40166
Oracle Database 10g
SQL Model Clause
Andy Witkowski, Architect
Thomas Kyte, VP
Oracle Corporation
What’s now in SQL for Modeling


Aggregation Enhancements
–
Cube, Rollup, Grouping Sets
–
New aggregates: Inverse Distribution,
FIRST/LAST,etc
Analytic Functions
–
Window Functions: Rank, Moving, Cumulative
–
Statistical Functions: Correlation, Linear
Regression,etc

Old tools still have more modeling power than
SQL
SQL
Model enhances SQL with modeling power
–
Spreadsheets, MOLAP engines
Case Study – Modeling with
Excel
 Excel fits well at the personal scale
–
–
–

UI and Formatting
Calculations (build-in functions, formulas)
What-If analysis
Excel fits poorly at corporate scale for
modeling
Cryptic row-column addressing
– No metadata, No standards, No mathematical
model
– 100s of spreadsheets and consolidation by hand
– Does not scale (1000’s formulas, TB of data)
Replace
Excel Modeling
with SQL
Modeling
– Perpetual
data exchange:
databases->Excel
–
Modeling with SQL Model
 Language: Spreadsheet-like calculations in SQL
–
–
–
–
–
–
–
Inter-row calculation. Treats relations as an N-Dim array
Symbolic references to cells and their ranges
Multiple Formulas over N-Dim arrays
Automatic Formula Ordering
Recursive Model Solving
Model is a relation & can be processed further in SQL
Multiple arrays with different dimensionality in one query
 Performance
–
–
–
Parallel Processing in partitioning & formulas
Multiple-self joins with one data access structure
Multiple UNIONs with one data access structure
 Why Better?
–
–
–
Automatic Consolidation (models as views – combine using
SQL)
Self Adjusting (as database changes no need to re-define)
One version of truth (calc directly over data base, no exchange)
SQL Model
Concepts
prod
time
vcr
dvd
2001
2001
Define Relation as Array
s
9
0
Relation
Array
SELECT prod, time, s FROM sales
1
2
3
4
1999
5
6
7
8
2000
9
0
1
2
2001
dvd
tv
pc
vcr
prod
DIMENSION BY (prod, time) MEASURES (s)
prod
time
vcr
dvd
2001
2001
Define Business Rules
s
9
0
Relation
Array
SELECT prod, time, s FROM sales
1
2
3
4
1999
5
6
7
8
2000
9
0
1
2
2001
dvd
tv
pc
vcr
DIMENSION BY (prod, time) MEASURES (s)
RULES UPSERT
(
Sales in 2000 2x of previous year s[ANY, 2000] = s[CV(prod), CV(time) - 1] * 2,
Predict vcr sales in 2002
s[vcr, 2002] = s[vcr, 2001] + s[vcr, 2000],
Predict dvd sales in 2002
s[dvd, 2002] =AVG(s) [CV(prod), time<2001]
)
prod
prod
time
vcr
dvd
2001
2001
Evaluate Formulas – 1st
s
9
0
Relation
Array
SELECT prod, time, s FROM sales
1
2
3
4
1999
2
4
6
8
2000
9
0
1
2
2001
dvd
tv
pc
vcr
DIMENSION BY (prod, time) MEASURES (s)
RULES UPSERT
(
Sales in 2000 2x of previous year s[ANY, 2000] = s[CV(prod), CV(time) - 1] * 2,
Predict vcr sales in 2002
s[vcr, 2002] = s[vcr, 2001] + s[vcr, 2000],
Predict dvd sales in 2002
s[dvd, 2002] = AVG(s) [CV(prod), time<2001]
)
prod
time
vcr
dvd
2001
2001
Evaluate Formulas – 2nd
s
9
0
Relation
SELECT prod, time, s FROM sales
1
2
3
4
1999
2
4
6
8
2000
9
0
1
2
2001
DIMENSION BY (prod, time) MEASURES (s)
2002
11
RULES UPSERT
(
Sales in 2000 2x of previous year s[ANY, 2000] = s[CV(prod), CV(time) - 1] * 2,
Predict vcr sales in 2002
s[vcr, 2002] = s[vcr, 2001] + s[vcr, 2000],
Predict dvd sales in 2002
s[dvd, 2002] = AVG(s) [CV(prod), time<2001]
)
vcr
dvd
tv
pc
prod
time
vcr
dvd
2001
2001
Evaluate Formulas – 3rd
s
9
0
Relation
SELECT prod, time, s FROM sales
1
2
3
4
1999
2
4
6
8
2000
9
0
1
2
2001
DIMENSION BY (prod, time) MEASURES (s)
2002
11 3
RULES UPSERT
(
Sales in 2000 2x of previous year s[ANY, 2000] = s[CV(prod), CV(time) - 1] * 2,
Predict vcr sales in 2002
s[vcr, 2002] = s[vcr, 2001] + s[vcr, 2000],
Predict dvd sales in 2002
s[dvd, 2002] = AVG(s) [CV(prod), time<2001]
)
vcr
dvd
tv
pc
prod
time
vcr
dvd
2001
2001
Return as Relation
s
9
0
Relation
SELECT prod, time, s FROM sales
1
2
3
4
1999
2
4
6
8
2000
9
0
1
2
2001
2002
11 3
vcr
dvd
DIMENSION BY (prod, time) MEASURES (s)
tv
pc
Self-join.
