Ex Parte Gustavson et al

Patent Trial and Appeal Board

Apr 18, 2013

11035933 (P.T.A.B. Apr. 18, 2013)

UNITED STATES PATENT AND TRADEMARK OFFICE
UNITED STATES DEPARTMENT OF COMMERCE
United States Patent and Trademark Office
Address: COMMISSIONER FOR PATENTS
P.O. Box 1450
Alexandria, Virginia 22313-1450
www.uspto.gov
APPLICATION NO. FILING DATE FIRST NAMED INVENTOR ATTORNEY DOCKET NO. CONFIRMATION NO.
11/035,933 01/14/2005 Fred Gehrung Gustavson YOR920040314US1
YOR.542
4272
48150 7590 04/19/2013
MCGINN INTELLECTUAL PROPERTY LAW GROUP, PLLC
8321 OLD COURTHOUSE ROAD
SUITE 200
VIENNA, VA 22182-3817
EXAMINER
MALZAHN, DAVID H
ART UNIT PAPER NUMBER
2193
MAIL DATE DELIVERY MODE
04/19/2013 PAPER
Please find below and/or attached an Office communication concerning this application or proceeding.
The time period for reply, if any, is set in the attached communication.
PTOL-90A (Rev. 04/07)

UNITED STATES PATENT AND TRADEMARK OFFICE
____________________

BEFORE THE PATENT TRIAL AND APPEAL BOARD
____________________

Ex parte FRED GEHRUNG GUSTAVSON and
JOHN A. GUNNELS
____________________

Appeal 2010-003918
Application 11/035,933
Technology Center 2100
____________________

Before ALLEN R. MacDONALD, LINDA E. HORNER,
SCOTT R. BOALICK, JASON V. MORGAN, and
MICHAEL J. STRAUSS, Administrative Patent Judges.

MacDONALD, Administrative Patent Judge.

DECISION ON APPEAL

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I. SUMMARY OF THE DECISION
Prosecution and Appeal History
Appellants appealed under 35 U.S.C. § 134(a) from rejections of
claims 1 and 3-21. We have jurisdiction under 35 U.S.C. § 6(b).
On June 3, 2009, the Examiner finally rejected claims 19 and 20 under
35 U.S.C. § 102(e) and finally rejected claims 1 and 3-21 under
35 U.S.C. § 101.
On September 14, 2009, Appellants filed an appeal brief appealing
from the final rejections under § 102(e) and § 101.
On December 22, 2009, in the Examiner’s Answer, the Examiner
maintained the rejection under § 102(e); however the Examiner withdrew
the rejection under 35 U.S.C. § 101. (Ans. 3-4).
On January 5, 2010, Appellants filed a reply brief responding to the
Examiner’s Answer.
We review the appealed rejection for error based upon the issues
identified by Appellants, and in light of the arguments and evidence
produced thereon. Cf. Ex Parte Frye, 94 USPQ2d 1072, 1075 (BPAI 2010)
(precedential) (citing In re Oetiker, 977 F.2d 1443, 1445 (Fed. Cir. 1992)).
Summary of Our New Ground of Rejection under § 101
of Method Claims 1, 3-11, and 21
Pursuant to 37 C.F.R. § 41.50(b), we enter a new ground of rejection
under 35 U.S.C. § 101. Our analysis as to the § 101 rejection is focused on
method claims 1, 3-11, and 21 and is summarized as follows:
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(1) Claim Interpretation
We begin by determining what, precisely, the applicant has invented
and is seeking to patent, and how claims 1, 3-11, and 21 relate to and define
that invention.
(2) Eligible Subject Matter Categories
We conclude that these claims are directed to a method (process) and,
as such, are within one of the four patent-eligible subject matter categories.
(3) Exceptions
For these method claims, relevant factors—both those in favor of
patent-eligibility and those against such a finding—should be weighed in
making the determination of whether the claimed invention, viewed as a
whole, is disqualified as being a claim to an abstract idea. We have
reviewed the particular machine factor and the transformation factor in light
of the presented evidence and argument, and have taken into consideration
the relevant statutes, regulations, authorities, and USPTO § 101 guidance.
We conclude that both the particular machine factor and the transformation
factor weigh against patent eligibility. We have similarly reviewed
additional method claim § 101 factors to determine whether the method
claims are patent-ineligible (i.e., directed to an abstract idea). We conclude
that when all the method claim § 101 factors are considered collectively they
weigh against subject matter eligibility.1

1 The phrases “patent eligibility” and “subject matter eligibility” are used
interchangeably herein.
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(4) Conclusion
We conclude that method claims 1, 3-11, and 21 do not qualify as a
statutory process. The detailed rationale for our decision as to the rejection
of method claims 1, 3-11, and 21 under 35 U.S.C. § 101 is discussed infra.
Summary of Our Other Decisions
We do not sustain the Examiner’s rejection of claims 19 and 20
under 35 U.S.C. § 102. We enter a new ground of rejection of computer
claims 12-14, medium claims 15-18, and apparatus claims 19 and 20 under
35 U.S.C. § 101.
The detailed rationales for these decisions are discussed infra.

