int PLA_Init(MPI_Comm comm) Purpose : Initialize PLAPACK library. IN comm base communicator to be used by PLAPACK
int PLA_Finalize ( ) Purpose : Exit PLAPACK library.
int PLA_Initialized (int *initialized ) Purpose : Check if PLAPACK is initialized. OUT initialized indicates whether PLAPACK is already initialized
int PLA_Base_comm(MPI_Comm *comm) Purpose : Extract the PLAPACK base communicator. OUT comm PLAPACK base communicator
int PLA_Comm_1D_to_2D(MPI_Comm comm1D, int nprows,
int npcols, MPI_Comm *comm2D)
Purpose : Create a communicator with a nprows by npcols topology.
IN comm1D communicator from which to create 2D communictor
IN nprows row dimension of 2D topology
IN npcols column dimension of 2D topology
OUT comm2D communicator with 2D topology
int PLA_Comm_1D_to_2D_ratio(MPI_Comm comm1D, float ratio,
MPI_Comm *comm2D)
Purpose : Create a communicator with a suggested ratio (nprows/npcols = ratio).
IN comm1D communicator from which to create 2D communictor
IN ratio suggested ratio of row and column dimensions
OUT comm2D communicator with 2D topology
int PLA_Temp_create(int nb, int zero_or_one,
PLA_Template *template)
Purpose : Create template for vector and matrix alignment
IN nb length of subvectors of inducing vector and vector template
IN zero_or_one indexing starts with zero or one
OUT template template for matrix and vector distribution
int PLA_Temp_free(PLA_Template *template)
Purpose : Free a template
IN/OUT template template for vector and matrix distribution
int PLA_Temp_comm_all_info(PLA_Template template, MPI_Comm *comm,
int *rank, int *numnodes)
Purpose : Extract communicator, calling node's rank in communicator,
and number of nodes in communicator.
IN template template for vector and matrix distribution OUT comm communicator of node mesh OUT rank rank of calling node within node mesh OUT numnodes number of nodes within node mesh
int PLA_Temp_comm_row_info(PLA_Template template, MPI_Comm *comm,
int *rank, int *numnodes)
Purpose : Extract row communictor, calling node's rank in communicator,
and number of nodes in communicator.
IN template template for vector and matrix distribution OUT comm communicator for calling node's row of nodes OUT rank rank of calling node within row of nodes OUT numnodes number of nodes within row of nodes
int PLA_Temp_comm_col_info(PLA_Template template, MPI_Comm *comm,
int *rank, int *numnodes)
Purpose : Extract column communictor, calling node's rank in communicator,
and number of nodes in communicator.
IN template template for vector and matrix distribution OUT comm communicator for calling node's column of nodes OUT rank rank of calling node within column of nodes OUT numnodes number of nodes within column of nodes
int PLA_Temp_nb (PLA_Template template, int *nb) Purpose : Extract template block sizeIN template template for vector and matrix distribution OUT nb block size of template
int PLA_Temp_zero_or_one (PLA_Template template, int *zero_or_one) Purpose : Extract index start parameter IN template template for vector and matrix distribution OUT zero_or_one indexing may start with zero or oneint PLA_Vector_create (MPI_Datatype datatype, int global_length, PLA_Template template, int global_align, PLA_Obj *new_obj) Purpose : Create distributed vector. IN datatype datatype of object IN global_length global length of vector IN template template for vector and matrix distribution IN global_align alignment to template OUT new_obj object describing created vector
int PLA_Mvector_create (MPI_Datatype datatype, int global_length, int global_width, PLA_Template template, int global_align, PLA_Obj *new_obj) Purpose : Create distributed multi-vector. IN datatype datatype of object IN global_length global length of multi-vector IN global_width global width of multi-vector IN template template for vector and matrix distribution IN global_align alignment to template OUT new_obj object describing created multi-vector
int PLA_Matrix_create (MPI_Datatype datatype, int global_length, int global_width, PLA_Template template, int global_align_row, int global_align_col, PLA_Obj *new_matrix) Purpose : Create distributed matrix. IN datatype datatype of object IN global_length global length of matrix IN global_width global width of matrix IN template template for vector and matrix distribution IN global_align_row row alignment to template IN global_align_col column alignment to template OUT new_matrix object describing created matrix
int PLA_Mscalar_create (MPI_Datatype datatype, int owner_row, int owner_col, int length, int width, PLA_Template template, PLA_Obj *new_mscalar) Purpose : Create distributed mutltiscalar. IN datatype datatype of object IN owner_row index of row of nodes with contains owning node(s) IN owner_col index of column of nodes with contains owning node(s) IN length length of mscalar IN width width of mscalar IN template template for vector and matrix distribution OUT new_mscalar object describing created multiscalar
int PLA_Pvector_create (MPI_Datatype datatype, int project_onto, int owner, int global_length, PLA_Template template, int global_align, PLA_Obj *new_proj_vector) Purpose : Create projected vector. IN datatype datatype of object IN project_onto direction onto which to project IN owner index of row or column of nodes wich containts projected vector IN global_length length of (projected) vector IN global_align alignment to template IN template template for vector and matrix distribution OUT new_proj_vector object describing created projected vector
int PLA_Pmvector_create (MPI_Datatype datatype, int project_onto, int owner, int global_proj_length, int global_proj_width, PLA_Template template, int global_align, PLA_Obj *new_proj_mvector) Purpose : Create projected multi-vector. IN datatype datatype of object IN project_onto direction onto which to project IN owner index of row or column of nodes wich containts projected vector IN global_proj_length length of (projected) vector IN global_proj_width width of (projected) vector IN global_align alignment to template IN template template for vector and matrix distribution OUT new_proj_mvector object describing created projected multi-vector
int PLA_Obj_free (PLA_Obj *obj) Purpose : Linear algebra object destructor. IN/OUT object object to be freet
int PLA_Obj_objtype (PLA_Obj obj, int *objtype) Purpose : Extract object type from object. IN obj object to be queried OUT objtype object type of object
int PLA_Obj_datatype (PLA_Obj obj, MPI_Datatype *datatype) Purpose : Extract datatype from object. IN obj object to be queried OUT datatype datatype of object
int PLA_Obj_template (PLA_Obj obj, PLA_Template *template) Purpose : Extract template from object. IN obj object to be queried OUT template template
int PLA_Obj_global_info (PLA_Obj obj, int *global_length, int *global_width, int *project_onto, int *owner_row, int *owner_col, int *global_align(_row), int *global_align_col) Purpose : Extract global information from linear algebra object.
