Mari missed Silas. Even though she understood why he ran away all those years ago, she would always be his big sister, she would always worry about him. He had cut out a place for himself though, found his calling as a park ranger and she respected that. She was happy for him. Every year she made time to come out and see him, in part to ensure for herself that he was doing ok but also just have a little of that sibling bonding time he used to find annoying. This year was different though, even as she sat on his couch laughing over a good beer there was still a cloud looming in the back of her mind reminding her of what was to come.Â
The next day she waited until he had left for work to gather her gear. She felt bad leaving him out of this but she had to do this alone and she wasnât quite sure this would even work. Silas had always wanted to know the truth about what happened, who wouldnât after their world got turned upside down and he didnât even know why. The running line was âanimal attackâ, that they were so lucky to get away with their lives. The siblings had never quite fallen for it, after all how could two small children get away from an animal that took out too grown adults. For Silas, that meant their parents were still alive but Mari had always suspected something darker.Â
Silas was too young at the time but Mari had known their parents were into something illegal. More than a few times sheâd been asked to hide something in her bag or seen something she shouldnât when she snuck out of bed. She never quite knew what but her father had made sure she knew how to protect herself and her brother, knew what to do if something went south, even if she never knew what that something was. After that night, the attack, whenever she attempted to remember anything all she felt was a darkness dropping into her stomach. She tried to tell herself that her parents were likely dead, that some vicious animal attack was the trauma that locked up her mind, that she didnât need to remember to know the truth and she put up a wall trying to close that night off forever.Â
Over the years, the wall had taken hits. She spot someone in a crowd she thought sheâd recognized and fear would come back. Eventually sheâd tell herself that she was crazy and revert back to âanimal attackâ mantra but sheâd still end up in the gym to keep up her sparring and checking the locks on her doors and windows every night. Seeing the knife in the camping shop though had been like a bulldozer to the wall, memories were seeping through and she finally realized it was time she stopped hiding from the truth. She needed to know what happened that night if she was going to move forward, if Silas was going to move forward.Â
Stepping into that fateful spot in the forest was honestly a bit anti-climatic. Sheâd imagined a wave of memories just hitting her like a mac truck but it didnât come. She remembered it for sure. As she walked around the small clearing in the trees she could almost see where they had set up her tents. She couldnât help but smile at their campsite, she could almost smell whatever concoction her father was cooking up over the fire. Everything else seemed distant, fractured as usual. Setting her back down she settled in, she wasnât going to give up this time. If she was going to do this she had to atleast give it a good try.Â
As the sun lowered in the sky she started a fire. Sheâd been running over what she could remember in her mind. Her parents, their life before all this happened, trying to think of any clue that might have led up to what happened that night but was coming up dry. A twig snapping nearby set her on edge and she pulled her hunting knife from its sheath crouching down trying to see who or what was there.Â
Just like that the floodgates let loose, her eyes shifted back to the camp but what was once just a fire transformed into their campsite. Her mother was arguing with someone, their back to her. It sound as though she was trying to work out a deal. Her eyes shifted to her father and a ripple of anger went through her. Fighting against the men that held him he was pleading not with them but with his wife to change her mind, not to go forward with this. Before she knew it, things had escalated quickly and she was jumping in to help, her knife sinking into one of the attackers. She was easily knocked away and then there was that knife again, glinting in the light of the fire. Searing pain made it hard to breathe, hard to focus but when she looked up her mother was no where to be seen and her father was screaming for her to run.Â
A hand on her arm brought her back to reality but in her fear she couldnât help but lash out. She missed but a voice called out to her, making her drop the knife all together. Silas. She crumbled as his arms wrapped around her, undoubtedly confused. âI remember Silas..I remember everything.âÂ
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Mariana woke suddenly, a cold sweat layered on her skin. If her neighborâs banging on her wall were any indication she had probably screamed. His voice echoed into her room, telling her to shut up as he cared more about his trouble sleeping then her own. Tugging herself out of bed her legs shook as she made her way to the bathroom. She should be used to these by now. Sheâd been having them for years. Her fractured memory trying to work itself out, trying to give her pieces of life that she was missing.
