Obtain

the BLAS routines rotg and rot for constructing and applying a Givens rotation.

These routines exist in both Fortran and C; they are available in the IMSL

Libraries or from CALGO (Collected Algorithms of the ACM; see the

Bibliography).

a)

Using these two routines, apply a Givens rotation to the matrix used in

Exercise 5.9 in Chap. 5,

Exercise

5.9

Determine

the Givens transformation matrix that will rotate the matrix

b)

Write a routine

»

Obtain

the BLAS routines rotg and rot for constructing and applying a Givens rotation.

These routines exist in both Fortran and C; they are available in the IMSL

Libraries or from CALGO (Collected Algorithms of the ACM; see the

Bibliography).

a)

Using these two routines, apply a Givens rotation to the matrix used in

Exercise 5.9 in Chap. 5,

Exercise

5.9

Determine

the Givens transformation matrix that will rotate the matrix

b)

Write a routine in Fortran or C that accepts as input a matrix and its

dimensions and uses the BLAS routines rotg and rot to produce its QR

decomposition. There are several design issues you should address: how the

output is returned (for purposes of this exercise, just return two arrays or

pointers to the arrays in full storage mode), how to handle nonfull rank matrices

(for this exercise, assume that the matrix is of full rank, so return an error

message in this case), how to handle other input errors (what do you do if the

user inputs a negative number for a dimension?), and others.

»

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