Note that the individual fields can be queried (separately) through calls to PLA_Obj_global(_field-name). IN obj object to be queried OUT global_length global row dimension of object OUT global_width global column dimension of object OUT project_onto direction of projection OUT owner_row row index of owning node(s) OUT owner_col column index of owning node(s) OUT global_align(_row) (row) alignment to template OUT global_align_col column alignment to template
int PLA_Obj_global_length (PLA_Obj obj, int *global_length ) Purpose : Extract global length from linear algebra object. IN obj object to be queried OUT global_length global row dimension of object
int PLA_Obj_global_width (PLA_Obj obj, int *global_width ) Purpose : Extract global width from linear algebra object. IN obj object to be queried OUT global_width global column dimension of object
int PLA_Obj_project_onto (PLA_Obj obj, int *project_onto ) Purpose : Extract projection information from linear algebra object. IN obj object to be queried OUT project_onto direction of projection
int PLA_Obj_owner_row (PLA_Obj obj, int *owner_row ) Purpose : Extract mesh row owner information rom linear algebra object. IN obj object to be queried OUT owner_row row index of owning node(s) OUT owner_col column index of owning node(s)
int PLA_Obj_owner_col (PLA_Obj obj, int *owner_col ) Purpose : Extract mesh column owner information rom linear algebra object. IN obj object to be queried OUT owner_col column index of owning node(s)
int PLA_Obj_global_align (PLA_Obj obj, int *global_align ) Purpose : Extract global alignment from linear algebra object. IN obj object to be queried OUT global_align Alignment to template
int PLA_Obj_global_align_row (PLA_Obj obj, int *global_align_row ) Purpose : Extract global row alignment from linear algebra object. IN obj object to be queried OUT global_align_row row alignment to template
int PLA_Obj_global_align_col (PLA_Obj obj, int *global_align_col ) Purpose : Extract global column alignment from linear algebra object. IN obj object to be queried OUT global_align_col column alignment to template
int PLA_Obj_local_info (PLA_Obj obj, int *local_length, int *local_width, void **local_buffer, int *local_stride, int *local_ldim) Purpose : Extract local information from linear algebra object.
Note that the individual fields can be queried (separately) through calls to PLA_Obj_local(_field-name). IN obj object to be queried OUT local_length local row dimension of object OUT local_width local column dimension of object OUT local_buffer address of local data OUT local_stride stride between entries in a column or vector OUT local_ldim leading dimension of array holding local data
int PLA_Obj_get_local_contents (PLA_Obj laobject, int transpose, int *rows_in_buf, int *cols_in_buf, void *buf, int leading_dim_buf, int stride_buf) Purpose : Extract the local data from the given object. IN laobject global object IN transpose indicates whether to transpose data OUT rows_in_buf row dimension of extracted data OUT cols_in_buf column dimension of extracted data OUT buf address where data is to be put IN leading_dim leading dimension of buffer where data is put IN stride_buf stride of buffer where data is put
PLA_Obj_set_local_contentsint PLA_Obj_set_local_contents (int transpose, int rows_in_buf, int cols_in_buf, void *buf, int leading_dim_buf, int stride_buf, PLA_Obj laobject) Purpose : Set the local data from the given object. IN transpose indicates whether to transpose data IN rows_in_buf row dimension of data buffer IN cols_in_buf column dimension of data buffer IN buf address of data buffer IN leading_dim leading dimension of data buffer IN stride_buf stride of data buffer where data is put IN/OUT laobject global object
int PLA_Obj_set (PLA_Obj obj, MPI_Datatype datatype, void *value ) Purpose : Sets all entries in the linear algebra object to value given by value. The value is cast to the given MPI_Datatype via the datatype parameter. IN/OUT obj linear algebra object IN datatype datatype of value IN *value value to be used for initialization
int PLA_Obj_set_to_zero (PLA_Obj obj) Purpose : Sets all entries in the linear algebra object to zero (0). The value is cast to the appropriate type (MPI_FLOAT, MPI_DOUBLE, etc.) where the datatype is the same as that of obj. IN/OUT obj linear algebra object
int PLA_Obj_set_to_one (PLA_Obj obj) Purpose : Sets all entries in the linear algebra object to one (1). The value is cast to the appropriate type (MPI_FLOAT, MPI_DOUBLE, etc.) where the datatype is the same as that of obj. IN/OUT obj linear algebra object
int PLA_Obj_set_to_minus_one (PLA_Obj obj) Purpose : Sets all entries in the linear algebra object to negative one (-1). The value is cast to the appropriate type (MPI_FLOAT, MPI_DOUBLE, etc.) where the datatype is the same as that of obj. IN/OUT obj linear algebra object
Chapter 3: Advanced Linear Algebra Object Manipulation
Back to Index to Chapters -- Back to Chapter 2 -- Forward to Chapter 4
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Section 3.1: Creating Views into Objects PLA_Obj_view PLA_Obj_view_all PLA_Obj_view_swap Section 3.2: Splitting of LAObjs PLA_Obj_split_4 PLA_Obj_horz_split_2 PLA_Obj_vert_split_2 Section 3.3: Shifting of LAObjs PLA_Obj_view_shift Section 3.4: Determining Where to Split PLA_Obj_split_size |
Section 3.5: Creating Objects "Conformal to" ... PLA_Vector_create_conf_to PLA_Mvector_create_conf_to PLA_Pvector_create_conf_to PLA_Pmvector_create_conf_to PLA_Matrix_create_conf_to PLA_Mscalar_create_conf_to PLA_Create_constants_conf_to Section 3.6: Annotating Object Orientation PLA_Obj_set_orientation PLA_Obj_get_orientation Section 3.7: Casting Object Types PLA_Obj_objtype_cast |
int PLA_Obj_view (PLA_Obj old_obj, int global_length,
int global_width, int align_row,
int align_col, PLA_Obj *new_obj)
Purpose : Create a view (reference) into an existing linear algebra
object.
IN old_obj object into which view is taken
IN global_length row dimension of view
IN global_width column dimension of view
IN align_row row index in old object of upper-left-hand element of view
IN align_col column index in old object of upper-left-hand element of view
IN/OUT new_obj created view
int PLA_Obj_view_all (PLA_Obj old_obj, PLA_Obj *new_obj) Purpose : Create a view (reference) into all of existing linear algebra object. IN old_obj object into which view is taken IN/OUT new_obj created view
int PLA_Obj_view_swap ( PLA_Obj *obj1, PLA_Obj *obj2) Purpose : Swaps two views. IN/OUT obj1 linear algebra object IN/OUT obj2 linear algebra object
int PLA_Obj_split_4 (PLA_Obj obj,
int length, int width,
PLA_Obj *upper_left_obj, PLA_Obj *upper_right_obj,
PLA_Obj *lower_left_obj, PLA_Obj *lower_right_obj)
Purpose : Split linear algebra object into four quadrants
IN obj object to be split
IN length row dimension of block (as indicated below)
IN width column dimension of block (as indicated below)
OUT upper_left_obj new object for upper-left block
OUT upper_right_obj new object for upper-right block
OUT lower_left_obj new object for lower-left block
OUT lower_right_obj new object for lower-right block
Here the value of length and width determine the size of one block while
their sign determines which block the length and widht refer to.
