1. Introduction to PETSc VIGRE Seminar, Wednesday, November 8, 2006

2. Parallel Computing How (basically) does it work?

3. Parallel Computing How (basically) does it work? Assign each processor a number

4. Parallel Computing How (basically) does it work? Assign each processor a number The same program goes to all

5. Parallel Computing How (basically) does it work? Assign each processor a number The same program goes to all Each uses separate memory

6. Parallel Computing How (basically) does it work? Assign each processor a number The same program goes to all Each uses separate memory They pass information back and forth as necessary

7. Parallel Computing Example 1: Matrix-Vector Product

8. Parallel Computing Example 1: Matrix-Vector Product and are inputs into the program. 0: 1: 2:

9. Parallel Computing Example 1: Matrix-Vector Product The control node (0) reads in the matrix and distributes the rows amongst the processors. 0: (a, b, c) 1: (d, e, f) 2: (g, h, i)

10. Parallel Computing Example 1: Matrix-Vector Product The control node also sends the vector to each processor’s memory. 0: (a, b, c) ; (j, k, l) 1: (d, e, f) ; (j, k, l) 2: (g, h, i) ; (j, k, l)

11. Parallel Computing Example 1: Matrix-Vector Product Each processor computes its own dot product. 0: (a, b, c) (j, k, l) = aj+bk+cl 1: (d, e, f) (j, k, l) = dj+ek+fl 2: (g, h, i) (j, k, l) = gj+hk+il

12. Parallel Computing Example 1: Matrix-Vector Product The processors send their results to the control node, which outputs. 0: (a, b, c) (j, k, l) = aj+bk+cl 1: (d, e, f) (j, k, l) = dj+ek+fl 2: (g, h, i) (j, k, l) = gj+hk+il

13. Parallel Computing Example 2: Matrix-Vector Product Suppose for memory reasons each processor only has part of the vector. 0: (a, b, c) ; j 1: (d, e, f) ; k 2: (g, h, i) ; l

14. Parallel Computing Example 2: Matrix-Vector Product Before the multiply, each processor sends the necessary information elsewhere. 0: (a, b, c) ; j ; (k from 1) ; (l from 2) 1: (d, e, f) ; (j from 0) ; k ; (l from 2) 2: (g, h, i) ; (j from 0) ; (k from 1) ; l

15. Parallel Computing Example 2: Matrix-Vector Product After the multiply, the space is freed again for other uses. 0: (a, b, c) ; j 1: (d, e, f) ; k 2: (g, h, i) ; l

16. Parallel Computing Example 3: Matrix-Matrix Product The previous case illustrates how to multiply matrices stored across multiple processors. 0: (a, b, c) ; (j, k, l) 1: (d, e, f) ; (m, n, o) 2: (g, h, i) ; (p, q, r)

17. Parallel Computing Example 3: Matrix-Matrix Product Each column is distributed for processing in turn. 1) (a, b, c)(j, m, p)=α 0: 2) (a, b, c)(k, n, q)=β 3) (a, b, c)(l, o, r)=γ 1) (d, e, f)(j, m, p)=δ 1: 2) (d, e, f)(k, n, q)=ε 3) (d, e, f)(l, o, r)=ζ 1) (g, h,i)(j, m, p)=η 2: 2) (g, h, i)(k, n, q)=θ 3) (g, h, i)(l, o, r)=ι

18. Parallel Computing Example 3: Matrix-Matrix Product The result is a matrix with the same parallel row structure as the first matrix and column structure as the right. 0: (α, β, γ) 1: (δ, ε, ζ) 2: (η, θ, ι)

19. Parallel Computing Example 3: Matrix-Matrix Product The original indices could also have been sub-matrices, as long as they were compatible. 0: (α, β, γ) 1: (δ, ε, ζ) 2: (η, θ, ι)

20. Parallel Computing Example 4: Block Diagonal Product Suppose the second matrix is block diagonal. 0: (A, B, C) ; (J, 0, 0) 1: (D, E, F) ; (0, K, 0) 2: (G, H, I) ; (0, 0, L)