join + UNION
join + UNION
RULES UPSERT
(
s[ANY, 2000] = s[CV(prod), CV(time) - 1] * 2,
s[vcr, 2002] = s[vcr, 2001] + s[vcr, 2000],
s[dvd, 2002] = AVG(s) [CV(prod), time<2001]
)
Relation again
vcr
dvd
2001
2001
9
0
vcr
dvd
2002
2002
11
3
Rows updated & inserted by the Model clause
Model Clause – Components
Model clause
Partitioning
SELECT region, prod, time, s
Dims of array
FROM sales
GROUP BY region, prod, time
MODEL PARTITION BY (region) DIMENSION BY (prod, time)
MEASURES (sum(sales) s, count(sales) c)
RULES ITERATE ( ) UNTIL ( )
Model options
(
s[ANY, 2000] = s[CV(prod), CV(time) - 1],
s[dvd, 2003] = s[dvd, 2002] + s[dvd, 2001],
Formulas
UPSERT s[vcr, 2003] = AVG(s) [vcr, time < 2001]
)
ORDER BY region, product, time, s;
Formula Options
Key Concepts (1)
 New SQL Model Clause:
–
–
–
Data as N-dim arrays with DIMENSIONS & MEASURES
Data can be PARTITION-ed - creates an array per partition
Formulas defined over the arrays express a (business) model
 Formulas within a Model:
–
–
–
–
–
Use symbolic addressing using familiar array notation
Can be ordered automatically based on dependency between
cells
Can be recursive with a convergence condition – recursive
models
Can UPDATE or UPSERT cells
Support most SQL functions including aggregates
Key Concepts (2)
 Result of a SQL Model is a relation
–
–
Can participate further in processing via joins, etc.
Can define views containing Model computations
 SQL Model is the last query clause
–
–
Executed after joins, aggregation, window
functions
Before ORDER BY
 Main Model and Reference Models
–
Can relate models of different dimensionality
Formula Fundamentals (1)
 Formulas: SQL expressions over cells with aggs, functions,
etc.
 Formula has a left and right side and represents assignment
–
–
s[‘vcr’, 2002] = s[‘vcr’, 2001] + s[‘vcr’, 2000]
s[‘vcr’, 2002] = AVG(s)[‘vcr’, t<2002]
– single ref
– multi ref on right
 Left side can qualify multiple cells
–
–
–
s[p IN (‘vcr’,’dvd’), t<2002] = 1000
– multi ref on left
s[ANY, t=2002] = 2 * s[CV(p), CV(t)-1]
– left-right
correlation
s[p IN (SELECT prod FROM prod_tb), 2000] = 1000
 Formula can operate in update or upsert mode
–
–
update s[‘vcr’, 2002] = s[‘vcr’, 2001] + s[‘vcr’, 2000]
upsert s[‘vcr’, 2002] = s[‘vcr’, 2001] + s[‘vcr’, 2000]
Formula Fundamentals (2)
 Function CV(dimension) propagates values from
left to the right side. In example, products in 2002
are sum of two previous years.
s[ANY, 2002] = s[CV(p), CV(t)-1] +s[CV(p), CV(t) – 2]
Formula Fundamentals (2)
 Function CV(dimension) propagates values from
left to the right side. In example, products in 2002
are sum of two previous years.
s[ANY, 2002] = s[CV(p), CV(t) -1] + s[CV(p), CV(t) – 2]
 Formula result can depend on processing order.