If :
length >= 0 width >= 0 upper_left_obj
length < 0 width >= 0 lower_left_obj
length >= 0 width < 0 upper_right_obj
length < 0 width < 0 lower_right_obj
int PLA_Obj_horz_split_2 ( PLA_Obj obj, int length,
PLA_Obj *upper_obj,
PLA_Obj *lower_obj)
Purpose : Split linear algebra object into top and bottom
IN obj object to be split
IN length row dimension of block (as indicated below)
OUT upper_obj new object for upper block
OUT lower_obj new object for lower block
If :
length >= 0 length specifies upper_obj
length < 0 length specifies lower_obj
int PLA_Obj_vert_split_2 ( PLA_Obj obj, int width,
PLA_Obj *left_obj, PLA_Obj *right_obj)
Purpose : Split linear algebra object into left and right
IN obj object to be split
IN width column dimension of block (as indicated below)
OUT left_obj new object for left block
OUT right_obj new object for right block
If :
width >= 0 width specifies left_obj
width < 0 width specifies right_obj
int PLA_Obj_view_shift (PLA_Obj obj, int length_top,
int width_left, int width_right,
int length_bottom)
Purpose : Shift the boundaries of the view of the linear algebra object
IN/OUT obj object to be grown [shifted]
IN length_top length to shift top boundary
IN width_left width to shift left boundary
IN width_right width to shift right boundary
IN length_bottom length to shift bottom boundary
Note : Positive is down/right negative is up/left (as if you were in quadrant IV
in the cartesian plane.
int PLA_Obj_split_size (PLA_Obj obj, int side,
int *size, int *owner)
Purpose :
IN obj object to be split
IN side side of split
OUT size size to next template subblock split
OUT owner index of row or column of nodes that owns the split block
Purpose : Compute size of split to next block boundary.
int PLA_Vector_create_conf_to (PLA_Obj obj, PLA_Obj *new_vector) Purpose : Create vector conformal to given object. IN obj original object OUT new_vector created object
int PLA_Mvector_create_conf_to (PLA_Obj obj, int global_width,
PLA_Obj *new_mvector)
Purpose : Create mvector conformal to given object.
IN obj original object
IN global_width number of vectors in mvector
OUT new_mvector created object
int PLA_Pvector_create_conf_to (PLA_Obj obj, int project_onto,
int owner, PLA_Obj *new_pvector)
Purpose : Create projected vector conformal to given object.
IN obj original object
IN project_onto mesh direction onto which to project
IN owner index of row or column of nodes which contains owning nodes
OUT new_pvector created object
int PLA_Pmvector_create_conf_to (PLA_Obj obj, int project_onto,
int owner, int num_vectors,
PLA_Obj *new_pmvector)
Purpose : Create projected mvector conformal to given object.
IN obj original object
IN project_onto mesh direction onto which to project
IN owner index of row or column of nodes which contains owning nodes
IN num_vectors number of vectors in multivector
OUT new_pmvector created object
int PLA_Matrix_create_conf_to (PLA_Obj matrix, PLA_Obj *new_matrix) Purpose : Create matrix conformal to given object (must be a matrix). IN matrix original object OUT new_matrix created object
int PLA_Mscalar_create_conf_to (PLA_Obj obj, int owner_row,
int owner_col, PLA_Obj *new_mscalar)
Purpose : Create multiscalar conformal to given object.
IN obj original object
IN owner_row index of row of nodes that contains owning node(s)
IN owner_col index of column of nodes that contains owning node(s)
OUT new_mscalar created object (multiscalar)
int PLA_Obj_objtype_cast (PLA_Obj obj, int obj_type) Purpose : Cast the linear algebra object to have given object type. IN/OUT obj original object IN objtype new object type
int PLA_Obj_set_orientation (PLA_Obj obj, int project_onto) Purpose : Set the orientation of a matrix panel. IN/OUT obj original object IN project_onto annotation indicating orientation
int PLA_Obj_get_orientation (PLA_Obj obj, int *project_onto) Purpose : Return the orientation of a matrix panel. IN/OUT obj original object IN project_onto annotation indicating orientation
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Section 4.2: API-Activation PLA_API_begin PLA_API_end PLA_API_state Section 4.3: Opening and Closing an Object PLA_Obj_API_open PLA_Obj_API_close PLA_Obj_API_mode |
Section 4.4: Accessing a Vector PLA_API_axpy_vector_to_global PLA_API_axpy_global_to_vector PLA_API_multi_axpy_vector_to_global PLA_API_multi_axpy_global_to_vector Section 4.5: Accessing a Matrix PLA_API_axpy_matrix_to_global PLA_API_axpy_global_to_matrix PLA_API_multi_axpy_matrix_to_global PLA_API_multi_axpy_global_to_matrix Section 4.6: Completion and Synchronization PLA_API_sync |
int PLA_API_begin() Purpose : Activites the API active state.
int PLA_API_end() Purpose : De-activates the API active state.
int PLA_API_state(int *state) Purpose : Determines the state of a linear algebra object. OUT state State of linear algebra object
int PLA_Obj_API_open(PLA_Obj obj) Purpose : Puts object into asynchronous mode(makes PLA_Obj_API_ operations on the object allowable). IN/OUT obj Linear algebra object (to be) placed in asynchronous mode.
int PLA_Obj_API_close(PLA_Obj obj) Purpose : Puts object into synchronous mode (disallows PLA_Obj_API_ operations on the object). IN/OUT obj Linear algebra object (to be) taken out of asynchronous mode.
int PLA_Obj_API_mode (PLA_Obj obj, int *mode) Purpose : Returns the mode of the linear algebra object (PLA_MODE_CLOSED or PLA_MODE_OPEN). IN obj Linear algebra object OUT mode Mode of linear algebra object
int PLA_API_axpy_vector_to_global( int size ,
void * alpha ,
void * local_obj ,
int local_inc ,
PLA_Obj laobj ,
int disp );
Purpose : Add local vector buffer data to global vector object.
IN size Length of vector
IN * alpha Scalar in axpy operation
IN * local_obj Local vector values
IN local_inc Local vector increment (stride)
IN/OUT laobj Global vector (target linear algebra object)
IN disp Global vector displacement
int PLA_API_axpy_global_to_vector(int size ,
void * alpha ,
PLA_Obj laobj ,
int displ ,
void * local_obj ,
int local_inc );
Purpose : Add piece of global vector object to local linear algebra
object.
IN size Length of vector
IN * alpha Scalar in axpy operation
IN laobj Global vector object
IN displ Displacement (in global object)
IN/OUT * local_obj Local linear algebra object (target) buffer
IN local_inc Local vector increment (stride)
int PLA_API_multi_axpy_vector_to_global(int nsub,
int * sizes ,
void * alpha ,
void * local_vector ,
int local_stride ,
PLA_Obj laobj ,
int * displs );
Purpose : Add local sub-vector buffer data chunks to global vector
object.