21. Parallel Computing Example 4: Block Diagonal Product Much less information needs to be passed between the processors. 1) AJ=α 0: 2) BK=β 3) CL=γ 1) DJ=δ 1: 2) EK=ε 3) FL=ζ 1) GJ=η 2: 2) HK=θ 3) IL=ι

22. Parallel Computing When is it worth it to parallelize?

23. Parallel Computing When is it worth it to parallelize? There is a time cost associated with passing messages

24. Parallel Computing When is it worth it to parallelize? There is a time cost associated with passing messages The amount of message passing is dependent on the problem and the program (algorithm)

25. Parallel Computing When is it worth it to parallelize? Therefore, the benefits depend more on the structure of the problem and the program than on the size/speed of the parallel network (diminishing returns).

26. Parallel Networks How do I use multiple processors?

27. Parallel Networks How do I use multiple processors? This depends on the network, but… Most networks use some variation of PBS, a job scheduler, and mpirun or mpiexec.

28. Parallel Networks How do I use multiple processors? This depends on the network, but… Most networks use some variation of PBS, a job scheduler, and mpirun or mpiexec. A parallel program needs to be submitted as a batch job.

29. Parallel Networks Suppose I have a program myprog, which gets data from data.dat, which I call in the following fashion when only using one processor:./myprog –f data.dat I would write a file myprog.pbs that looks like the following:

30. Parallel Networks #PBS –q compute (name of the processing queue [not necessary on all networks]) #PBS -N myprog (the name of the job) #PBS –l nodes=2:ppn=1,walltime=00:10:00 (number of nodes and number of processes per node, maximum time to allow the program to run) #PBS -o /home/me/mydir/myprog.out (where the output of the program should be written) #PBS -e /home/me/mydir/myprog.err (where the error stream should be written) These are the headers that tell the job scheduler how to handle your job.

31. Parallel Networks Although what follows depends on the MPI software that the network runs, it should look something like this: cd $PBS_O_WORKDIR (makes the processors run the program in the directory where myprog.pbs is saved) mpirun –machinefile $PBS_NODEFILE –np 2 myprog –f mydata.dat (tells the MPI software which processes to use and how many processes to start: notice that command line arguments follows as usual)

32. Parallel Networks Once the.pbs file is written, it can be submitted to the job scheduler with qsub: qsub myprog.pbs

33. Parallel Networks Once the.pbs file is written, it can be submitted to the job scheduler with qsub: qsub myprog.pbs You can check to see if your job is running with the command qstat.

34. Parallel Networks Some systems (but not all) will allow you to simulate running your program in parallel on one processor, which is useful for debugging: mpirun –np 3 myprog –f mydata.dat

35. Parallel Networks What parallel systems are available?

36. Parallel Networks What parallel systems are available? RTC : Rice Terascale Cluster: 244 processors.

37. Parallel Networks What parallel systems are available? RTC : Rice Terascale Cluster: 244 processors. ADA : Cray XD1: 632 processors.

38. Parallel Networks What parallel systems are available? RTC : Rice Terascale Cluster: 244 processors. ADA : Cray XD1: 632 processors. caamster: CAAM department exclusive: 8(?) processors.

39. PETSc What do I use PETSc for?

40. PETSc What do I use PETSc for? File I/O with “minimal” understanding of MPI

41. PETSc What do I use PETSc for? File I/O with “minimal” understanding of MPI Vector and matrix based data management (in particular: sparse)

42. PETSc What do I use PETSc for? File I/O with “minimal” understanding of MPI Vector and matrix based data management (in particular: sparse) Linear algebra routines familiar from the famous serial packages

43. PETSc At the moment, ada and caamster (and harvey) have PETSc installed

44. PETSc At the moment, ada and caamster (and harvey) have PETSc installed You can download and install PETSc on your own machine (requires cygwin for Windows), for educational and debugging purposes

45. PETSc PETSc builds on existing software BLAS and LAPACK: which implementations to use can be specified at configuration

46. PETSc PETSc builds on existing software BLAS and LAPACK: which implementations to use can be specified at configuration Has (slower) debugging configuration and (faster, tacit) optimized configuration

47. PETSc Installation comes with documentation, examples, and manual pages.

48. PETSc Installation comes with documentation, examples, and manual pages. The biggest part of learning how to use PETSc is learning how to use the manual pages.