Can specify order in each formula. E.g., shift by
time:
s[‘vcr’, ANY] ORDER BY t = s[‘vcr’, CV(t) - 1]
Formula Fundamentals (2)
 Function CV(dimension) propagates values from
left to the right side. In example, products in 2002
are sum of two previous years.
s[ANY, 2002] = s[CV(p), CV(t) -1] + s[CV(p), CV(t) – 2]
 Formula result can depend on processing order.
Can specify order in each formula. E.g., shift by
time:
s[‘vcr’, ANY] ORDER BY t = s[‘vcr’, CV(t) - 1]
vcr
vcr
vcr
vcr
vcr
2001
2002
2003
2004
2005
300.00
0
350.00 300.00
400.00
450.00
500.00
ORDER BY t
Formula Fundamentals (2)
 Function CV(dimension) propagates values from
left to the right side. E.g, products in 2002 are
sum of two previous years
s[ANY, 2002] = s[CV(p), CV(t) -1] + s[CV(p), CV(t) – 2]
 Formula result can depend on processing order.
Can specify order in each formula. E.g., shift by
time:
s[‘vcr’, ANY] ORDER BY t = s[‘vcr’, CV(t) - 1]
vcr
vcr
vcr
vcr
vcr
2001
2002
2003
2004
2005
300.00
0
350.00 300.00
400.00 350.00
450.00
500.00
ORDER BY t
Formula Fundamentals (2)
 Function CV(dimension) propagates values from
left to the right side. E.g, products in 2002 are
sum of two previous years
s[ANY, 2002] = s[CV(p), CV(t) -1] + s[CV(p), CV(t) – 2]
 Formula result can depend on processing order.
Can specify order in each formula. E.g., shift by
time:
s[‘vcr’, ANY] ORDER BY t = s[‘vcr’, CV(t) - 1]
vcr
vcr
vcr
vcr
vcr
2001
2002
2003
2004
2005
300.00
350.00
400.00
450.00
500.00
ORDER BY t
0
300.00
350.00
400.00
450.00
Model Options – Fundamentals
global options
MODEL
[ UNIQUE DIMENSIONS | UNIQUE SINGLE REFERENCE ]
[ IGNORE NAV | KEEP NAV ]
PARTITION BY (r) DIMENSION BY (p, t) MEASURES (s)
RULES [ UPDATE | UPSERT ]
rule
[ AUTOMATIC ORDER | SEQUENTIAL ORDER ]
(
s[ANY, 2002] = 1.2 * s[CV(product), 2002],
s[‘dvd’, 2003] = s[‘dvd’, 2002] + s[‘dvd’, 2001],
s[‘vcr’, 2003] = AVG(s) [‘vcr’, t BETWEEN 1995 AND 2000],
s[‘video’, 2003] = s[‘dvd’, 2003], s[‘vcr’, 2003]
)
options
NAV Options: Handling Sparse
Data
West dvd 2001
300.00
West tv
West vcr
West vcr
2002
2001
2002
500.00
200.00
400.00
MODEL KEEP NAV PARTITION BY (r) DIMENSION BY (p, t) MEASURES (s)
RULES UPSERT
(
s[‘dvd’, 2003] = s[‘dvd’, 2002] + s[‘dvd’, 2001]
s[‘tv’ ,2003] = sum(s) [‘tv’, t BETWEEN 2001 AND 2002]
)
keep nav
2001 ?
West
West
West
West
West
West
dvd
tv
dvd
tv
vcr
vcr
2001
2002
2003
2003
2001
2002
300.00
500.00
500.00
200.00
400.00
NAV Options: Handling Sparse
Data
West dvd 2001
300.00
West tv
West vcr
West vcr
2002
2001
2002
500.00
200.00
400.00
MODEL INGNORE NAV PARTITION BY (r) DIMENSION BY (p, t) MEASURES (s)
RULES UPSERT
(
s[‘dvd’, 2003] = s[‘dvd’, 2002] + s[‘dvd’, 2001]
s[‘tv’ ,2003] = sum(s) [‘tv’, t BETWEEN 2001 AND 2002]
)
ignore nav
assume 0
West
West
West
West
West
West
dvd
tv
dvd
tv
vcr
vcr
2001
2002
2003
2003
2001
2002
300.00
500.00
300.00
500.00
200.00
400.00
NAV Options: Handling Sparse
Data
West dvd 2001
300.00
West tv
West vcr
West vcr
2002
2001
2002
500.00
200.00
400.00
MODEL KEEP NAV PARTITION BY (r) DIMENSION BY (p, t) MEASURES (s)
RULES UPSERT
(
s[‘dvd’, 2003] = s[‘dvd’, 2002] + s[‘dvd’, 2001]
s[‘tv’ ,2003] = sum(s) [‘tv’, t BETWEEN 2001 AND 2002]
)
keep nav
ignore nav
assume 0
2001 ?