What happened to their family in the woods was still a mystery. When she and her brother, Silas, had been found they were in bad shape, Mari herself wounded. The Vargasâs had said that when the pair had stumbled upon their camp, the kids were scared, Mari in front of her brother brandishing a knife she was too weak to really use. After getting them to the hospital, Mari had been in and out and they really only had Silasâs point of view to go on. Heâd said that the siblings had gone on a hike together, out to a waterfall and back. Mari knew the forest well, so their parents had let her take her brother out there alone. When they made it back to camp something was wrong. Things were strewn about and a large shape seemed to be in one of the tents. Silas hadnât seen it, not up close, Mari had told him to crouch down and hide among a set of logs nearby but he was sure it was a bear. He said that his sister went to go investigate alone and a few minutes later he heard her screams. By the time she ran out of camp screaming for him to run heâd convinced himself that some monstrous bear had attacked their camp and never looked back.
When Mari woke she wasnât much help. She remembered bits and pieces of their trip but the doctors didnât want her to push more. The Park Rangers said the wounds were inconclusive and despite blood at the camp they couldnât say what had happened to their parents. A search party had continued to look but everyone was convinced they were dead. Their uncle had even come to town, long enough to play the picture of the childrenâs savior, come to take them home but when the estate was finalized and their life insurance came in he was long gone. Mari couldnât say she was surprised. Despite the perfect little family they seemed to be, that Silas thought they were she was old enough to have seen the darker side of her father and his side of the family. They werenât the saints her brother made them out to be and while he was convinced that their parents were alive, somewhere out there trying to make their way back, something in Mari knew that even if her parents were alive, she doubted theyâd come back to town, not even for their kids.
The Vargas family was kind enough to step in, building the kids a home. They tried to help the siblings deal with that night. Both children went into therapy but it didnât stick for either. As much as Mari wanted to remember, to know what truly happened the sessions only made her nightmares more vivid. Eventually they stopped making her go and Mari stopped trying, tired of sleepless nights. For a while the nightmares stopped or atleast were less prevalent. She tried to move forward with her life. Remembering wouldnât bring them back and she doubted even the truth could make her brother come home.
That was until the other week. A trip to the camping store had flipped a switch in her mind. Her eyes had landed on a knife in a display cabinet and something about the serrated edge, something about its glint was so familiar to her. The memory hit her like a flash, the darkened camp, her falling as someone grabbed at her, then that knife and the hand that wielded it followed by searing pain. It was overwhelming, sheâd stumbled into the storeâs bathroom and found herself heaving into the toilet. When sheâd composed herself, sheâd brushed it off as something she ate to those watching her concerned but ever since, those nightmares had returned, new images starting to form and now she was questioning everything about that camping trip. Gripping her sink she grabbed the meds tucked away in the cabinet, meant to help her anxiety and downed a dose, praying it slowed her speeding heart. Sinking back against the cool bathroom floor she sighed. She wasnât going to be able to push this down this time. It was time she figured it all out. But she was going to need help.
Review: Computational Study of Sparse Matrix Storage Schemes
This dissertation is by Sardar Ansul Haque, University of Lethbridge, Alberta, Canada.Â
I'll be doing this review in stages as I go through the dissertation in parts during the next few days. The review will contain content from the dissertation as well as some of my own input.
The SpMV problem is solving Ax=y; where A is a matrix that is mostly zeros and x is a dense vector. This kernel displays irregular vector writes but regular matrix reads and regular vector (y) writes. The problem is natural memory bound and providing intuition into data reuse is hard particularly when the sparsity is unknown prior to run time. This irregular access leads to a large number of cache misses. This is intensified when the matrix and vector do not fit inside of cache. Several machine learning algorithms, PDEs, mesh calculations, and several computational problems utilize sparse structures where sparsity structure is not really known until during runtime. (Hint hint: we need better Top500 benchmarks ;) )
Most data structures for storing sparse matrices use array-based data structures to introduce some sort of regularity into the data access patterns. Most commonly, column indices and row indices of every non zero element are stored into arrays leading to a form of compressed storage. Compressed Row Storage and Compressed Column Storage are some of the popular storage formats. The whole point of these different storages is to regularize data access and ensure either Spatial or Temporal Locality. Spatial locality of A is reordering A such that the nonzeros in each row are consecutive. This improves the regularity of accessing A. Temporal locality says that the data (parts of the vector) recently used will be used again by A.
In the next posts I will review different storage techniques as presented in the thesis and also go through the MatMult algorithm for each storage technique. Later posts will be on columns reordering algorithms (something I myself am rather new to :) ).