const QString CPrinter::entryLink(const KeyTreeItem& item, CSwordModuleInfo* module) {
Q_ASSERT(module);
if (module->type() == CSwordModuleInfo::Bible) {
CSwordVerseKey vk(module);
vk = item.key();
switch (item.settings().keyRenderingFace) {
case KeyTreeItem::Settings::CompleteShort:
return QString::fromUtf8(vk.getShortText());
case KeyTreeItem::Settings::CompleteLong:
return vk.key();
case KeyTreeItem::Settings::NoKey:
return QString::null;
case KeyTreeItem::Settings::SimpleKey: //fall through
default:
return QString::number(vk.Verse());
}
}
return item.key();
}
QString CrossRefRendering::entryLink(const KeyTreeItem &item,
const CSwordModuleInfo *module)
{
QString linkText;
const bool isBible = module && (module->type() == CSwordModuleInfo::Bible);
CSwordVerseKey vk(module); //only valid for bible modules, i.e. isBible == true
if (isBible) {
vk.setKey(item.key());
}
switch (item.settings().keyRenderingFace) {
case KeyTreeItem::Settings::NoKey: {
linkText = QString::null;
break; //no key is valid for all modules
}
case KeyTreeItem::Settings::CompleteShort: {
if (isBible) {
linkText = QString::fromUtf8(vk.getShortText());
break;
}
//fall through for non-Bible modules
}
case KeyTreeItem::Settings::CompleteLong: {
if (isBible) {
linkText = vk.key();
break;
}
//fall through for non-Bible modules
}
case KeyTreeItem::Settings::SimpleKey: {
if (isBible) {
linkText = QString::number(vk.getVerse());
break;
}
//fall through for non-Bible modules
}
default: { //default behaviour to return the passed key
linkText = item.key();
break;
}
}
if (!linkText.isEmpty()) { //if we have a valid link text
// qWarning("rendering");
return QString("<a href=\"%1\">%2</a>")
.arg(
ReferenceManager::encodeHyperlink(
module->name(),
item.key(),
ReferenceManager::typeFromModule(module->type())
)
)
.arg(linkText);
}
return QString::null;
}
/** Copies the current chapter into the clipboard. */
void CBibleReadWindow::copyDisplayedText() {
CSwordVerseKey dummy(*verseKey());
dummy.setVerse(1);
CSwordVerseKey vk(*verseKey());
vk.setLowerBound(dummy);
const CSwordBibleModuleInfo* bible = dynamic_cast<const CSwordBibleModuleInfo*>(modules().first());
dummy.setVerse(bible->verseCount(dummy.book(), dummy.getChapter()));
vk.setUpperBound(dummy);
CExportManager mgr(false, tr("Copying"), filterOptions(), displayOptions());
mgr.copyKey(&vk, CExportManager::Text, true);
}
BtBookmarkItem::BtBookmarkItem(CSwordModuleInfo* module, QString key, QString& description)
:m_description(description),
m_moduleName(module ? module->name() : QString::null)
{
if (((module && (module->type() == CSwordModuleInfo::Bible)) || (module->type() == CSwordModuleInfo::Commentary)) ) {
CSwordVerseKey vk(0);
vk.key(key);
vk.setLocale("en");
m_key = vk.key(); //the m_key member is always the english key!