West
West
West
West
West
West
dvd
tv
dvd
tv
vcr
vcr
2001
2002
2003
2003
2001
2002
300.00
500.00
500.00
200.00
400.00
West
West
West
West
West
West
dvd
tv
dvd
tv
vcr
vcr
2001
2002
2003
2003
2001
2002
300.00
500.00
300.00
500.00
200.00
400.00
Automatic Formula Ordering
MODEL PARTITION BY (r) DIMENSION BY (p, t) MEASURES (s)
RULES UPDATE AUTOMATIC ORDER
(
F1: s[‘vcr’, 2003] = AVG(s) [‘vcr’, t BETWEEN 1995 AND 2002],
F2: s[‘dvd’, 2003] = s[‘dvd’, 2002] + s[‘dvd’, 2001],
F3: s[ANY, 2002] = s[CV(p), 2001] + s[CV(p), 1999]
)
Automatic Formula Ordering
MODEL PARTITION BY (r) DIMENSION BY (p, t) MEASURES (s)
RULES UPDATE AUTOMATIC ORDER
(
F1: s[‘vcr’, 2003] = AVG(s) [‘vcr’, t BETWEEN 1995 AND 2002],
F2: s[‘dvd’, 2003] = s[‘dvd’, 2002] + s[‘dvd’, 2001],
F3: s[ANY, 2002] = s[CV(p), 2001] + s[CV(p), 1999]
)
F1 depends on F3 and F2 depends on F3, thus F3 automatically first:
Automatic Formula Ordering
MODEL PARTITION BY (r) DIMENSION BY (p, t) MEASURES (s)
RULES UPDATE AUTOMATIC ORDER
(
F1: s[‘vcr’, 2003] = AVG(s) [‘vcr’, t BETWEEN 1995 AND 2002],
F2: s[‘dvd’, 2003] = s[‘dvd’, 2002] + s[‘dvd’, 2001],
F3: s[ANY, 2002] = s[CV(p), 2001] + s[CV(p), 1999]
)
F1 depends on F3 and F2 depends on F3, thus F3 automatically first:
RULES UPDATE AUTOMATIC ORDER
(
F3: s[ANY, 2002] = s[CV(p), 2001] + s[CV(p), 1999]
F2: s[‘dvd’, 2003] = s[‘dvd’, 2002] + s[‘dvd’, 2001],
F1: s[‘vcr’, 2003] = AVG(s) [‘vcr’, t BETWEEN 1995 AND 2000]
)
UPDATE, UPSERT & Partitions
Region
East
East
East
West
Product Time
dvd
2001
dvd
2002
vcr
2002
dvd
2001
s
100
150
100
200
MODEL PARTITION BY (r) DIMENSION BY (p,t) MEASURES (s)
RULES UPDATE IGNORE NAV
(
UPDATE s[‘vcr’, 2002] = s[‘vcr’, 2002] * 1.2,
UPSERT s[‘dvd’, 2003] = s[‘dvd’, 2002] + s[‘dvd’, 2001]
)
UPDATE, UPSERT & Partitions
Region
East
East
East
West
Product Time
dvd
2001
dvd
2002
vcr
2002
dvd
2001
s
100
150
100
200
MODEL PARTITION BY (r) DIMENSION BY (p,t) MEASURES (s)
RULES UPDATE IGNORE NAV
(
UPDATE s[‘vcr’, 2002] = s[‘vcr’, 2002] * 1.2,
UPSERT s[‘dvd’, 2003] = s[‘dvd’, 2002] + s[‘dvd’, 2001]
)
Region
East
East
East
Product Time
dvd
2001
dvd
2002
vcr
2002
West
dvd
2001
Old s
100
150
100
200
New s
100
100
120
200
updated
UPDATE, UPSERT & Partitions
Region
East
East
East
West
Product Time
dvd
2001
dvd
2002
vcr
2002
dvd
2001
s
100
150
100
200
MODEL PARTITION BY (r) DIMENSION BY (p,t) MEASURES (s)
RULES UPDATE IGNORE NAV
(
UPDATE s[‘vcr’, 2002] = s[‘vcr’, 2002] * 1.2,
UPSERT s[‘dvd’, 2003] = s[‘dvd’, 2002] + s[‘dvd’, 2001]
)
Region
East
East
East
East
West
West
Product Time
dvd
2001
dvd
2002
vcr
2002
dvd
2003
dvd
2001
dvd
2003
Old s
100
150
100
200
-
New s
100
100
120
250
200
200
updated
upserted
Different dimensions: Reference
Relate Models with different dimensions. Represent each as ndimensional array: one main, others as reference or lookup arrays.
