SVSOL

The SVSOL function uses " back-substitution" to solve a set of simultaneous linear equations Ax = b , given the U , W , and V arrays returned by the SVDC procedure. None of the input arguments are modified, making it possible to call SVSOL multiple times with different right hand vectors, B .

SVSOL is based on the routine


svbksb

described in section 2.6 of Numerical Recipes in C: The Art of Scientific Computing (Second Edition), published by Cambridge University Press, and is used by permission.

Arguments

U

An n -column, m -row orthogonal array used in the decomposition of A . Normally, U is returned from the SVDC procedure.

W

An n -element vector containing "singular values." Normally, W is returned from the SVDC procedure. Small values (close to machine floating-point precision) should be set to zero prior to calling SVSOL.

V

An n -column, n -row orthogonal array used in the decomposition of A . Normally, V is returned from the SVDC procedure.

B

An m -element vector containing the right hand side of the linear system Ax = b .

Keywords

COLUMN

Set this keyword if the input arrays U and V are in column-major format (composed of column vectors) rather than in row-major format (composed of row vectors).

DOUBLE

Set this keyword to force the computation to be done in double-precision arithmetic.

Example

To solve the linear system Ax = b using Singular-value decomposition and back substitution, begin with an array A which serves as the coefficient array:

A = [[1.0, 2.0, -1.0, 2.5], $ ; Define the array A.

[1.5, 3.3, -0.5, 2.0], $

[3.1, 0.7, 2.2, 0.0], $

[0.0, 0.3, -2.0, 5.3], $

[2.1, 1.0, 4.3, 2.2], $

[0.0, 5.5, 3.8, 0.2]]

B = [0.0, 1.0, 5.3, -2.0, 6.3, 3.8] ; Define the right-hand side vector B.

SVDC, A, W, U, V ; Decompose A.

PRINT, SVSOL(U, W, V, B) ; Compute the solution and print the result.

IDL prints:

1.00095 0.00881170 0.984176 -0.0100954

This is the correct solution.