IN nsub Number of subvectors
IN * size Length of subvectors
IN * alpha Scalar in axpy operation
IN * local_vector Local vector values
IN local_stride Local vector increment (stride)
IN/OUT laobj Global vector (target linear algebra object)
IN * displs Global vector displacements
int PLA_API_multi_axpy_global_to_vector(int nsub ,
int * sizes ,
void * alpha ,
PLA_Obj laobj ,
int * displs ,
void * local_vector ,
int local_stride );
Purpose : Add pieces of global vector object to local vector.
IN nsub Number of subvectors
IN * size Length of subvectors
IN * alpha Scalar in axpy operation
IN laobj Global vector object
IN * displs Displacements (in global object)
IN/OUT * local_vector Local linear algebra object (target) buffer
IN local_stride Local vector increment (stride)
int PLA_API_axpy_matrix_to_global( int size_row ,
int size_col ,
void * alpha ,
void * local_matrix ,
int local_ldim ,
PLA_Obj obj ,
int disp_row,
int disp_col );
Purpose : Add local matrix buffer data to global matrix object.
IN size_row Length of matrix
IN size_col Width of matrix
IN * alpha Scalar in axpy operation
IN * local_obj Local matrix values (buffer)
IN local_ldim Local matrix leading dimension
IN/OUT obj Global matrix (target linear algebra object)
IN disp_row Global matrix row displacement
IN disp_col Global matrix column displacement
int PLA_API_axpy_global_to_matrix(int size_row ,
int size_col ,
void * alpha ,
PLA_Obj obj ,
int displ_row ,
int displ_col,
void * local_matrix ,
int local_ldim );
Purpose : Add piece of global matrix object to local linear algebra
object (matrix).
IN size_row Length of matrix
IN size_col Width of matrix
IN * alpha Scalar in axpy operation
IN obj Global vector object
IN displ_row Row displacement (in global object)
IN displ_col Column displacement (in global object)
IN/OUT * local_matrix Local linear algebra object (target) buffer
IN local_ldim Local matrix leading dimension
int PLA_API_multi_axpy_matrix_to_global( int nsub_row,
int nsub_col,
int * size_row ,
int * size_col ,
void * alpha ,
void * local_matrix ,
int local_ldim ,
PLA_Obj obj ,
int * disp_row,
int * disp_col );
Purpose : Add local sub-matrix buffer data chunks to global matrix
object.
IN nsub_row Number of row subblocks to map
IN nsub_row Number of column subblocks to map
IN * size_row Row block lengths
IN * size_col Column block widths
IN * alpha Scalar in axpy operation
IN * local_matrix Local matrix values
IN local_ldim Local matrix leading dimension
IN/OUT obj Global matrix (target linear algebra object)
IN * disp_row Global matrix row displacements
IN * disp_col Global matrix column displacements
int PLA_API_multi_axpy_global_to_matrix( int nsub_row ,
int nsub_col
int * size_row ,
int * size_col ,
void * alpha ,
PLA_Obj obj ,
int * disp_row ,
int * disp_col ,
void * local_matrix ,
int local_ldim );
Purpose : Add pieces of global matrix object to local matrix.
IN nsub_row Number of row subblocks to map
IN nsub_row Number of column subblocks to map
IN * size_row Row block lengths
IN * size_col Column block widths
IN * alpha Scalar in axpy operation
IN obj Global matrix
IN * disp_row Global matrix row displacements
IN * disp_col Global matrix column displacements
IN/OUT * local_matrix Local matrix values
IN local_ldim Local matrix leading dimension
int PLA_API_sync(PLA_Obj laboj) Purpose : Synchronizes all nodes w.r.t. the given object and completes all pending "API_axpy" operations on the object. IN/OUT laobj Linear algebra object
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Section 5.1: Copy PLA_Copy PLA_Copy_x Section 5.2: Reduce PLA_Reduce PLA_Reduce_x |
Section 5.3: Pipelining Computation and Communication PLA_Temp_set_comm_dir PLA_Temp_get_comm_dir |
int PLA_Copy(PLA_Obj obj_from, PLA_Obj obj_to) Purpose : Copies the contents (not description) between linear algebra objects. IN obj_from object to be copied IN/OUT obj_to object into which to copy
int PLA_Copy_x(int shape, PLA_Obj obj_from, PLA_Obj obj_to) Purpose : Copy contents between linear algebra objects. This version allows a shape to be given for the input object, copying only part of the contents. IN shape shape of object IN obj_from object to be copied IN/OUT obj_to object into which to copy
int PLA_Reduce(PLA_Obj obj_from, MPI_Op op, PLA_Obj obj_to) Purpose : Reduce, using operator given by op, the contents in the duplicated object given by obj_from and overwrite obj_to with the result. IN obj_from object to be reduced IN op reduce operator to be used IN/OUT obj_to object into which to reduce
int PLA_Reduce_x(int shape, PLA_Obj obj_from,
PLA_Obj alpha, PLA_Obj obj_to)
Purpose : Reduce, using summation, the contents in the duplicated object
given by obj_from and overwrite obj_to with the result. This verson reduces
part of the contents, as indicated by shape, and also scales the target
object by alpha before the reduce.
IN shape shape of object
IN obj_from object to be reduced
IN alpha scaling factor for target object
IN/OUT obj_to object into which to reduce
int PLA_Temp_set_comm_dir(PLA_Template template, int mesh_dimension,
int direction )
Purpose : Passes "hints" the the PLA_Copy* and PLA_Reduce*
operations to indicate the direction that data should flow along the processor
mesh. Note that there is no guarantee that the library will obey these
directives. The directions may be up/down/right/left.
IN/OUT template template for computation
IN mesh_dimension dimension of node mesh (row or column)
IN direction direction of flow of computation
int PLA_Temp_get_comm_dir(PLA_Template template, int mesh_dimension,
int *direction )
Purpose : Determines the current status of the "hints" passed
to the PLA_Copy* and PLA_Reduce* operations through PLA_Temp_set_comm_dir().