Sales Table
c
p
USA
dvd
USA
tv
Poland vcr
France vcr
Conv table converts currency to $
t
2001
2001
2001
2001
s
300.00 $
500.00 $
200.00 zl
100.00 fr
c
USA
Poland
France
ratio
1
0.24
0.12
SELECT c, p, t, s FROM sales
MODEL
REFERENCE convert ON (SELECT c, ratio FROM conv) DBY (c) MEASURES(r)
MAIN DIMENSION BY (c,p,t) MEASURES (s)
RULES UPSERT
(
s[ANY, ANY, ANY] = r[CV(c)] * s[CV(c), CV(p), CV(t)]
)
Different dimensions: Reference
Sales Table
c
p
USA
dvd
USA
tv
Poland vcr
France vcr
t
2001
2001
2001
2001
Conv table converts currency to $
c
ratio
USA 1
Poland 0.24
France 0.12
s
300.00 $
500.00 $
200.00 zl
100.00 fr
SELECT c, p, t, s FROM sales
MODEL
REFERENCE convert ON (SELECT c, ratio FROM conv) DBY (c) MEASURES(r)
MAIN DIMENSION BY (c,p,t) MEASURES (s)
RULES UPSERT
(
s[ANY, ANY, ANY] = r[CV(c)] * s[CV(c), CV(p), CV(t)]
)
USA
dvd
USA
tv
Poland vcr
France vcr
2001
2001
2001
2001
300.00 $
500.00 $
48.00 $
12.00 $
Converted values
Recursive Model Solving

Model can contain cyclic (recursive) formulas.
- If cyclic formulas desired, use ITERATE option
- If ITERATE not present, cyclic formulas automatically
detected, and an error reported.
 Use ITERATE clause to specify # of iterations or
 Use UNTIL clause to specify convergence conditions
SELECT x, s FROM dual
MODEL DIMENSION BY (1 x) MEASURES (1024 s)
RULES ITERATE (8)
(
s[1] = s[1] / 2
)
Iteration
1
2
S value 1024 512
3
128
4
64
5
32
6
16
7
8
8
4
Recursive Model Solving

Model can contain cyclic (recursive) formulas.
- If cyclic formulas desired, use ITERATE option
- If ITERATE not present, cyclic formulas automatically
detected, and an error reported.
 Use ITERATE clause to specify # of iterations or
 Use UNTIL clause to specify convergence conditions
SELECT x, s FROM dual
MODEL DIMENSION BY (1 x) MEASURES (1024 s)
RULES ITERATE (8)
(
s[1] = s[1] / 2
)
Iteration
1
2
S value 1024 512
3
128
4
64
5
32
6
16
7
8
8
4
Recursive Model Solving

Model can contain cyclic (recursive) formulas.
- If cyclic formulas desired, use ITERATE option
- If ITERATE not present, cyclic formulas automatically
detected, and an error reported.
 Use ITERATE clause to specify # of iterations or
 Use UNTIL clause to specify convergence conditions
SELECT x, s FROM dual
MODEL DIMENSION BY (1 x) MEASURES (1024 s)
RULES ITERATE (8)
(
s[1] = s[1] / 2
)
Iteration
1
2
S value 1024 512
3
128
4
64
5
32
6
16
7
8
8
4
Recursive Model Solving

Model can contain cyclic (recursive) formulas.
- If cyclic formulas desired, use ITERATE option
- If ITERATE not present, cyclic formulas automatically
detected, and an error reported.