49. PETSc It is extremely useful to have an environmental variable PETSC_DIR in you shell of choice, which gives the path to the installation of PETSc, e.g. PETSC_DIR=/usr/local/src/petsc-2.3.1-p13/ export PETSC_DIR

50. PETSc Makefile

51. PETSc Makefile You can pretty much copy/paste/modify the makefiles in the examples, but here is the basic setup:

52. PETSc Makefile (…) (Other definitions for CFLAGS, etc.) LOCDIR = ~/mydir include ${PETSC_DIR}/bmake/common/base (This is why it is useful to have this variable saved) myprog: myprog.o chkopts -${CLINKER} -o myprog myprog.o ${PETSC_LIB} ${RM} myprog.o

53. PETSc Headers

54. PETSc Headers #include “petsc.h” in all files, unless the routines that you use need more specific headers.

55. PETSc Headers #include “petsc.h” in all files, unless the routines that you use need more specific headers. How do you know? Consult the manual pages!

56. PETSc Data Types

57. PETSc Data Types PETSc has a slew of its own data types: PetscInt, PetscReal, PetscScalar, etc.

58. PETSc Data Types PETSc has a slew of its own data types: PetscInt, PetscReal, PetscScalar, etc. Usually aliases of normal data types: PetscInt ~ int, PetscReal ~ double

59. PETSc Data Types PETSc has a slew of its own data types: PetscInt, PetscReal, PetscScalar, etc. Usually aliases of normal data types: PetscInt ~ int, PetscReal ~ double Safer to use for compatibility

60. PETSc Usage in C/C++

61. PETSc Usage in C/C++ The top program should begin: Static char[] help=“Your message here.” int main(int argc,char **argv){ (… declarations) PetscInitialize(&argc,&argv,PETSC_NULL,help)

62. PETSc Usage in C/C++ The top program should end: (…) PetscFinalize(); return(0); }

63. PETSc Usage in C/C++ When first programming, include the following variable: PetscErrorCode ierr; Where you’d call a PETSc routine, Routine(arg); write instead ierr=Routing(arg);CHKERRQ(ierr);

64. PETSc Usage in C/C++ When you try to run your program, you will be informed of any problems with incompatible data types/dimensions/etc.

65. PETSc Data Anything data type larger than a scalar has a Create and a Destroy routine.

66. PETSc Data Anything data type larger than a scalar has a Create and a Destroy routine. If you run./myprog –log_summary, you get # created and # destroyed for each data type, to find memory leaks.

67. PETSc Example: Vec

68. PETSc Example: Vec Two types: global and local

69. PETSc Example: Vec Two types: global and local Dependent on function: do other processors need to see this data?

70. PETSc Example: Vec Two types: global and local Dependent on function: do other processors need to see this data? Basic usage: Vec X; VecCreate( [ PETSC_COMM_WORLD / PETSC_COMM_SELF ], &X);

71. PETSc Example: Vec Advanced usage:

72. PETSc Example: Vec Advanced usage: VecCreateSeq(PETSC_COMM_SELF,n,&X);

73. PETSc Example: Vec Advanced usage: VecCreateSeq(PETSC_COMM_SELF,n,&X); VecCreateSeqWithArray(PETSC_COMM_SELF,n,vals,&X);

74. PETSc Example: Vec Advanced usage: VecCreateSeq(PETSC_COMM_SELF,n,&X); VecCreateSeqWithArray(PETSC_COMM_SELF,n,vals,&X); VecLoad(instream,VECSEQ,&X);