II. STATEMENT OF CASE
Exemplary Claims
Exemplary claims 1, 12, and 15 (not currently rejected by the
Examiner), and claim 19 on appeal read as follows:

1. A method of improving at least one of efficiency and a speed of
processing for transposing data of a rectangular matrix A to form a transpose
A' of said matrix A in a computer, where Aij resides at a memory location
(i,j) = location (0,0) + i + LDA*j, 0 ≤ j, < LDA-1, where LDA is a leading
dimension of the matrix A, location (0,0) is a starting location in memory of
said rectangular matrix A, as stored in one of a row major or column major
format, said method comprising:
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determining, using a processor on said computer, a largest order
square submatrix within a residual of said rectangular matrix A not yet
transposed;
subdividing said residual of said rectangular matrix A into one or
more square submatrices Aij , each having said largest order;
executing an in-place transposition of each of said square submatrices
Aij; and
storing said transposed square submatrices Aij in a memory as data
structures representing said transposed square submatrices, said data
structures mapped as being concatenated in a formation of said transpose A'.

12. A computer, comprising:
a memory to store a matrix data to be transposed, said matrix having
size m x n, where m and n are two integers, said matrix data being stored in
said memory in one of a row major or column major format in a format
memory location (i,j) = location (0,0) + i + LDA*j, where 0 ≤ j ≤ (LDA-1),
LDA is defined as a leading dimension of the matrix, and location (0,0) is a
starting location in memory of said matrix;
a square sub-divider module, as executed by a processor of said
computer, to subdivide said matrix data into at least one square submatrix;
and
an in-place square transpose module, executed by said processor, to
transpose each said at least one square submatrix to form a transposed
square submatrix,
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wherein said square sub-divider module determines a size of a largest
square submatrix of a residual amount of said matrix data not yet transposed
and uses said determined size for the subdividing.
15. A storage medium tangibly embodying a program of machine-
readable instructions executable by a digital processing apparatus to perform
a method of transposing data of a matrix, said instructions comprising at
least one of:
a square sub-divider module to determine a largest residual square
submatrix in a matrix stored as matrix data in a memory in one of a row
major or column major format and to subdivide said matrix data into at least
one square submatrix;
an in-place square transpose module to transpose each said at least
one square submatrix to form a transposed square submatrix;
a re-organizer module to determine how each said transposed square
submatrix is fitted back to form transposed matrix data;
an extra space module to determine an amount of extra memory space
to be reserved for a residual portion of said matrix data; and
a control module to supervise and coordinate an operation of one or
more of said square sub-divider module, said in-place square transpose
module, said re-organizer module, and said extra space module.
19. An apparatus, comprising:
means for subdividing a matrix data into one or more square
submatrices of data, said matrix having size m x n, where m and n are two
integers, including means to determine a largest square submatrix of a
residual amount of matrix data not yet transposed;
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means for executing an in-place square matrix transposition of data
subdivided from said matrix data; and
means for selectively repeating said subdividing by determining a
remaining largest square submatrix and executing said in-place square
matrix transposition until said matrix data is completely transposed.
Rejection on Appeal
The Examiner rejected claims 19 and 20 under 35 U.S.C. § 102(b) as
being anticipated by Lao (US 7,031,994 B2).2
Appellants’ Contention
Appellants contend that the Examiner erred because Lao fails to
describe “determining a remaining largest square submatrix” from the
residual portion of the matrix. (App. Br 15-16 and Reply Br. 2).

Issue on Appeal
Did the Examiner err in rejecting claims 19 and 20 as being
anticipated because Lao fails to describe “determining a remaining largest
square submatrix” as claimed?

III. ANALYSIS OF APPEALED REJECTION
We have reviewed the Examiner’s § 102 rejection in light of
Appellants’ above contention of error in the rejection.3

2 Separate patentability is not argued for claim 20.
3 Appellants do not dispute the Examiner’s finding that Lao teaches
that so called in-place matrix transpose operations are known in the art.
We particularly note Lao’s discussion of the tradeoffs between utilizing
out-of-place transpose versus in-place transpose. (Lao, col. 1, l. 48, through
col. 2, l. 5).
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Although we agree with Examiner’s findings that Lao describes
every other feature of Appellants’ claim 19, we do not agree with the
Examiner that Lao describes “determining a remaining largest square
submatrix” as claimed. We agree with Appellants that the rejection
under 35 U.S.C. § 102(e) is in error.

IV. NEW GROUND OF REJECTION
We reject claims 1 and 3-21 under 35 U.S.C. § 101 as being directed
to non-statutory subject matter. We make this rejection in light of the
presented evidence and argument, and upon consideration of the relevant
statutes, regulations, authorities, and USPTO § 101 guidance.