IN/OUT template template for computation
IN mesh_dimension dimension of node mesh (row or column)
IN direction direction of flow of computation
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Local level-1 BLAS: PLA_Local_copy PLA_Local_swap PLA_Local_scal PLA_Local_inv_scal PLA_Local_axpy PLA_Local_dot PLA_Local_nrm2 PLA_Local_asum PLA_Local_iamax |
Global level-1 BLAS: PLA_Swap PLA_Scal PLA_Inv_scal PLA_Axpy PLA_Dot PLA_Nrm2 PLA_Asum PLA_Iamax |
int PLA_Local_copy(PLA_Obj obj_from, PLA_Obj obj_to) Purpose : Copies the local contents of one linear algebra object into another (i.e. copies the local buffer of one object into the local buffer of another). IN obj_from object to be copied IN/OUT obj_to object into which to copy
Note : The Global copy, PLA_Copy() is covered in Chapter5 and is not repeated on this web page.
int PLA_Local_swap(PLA_Obj obj_x, PLA_Obj obj_y) Purpose : Swaps the local contents of two linear algebra objects (i.e. copies the local buffer of one object into the local buffer of the other and vice versa). IN/OUT obj_x linear algebra object 1 IN/OUT obj_y linear algebra object 2
int PLA_Local_scal(PLA_Obj alpha, PLA_Obj x) Purpose : Scales the local contents of a linear algebra object (i.e. scales its buffer contents through multiplication by alpha). IN alpha scaling factor (multiscalar) IN/OUT x linear algebra object to scale
int PLA_Local_inv_scal(PLA_Obj alpha, PLA_Obj x) Purpose : Scales the local contents of a linear algebra object (i.e. scales its buffer contents through multiplication by 1/alpha). IN alpha (inverse of) scaling factor (multiscalar) IN/OUT x linear algebra object to scale
int PLA_Local_axpy(PLA_Obj alpha, PLA_Obj x,
PLA_Obj y)
Purpose : local(y) = alpha * local(x) + local(y)
IN alpha scaling factor (multiscalar)
IN x linear algebra object to scale
IN/OUT y target
int PLA_Local_dot(PLA_Obj x, PLA_Obj y,
PLA_Obj alpha)
Purpose : local(alpha) = local(x)T * local(y)
IN x vector x (linear algebra object)
IN y vector y (linear algebra object)
IN/OUT alpha local contribution to result of xT * y
int PLA_Local_nrm2(PLA_Obj x, PLA_Obj alpha) Purpose : local(alpha) = ||local(x)|| 2 IN x vector x (linear algebra object) IN/OUT alpha local contribution to ||x||2
int PLA_Local_asum(PLA_Obj x, PLA_Obj alpha) Purpose : local(alpha) = ||local(Re(x))||1 + ||local(Im(x))||1 IN x vector x (linear algebra object) IN/OUT alpha local contribution to ||x||1
int PLA_Local_iamax(PLA_Obj x, PLA_Obj xmax,
PLA_Obj k)
Purpose : local(xmax) = x(k) where |x(k)| = max(|x(j)|) for j ranging
from 1-size of local(x).
IN x vector x (linear algebra object)
IN/OUT xmax local maximum
IN/OUT k global index of local maximum
int PLA_Swap(PLA_Obj x, PLA_Obj y)
Purpose : Swaps the contents (globally) of two linear algebra objects.
NOTE : Does not change any part of either object except the buffer (i.e.
global_length before = global length after etc.).
IN/OUT x linear algebra object ("vector" x)
IN/OUT y linear algebra object ("vector" y)
int PLA_Scal(PLA_Obj alpha, PLA_Obj x) Purpose : Scales the local contents of a linear algebra object : x <- alpha * x IN alpha scaling factor (multiscalar) IN/OUT x linear algebra object to scale
int PLA_Inv_scal(PLA_Obj alpha, PLA_Obj x) Purpose : Scales the local contents of a linear algebra object x <- 1/alpha * x (i.e. scales its buffer contents through multiplication by 1/alpha). IN alpha (inverse of) scaling factor (multiscalar) IN/OUT x linear algebra object to scale
int PLA_Axpy(PLA_Obj alpha, PLA_Obj x,
PLA_Obj y)
Purpose : y = alpha * x + y
IN alpha scaling factor (multiscalar)
IN x linear algebra object to scale
IN/OUT y target
int PLA_Dot(PLA_Obj x, PLA_Obj y,
PLA_Obj alpha)
Purpose : alpha = xT * y
IN x vector x (linear algebra object)
IN y vector y (linear algebra object)
IN/OUT alpha result of xT * y
int PLA_Nrm2(PLA_Obj x, PLA_Obj alpha) Purpose : alpha = ||x|| 2 IN x vector x (linear algebra object) IN/OUT alpha result : ||x||2
int PLA_Asum(PLA_Obj x, PLA_Obj alpha) Purpose : alpha = ||Re(x)||1 + ||Im(x)||1 IN x vector x (linear algebra object) IN/OUT alpha result : ||x||1
int PLA_Iamax(PLA_Obj x, PLA_Obj xmax,
PLA_Obj k)
Purpose : xmax = x(k) where |x(k)| = max(|x(j)|) for j ranging from
1-size of x.
IN x vector x (linear algebra object)
IN/OUT xmax global maximum
IN/OUT k global index of global maximum
|
Local level-2 BLAS: PLA_Local_gemv PLA_Local_symv PLA_Local_trmv PLA_Local_trsv PLA_Local_ger PLA_Local_syr PLA_Local_syr2 |
Global level-2 BLAS: PLA_Gemv PLA_Symv PLA_Trmv PLA_Trsv PLA_Ger PLA_Syr PLA_Syr2 |
int PLA_Local_gemv(int trans, PLA_Obj alpha, PLA_Obj a,
PLA_Obj x, PLA_Obj beta, PLA_Obj y)
Purpose : local(y) <- a* local(A)*local(x)
+ b*local(y) OR local(y) <- a*
local(A)T*local(x) + b*local(y).
IN trans transpose (or no transpose) A (a)
IN alpha scaling factor for A*x
IN a matrix A
IN x "vector" x
IN beta scaling factor for y
IN/OUT y "vector" y
int PLA_Local_symv(int uplo, PLA_Obj alpha, PLA_Obj a,
PLA_Obj x, PLA_Obj beta, PLA_Obj y)
Purpose : local(y) <- a* local(A)*local(x)
+ b*local(y) with only the upper or lower portion
of (local) A stored in object a.
IN uplo use only upper or lower triangular portion of A
IN alpha scaling factor for A*x
IN a matrix A
IN x "vector" x
IN beta scaling factor for y
IN/OUT y "vector" y
int PLA_Local_trmv(int uplo, int trans, int diag,
PLA_Obj a, PLA_Obj x)
Purpose : local(x) <- local(A)*local(x) OR local(x) <- local(A)T
where local A is upper or lower triangular and may have a unit diagonal.
IN uplo (local) A is upper or lower triangular
IN trans transpose (or no transpose) A (a)
IN diag local A has unit or non-unit diagonal
IN a matrix A
IN x "vector" x
int PLA_Local_trsv(int uplo, int trans, int diag,
PLA_Obj a, PLA_Obj x)
Purpose : local(x) <- local(A)-1*local(x) OR local(x)
<- local(A)-T*local(x) OR local(x) <- local(A)-H*local(x)
where local A is upper or lower triangular and may have a unit diagonal.