75. PETSc Example: Vec Advanced usage: VecCreateSeq(PETSC_COMM_SELF,n,&X); VecCreateSeqWithArray(PETSC_COMM_SELF,n,vals,&X); VecLoad(instream,VECSEQ,&X); VecCreateMPI(PETSC_COMM_WORLD,n,PETSC_DETERMINE,&X);

76. PETSc Example: Vec Advanced usage: VecCreateSeq(PETSC_COMM_SELF,n,&X); VecCreateSeqWithArray(PETSC_COMM_SELF,n,vals,&X); VecLoad(instream,VECSEQ,&X); VecCreateMPI(PETSC_COMM_WORLD,n,PETSC_DETERMINE,&X); VecCreateMPI(PETSC_COMM_WORLD,PETSC_DECIDE,N,&X);

77. PETSc Example: Vec Advanced usage: VecCreateSeq(PETSC_COMM_SELF,n,&X); VecCreateSeqWithArray(PETSC_COMM_SELF,n,vals,&X); VecLoad(instream,VECSEQ,&X); VecCreateMPI(PETSC_COMM_WORLD,n,PETSC_DETERMINE,&X); VecCreateMPI(PETSC_COMM_WORLD,PETSC_DECIDE,N,&X); VecCreateMPIWithArray(PETSC_COMM_WORLD,n,N,vals,&X);

78. PETSc Example: Vec Advanced usage: VecCreateSeq(PETSC_COMM_SELF,n,&X); VecCreateSeqWithArray(PETSC_COMM_SELF,n,vals,&X); VecLoad(instream,VECSEQ,&X); VecCreateMPI(PETSC_COMM_WORLD,n,PETSC_DETERMINE,&X); VecCreateMPI(PETSC_COMM_WORLD,PETSC_DECIDE,N,&X); VecCreateMPIWithArray(PETSC_COMM_WORLD,n,N,vals,&X); VecLoad(instream,VECMPI,&X);

79. PETSc Example: Vec Advanced usage: VecCreateSeq(PETSC_COMM_SELF,n,&X); VecCreateSeqWithArray(PETSC_COMM_SELF,n,vals,&X); VecLoad(instream,VECSEQ,&X); VecCreateMPI(PETSC_COMM_WORLD,n,PETSC_DETERMINE,&X); VecCreateMPI(PETSC_COMM_WORLD,PETSC_DECIDE,N,&X); VecCreateMPIWithArray(PETSC_COMM_WORLD,n,N,vals,&X); VecLoad(instream,VECMPI,&X); VecDuplicate(Y,&X);

80. PETSc Example: Vec Advanced usage: VecCreateSeq(PETSC_COMM_SELF,n,&X); VecCreateSeqWithArray(PETSC_COMM_SELF,n,vals,&X); VecLoad(instream,VECSEQ,&X); VecCreateMPI(PETSC_COMM_WORLD,n,PETSC_DETERMINE,&X); VecCreateMPI(PETSC_COMM_WORLD,PETSC_DECIDE,N,&X); VecCreateMPIWithArray(PETSC_COMM_WORLD,n,N,vals,&X); VecLoad(instream,VECMPI,&X); VecDuplicate(Y,&X); MatGetVecs(M,&X,PETSC_NULL);

81. PETSc Example: Vec Advanced usage: VecCreateSeq(PETSC_COMM_SELF,n,&X); VecCreateSeqWithArray(PETSC_COMM_SELF,n,vals,&X); VecLoad(instream,VECSEQ,&X); VecCreateMPI(PETSC_COMM_WORLD,n,PETSC_DETERMINE,&X); VecCreateMPI(PETSC_COMM_WORLD,PETSC_DECIDE,N,&X); VecCreateMPIWithArray(PETSC_COMM_WORLD,n,N,vals,&X); VecLoad(instream,VECMPI,&X); VecDuplicate(Y,&X); MatGetVecs(M,&X,PETSC_NULL); MatGetVecs(M,PETSC_NULL,&X);

82. PETSc Example: Vec If not created with array or loaded from file, values still needed:

83. PETSc Example: Vec If not created with array or loaded from file, values still needed To copy the values of another Vec, with the same parallel structure, use VecCopy(Y,X).