A. Findings of Fact (FF)
Field of Appellants’ Invention
1. Appellants state:
The present invention generally relates to providing
efficiency in linear algebra subroutines. More specifically, a
novel method saves both computer memory and improves
performance by forming the transpose of a matrix A by
subdividing the matrix A into one or more square submatrices
Aij along a row or column direction, performing an in-place
square matrix transposition on each square submatrix Aij, to
form transposed square submatrices Aij' and then forming, on
the possible remaining leftover rectangular piece B of A, its
transpose matrix B' by using a standard out-of-place transpose
algorithm. The final transpose of matrix A is formed by
connecting the square transposed part(s) Aij of the original of
matrix A with B'.
(Appellants’ Spec. 1:18-26) (emphasis added).
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Related Art to Appellants’ Invention
2. Appellants state:
Scientific computing relies heavily on linear algebra. In
fact, the whole field of engineering and scientific computing
takes advantage of linear algebra for computations. Linear
algebra routines are also used in games and graphics rendering.
Typically, these linear algebra routines reside in a math
library of a computer system that utilizes one or more linear
algebra routines as a part of its processing.
(Appellants’ Spec. 1:29-2:3) (emphasis added).
3. Appellants state:
The applications of the present invention include the
matrix operation of transposition and is [sic] applicable in any
environment in which used [sic] transposition is performed.
(Appellants’ Spec. 2:13-15) (emphasis added).
4. Appellants further state:
Matrix transposition is an important sub-operation
appearing in many matrix algorithms, such as solving dense
linear systems, matrix multiply, and eigenvalue computations.
(Appellants’ Spec. 3:21-23).
Brief Description of Appellants’ Drawings
5. Appellants state (Spec. 6:16):
Figure 1 [shown below] shows a conventional matrix
transposition process 100;

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6. Appellants state (Spec. 6:17-18):
Figure 2 [shown below] shows how a matrix
transposition process 200 of a square matrix can be executed in
place.

7. Appellants further state (Spec. 7:16-18):
Figure 7 [shown below] shows visually a process 700 of
how the transposed submatrices resultant from the process 600
in Figures 6A-6C are viewed as concatenated in the manner
complementary to the manner in which the submatrices were
split apart.
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8. Appellants further state (Spec. 6:19-20):
Figure 3 [shown below] shows a flowchart 300 that
summarizes a technique of transposition for any matrix A in
accordance with the method of the present invention.

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9. Appellants further state (Spec. 8:3-4):
Figure 11 [shown below] shows an exemplary block
diagram 1100 of a software module that might be implemented
to execute the transposition technique of the present invention.

10. Appellants further state (Spec. 8:5-6):
Figure 12 [shown below] illustrates an exemplary
hardware/information handling system 1200 for incorporating
the present invention therein. (Figure 13 is also shown below).

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11. Appellants further state (Spec. 23:1-24:4)(emphasis added):
[T]he present invention could be implemented by custom
designing a computer in accordance with the principles of the
present invention. . . .
[T]he present invention could be implemented by
modifying standard matrix processing modules, such as
described by LAPACK, so as to be based on the principles of
the present invention. . . .
Moreover, the principles and methods of the present
invention could be embodied as a computerized tool stored on a
memory device, such as independent diskette 1300, that
contains a series of matrix subroutines to solve scientific and
engineering problems using matrix processing, as modified by
the technique described above. . . .
It should also be obvious to one of skill in the art that the
instructions for the technique described herein can be
downloaded through a network interface from a remote storage
facility.
All of these various embodiments are intended as
included in the present invention, since the present invention
should be appropriately viewed as a method to enhance the
computation of matrix subroutines, as based upon recognizing
how linear algebra processing can be more efficient by using
the principles of the present invention
12. Appellants further state (Spec. 24:9-15) (emphasis added):
[I]t is understood that an end user desiring a solution of a
scientific or engineering problem may undertake to directly use
a computerized linear algebra processing method that
incorporates the method of the present invention. Alternatively,
the end user might desire that a second party provide the end
user the desired solution to the problem by providing the results
of a computerized linear algebra processing method that
incorporates the method of the present invention.
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B. Principles of Law and Examination Guidelines
When statutory subject matter concerns are raised for a process claim,
an examiner is required to provide appellants with a clear analysis as to why
their claims are not directed to statutory subject matter. Towards that goal,
the USPTO issued § 101 subject matter eligibility determination guidance to
all USPTO examiners on August 24, 2009 (Memo 1 hereinafter)4 and July
27, 2010 (Memo 2 hereinafter).5 Memo 1 was directed to examination of all
claims including method claims. Memo 2 provided factors to consider in
determining subject matter eligibility of method claims in view of the
abstract idea exception and superseded the guidance of Memo 1 on such
determinations.6 The guidance of Memo 1 and Memo 2 was incorporated in
Revision 9 of the Eighth Edition of The Manual of Patent Examining
Procedure (MPEP) issued in August 2012. (See MPEP § 2106; 8th Ed.,
Rev. 9).

