**1. NAME AND TITLE**

FERDO/FERD: Multichannel Neutron and Gamma-Ray Spectrum Matrix Unfolding Code
Systems.

**2. CONTRIBUTOR**

Oak Ridge National Laboratory, Oak Ridge, Tennessee.

**3. CODING LANGUAGE AND COMPUTER**

Fortran IV; IBM 3033.

**4. NATURE OF PROBLEM SOLVED**

FERDO and FERD solve the integral equation which relates a measured pulse-height distribution
and associated uncertainties to the true energy spectrum of the incident radiation.

**5. METHOD OF SOLUTION**

FERDO uses the method of constrained least-squares and biased estimation to solve a discretized
representation of the integral unfolding problem and to compute a 2-sigma confidence interval for the
true energy spectrum. FERD improves the FERDO solution by iteratively modifying the biased
estimator.

**6. RESTRICTIONS OR LIMITATIONS**

FERDO/FERD require accurate estimations of the actual detector response and the idealized
detector response (normally the detector energy resolution). In-core memory requirements are roughly
three times the size of the response matrix (number of rows times the number of columns) for FERDO
and four times the size of the response matrix for FERD. Additionally, a scratch storage device must
be specified for both FERDO and FERD.

**7. TYPICAL RUNNING TIME**

Running time depends most strongly on the size of the response matrix. An 87 x 88 matrix problem
required 4.5 s of IBM 3033 CPU time for FERDO and 15.2 s for FERD.

**8. COMPUTER HARDWARE REQUIREMENTS**

FERDO/FERD is operable on the IBM 3033 computer.

**9. COMPUTER SOFTWARE REQUIREMENT**

FERDO/FERD uses the proprietary DISSPLA graphics software package available from ISSCO,
San Diego, California. It has been successfully run on the IBM 3033 computer under control of the
MVS-JES2 Operating System. A Fortran IV compiler is required.

**10. REFERENCE**

B. W. Rust, D. T. Ingersoll, and W. R. Burrus, "A User's Manual for the FERDO and FERD
Unfolding Codes," ORNL/TM-8720 (September 1983).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced document and one (1.2MB) DOS diskette which contains the source
code and sample problem input and output.

**12. DATE OF ABSTRACT**

October 1983.

**KEYWORDS**: UNFOLDING; GAMMA-RAY SPECTRUM ANALYSIS