IN uplo (local) A is upper or lower triangular
IN trans transpose (or no transpose) A (a)
IN diag local A has unit or non-unit diagonal
IN a matrix A
IN x "vector" x
int PLA_Local_ger (PLA_Obj alpha, PLA_Obj x,
PLA_Obj y, PLA_Obj a)
Purpose : local(A) <- a*local(x)*local(y)T
+ local(A).
IN alpha scaling factor
IN x "vector" x
IN y "vector" y
IN/OUT a matrix A
int PLA_Local_syr (int uplo, PLA_Obj alpha,
PLA_Obj x, PLA_Obj a)
Purpose : local(A) <- a*local(x)*local(x)T
+ local(A) with only the upper or lower portion of (local) A stored in
object a.
IN uplo use only the upper or lower portion of local A
IN alpha scaling factor for A*x
IN x "vector" x
IN/OUT a matrix A
int PLA_Local_syr2 (int uplo, PLA_Obj alpha, PLA_Obj x,
PLA_Obj y, PLA_Obj a)
Purpose : local(A) <- a*local(x)*local(y)T
+ local(A) with only the upper or lower portion of (local) A stored in
object a.
IN uplo use only the upper or lower portion of local A
IN alpha scaling factor for A*x
IN x "vector" x
IN y "vector" y
IN/OUT a matrix A
int PLA_Gemv(int trans, PLA_Obj alpha, PLA_Obj a,
PLA_Obj x, PLA_Obj beta, PLA_Obj y)
Purpose : y <- a* A*x + b*y
OR y <- a* AT*x + b*y.
IN trans transpose (or no transpose) A (a)
IN alpha scaling factor for A*x
IN a matrix A
IN x "vector" x
IN beta scaling factor for y
IN/OUT y "vector" y
int PLA_Symv(int uplo, PLA_Obj alpha, PLA_Obj a,
PLA_Obj x, PLA_Obj beta, PLA_Obj y)
Purpose : y <- a* A*x + b*y
with only the upper or lower portion of A stored in object a.
IN uplo use only upper or lower triangular portion of A
IN alpha scaling factor for A*x
IN a matrix A
IN x "vector" x
IN beta scaling factor for y
IN/OUT y "vector" y
int PLA_Trmv(int uplo, int trans, int diag,
PLA_Obj a, PLA_Obj x)
Purpose : x <- A*x OR x <- AT where A is upper or
lower triangular and may have a unit diagonal.
IN uplo A is upper or lower triangular
IN trans transpose (or no transpose) A (a)
IN diag A has unit or non-unit diagonal
IN a matrix A
IN x "vector" x
int PLA_Trsv(int uplo, int trans, int diag,
PLA_Obj a, PLA_Obj x)
Purpose : x <- A-1*x OR x <- A-T*x OR x
<- A-H*x where A is upper or lower triangular and may have
a unit diagonal.
IN uplo A is upper or lower triangular
IN trans transpose (or no transpose) A (a)
IN diag A has unit or non-unit diagonal
IN a matrix A
IN x "vector" x
int PLA_Ger (PLA_Obj alpha, PLA_Obj x,
PLA_Obj y, PLA_Obj a)
Purpose : A <- a*x*yT + A.
IN alpha scaling factor
IN x "vector" x
IN y "vector" y
IN/OUT a matrix A
int PLA_Syr (int uplo, PLA_Obj alpha,
PLA_Obj x, PLA_Obj a)
Purpose : A <- a*x*xT + A
with only the upper or lower portion of A stored in object a.
IN uplo use only the upper or lower portion of A
IN alpha scaling factor for A*x
IN x "vector" x
IN/OUT a matrix A
int PLA_Syr2 (int uplo, PLA_Obj alpha, PLA_Obj x,
PLA_Obj y, PLA_Obj a)
Purpose : A <- a*x*yT + A
with only the upper or lower portion of A stored in object a.
IN uplo use only the upper or lower portion of A
IN alpha scaling factor for A*x
IN x "vector" x
IN y "vector" y
IN/OUT a matrix A
|
Local level-3 BLAS: PLA_Local_gemm PLA_Local_symm PLA_Local_syrk PLA_Local_syr2k PLA_Local_trmm PLA_Local_trsm |
Global level-3 BLAS: PLA_Gemm PLA_Symm PLA_Syrk PLA_Syr2k PLA_Trmm PLA_Trsm |
int PLA_Local_gemm ( int transa, int transb, PLA_Obj alpha, PLA_Obj A, PLA_Obj B, PLA_Obj beta, PLA_Obj C) Purpose : Local matrix multiplication IN transa integer, PLA_TRANSPOSE or PLA_NO_TRANSPOSE IN transb integer, PLA_TRANSPOSE or PLA_NO_TRANSPOSE IN alpha multiscalar, scale factor for A and B IN A any object type, factor in product IN B any object type, factor in product IN beta multiscalar, scale factor for C IN/OUT C any object type, overwritten with alpha*opA(A)*opB(B)+beta*C
int PLA_Gemm ( int transa,
int transb,
PLA_Obj alpha,
PLA_Obj A,
PLA_Obj B,
PLA_Obj beta,
PLA_Obj C)
Purpose : Parallel matrix multiplication
IN transa integer, PLA_TRANSPOSE or PLA_NO_TRANSPOSE
IN transb integer, PLA_TRANSPOSE or PLA_NO_TRANSPOSE
IN alpha multiscalar, scale factor for A and B
IN A matrix, factor in product
IN B matrix, factor in product
IN beta multiscalar, scale factor for C
IN/OUT C matrix, overwritten with alpha*opA(A)*opB(B)+beta*C
int PLA_Local_symm ( int side, int uplo, PLA_Obj alpha, PLA_Obj A, PLA_Obj B, PLA_Obj beta, PLA_Obj C) Purpose : Local symmetric matrix multiplication IN side integer, PLA_SIDE_LEFT or PLA_SIDE_RIGHT IN uplo integer, PLA_UPPER_TRIANGULAR or PLA_LOWER_TRIANGULAR IN alpha multiscalar, scale factor for A and B IN A any object type, factor in product IN B any object type, factor in product IN beta multiscalar, scale factor for C IN/OUT C any object type, overwritten with alpha*opA(A)*opB(B)+beta*C
int PLA_Symm ( int side,
int uplo,
PLA_Obj alpha,
PLA_Obj A,
PLA_Obj B,
PLA_Obj beta,
PLA_Obj C)
Purpose : Parallel symmetric matrix multiplication
IN side integer, PLA_SIDE_LEFT or PLA_SIDE_RIGHT
IN uplo integer, PLA_UPPER_TRIANGULAR or PLA_LOWER_TRIANGULAR
IN alpha multiscalar, scale factor for A and B
IN A matrix, factor in product
IN B matrix, factor in product
IN beta multiscalar, scale factor for C
IN/OUT C matrix, overwritten with alpha*opA(A)*opB(B)+beta*C