}
else {
m_key = key;
};
update();
}
/** Saves the chapter as valid HTML page. */
void CBibleReadWindow::saveChapterPlain() {
//saves the complete chapter to disk
CSwordVerseKey vk(*verseKey());
CSwordVerseKey dummy(*verseKey());
dummy.setVerse(1);
vk.setLowerBound(dummy);
const CSwordBibleModuleInfo* bible = dynamic_cast<const CSwordBibleModuleInfo*>(modules().first());
dummy.setVerse(bible->verseCount(dummy.book(), dummy.getChapter()));
vk.setUpperBound(dummy);
CExportManager mgr(true, tr("Saving"), filterOptions(), displayOptions());
mgr.saveKey(&vk, CExportManager::Text, true);
}
QString BtBookmarkItem::key()
{
const QString englishKeyName = englishKey();
if (!module()) {
return englishKeyName;
}
QString returnKeyName = englishKeyName;
if ((module()->type() == CSwordModuleInfo::Bible) || (module()->type() == CSwordModuleInfo::Commentary)) {
CSwordVerseKey vk(0);
vk.key(englishKeyName);
vk.setLocale(CPointers::backend()->booknameLanguage().toLatin1() );
returnKeyName = vk.key(); //the returned key is always in the currently set bookname language
}
return returnKeyName;
}
QString CDisplayRendering::entryLink(const KeyTreeItem &item,
const CSwordModuleInfo * module)
{
QString linkText;
const bool isBible = module && (module->type() == CSwordModuleInfo::Bible);
CSwordVerseKey vk(module); //only valid for bible modules, i.e. isBible == true
vk.setIntros(true);
if (isBible) {
vk.setKey(item.key());
}
if (isBible && (vk.getVerse() == 0)) {
return QString::null; //Warning: return already here
}
switch (item.settings().keyRenderingFace) {
case KeyTreeItem::Settings::NoKey: {
linkText = QString::null;
break; //no key is valid for all modules
}
case KeyTreeItem::Settings::CompleteShort: {
if (isBible) {
linkText = QString::fromUtf8(vk.getShortText());
break;
}
//fall through for non-Bible modules
}
case KeyTreeItem::Settings::CompleteLong: {
if (isBible) {
linkText = vk.key();
break;
}
//fall through for non-Bible modules
}
case KeyTreeItem::Settings::SimpleKey: {
if (isBible) {
linkText = QString::number(vk.getVerse());
break;
}
//fall through for non-Bible modules
}
default: { //default behaviour to return the passed key
linkText = item.key();
break;
}
}
if (linkText.isEmpty()) {
return QString("<a name=\"").append(keyToHTMLAnchor(item.key())).append("\"></a>");
}
else {
return QString("<a name=\"").append(keyToHTMLAnchor(item.key())).append("\" ")
.append("href=\"")
.append(ReferenceManager::encodeHyperlink(
module->name(), item.key(), ReferenceManager::typeFromModule(module->type()))
)
.append("\">").append(linkText).append("</a>\n");
}
return QString::null;
}
void SkinningAppVk::initRendering(void) {
setGLDrawCallbacks(this);
VkResult result = VK_ERROR_INITIALIZATION_FAILED;
NvAssetLoaderAddSearchPath("vk10-kepler/SkinningAppVk");
mMesh.initRendering(vk());
SkinnedMesh::UBOBlock& ubo = *mMesh.mUBO;
ubo.mRenderMode[2] = 0;
ubo.mLightDir0 = nv::vec4f(0.267f, 0.535f, 0.802f, 0.0f);
ubo.mLightDir1 = nv::vec4f(-0.408f, 0.816f, -0.408f, 0.0f);
mMesh.mUBO.Update();
VkPipelineLayoutCreateInfo pipelineLayoutCreateInfo = { VK_STRUCTURE_TYPE_PIPELINE_LAYOUT_CREATE_INFO };
pipelineLayoutCreateInfo.setLayoutCount = 1;
pipelineLayoutCreateInfo.pSetLayouts = &mMesh.mDescriptorSetLayout;
result = vkCreatePipelineLayout(device(), &pipelineLayoutCreateInfo, 0, &mPipelineLayout);
