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## Unit1.1.2Outline Week 1

• 1.1 Opening Remarks

• 1.1.1 Launch

• 1.1.2 Outline Week 1

• 1.1.3 What you will learn

• 1.2 Loop Orderings

• 1.2.1 Mapping matrices to memory

• 1.2.2 The leading dimension

• 1.2.3 A convention regarding the letters used for the loop index

• 1.2.4 Ordering the loops

• 1.3 Layering Matrix-Matrix Multiplication

• 1.3.1 Notation

• 1.3.2 The dot product (inner product)

• 1.3.3 Matrix-vector multiplication via dot products

• 1.3.4 The axpy operation

• 1.3.5 Matrix-vector multiplication via axpy operations

• 1.3.6 Matrix-matrix multiplication via matrix-vector multiplications

• 1.4 Layering Matrix-Matrix Multiplication: Alternatives

• 1.4.1 Rank-1 update (rank-1)

• 1.4.2 Matrix-matrix multiplication via rank-1 updates

• 1.4.3 Row-times-matrix multiplications

• 1.4.4 Matrix-matrix multiplication via row-times-matrix multiplications

• 1.4.5 Comparison

• 1.5 Enrichments

• 1.5.1 The Basic Linear Algebra Subprograms

• 1.5.2 The BLAS-like Library Instantiation Software

• 1.5.3 Counting flops

• 1.6 Wrap Up

• 1.6.1 Additional exercises

• 1.6.2 Summary