4 Memorandum from Andrew H. Hirshfeld, Acting Deputy Comm’r for
Patent Examination Policy, U.S. Patent and Trademark Office (to the
Technology Center Directors), New Interim Patent Subject Matter Eligibility
Examination Instructions (August 24, 2009) available at
http://www.uspto.gov/web/offices/pac/dapp/opla/2009-08-25_interim_101_
instructions.pdf.
5 Memorandum from Robert W. Bahr, Acting Assoc. Comm’r for Patent
Examination Policy, U.S. Patent and Trademark Office (to the Patent
Examining Corps), Interim Guidance for Determining Subject Matter
Eligibility for Process Claims in View of Bilski v. Kappos (July 27, 2010)
available at http://www.uspto.gov/patents/law/exam/bilski_guidance_
27jul2010.pdf (including Interim Guidance for Determining Subject Matter
Eligibility for Process Claims in View of Bilski v. Kappos, 75 Fed. Reg.
43,922 (July 27, 2010)(notice)).
6 The Examiner rejected the claims currently before us on appeal under
§ 101 on December 29, 2008, before either guidance memo was issued.
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Examiners are instructed to use a two-step analysis, discussed infra, to
evaluate these subject matter eligibility criteria. “There are two criteria for
determining subject matter eligibility and both must be satisfied. The
claimed invention (1) must be directed to one of the four statutory
categories, and (2) must not be wholly directed to subject matter
encompassing a judicially recognized exception . . . .” (MPEP § 2106; 8th
Ed., Rev. 9).
(Preliminary Step) However, as a preliminary step prior to focusing
on any specific statutory requirements, examiners are also instructed to
begin examination by determining what, precisely, the applicant has
invented and is seeking to patent, and how the claims relate to and define
that invention. (MPEP § 2103 I; 8th Ed., Rev. 9). Examiners must give
claims their broadest reasonable interpretation in light of the supporting
disclosure. (MPEP § 2111; 8th Ed., Rev. 9).
[W]hen evaluating the scope of a claim, every limitation in the
claim must be considered. [An examiner] may not dissect a
claimed invention into discrete elements and then evaluate the
elements in isolation. Instead, the claim as a whole must be
considered. See, e.g., Diamond v. Diehr, 450 U.S. 175, 188-89,
209 USPQ 1, 9 (1981) (“In determining the eligibility of
respondents’ claimed process for patent protection under § 101,
their claims must be considered as a whole. It is inappropriate
to dissect the claims into old and new elements and then to
ignore the presence of the old elements in the analysis. This is
particularly true in a process claim because a new combination
of steps in a process may be patentable even though all the
constituents of the combination were well known and in
common use before the combination was made.”).
(MPEP § 2103 I. C.; 8th Ed., Rev. 9).
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(Step One – Eligible Subject Matter Categories) Once the examiner
has determined what the applicant has invented and is seeking to patent, the
examiner is instructed to determine if the claim is directed to one of the four
patent-eligible subject matter categories: process, machine, manufacture, or
composition of matter. If the subject matter of the claim is not to one of the
four patent-eligible subject matter categories, then it should be rejected
under 35 U.S.C. § 101, for at least this reason. (See MPEP § 2106 I; 8th Ed.,
Rev. 9).
(Step Two – Subject Matter Eligibility – Exceptions) If the claim is
within one of the four subject matter categories, the examiner is instructed to
determine if the claim wholly embraces a judicially recognized exception,
which includes laws of nature, physical phenomena, and abstract ideas, or
alternatively, if it is a particular practical application of a judicial exception.
(See MPEP § 2106 II; 8th Ed., Rev. 9).
In addition to the terms laws of nature, physical
phenomena, and abstract ideas, judicially recognized exceptions
have been described using various other terms, including
natural phenomena, scientific principles, systems that depend
on human intelligence alone, disembodied concepts, mental
processes and disembodied mathematical algorithms and
formulas, for example. The exceptions reflect the courts’ view
that the basic tools of scientific and technological work are not
patentable.
The claimed subject matter must not be wholly directed
to a judicially recognized exception. If it is, the claim is not
eligible for patent protection and should be rejected under
35 U.S.C. 101. However, a claim that is limited to a particular
practical application of a judicially recognized exception is
eligible for patent protection. A “practical application” relates
to how a judicially recognized exception is applied in a real
world product or a process, and not merely to the result
achieved by the invention. When subject matter has been
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reduced to a particular practical application having a real world
use, the claimed practical application is evidence that the
subject matter is not abstract (e.g., not purely mental) and does
not encompass substantially all uses (preemption) of a law of
nature or a physical phenomenon. See, e.g., Ultramercial v.
Hulu, 657 F.3d 1323, 1329, 100 USPQ2d 1140, 1145 (Fed. Cir.
2011)(stating that the patent “does not claim a mathematical
algorithm, a series of purely mental steps, or any similarly
abstract concept. It claims a particular method . . . a practical
application of the general concept.”).
(MPEP § 2106 II; 8th Ed., Rev. 9).
In Step Two, if the claim is a process (method) claim, the guidance of
MPEP § 2106 II B “presents factors that are to be considered when
evaluating patent-eligibility of method claims.”7
The factors include inquiries from the machine-or-
transformation test, which remains a useful investigative tool,
and inquiries gleaned from Supreme Court precedent. See In re
Bilski, 545 F.3d 943, 954 (Fed. Cir. 2009) (stating that “[a]
claimed process is surely patent-eligible under § 101 if: (1) it is
tied to a particular machine or apparatus, or (2) it transforms a
particular article into a different state or thing.”); and Bilski,
130 S. Ct. at 3227 (stating, “This Court’s precedents establish
that the machine-or-transformation test is a useful and