CHECK_VK_RESULT();
// Create static state info for the mPipeline.
// set dynamically
VkPipelineViewportStateCreateInfo vpStateInfo = { VK_STRUCTURE_TYPE_PIPELINE_VIEWPORT_STATE_CREATE_INFO };
vpStateInfo.pNext = 0;
vpStateInfo.viewportCount = 1;
vpStateInfo.scissorCount = 1;
VkPipelineRasterizationStateCreateInfo rsStateInfo = { VK_STRUCTURE_TYPE_PIPELINE_RASTERIZATION_STATE_CREATE_INFO };
rsStateInfo.depthClampEnable = VK_TRUE;
rsStateInfo.rasterizerDiscardEnable = VK_FALSE;
rsStateInfo.polygonMode = VK_POLYGON_MODE_FILL;
rsStateInfo.cullMode = VK_CULL_MODE_BACK_BIT;
rsStateInfo.frontFace = VK_FRONT_FACE_COUNTER_CLOCKWISE;
VkPipelineColorBlendAttachmentState attachments[1] = {};
attachments[0].blendEnable = VK_FALSE;
attachments[0].colorWriteMask = ~0;
VkPipelineColorBlendStateCreateInfo cbStateInfo = { VK_STRUCTURE_TYPE_PIPELINE_COLOR_BLEND_STATE_CREATE_INFO };
cbStateInfo.logicOpEnable = VK_FALSE;
cbStateInfo.attachmentCount = ARRAY_SIZE(attachments);
cbStateInfo.pAttachments = attachments;
VkPipelineDepthStencilStateCreateInfo dsStateInfo = { VK_STRUCTURE_TYPE_PIPELINE_DEPTH_STENCIL_STATE_CREATE_INFO };
dsStateInfo.depthTestEnable = VK_TRUE;
dsStateInfo.depthWriteEnable = VK_TRUE;
dsStateInfo.depthCompareOp = VK_COMPARE_OP_LESS_OR_EQUAL;
dsStateInfo.depthBoundsTestEnable = VK_FALSE;
dsStateInfo.stencilTestEnable = VK_FALSE;
dsStateInfo.minDepthBounds = 0.0f;
dsStateInfo.maxDepthBounds = 1.0f;
VkPipelineMultisampleStateCreateInfo msStateInfo = { VK_STRUCTURE_TYPE_PIPELINE_MULTISAMPLE_STATE_CREATE_INFO };
msStateInfo.rasterizationSamples = VK_SAMPLE_COUNT_1_BIT;
msStateInfo.alphaToCoverageEnable = VK_FALSE;
msStateInfo.sampleShadingEnable = VK_FALSE;
msStateInfo.minSampleShading = 1.0f;
uint32_t smplMask = 0x1;
msStateInfo.pSampleMask = &smplMask;
VkPipelineTessellationStateCreateInfo tessStateInfo = { VK_STRUCTURE_TYPE_PIPELINE_TESSELLATION_STATE_CREATE_INFO };
tessStateInfo.patchControlPoints = 0;
VkPipelineDynamicStateCreateInfo dynStateInfo;
VkDynamicState dynStates[] = { VK_DYNAMIC_STATE_VIEWPORT, VK_DYNAMIC_STATE_SCISSOR };
memset(&dynStateInfo, 0, sizeof(dynStateInfo));
dynStateInfo.sType = VK_STRUCTURE_TYPE_PIPELINE_DYNAMIC_STATE_CREATE_INFO;
dynStateInfo.dynamicStateCount = 2;
dynStateInfo.pDynamicStates = dynStates;
// Shaders
VkPipelineShaderStageCreateInfo shaderStages[2];
uint32_t shaderCount = 0;
#ifdef SOURCE_SHADERS
shaderCount = vk().createShadersFromSourceFile(
NvAssetLoadTextFile("src_shaders/skinning.glsl"), shaderStages, 2);
#else
{
int32_t length;
char* data = NvAssetLoaderRead("shaders/skinning.nvs", length);
shaderCount = vk().createShadersFromBinaryFile((uint32_t*)data,
length, shaderStages, 2);
}
#endif
// Create mPipeline state VI-IA-VS-VP-RS-FS-CB
VkGraphicsPipelineCreateInfo pipelineInfo = { VK_STRUCTURE_TYPE_GRAPHICS_PIPELINE_CREATE_INFO };
pipelineInfo.pVertexInputState = &mMesh.mVIStateInfo;
pipelineInfo.pInputAssemblyState = &mMesh.mIAStateInfo;
pipelineInfo.pViewportState = &vpStateInfo;
pipelineInfo.pRasterizationState = &rsStateInfo;
pipelineInfo.pColorBlendState = &cbStateInfo;
pipelineInfo.pDepthStencilState = &dsStateInfo;
pipelineInfo.pMultisampleState = &msStateInfo;
pipelineInfo.pTessellationState = &tessStateInfo;
pipelineInfo.pDynamicState = &dynStateInfo;