84. PETSc Example: Vec If not created with array or loaded from file, values still needed To copy the values of another Vec, with the same parallel structure, use VecCopy(Y,X). To set all values to a single scalar value, use VecSet(X,alpha).

85. PETSc Example: Vec There are routines for more complicated ways to set values

86. PETSc Example: Vec There are other routines for more complicated ways to set values PETSc guards the block of data where the actual values are stored very closely

87. PETSc Example: Vec There are other routines for more complicated ways to set values PETSc guards the block of data where the actual values are stored very closely An assembly routine must be called after these other routines

88. PETSc Example: Vec Other routines:

89. PETSc Example: Vec Other routines: VecSetValue

90. PETSc Example: Vec Other routines: VecSetValue VecSetValueLocal (different indexing used)

91. PETSc Example: Vec Other routines: VecSetValue VecSetValueLocal (different indexing used) VecSetValues

92. PETSc Example: Vec Other routines: VecSetValue VecSetValueLocal (different indexing used) VecSetValues VecSetValuesLocal

93. PETSc Example: Vec Other routines: VecSetValue VecSetValueLocal (different indexing used) VecSetValues VecSetValuesLocal VecSetValuesBlocked

94. PETSc Example: Vec Other routines: VecSetValue VecSetValueLocal (different indexing used) VecSetValues VecSetValuesLocal VecSetValuesBlocked VecSetValuesBlockedLocal

95. PETSc Example: Vec Once a vector is assembled, there are routines for (almost) every function we could want from a vector: AXPY, dot product, absolute value, pointwise multiplication, etc.

96. PETSc Example: Vec Once a vector is assembled, there are routines for (almost) every function we could want from a vector: AXPY, dot product, absolute value, pointwise multiplication, etc. Call VecDestroy(X) to free its array when it isn’t needed anymore.

97. PETSc Example: Mat

98. PETSc Example: Mat Like Vec, a Mat can be global or local (MPI/Seq)

99. PETSc Example: Mat Like Vec, a Mat can be global or local (MPI/Seq) A Mat can take on a large number of data structures to optimize * and \, even though the same routine is used on all structures.

100. PETSc Example: Mat Row compressed Block row compressed Symmetric block row compressed Block diagonal And even dense

101. PETSc File I/O

102. PETSc File I/O The equivalent to a stream is a viewer.

103. PETSc File I/O PETSc has equivalent routines to printf, but you must decide if you want every node to print or just the control node

104. PETSc File I/O PETSc has equivalent routines to printf, but you must decide if you want every node to print or just the control node To ensure clarity when multiple nodes print, use PetscSynchronizedPrintf followed by PetscSynchronizedFlush.

105. PETSc File I/O The equivalent to a stream is a “viewer”, but a viewer organizes data across multiple processors.

106. PETSc File I/O The equivalent to a stream is a “viewer”, but a viewer organizes data across multiple processors. A viewer combines an output location (file/stdout/stderr), with a format.

107. PETSc File I/O The equivalent to a stream is a “viewer”, but a viewer organizes data across multiple processors. A viewer combines an output location (file/stdout/stderr), with a format. Most data types have a View routine such as MatView(M,viewer)

108. PETSc File I/O On a batch server, ASCII I/O can be horrendously slow.

109. PETSc File I/O On a batch server, ASCII I/O can be horrendously slow. PETSc only reads into a parallel format data which is stored in binary form.

110. PETSc File I/O On a batch server, ASCII I/O can be horrendously slow. PETSc only reads into a parallel format data which is stored in binary form. Lots of output data is likely: binary is more compressed than ASCII.

111. PETSc I have ASCII input data: solution?

112. PETSc I have ASCII input data: solution? Write a wrapper program Runs on one processor Creates the data to be used in parallel, and “views” it to a binary input file In parallel, it will be automatically distributed

113. PETSc Next Time, Issues for Large Dynamical Systems: Time Stepping Updating algebraically Managing lots of similar equations (Scattering/Gathering)