7 MPEP § 2106 II B goes on to state:
While the Supreme Court in Bilski did not set forth detailed
guidance, there are many factors to be considered when
determining whether there is sufficient evidence to support a
determination that a method claim is directed to an abstract
idea. The following factors are intended to be useful examples
and are not intended to be exclusive or limiting. It is
recognized that new factors may be developed, particularly for
emerging technologies. It is anticipated that the factors will be
modified and changed to take into account developments in
precedential case law and to accommodate prosecution issues
that may arise in implementing this new practice.
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important clue, an investigative tool, for determining whether
some claimed inventions are processes under § 101. The
machine-or-transformation test is not the sole test for deciding
whether an invention is a patent-eligible ‘process.’”).
(MPEP § 2106 II B; 8th Ed., Rev. 9).8
In Step Two, MPEP §2106 II B instructs an examiner to “determine
whether the claimed invention, viewed as a whole, is disqualified as being a
claim to an abstract idea.”
Relevant factors—both those in favor of patent-eligibility and
those against such a finding—should be weighed in making the
determination. Factors that weigh in favor of patent-eligibility
satisfy the criteria of the machine-or-transformation test or
provide evidence that the abstract idea has been practically
applied. Factors that weigh against patent-eligibility neither
satisfy the criteria of the machine-or-transformation test nor
provide evidence that the abstract idea has been practically
applied. Each case will present different factors, and it is likely
that only some of the factors will be present in each application.
It would be improper to make a conclusion based on one factor
while ignoring other factors.
(MPEP §2106 II B; 8th Ed., Rev. 9).9

8 When determining patent eligibility of a method claim, the machine-or-
transformation factors should be weighed even where “technology without
anchors in physical structures and mechanical steps” may “defy easy
classification under the machine-or-transformation categories.”
Ultramercial, LLC v. Hulu, LLC, 657 F.3d 1323, 1327 (Fed. Cir. 2011).
9 MPEP §2106 II B also states that:
With respect to the factors listed below, a “field-of-use”
limitation does not impose actual boundaries on the scope of
the claimed invention. A field-of-use limitation merely
indicates that the method is for use in a particular environment,
such as “for use with a machine” or “for transforming an
article”, which would not require that the machine implement
the method or that the steps of the method cause the article to
transform. A field-of-use limitation does not impose a
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The factors that an examiner is instructed to consider in an abstract
idea determination of a method claim include the following (see MPEP
§ 2106 II.B.1.):
(a) Whether the method involves or is executed by a particular
machine or apparatus.
(i) The particularity or generality of the elements of the
machine or apparatus.
(ii) Whether the machine or apparatus implements the steps of
the method.
(iii) Whether the machine or apparatus involvement is
extrasolution activity or a field-of-use, i.e., the extent to which
(or how) the machine or apparatus imposes meaningful limits
on the execution of the claimed method steps.
(b) Whether performance of the claimed method results in or
otherwise involves a transformation of a particular article.
(i) The particularity or generality of the transformation.
(ii) The degree to which the recited article is particular.
(iii) The nature of the transformation in terms of the type or
extent of change in state or thing.
(iv) The nature of the article transformed, i.e., whether it is an
object or substance.
(v) Whether the transformation involvement is extrasolution
activity or a field-of-use, i.e., the extent to which (or how) the
transformation imposes meaningful limits on the execution of
the claimed method steps.

meaningful limit on the claimed invention. Insignificant “extra-
solution” activity means activity that is not central to the
purpose of the method invented by the applicant. For example,
gathering data to use in the method when all applications of the
method would require some form of data gathering would not
impose a meaningful limit on the claim.
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(c) Whether performance of the claimed method involves an
application of a law of nature, even in the absence of a particular
machine, apparatus, or transformation.
(i) The particularity or generality of the application.
(ii) Whether the claimed method recites an application of a law
of nature solely involving subjective determinations; e.g., ways
to think about the law of nature.
(iii) Whether its involvement is extrasolution activity or a field-
of-use, i.e., the extent to which (or how) the application
imposes meaningful limits on the execution of the claimed
method steps.
(d) Whether a general concept (which could also be recognized in
such terms as a principle, theory, plan or scheme) is involved in
executing the steps of the method. 10
(i) The extent to which use of the concept, as expressed in the
method, would preempt its use in other fields.
(ii) The extent to which the claim is so abstract and sweeping as
to cover both known and unknown uses of the concept, and be
performed through any existing or future-devised machinery, or
even without any apparatus.