pipelineInfo.stageCount = shaderCount;
pipelineInfo.pStages = shaderStages;
pipelineInfo.renderPass = vk().mainRenderTarget()->clearRenderPass();
pipelineInfo.subpass = 0;
pipelineInfo.layout = mPipelineLayout;
result = vkCreateGraphicsPipelines(device(), VK_NULL_HANDLE, 1, &pipelineInfo, NULL, &mPipeline);
CHECK_VK_RESULT();
mMesh.UpdateDescriptorSet(vk());
}
void SkinningAppVk::draw(void)
{
VkResult result = VK_ERROR_INITIALIZATION_FAILED;
NvSimpleUBO<SkinnedMesh::UBOBlock>& uboObj = mMesh.mUBO;
SkinnedMesh::UBOBlock& ubo = *uboObj;
// Compute and update the ModelViewProjection matrix
nv::perspectiveLH(ubo.mMVP, 45.0f, (float)m_width / (float)m_height, 0.1f, 100.0f);
ubo.mMVP *= m_transformer->getModelViewMat();
// Compute and update the bone matrices
computeBones(mTime, ubo);
mTime += mTimeScalar * getFrameDeltaTime();
// Update other uniforms
ubo.mRenderMode[0] = (int32_t)mSingleBoneSkinning;
ubo.mRenderMode[1] = (int32_t)mRenderMode;
uboObj.Update();
VkCommandBuffer cmd = vk().getMainCommandBuffer();
VkRenderPassBeginInfo renderPassBeginInfo = { VK_STRUCTURE_TYPE_RENDER_PASS_BEGIN_INFO };
renderPassBeginInfo.renderPass = vk().mainRenderTarget()->clearRenderPass();
renderPassBeginInfo.framebuffer = vk().mainRenderTarget()->frameBuffer();
renderPassBeginInfo.renderArea.offset.x = 0;
renderPassBeginInfo.renderArea.offset.y = 0;
renderPassBeginInfo.renderArea.extent.width = m_width;
renderPassBeginInfo.renderArea.extent.height = m_height;
VkClearValue clearValues[2];
clearValues[0].color.float32[0] = 0.33f;
clearValues[0].color.float32[1] = 0.44f;
clearValues[0].color.float32[2] = 0.66f;
clearValues[0].color.float32[3] = 1.0f;
clearValues[1].depthStencil.depth = 1.0f;
clearValues[1].depthStencil.stencil = 0;
renderPassBeginInfo.pClearValues = clearValues;
renderPassBeginInfo.clearValueCount = 2;
vkCmdBeginRenderPass(cmd, &renderPassBeginInfo, VK_SUBPASS_CONTENTS_INLINE);
{
// Bind the mPipeline state
vkCmdBindPipeline(cmd, VK_PIPELINE_BIND_POINT_GRAPHICS, mPipeline);
VkViewport vp;
VkRect2D sc;
vp.x = 0;
vp.y = 0;
vp.height = (float)(m_height);
vp.width = (float)(m_width);
vp.minDepth = 0.0f;
vp.maxDepth = 1.0f;
sc.offset.x = 0;
sc.offset.y = 0;
sc.extent.width = vp.width;
sc.extent.height = vp.height;
vkCmdSetViewport(cmd, 0, 1, &vp);
vkCmdSetScissor(cmd, 0, 1, &sc);
mMesh.draw(mPipelineLayout, cmd);
}
vkCmdEndRenderPass(cmd);
vk().submitMainCommandBuffer();
}
void CalculateAngleDerivativesE2(vtkPolyData* mesh, const arma::sp_mat& edge_lengths, const arma::vec& radii) {
//calculate the power center for each triangle as follows
//for 2 circles centered at c1 and c2 solve for p:
//|p-c1|^2 - r1^2 = |p-c2|^2 - r2^2 -- this is power line
//add one more condition for the third circle to get one point
// Funny part: the paper says that the circle of radius sqrt(|c1-p|^2 - r1^2)
// is perpendicular to all three circles. But this works only when the 3 circles do not intersect
const int npts = mesh->GetNumberOfPoints();
const int ncells = mesh->GetNumberOfCells();
vtkSmartPointer<vtkIdList> cellIdList = vtkSmartPointer<vtkIdList>::New();
vtkSmartPointer<vtkIdList> pointIdList = vtkSmartPointer<vtkIdList>::New();
//for every face calculate gamma_ijk
arma::vec gamma_percell(ncells);
for (vtkIdType i = 0; i < ncells; i++) {
pointIdList->Reset();