int PLA_Local_syrk ( int uplo, int trans, PLA_Obj alpha, PLA_Obj A, PLA_Obj beta, PLA_Obj C) Purpose : Local symmetric rank-k update IN uplo integer, PLA_UPPER_TRIANGULAR or PLA_LOWER_TRIANGULAR IN trans integer, PLA_TRANSPOSE or PLA_No_TRANPOSE IN alpha multiscalar, scale factor for A IN A any object type, factor in product IN beta multiscalar, scale factor for C IN/OUT C any object type, overwritten with alpha A*A^T + beta C
int PLA_Syrk ( int uplo,
int trans,
PLA_Obj alpha,
PLA_Obj A,
PLA_Obj beta,
PLA_Obj C)
Purpose : Parallel symmetric rank-k update
IN uplo integer, PLA_UPPER_TRIANGULAR or PLA_LOWER_TRIANGULAR
IN trans integer, PLA_TRANSPOSE or PLA_No_TRANPOSE
IN alpha multiscalar, scale factor for A
IN A matrix, factor in product
IN beta multiscalar, scale factor for C
IN/OUT C symmetric matrix, overwritten with alpha A*A^T + beta C
int PLA_Local_syr2k ( int uplo,
int trans,
PLA_Obj alpha,
PLA_Obj A,
PLA_Obj B,
PLA_Obj beta,
PLA_Obj C)
Purpose : Local symmetric double rank-k update
IN uplo integer, PLA_UPPER_TRIANGULAR or PLA_LOWER_TRIANGULAR
IN trans integer, PLA_TRANSPOSE or PLA_No_TRANPOSE
IN alpha multiscalar, scale factor for A and B
IN A any object type, factor in product
IN B any object type, factor in product
IN beta multiscalar, scale factor for C
IN/OUT C any object type, overwritten with
alpha*(A*B^T + B*A^T)+beta*C
int PLA_Syr2k ( int uplo,
int trans,
PLA_Obj alpha,
PLA_Obj A,
PLA_Obj B,
PLA_Obj beta,
PLA_Obj C)
Purpose : Parallel symmetric double rank-k update
IN uplo integer, PLA_UPPER_TRIANGULAR or PLA_LOWER_TRIANGULAR
IN trans integer, PLA_TRANSPOSE or PLA_No_TRANPOSE
IN alpha multiscalar, scale factor for A and B
IN A matrix, factor in product
IN B matrix, factor in product
IN beta multiscalar, scale factor for C
IN/OUT C symmetric matrix, overwritten with
alpha*(A*B^T + B*A^T)+beta*C
int PLA_Local_trmm ( int side,
int uplo,
int trans,
int diag,
PLA_Obj alpha,
PLA_Obj A,
PLA_Obj B)
Purpose : Local triangular matrix multiply
IN side integer, PLA_SIDE_LEFT or PLA_SIDE_RIGHT
IN uplo integer, PLA_UPPER_TRIANGULAR or PLA_LOWER_TRIANGULAR
IN trans integer, PLA_TRANSPOSE or PLA_No_TRANPOSE
IN diag integer, PLA_UNIT_DIAG or PLA_NONUNIT_DIAG
IN alpha multiscalar, scale factor
IN A any object type, factor in product
IN/OUT B any object type, factor in product
int PLA_Trmm ( int side,
int uplo,
int trans,
int diag,
PLA_Obj alpha,
PLA_Obj A,
PLA_Obj B)
Purpose : Parallel triangular matrix multiplication
IN side integer, PLA_SIDE_LEFT or PLA_SIDE_RIGHT
IN uplo integer, PLA_UPPER_TRIANGULAR or PLA_LOWER_TRIANGULAR
IN trans integer, PLA_TRANSPOSE or PLA_No_TRANPOSE
IN diag integer, PLA_UNIT_DIAG or PLA_NONUNIT_DIAG
IN alpha multiscalar, scale factor
IN A matrix, factor in product
IN/OUT B matrix, factor in product
int PLA_Local_trsm ( int side,
int uplo,
int trans,
int diag,
PLA_Obj alpha,
PLA_Obj A,
PLA_Obj B)
Purpose : Local triangular solve with multiple right hand sides
IN side integer, PLA_SIDE_LEFT or PLA_SIDE_RIGHT
IN uplo integer, PLA_UPPER_TRIANGULAR or PLA_LOWER_TRIANGULAR
IN trans integer, PLA_TRANSPOSE or PLA_No_TRANPOSE
IN diag integer, PLA_UNIT_DIAG or PLA_NONUNIT_DIAG
IN alpha multiscalar, scale factor
IN A any object type, triangular matrix
IN/OUT B any object type, right hand sides
int PLA_Trsm ( int side,
int uplo,
int trans,
int diag,
PLA_Obj alpha,
PLA_Obj A,
PLA_Obj B)
Purpose : Parallel triangular solve with multiple right hand sides
IN side integer, PLA_SIDE_LEFT or PLA_SIDE_RIGHT
IN uplo integer, PLA_UPPER_TRIANGULAR or PLA_LOWER_TRIANGULAR
IN trans integer, PLA_TRANSPOSE or PLA_No_TRANPOSE
IN diag integer, PLA_UNIT_DIAG or PLA_NONUNIT_DIAG
IN alpha multiscalar, scale factor
IN A matrix, triangular matrix
IN/OUT B matrix, right hand sides (overwritten with solution)
|
PLA_Create_constants_conf_to PLA_Obj_set_to_identity PLA_Local_equal_zero PLA_Local_sign PLA_Local_invert_sign |
int PLA_Create_constants_conf_to (PLA_Obj obj, PLA_Obj *minus_one,
PLA_Obj *zero, PLA_Obj *one)
Purpose : Create multiscalars of the same datatype as the given object.
IN obj original object
OUT minus_one mscalar containing -1
OUT zero mscalar containing 0
OUT one mscalar containing 1
int PLA_Obj_set_to_identity (PLA_Obj obj) Purpose : Set object to identity matrix. IN/OUT obj linear algebra object
int PLA_Local_equal_zero(PLA_Obj x) Purpose : Return TRUE (=1) or FALSE (=0) depending on whether the local (scalar) object equals zero. IN x scalar for which to determine if zero RETURN value: TRUE iff x == 0
int PLA_Local_sign(PLA_Obj x, PLA_Obj sign_x )
Purpose : local( sign_x ) = sign( local(x)
IN x scalar for which to determine sign
IN/OUT sign_x scalar = sign of x ( = x / | x | so complex is
covered )
int PLA_Local_invert_sign( PLA_Obj x )
Purpose : local( x ) = - local(x)
IN/OUT x object for which sign(s) of element(s) are
to be inverted.
|
General Solve:
Symmetric Positive Definite Solve: |
Linear Least Squares Solve: |
int PLA_General_solve(PLA_Obj A, PLA_Obj ipiv, PLA_Obj B )
Purpose : Solve linear system of equations A X = B, overwriting B
with X, using LU factorization with partial pivoting. B may have
more than one column.