10 Examples of general concepts include, but are not limited to:
• Basic economic practices or theories (e.g., hedging, insurance,
financial transactions, marketing);
• Basic legal theories (e.g., contracts, dispute resolution, rules
of law);
• Mathematical concepts (e.g., algorithms, spatial relationships,
geometry);
• Mental activity (e.g., forming a judgment, observation,
evaluation, or opinion);
• Interpersonal interactions or relationships (e.g., conversing,
dating);
• Teaching concepts (e.g., memorization, repetition);
• Human behavior (e.g., exercising, wearing clothing, following
rules or instructions);
• Instructing “how business should be conducted.”
See MPEP § 2106 II.B.1(d).
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(iii) The extent to which the claim would effectively cover all
possible solutions to a particular problem; i.e., that the claim is
a statement of the problem versus a description of a particular
solution to the problem.
(iv) Whether the concept is disembodied or whether it is
instantiated; i.e., implemented, in some tangible way.
(v) The mechanism(s) by which the steps are implemented; e.g.,
whether the performance of the process is observable and
verifiable rather than subjective or imperceptible.
Lastly, in Step Two the examiner is instructed to weigh all of these
factors to make a proper determination as to whether the claim wholly
embraces a judicially recognized exception:
Each of the factors relevant to the particular patent
application should be weighed to determine whether the method
is claiming an abstract idea by covering a general concept, or
combination of concepts, or whether the method is limited to a
particular practical application of the concept. The presence or
absence of a single factor will not be determinative as the
relevant factors need to be considered and weighed to make a
proper determination as to whether the claim as a whole is
drawn to an abstract idea such that the claim would effectively
grant a monopoly over an abstract idea and be ineligible for
patent protection.
(MPEP § 2106 II.B.2; 8th Ed., Rev. 9).