mesh->GetCellPoints(cellIdList->GetId(i), pointIdList);
const int ind_i = pointIdList->GetId(0);
const int ind_j = pointIdList->GetId(1);
const int ind_k = pointIdList->GetId(2);
const double ri = radii[ind_i];
const double rj = radii[ind_j];
const double rk = radii[ind_k];
arma::vec ci(3), cj(3), ck(3);
mesh->GetPoint(ind_i, ci.memptr());
mesh->GetPoint(ind_j, cj.memptr());
mesh->GetPoint(ind_k, ck.memptr());
//create local 2D coordinates, and map vertices
arma::vec vji = cj - ci;
arma::vec v = ck - ci;
arma::vec n = arma::cross(vji, v); //normal
arma::vec vki = arma::cross(n, vji); //creates local y' axis
const double lenX = arma::norm(vji,2);
const double lenY = arma::norm(vki,2);
vji /= lenX; //normalize axes
vki /= lenY;
//2D coordinates
arma::vec vi(3,0); //(0,0)
arma::vec vj(3);
arma::vec vk(3);
vj(0) = lenX;
vj(1) = 0.0;
vk(0) = arma::dot(v, vji);
vk(1) = arma::dot(v, vki);
//form matrices for system of linear equations and solve
//A = [2*(c2-c1)'; 2*(c2-c3)'];
//B = [ c2'*c2 - c1'*c1 + r1^2 - r2^2; c2'*c2 - c3'*c3 + r3^2 - r2^2];
//P = A\B;
arma::mat A(2,2);
arma::vec B(2);
A.insert_rows( 0, 2.0*(cj-ci) );
A.insert_rows( 1, 2.0*(cj-ck) );
B(0) = arma::dot(cj, cj) - arma::dot(ci, ci) + ri*ri - rj*rj;
B(1) = arma::dot(cj, cj) - arma::dot(ck, ck) + rk*rk - rj*rj;
arma::vec P = arma::solve( A, B );
//calculate distance from P to all the edges: hi, hj, hk
//http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html
const double hi = arma::norm( arma::cross(cj-ck, ck-P), 2 ) / arma::norm(cj-ck, 2);
const double hj = arma::norm( arma::cross(ci-ck, ck-P), 2 ) / arma::norm(ci-ck, 2);
const double hk = arma::norm( arma::cross(cj-ci, ci-P), 2 ) / arma::norm(cj-ci, 2);
const double li = edge_lengths(ind_j, ind_k);
const double lj = edge_lengths(ind_i, ind_k);
const double lk = edge_lengths(ind_i, ind_j);
const double dTi_duj = hk/lk;
const double dTj_duk = hi/li;
const double dTk_dui = hj/lj;
const double dTi_dui = - dTi_duj - dTk_dui;
const double dTj_duj = - dTj_duk - dTi_duj;
const double dTk_duk = - dTj_duk - dTk_dui;
}
}
int
Stokhos::GMRESDivisionExpansionStrategy<ordinal_type,value_type,node_type>::
GMRES(const Teuchos::SerialDenseMatrix<int, double> & A, Teuchos::SerialDenseMatrix<int,double> & X, const Teuchos::SerialDenseMatrix<int,double> & B, int max_iter, double tolerance, int prec_iter, int order, int dim, int PrecNum, const Teuchos::SerialDenseMatrix<int, double> & M, int diag)
{
int n = A.numRows();
int k = 1;
double resid;
Teuchos::SerialDenseMatrix<int, double> P(n,n);
Teuchos::SerialDenseMatrix<int, double> Ax(n,1);
Ax.multiply(Teuchos::NO_TRANS,Teuchos::NO_TRANS,1.0, A, X, 0.0);
Teuchos::SerialDenseMatrix<int, double> r0(B);
r0-=Ax;
resid=r0.normFrobenius();
//define vector v=r/norm(r) where r=b-Ax
Teuchos::SerialDenseMatrix<int, double> v(n,1);
r0.scale(1/resid);
Teuchos::SerialDenseMatrix<int, double> h(1,1);
//Matrix of orthog basis vectors V
Teuchos::SerialDenseMatrix<int, double> V(n,1);
//Set v=r0/norm(r0) to be 1st col of V
for (int i=0; i<n; i++) {
V(i,0)=r0(i,0);
}
//right hand side
Teuchos::SerialDenseMatrix<int, double> bb(1,1);
bb(0,0)=resid;
Teuchos::SerialDenseMatrix<int, double> w(n,1);
Teuchos::SerialDenseMatrix<int, double> c;
Teuchos::SerialDenseMatrix<int, double> s;
while (resid > tolerance && k < max_iter) {
