvec > nloc) SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_WRONG, "In QR factorization, the number of local rows should be greater or equal to the number of columns");
pas = 1;
k = 0;
/* Copy the vectors of the basis */
for (j = 0; j < nvec; j++) {
ierr = VecGetArray(VEC_V(j), &col);CHKERRQ(ierr);
PetscStackCallBLAS("BLAScopy",BLAScopy_(&nloc, col, &pas, &Qloc[j*nloc], &pas));
ierr = VecRestoreArray(VEC_V(j), &col);CHKERRQ(ierr);
}
/* Each process performs a local QR on its own block */
for (j = 0; j < nvec; j++) {
len = nloc - j;
Ajj = Qloc[j*nloc+j];
rho = -PetscSign(Ajj) * BLASnrm2_(&len, &(Qloc[j*nloc+j]), &pas);
if (rho == 0.0) tloc[j] = 0.0;
else {
tloc[j] = (Ajj - rho) / rho;
len = len - 1;
val = 1.0 / (Ajj - rho);
PetscStackCallBLAS("BLASscal",BLASscal_(&len, &val, &(Qloc[j*nloc+j+1]), &pas));
Qloc[j*nloc+j] = 1.0;
len = len + 1;
for (k = j + 1; k < nvec; k++) {
PetscStackCallBLAS("BLASdot",tt = tloc[j] * BLASdot_(&len, &(Qloc[j*nloc+j]), &pas, &(Qloc[k*nloc+j]), &pas));
PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&len, &tt, &(Qloc[j*nloc+j]), &pas, &(Qloc[k*nloc+j]), &pas));
}
Qloc[j*nloc+j] = rho;
}
}
/*annihilate undesirable Rloc, diagonal by diagonal*/
for (d = 0; d < nvec; d++) {
len = nvec - d;
if (rank == First) {
PetscStackCallBLAS("BLAScopy",BLAScopy_(&len, &(Qloc[d*nloc+d]), &nloc, &(wbufptr[d]), &pas));
ierr = MPI_Send(&(wbufptr[d]), len, MPIU_SCALAR, rank + 1, tag, comm);CHKERRQ(ierr);
} else {
ierr = MPI_Recv(&(wbufptr[d]), len, MPIU_SCALAR, rank - 1, tag, comm, &status);CHKERRQ(ierr);
/*Elimination of Rloc(1,d)*/
c = wbufptr[d];
s = Qloc[d*nloc];
ierr = KSPAGMRESRoddecGivens(&c, &s, &rho, 1);
/*Apply Givens Rotation*/
for (k = d; k < nvec; k++) {
old = wbufptr[k];
wbufptr[k] = c * old - s * Qloc[k*nloc];
Qloc[k*nloc] = s * old + c * Qloc[k*nloc];
}
Qloc[d*nloc] = rho;
if (rank != Last) {
ierr = MPI_Send(& (wbufptr[d]), len, MPIU_SCALAR, rank + 1, tag, comm);CHKERRQ(ierr);
}
/* zero-out the d-th diagonal of Rloc ...*/
for (j = d + 1; j < nvec; j++) {
/* elimination of Rloc[i][j]*/
i = j - d;
c = Qloc[j*nloc+i-1];
s = Qloc[j*nloc+i];
ierr = KSPAGMRESRoddecGivens(&c, &s, &rho, 1);CHKERRQ(ierr);
for (k = j; k < nvec; k++) {
old = Qloc[k*nloc+i-1];
Qloc[k*nloc+i-1] = c * old - s * Qloc[k*nloc+i];
Qloc[k*nloc+i] = s * old + c * Qloc[k*nloc+i];
}
Qloc[j*nloc+i] = rho;
}
if (rank == Last) {
PetscStackCallBLAS("BLAScopy",BLAScopy_(&len, &(wbufptr[d]), &pas, RLOC(d,d), &N));
for (k = d + 1; k < nvec; k++) *RLOC(k,d) = 0.0;
}
}
}
if (rank == Last) {
for (d = 0; d < nvec; d++) {
pos = nvec - d;
sgn[d] = PetscSign(*RLOC(d,d));
PetscStackCallBLAS("BLASscal",BLASscal_(&pos, &(sgn[d]), RLOC(d,d), &N));
}
}
/*BroadCast Rloc to all other processes
* NWD : should not be needed
*/
ierr = MPI_Bcast(agmres->Rloc,N*N,MPIU_SCALAR,Last,comm);CHKERRQ(ierr);
ierr = PetscLogEventEnd(KSP_AGMRESRoddec,ksp,0,0,0);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