C. New Ground of Rejection Analysis
Method Claims 1, 3-11, and 21
We reject method claims 1, 3-11, and 21 under 35 U.S.C. § 101 as
being directed to non-statutory subject matter.
(Preliminary Step) Applying the Office’s multi-step § 101 analysis,
we first determine the broadest reasonable interpretation of claim 1 on
appeal. See In re Fout, 675 F.2d 297, 300 (CCPA 1982) (“Claims must
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always be read in light of the specification. Here, the specification makes
plain what the appellants did and did not invent ....”); Philips v. AWH Corp.
415 F.3d 1303, 1313 (Fed. Cir. 2005) (“Importantly, the person of ordinary
skill in the art is deemed to read the claim term not only in the context of the
particular claim in which the disputed term appears, but in the context of the
entire patent, including the specification.”).
We conclude that claim 1 as a whole is directed to a sequence of steps
performed within a general purpose computer system. Appellants indicate
that claim 1 is illustrated by Figure 3 (see FF 8) and Figure 7 (see FF 7).
(App. Br. 3). Particularly, Appellants point to items 303, 309, and 307(1) of
Figure 3 to illustrate the functions of determining a largest order square
matrix and executing an in-place transposition. Although Appellants do not
point to Figures 11 and 12 in the discussion of claim 1 at page 3 of the
Appeal Brief, Appellants’ claim 1 explicitly recites a “computer” (claim 1,
line 3) and Appellants state that “Figure 12 illustrates a typical hardware
configuration of an information handling/ computer system in accordance
with the invention.” (Spec. 21:11-12). An artisan would recognize that the
system of Appellants’ Figure 12 is a typical general purpose computer
system in the form of a “hardware/software environment.” (Spec. 21:23).
Further, Appellants state that “Figure 11 shows an exemplary software
program block diagram 1100 that might be used to implement the method of
the present invention. It is noted that Figure 3 and Figure 11 are related.”
(Spec. 20:10-12).
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We also conclude that the steps of claim 1 recite mathematical
constructs in the form of “a rectangular matrix A” and “one or more square
submatrices Aij.” In mathematics, a “matrix” is:
11. Math. a rectangular array of numbers, algebraic symbols, or
mathematical functions, esp. when such arrays are added or
multiplied according to certain rules.
The Random House Dictionary of the English Language, © Random House,
Inc. 1987, p.1186. Similarly, the IEEE description of a “matrix” includes:
(2) (mathematics). (A) A two-dimensional rectangular array of
quantities. Matrices are manipulated in accordance with the rules of
matrix algebra.
IEEE Standard Dictionary of Electrical and Electronic Terms, 4th Ed.,
Newly Revised and Expanded, © The Institute of Electrical and Electronics
Engineers, Inc. 1988, p. 571. These definitions of “matrix” are consistent
with Appellants’ use of the term throughout the entire patent application
before us. (See FF 1-2 and FF 4).
We also conclude that the steps of claim 1 recite a mathematical
operation in the form of “transposing” a matrix. In mathematics, to
“transpose” a matrix is “to interchange the rows and columns of a matrix,”
and the “transpose” of a matrix is “the matrix derived from a given matrix
by interchanging the rows and columns; the transpose of M is often denoted
as MT.” HarperCollins Dictionary of Mathematics, © Borowski and
Borwein, 1991, p. 598. These definitions of “transpose” are consistent with
Appellants’ use of the term. (See FF 7).
In summary, we conclude that Appellants’ claim 1 applies a
mathematical operation to transpose a rectangular matrix by subdividing the
rectangular matrix into one or more square submatrices and performing
transposition of each of said square submatrices. We conclude that the
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specific facts before us establish that the broadest reasonable interpretation
of the claim as a whole is that the transpose is performed within a general
purpose computer system.
Having determined what applicant has invented and is seeking to
patent, we now review whether the method claims recite patent-eligible
subject matter by (1) determining at Step One below whether the method
claims are within one of the four patent-eligible subject matter categories,
and if so, then, (2) determining at Step Two below whether the method
claims are directed nonetheless to an abstract idea.
(Step One) Reviewing claim 1 as a whole, we conclude that the claim
is directed to a process (method) and, as such, is within one of the four
patent-eligible subject matter categories. Having reached this conclusion,
we now determine if claim 1 wholly embraces a judicially recognized
exception.
(Step Two) We determine whether the method claims are directed
nonetheless to an abstract idea by reviewing factors that are to be considered
when evaluating patent-eligibility of method claims. These § 101 factors
include inquiries from the machine-or-transformation test, which remains a
useful investigative tool, and inquiries gleaned from Supreme Court
precedent. We begin our analysis in Step Two by reviewing factors directed
to determining if the process (method) claim passes muster under either of
the two prongs of the machine-or-transformation test.
(Step Two – Machine Factor) Contrary to arguments by Appellants, it
is readily apparent that claim 1 does not require the method to be executed
(performed) by a particular machine or apparatus. Beyond generic structure
in the form of “a computer,” “a processor,” and “a memory,” the claim
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recites no particular machine for performing the method steps. Neither the
recited computer, nor the recited processor, nor the recited memory is a
particular machine. See Gottschalk v. Benson, 409 U.S. 63, 64 (1972)
(Method for converting binary-coded-decimal (BCD) numerals into pure
binary numerals tied to a general-purpose digital computer of any type, not a
particular machine.); Ex parte Gutta, 93 USPQ2d 1025, 1032-33, 1036
(BPAI 2009) (precedential) (“[T]he combined processor and memory are
tantamount to a general-purpose computer.”); Ex parte Langemyr, 89
USPQ2d 1988, 1997-98 (BPAI 2008) (informative) (Recitation of an
algorithm performed on a general-purpose computer does not tie the method
to a particular machine.). Moreover, Appellants acknowledge that the scope
of the claimed invention is directed to various embodiments that encompass
anything from custom-designed computers to instructions downloaded
through a network interface (FF 9-11), rather than being directed to a
particular machine or apparatus.
We conclude that the claim does not involve and is not executed by a
particular machine or apparatus, and this machine factor weighs against
patent eligibility.
(Step Two – Transformation Factor) As discussed above, we conclude
that claim 1 generates a “transpose A'” from a “rectangular matrix A.” We
consider specifically whether performance of the claimed method results in
or otherwise involves a transformation of a particular article. We conclude
that the mathematical operation is not practically applied to a physical entity
(article) in the claim. As discussed above, the claimed rectangular matrix A
is a first mathematical construct from which the method generates a second
mathematical construct.
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We also conclude that: (1) the matrix being transposed is not an
object (e.g., physical entity); (2) the matrix being transposed is not particular
and does not represent anything particular; and (3) the method does not
involve a change in state (e.g., objectively different function or use). We
conclude that Appellants’ claim 1 does not transform a particular article and
this transformation factor weighs against patent eligibility.
(Step Two – Law of Nature Factor) We also consider additional
factors to determine whether claim 1 is patent-ineligible (i.e., is an abstract
idea). We consider whether performance of the claimed method involves an
application of a law of nature. We conclude that claim 1 does not involve an
application of a law of nature, so we conclude that this factor is not relevant
to our analysis of this claim.
(Step Two – General Concept Factor) We now consider whether a
general concept is involved in executing the steps of the method. We repeat
that claim 1 applies a mathematical operation to transpose a rectangular
matrix by subdividing the rectangular matrix into one or more square
submatrices and performing transposition of each of said square
submatrices. Furthermore, Appellants acknowledge that matrix
transposition is an important sub-operation in many matrix algorithms (FF
4), having applications in the fields of engineering, scientific computing,
games, and graphics rendering (FF 2) (see also FF 11-12). Yet, claim 1 does
not recite any practical application or use of the recited method of matrix
transposition.
We conclude that even though the transpose is recited as being
performed within a general purpose computer system: (1) the concept as
expressed in the method would preempt its use in all fields; and (2) the claim
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is so abstract and sweeping so as to cover both known and unknown uses of
the concept. We conclude that, as to Appellants’ claim 1, this concept factor
weighs against patent eligibility.
(Step Two – Determine Subject Matter Eligibility) We have reviewed
method claim § 101 factors to determine if they weigh in favor of patent-
eligibility by satisfying the criteria of the machine-or-transformation test or
providing evidence that an abstract idea has been practically applied; or if
these factors instead weigh against patent-eligibility because they neither
satisfy the criteria of the machine-or-transformation test nor provide
evidence that an abstract idea has been practically applied. We have found
that even though the claimed method does not involve an application of a
law of nature, the claimed method is not tied to any particular machine or
apparatus, the claimed method does not transform any particular article, and
the claimed method does not recite any practical application, but is directed
to a general concept. We conclude that when these numerous method claim
§ 101 factors are considered collectively they weigh against eligibility.
We conclude that method claim 1 is not directed to patent eligible
subject matter.11 Claims 3-11 and 21 depend from claim 1 and do not add
subject matter to claim 1 that would change the analysis of subject matter
eligibility set forth supra.