IN/OUT A Matrix A. Overwritten with LU factorization.
(PLA_MATRIX of size nxn)
IN/OUT ipiv Object in which to store pivots encountered
during LU factorization.
(PLA_MSCALAR of size 1xn, duplicated on all nodes)
IN/OUT B (Multiple)right-hand-side(s). Overwritten with
solution(s)
(PLA_MVECTOR or PLA_MATRIX with n rows)
|
PLA_Pos_def_solve PLA_Chol |
int PLA_Pos_def_solve(int uplo, PLA_Obj A, PLA_Obj B )
Purpose : Solve linear system of equations A X = B, overwriting B
with X, using Cholesky factorization. Matrix A must be symmetric
positive definite. B may have more than one column.
IN uplo If PLA_LOWER_TRIANGULAR or PLA_UPPER_TRIANGULAR,
A is stored in lower or upper triangular part of
object A, respectively.
IN/OUT A Matrix A. Overwritten with Cholesky factorization.
(PLA_MATRIX of size nxn)
IN/OUT B (Multiple)right-hand-side(s). Overwritten with
solution(s)
(PLA_MVECTOR or PLA_MATRIX with n rows)
int PLA_Chol( int uplo, PLA_Obj A )
Purpose : Compute Cholesky factorization A -> L L^T of positive
symmetric matrix A. Currently, only uplo = PLA_LOWER_TRIANGULAR
is supported, which means that the symmetric matrix is stored
in the the lower triangle of A and it is this part of A that
is overwritten with factor L.
IN uplo If PLA_LOWER_TRIANGULAR or PLA_UPPER_TRIANGULAR,
A is stored in lower or upper triangular part of
object A, respectively.
IN/OUT A Matrix A. Overwritten with Cholesky factorization.
(PLA_MATRIX of size nxn)
|
PLA_Least_sqr_solve PLA_QR PLA_Compute_House_v PLA_Compute_W_Y PLA_Apply_W_Y PLA_Form_Q PLA_Q_solve |
int PLA_Least_sqr_solve(PLA_Obj A, PLA_Obj s, PLA_Obj Q, PLA_Obj B )
Purpose : Solve linear least squares problem min || A X - B ||_2
using QR factorization. B may have more than one column.
IN/OUT A Matrix A. Overwritten with R and the Householder
vectors.
(PLA_MATRIX of size mxn)
IN/OUT s Object for storing the scaling factors for
the Householder transforms.
(PLA_Mvector of size nx1)
IN/OUT Q Object for storing Q. If it equals PLA_DUMMY,
Q is not computed.
(PLA_MATRIX of size mxm)
IN/OUT B (Multiple)right-hand-side(s). Overwritten with
solution(s)
(PLA_MVECTOR or PLA_MATRIX with m rows)
int PLA_QR(PLA_Obj A, PLA_Obj s )
Purpose : Factor A -> Q R, overwriting the uppertriangular part of
A with R and leaving the Householder vectors stored below the
diagonal and in s.
IN/OUT A Matrix A. Overwritten with R and the Householder
vectors.
(PLA_MATRIX of size mxn)
IN/OUT s Object for storing the scaling factors for
the Householder transforms.
(PLA_Mvector of size nx1)
int PLA_Compute_House_v(PLA_Obj x, PLA_Obj beta )
Purpose : Compute vector u so that
( I - beta u u^T ) x = +- || x ||_2 e_1
u is normalized to have unit first element and beta = 2 / || u ||_2^2.
IN/OUT x Vector x. Overwritten with first entry +-|| x ||_2
and the rest of the entries of u.
(PLA_MVECTOR of width 1)
IN/OUT beta Object for storing the scaling factor beta.
(1x1 PLA_MSCALAR duplicated to all nodes)
int PLA_Compute_W_Y(PLA_Obj Amv, PLA_Obj s, PLA_Obj Wmv, PLA_Obj Ymv )
Purpose : Compute WY transform from Householder vectors stored
below diagonal of Amv and s.
IN Amv Panel of matrix which stores the current Householder
vectors from which to compute WY transform.
(mxn PLA_MVECTOR)
IN s Scaling factors for Householder transforms.
(nx1 PLA_MSCALAR duplicated to all nodes)
IN/OUT Wmv, Ymv Matrices in which to compute W and Y.
(mxn PLA_MVECTOR)
int PLA_Apply_W_Y(int side, int trans,
PLA_Obj Wmv, PLA_Obj, Ymv, PLA_Obj A )
Purpose : Compute one of the following:
OPERATION SIDE TRANS
----------------------------------------------
A <-- (1 + W Y') A PLA_SIDE_LEFT PLA_NO_TRANS
A <-- A (1 + W Y') PLA_SIDE_RIGHT PLA_NO_TRANS
A <-- (1 + Y W') A PLA_SIDE_LEFT PLA_TRANS
A <-- A (1 + Y W') PLA_SIDE_RIGHT PLA_TRANS
IN side Side from which to apply WY transform.
(int)
IN trans Indicates whether to transpose WY transform.
(int)
IN Wmv, Ymv Matrices W and Y.
(mxn PLA_MVECTOR)
IN/OUT A Matrix to be updated.
(PLA_MATRIX)
int PLA_Form_Q(int trans, PLA_Obj A, PLA_Obj s, PLA_Obj Q )
Purpose : Compute Q = H_1 * H_2 * ... * H_n-1 where H_i is
the ith Householder transform stored in the ith column of A and
ith entry in s. If trans = PLA_NO_TRANS, Q is computed.
Otherwise, Q^T is computed.
IN trans Indicates whether to compute Q or Q^T.
(int)
IN A Householder vectors are stored below diagonal of A.
(PLA_MATRIX)
IN s Scaling factors for Householder transformations.
(PLA_MVECTOR of width 1)
IN/OUT Q Matrix in which to form Q.
(PLA_MATRIX)
int PLA_Q_solve( int side, int trans, PLA_Obj A, PLA_Obj s, PLA_Obj B )
Purpose: Solve one of the following:
OPERATION SIDE TRANS
----------------------------------------------
Q X = B PLA_SIDE_LEFT PLA_NO_TRANS
Q^T X = B PLA_SIDE_LEFT PLA_TRANS
X Q = B PLA_SIDE_RIGHT PLA_NO_TRANS
X Q^T = B PLA_SIDE_RIGHT PLA_TRANS
where Q is stored as Householder vectors below the diagonal of A and in s
and B is given. The solution X overwrites B.
IN side Indicates whether Q appears to left or right of X.
IN trans Indicates whether to transpose Q.
IN A Householder vectors are stored below diagonal of A.
(PLA_MATRIX)
IN s Scaling factors for Householder transformations.
(PLA_MVECTOR of width 1)
IN/OUT B Right-hand-sides.
(PLA_MATRIX or PLA_MVECTOR)