h.reshape(k+1,k);
//Arnoldi iteration(Gram-Schmidt )
V.reshape(n,k+1);
//set vk to be kth col of V
Teuchos::SerialDenseMatrix<int, double> vk(Teuchos::Copy, V, n,1,0,k-1);
//Preconditioning step: solve Mz=vk
Teuchos::SerialDenseMatrix<int, double> z(vk);
if (PrecNum == 1) {
Stokhos::DiagPreconditioner precond(M);
precond.ApplyInverse(vk,z,prec_iter);
}
else if (PrecNum == 2) {
Stokhos::JacobiPreconditioner precond(M);
precond.ApplyInverse(vk,z,2);
}
else if (PrecNum == 3) {
Stokhos::GSPreconditioner precond(M,1);
precond.ApplyInverse(vk,z,1);
}
else if (PrecNum == 4) {
Stokhos::SchurPreconditioner precond(M, order, dim, diag);
precond.ApplyInverse(vk,z,prec_iter);
}
w.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1, A, z, 0.0);
Teuchos::SerialDenseMatrix<int, double> vi(n,1);
Teuchos::SerialDenseMatrix<int, double> ip(1,1);
for (int i=0; i<k; i++) {
//set vi to be ith col of V
Teuchos::SerialDenseMatrix<int, double> vi(Teuchos::Copy, V, n,1,0,i);
//Calculate inner product
ip.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, vi, w, 0.0);
h(i,k-1)= ip(0,0);
//scale vi by h(i,k-1)
vi.scale(ip(0,0));
w-=vi;
}
h(k,k-1)=w.normFrobenius();
w.scale(1.0/h(k,k-1));
//add column vk+1=w to V
for (int i=0; i<n; i++) {
V(i,k)=w(i,0);
}
//Solve upper hessenberg least squares problem via Givens rotations
//Compute previous Givens rotations
for (int i=0; i<k-1; i++) {
double q=c(i,0)*h(i,k-1)+s(i,0)*h(i+1,k-1);
h(i+1,k-1)=-1*s(i,0)*h(i,k-1)+c(i,0)*h(i+1,k-1);
h(i,k-1)=q;
}
//Compute next Givens rotations
c.reshape(k,1);
s.reshape(k,1);
bb.reshape(k+1,1);
double l = sqrt(h(k-1,k-1)*h(k-1,k-1)+h(k,k-1)*h(k,k-1));
c(k-1,0)=h(k-1,k-1)/l;
s(k-1,0)=h(k,k-1)/l;
// Givens rotation on h and bb
h(k-1,k-1)=l;
h(k,k-1)=0;
bb(k,0)=-s(k-1,0)*bb(k-1,0);
bb(k-1,0)=c(k-1,0)*bb(k-1,0);
//Determine residual
resid = fabs(bb(k,0));
k++;
}
//Extract upper triangular square matrix
bb.reshape(h.numRows()-1 ,1);
//Solve linear system
int info;
Teuchos::LAPACK<int, double> lapack;
lapack.TRTRS('U', 'N', 'N', h.numRows()-1, 1, h.values(), h.stride(), bb.values(), bb.stride(),&info);
Teuchos::SerialDenseMatrix<int, double> ans(X);
V.reshape(n,k-1);
ans.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, V, bb, 0.0);
if (PrecNum == 1) {
Stokhos::DiagPreconditioner precond(M);
precond.ApplyInverse(ans,ans,prec_iter);
}
else if (PrecNum == 2) {
Stokhos::JacobiPreconditioner precond(M);
precond.ApplyInverse(ans,ans,2);
}
else if (PrecNum == 3) {
Stokhos::GSPreconditioner precond(M,1);
precond.ApplyInverse(ans,ans,1);
}
else if (PrecNum == 4) {
Stokhos::SchurPreconditioner precond(M, order, dim, diag);
precond.ApplyInverse(ans,ans,prec_iter);
}
X+=ans;
std::cout << "iteration count= " << k-1 << std::endl;
return 0;
}
//GMRES
int gmres(const Teuchos::SerialDenseMatrix<int, double> & A, Teuchos::SerialDenseMatrix<int,double> X,const Teuchos::SerialDenseMatrix<int,double> & B, int max_iter, double tolerance)
{
int n;
int k;
double resid;
k=1;
n=A.numRows();
std::cout << "A= " << A << std::endl;
std::cout << "B= " << B << std::endl;
//Teuchos::SerialDenseMatrix<int, double> Ax(n,1);
//Ax.multiply(Teuchos::NO_TRANS,Teuchos::NO_TRANS,1.0, A, X, 0.0);
Teuchos::SerialDenseMatrix<int, double> r0(B);
//r0-=Ax;
resid=r0.normFrobenius();
std::cout << "resid= " << resid << std::endl;