11 We note that Appellants’ Appeal Brief presented numerous arguments that
the Examiner’s § 101 rejection (now withdrawn) was in error. We do not
attempt to address these arguments herein. Given that many of the
arguments were mere straw men arguing points the Examiner never made,
were inconsistent with Appellants’ own Specification, or were contradictory
to the very case law Appellants cited, we leave it to Appellants to carefully
select which of these now moot arguments they may wish to present again.
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“Computer” Claims 12-14; “Medium” Claims 15-18; and
“Apparatus (means plus function)” Claims 19-20
We reject claims 12-20 under 35 U.S.C. § 101 as being directed to
non-statutory subject matter.
Claims 12-20 are merely the transpose operation of method claim 1
written to cover alternative claim categories. We reach this conclusion in
principle part due to Appellants’ Summary of the Invention at pages 3-5 of
the Appeal Brief. As we stated supra when construing Appellants’ method
claim 1:
Appellants indicate that claim 1 is illustrated by Figure 3 (see
FF 8) and Figure 7 (see FF 7). (App. Br. 3). Particularly,
Appellants point to items 303, 309, and 307(1) of Figure 3 to
illustrate the functions of determining a largest order square
matrix and executing an in-place transposition. Although
Appellants do not point to Figures 11 and 12 in the discussion
of claim 1 at page 3 of the Appeal Brief, Appellants’ claim 1
explicitly recites a “computer” (claim 1, line 3) and Appellants
state that “Figure 12 illustrates a typical hardware configuration
of an information handling/ computer system in accordance
with the invention.” (Spec. 21:11-12). An artisan would
recognize that the system of Appellants’ Figure 12 is a typical
general purpose computer system in the form of a
“hardware/software environment.” (Spec. 21:23). Further,
Appellants state that “Figure 11 shows an exemplary software
program block diagram 1100 that might be used to implement
the method of the present invention. It is noted that Figure 3
and Figure 11 are related.” (Spec. 20:10-12).
In discussing claims 12, 15, and 19, at pages 3-5 of the Appeal Brief,
Appellants explicitly reference the same items in Figure 3, 11, and 12, which
they have referenced when describing claim 1 or its limitations. “Regardless
of what statutory category (‘process, machine, manufacture, or composition
of matter,’ 35 U.S.C. § 101) a claim’s language is crafted to literally invoke,
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we look to the underlying invention for patent-eligibility purposes.”
CyberSource Corp. v. Retail Decisions, Inc., 654 F.3d 1366, 1374
(Fed. Cir. 2011). Given that we find no meaningful differentiation in
Appellants’ descriptions of claims 1, 12, 15, and 19, we conclude that for
patent-eligibility purposes, all of these claims are directed to the same
underlying invention. Due to their “broad” and “functionally-defined”
nature, treating claims 12-20 as apparatus or article claims would exalt
form over substance since the claims are really to the method itself. See
CyberSource 654 F.3d at 1374 (citing In re Abele, 684 F.2d 902, 909 (CCPA
1982)). We therefore reject claims 12-20 on the same basis as claim 1.
We further note that should Appellants wish to contest this rejection,
the burden is on Appellants to demonstrate that these claims are truly drawn
to a specific apparatus or article distinct from other apparatuses capable of
performing the identical functions. Cf. CyberSource 654 F.3d at 1374 (citing
In re Abele, 684 F.2d 902, 909 (CCPA 1982)).

D. 37 C.F.R. § 41.50(b)
This decision contains a new ground of rejection pursuant to 37
C.F.R. § 41.50(b). 37 C.F.R. § 41.50(b) provides “[a] new ground of
rejection pursuant to this paragraph shall not be considered final for judicial
review.”
37 C.F.R. § 41.50(b) also provides that Appellant, WITHIN TWO
MONTHS FROM THE DATE OF THE DECISION, must exercise one of
the following two options with respect to the new grounds of rejection to
avoid termination of the appeal as to the rejected claims:
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(1) Reopen prosecution. Submit an appropriate
amendment of the claims so rejected or new evidence relating
to the claims so rejected, or both, and have the matter
reconsidered by the examiner, in which event the proceeding
will be remanded to the examiner. . . .
(2) Request rehearing. Request that the proceeding be
reheard under § 41.52 by the Board upon the same record. . . .

V. CONCLUSIONS
(1) Appellants have established that the Examiner erred in rejecting
claims 19 and 20 as being unpatentable under 35 U.S.C. § 102(e).
(2) Claims 1 and 3-21 are not patentable.

VI. DECISION
The Examiner’s rejection of claims 19 and 20 under 35 U.S.C. § 102
is reversed.
We enter a new ground of rejection of claims 1 and 3-21 under
35 U.S.C. § 101.

No time period for taking any subsequent action in connection with
this appeal may be extended under 37 C.F.R. § 1.136(a)(1)(iv).

REVERSED
37 C.F.R. § 41.50(b)

msc