//define vector v=r/norm(r) where r=b-Ax
r0.scale(1/resid);
Teuchos::SerialDenseMatrix<int, double> h(1,1);
//Matrix of orthog basis vectors V
Teuchos::SerialDenseMatrix<int, double> V(n,1);
//Set v=r0/norm(r0) to be 1st col of V
for (int i=0; i<n; i++){
V(i,0)=r0(i,0);
}
//right hand side
Teuchos::SerialDenseMatrix<int, double> bb(1,1);
bb(0,0)=resid;
Teuchos::SerialDenseMatrix<int, double> w(n,1);
Teuchos::SerialDenseMatrix<int, double> c;
Teuchos::SerialDenseMatrix<int, double> s;
while (resid > tolerance && k < max_iter){
std::cout << "k = " << k << std::endl;
h.reshape(k+1,k);
//Arnoldi iteration(Gram-Schmidt )
V.reshape(n,k+1);
//set vk to be kth col of V
Teuchos::SerialDenseMatrix<int, double> vk(Teuchos::Copy, V, n,1,0,k-1);
w.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, A, vk, 0.0);
Teuchos::SerialDenseMatrix<int, double> vi(n,1);
Teuchos::SerialDenseMatrix<int, double> ip(1,1);
for (int i=0; i<k; i++){
//set vi to be ith col of V
Teuchos::SerialDenseMatrix<int, double> vi(Teuchos::Copy, V, n,1,0,i);
//Calculate inner product
ip.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, vi, w, 0.0);
h(i,k-1)= ip(0,0);
//scale vi by h(i,k-1)
vi.scale(ip(0,0));
w-=vi;
}
h(k,k-1)=w.normFrobenius();
w.scale(1.0/w.normFrobenius());
//add column vk+1=w to V
for (int i=0; i<n; i++){
V(i,k)=w(i,0);
}
//Solve upper hessenberg least squares problem via Givens rotations
//Compute previous Givens rotations
for (int i=0; i<k-1; i++){
// double hi=h(i,k-1);
// double hi1=h(i+1,k-1);
// h(i,k-1)=c(i,0)*h(i,k-1)+s(i,0)*h(i+1,k-1);
// h(i+1,k-1)=-1*s(i,0)*h(i,k-1)+c(i,0)*h(i+1,k-1);
// h(i,k-1)=c(i,0)*hi+s(i,0)*hi1;
// h(i+1,k-1)=-1*s(i,0)*hi+c(i,0)*hi1;
double q=c(i,0)*h(i,k-1)+s(i,0)*h(i+1,k-1);
h(i+1,k-1)=-1*s(i,0)*h(i,k-1)+c(i,0)*h(i+1,k-1);
h(i,k-1)=q;
}
//Compute next Givens rotations
c.reshape(k,1);
s.reshape(k,1);
bb.reshape(k+1,1);
double l = sqrt(h(k-1,k-1)*h(k-1,k-1)+h(k,k-1)*h(k,k-1));
c(k-1,0)=h(k-1,k-1)/l;
s(k-1,0)=h(k,k-1)/l;
std::cout << "c " << c(k-1,0)<<std::endl;
std::cout << "s " << s(k-1,0)<<std::endl;
// Givens rotation on h and bb
// h(k-1,k-1)=l;
// h(k,k-1)=0;
double hk=h(k,k-1);
double hk1=h(k-1,k-1);
h(k-1,k-1)=c(k-1,0)*hk1+s(k-1,0)*hk;
h(k,k-1)=-1*s(k-1,0)*hk1+c(k-1,0)*hk;
std::cout << "l = " << l <<std::endl;
std::cout << "h(k-1,k-1) = should be l " << h(k-1,k-1) <<std::endl;
std::cout << "h(k,k-1) = should be 0 " << h(k,k-1) <<std::endl;
bb(k,0)=-1*s(k-1,0)*bb(k-1,0);
bb(k-1,0)=c(k-1,0)*bb(k-1,0);
//Determine residual
resid =fabs(bb(k,0));
std::cout << "resid = " << resid <<std::endl;
k++;
}
//Extract upper triangular square matrix
bb.reshape(h.numRows()-1 ,1);
//Solve linear system
int info;
std::cout << "bb pre solve = " << bb << std::endl;
std::cout << "h= " << h << std::endl;
Teuchos::LAPACK<int, double> lapack;
lapack.TRTRS('U', 'N', 'N', h.numRows()-1, 1, h.values(), h.stride(), bb.values(), bb.stride(),&info);
V.reshape(n,k-1);
std::cout << "V= " << V << std::endl;
std::cout << "y= " << bb << std::endl;
X.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, V, bb, 1.0);
std::cout << "X= " << X << std::endl;
//Check V is orthogoanl
// Teuchos::SerialDenseMatrix<int, double> vtv(V);
// vtv.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, V, V, 0.0);
// std::cout << "Vtv" << vtv << std::endl;
return 0;
}
//Mean-Based Preconditioned GMRES
int pregmres(const Teuchos::SerialDenseMatrix<int, double> & A, const Teuchos::SerialDenseMatrix<int,double> & X,const Teuchos::SerialDenseMatrix<int,double> & B, int max_iter, double tolerance)
{
int n;
int k;
double resid;
k=1;
n=A.numRows();
std::cout << A << std::endl;
Teuchos::SerialDenseMatrix<int, double> D(n,1);
//Get diagonal entries of A
for (int i=0; i<n; i++){
D(i,0)=A(i,i);
}
Teuchos::SerialDenseMatrix<int, double> Ax(n,1);
Ax.multiply(Teuchos::NO_TRANS,Teuchos::NO_TRANS,1.0, A, X, 0.0);
Teuchos::SerialDenseMatrix<int, double> r0(B);
r0-=Ax;
resid=r0.normFrobenius();
//define vector v=r/norm(r) where r=b-Ax
Teuchos::SerialDenseMatrix<int, double> v(n,1);
r0.scale(1/resid);
Teuchos::SerialDenseMatrix<int, double> h(1,1);
//Matrix of orthog basis vectors V
Teuchos::SerialDenseMatrix<int, double> V(n,1);
//Set v=r0/norm(r0) to be 1st col of V
for (int i=0; i<n; i++){
V(i,0)=r0(i,0);
}
//right hand side
Teuchos::SerialDenseMatrix<int, double> bb(1,1);
bb(0,0)=resid;
Teuchos::SerialDenseMatrix<int, double> w(n,1);
Teuchos::SerialDenseMatrix<int, double> c;
Teuchos::SerialDenseMatrix<int, double> s;
while (resid > tolerance && k < max_iter){
std::cout << "k = " << k << std::endl;
h.reshape(k+1,k);
//Arnoldi iteration(Gram-Schmidt )
V.reshape(n,k+1);
//set vk to be kth col of V
Teuchos::SerialDenseMatrix<int, double> vk(Teuchos::Copy, V, n,1,0,k-1);
//Preconditioning step w=AMj(-1)vj
w.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1/D(k-1,0), A, vk, 0.0);
Teuchos::SerialDenseMatrix<int, double> vi(n,1);
Teuchos::SerialDenseMatrix<int, double> ip(1,1);
for (int i=0; i<k; i++){
//set vi to be ith col of V
Teuchos::SerialDenseMatrix<int, double> vi(Teuchos::Copy, V, n,1,0,i);
//Calculate inner product
ip.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, vi, w, 0.0);
h(i,k-1)= ip(0,0);
//scale vi by h(i,k-1)
vi.scale(ip(0,0));
w-=vi;
}
h(k,k-1)=w.normFrobenius();
w.scale(1.0/w.normFrobenius());
//add column vk+1=w to V
for (int i=0; i<n; i++){
V(i,k)=w(i,0);
}
//Solve upper hessenberg least squares problem via Givens rotations
//Compute previous Givens rotations
for (int i=0; i<k-1; i++){
h(i,k-1)=c(i,0)*h(i,k-1)+s(i,0)*h(i+1,k-1);
h(i+1,k-1)=-s(i,0)*h(i,k-1)+c(i,0)*h(i+1,k-1);
}
//Compute next Givens rotations
c.reshape(k,1);
s.reshape(k,1);
bb.reshape(k+1,1);
double l = sqrt(h(k-1,k-1)*h(k-1,k-1)+h(k,k-1)*h(k,k-1));
c(k-1,0)=h(k-1,k-1)/l;
s(k-1,0)=h(k,k-1)/l;
std::cout <<" h(k,k-1)= " << h(k,k-1) << std::endl;
// Givens rotation on h and bb
h(k-1,k-1)=l;
h(k,k-1)=0;
bb(k-1,0)=c(k-1,0)*bb(k-1,0);
bb(k,0)=-s(k-1,0)*bb(k-1,0);
//Determine residual
resid = fabs(bb(k,0));
std::cout << "resid = " << resid << std::endl;
k=k+1;
}
//Extract upper triangular square matrix
bb.reshape(h.numRows()-1 ,1);
//Solve linear system
int info;
Teuchos::LAPACK<int, double> lapack;
lapack.TRTRS('U', 'N', 'N', h.numRows()-1, 1, h.values(), h.stride(), bb.values(), bb.stride(),&info);
//Found y=Mx
for (int i=0; i<k-1; i++){
bb(i,0)=bb(i,0)/D(i,0);
}
V.reshape(n,k-1);
Teuchos::SerialDenseMatrix<int, double> ans(X);
ans.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, V, bb, 1.0);
std::cout << "ans= " << ans << std::endl;
std::cout << "h= " << h << std::endl;
return 0;
}