 Use ITERATE clause to specify # of iterations or
 Use UNTIL clause to specify convergence conditions
SELECT x, s FROM dual
MODEL DIMENSION BY (1 x) MEASURES (1024 s)
RULES ITERATE (8)
(
s[1] = s[1] / 2
)
Iteration
1
2
S value 1024 512
3
128
4
64
5
32
6
16
7
8
8
4
Recursive Model Solving with
Until
 Model can contain cyclic (recursive) formulas.
- If cyclic formulas desired, use ITERATE option
- If ITERATE not present, cyclic formulas automatically
detected, and an error reported.
 Use ITERATE clause to specify # of iterations or
 Use UNTIL clause to specify convergence conditions
SELECT x, s FROM dual
MODEL DIMENSION BY (1 x) MEASURES (1024 s)
RULES ITERATE (10000) UNTIL (PREVIOUS(s[1]) – s[1] <= 1)
(
s[1] = s[1] / 2
)
Iteration
1
2
S value 1024 512
3
256
previous(s[1]) - s[1] = 512
4
128
5
64
6
32
7
16
8
8
9
4
10
2
Recursive Model Solving with
Until
 Model can contain cyclic (recursive) formulas.
- If cyclic formulas desired, use ITERATE option
- If ITERATE not present, cyclic formulas automatically
detected, and an error reported.
 Use ITERATE clause to specify # of iterations or
 Use UNTIL clause to specify convergence conditions
SELECT x, s FROM dual
MODEL DIMENSION BY (1 x) MEASURES (1024 s)
RULES ITERATE (10000) UNTIL (PREVIOUS(s[1]) – s[1] <= 1)
(
s[1] = s[1] / 2
)
Iteration
1
2
S value 1024 512
3
256
previous(s[1]) - s[1] = 256
4
128
5
64
6
32
7
16
8
8
9
4
10
2
Recursive Model Solving with
Until
 Model can contain cyclic (recursive) formulas. They are
automatically detected, and error is reported. Unless cycles
are intentional which is indicated with ITERATE option

Use ITERATE clause to specify # of iterations or

Use UNTIL to specify convergence conditions. Stop if
true.
SELECT x, s FROM dual
MODEL DIMENSION BY (1 x) MEASURES (1024 s)
RULES ITERATE (10000) UNTIL (PREVIOUS(s[1]) – s[1] <= 1)
(
s[1] = s[1] / 2
)
Iteration
1
2
S value 1024 512
3
256
4
128
5
64
6
32
7
16
8
8
9
4
10
2
previous(s[1]) - s[1] = 4
SQL Model
Business Examples
Time Series Calculation (1)
Compute the ratio of current month sales of each product to
sales one year ago, one quarter ago and one month ago.
Assume: Sales cube with product sales per year, quarter, and month
& a time table mapping periods to prior year, quarter and month
time table: maps t to y_ago, q_ago, m_ago
Sales cube: prod sales per y, q, m
t
y_ago
q_ago
m_ago
t
product
sales
1999m01
1998m01
1998m10
1998m12
1999m01
vcr
100.00
1999m02
1998m02
1998m11
1999m01
1999m02
vcr
120.00
…
…
…
…
…
…
…
1999q01
1998q01
1998q04
NULL
1999q01
vcr
360.00
…
…
…
…
…
…
…
Time Series Calculation (2)
• Reference model with Time table acts like look-up table
• CV carries values from the left side to the right side
• Without Model, you need 3 outer joins and a regular join
SELECT product, sales, r_y_ago, r_q_ago, r_m_ago
FROM sales_cube
MODEL REFERENCE r ON (SELECT * from time)
DIMENSION BY (t) MEASURES (y_ago, q_ago, m_ago)
MAIN PARTITION BY (product) DIMENSION BY (t)
MEASURES (sales, 0 r_y_ago, 0 r_q_ago, 0 r_m_ago)
RULES
(
r_y_ago[ANY] = s[CV(t)] / s[ y_ago[CV(t)] ],
-- year ago
r_q_ago[ANY] = s[CV(t)] / s[ q_ago[CV(t)] ], -- quarter ago
r_m_ago[ANY] = s[CV(t)] / s[ m_ago[CV(t)] ] -- month ago
);
Time Series Calculation (3)
Compute the ratio of current period sales of each product to sales a
year ago, quarter ago and a month ago.
For each row, we use the reference Model to find 3 other rows.
Sales cube: prod sales per y, q, m
t
product
sales
r_y_ago
r_q_ago
a_m_ago
1999m01
vcr
100.00
0.050
0.280
0.830
1999m02
vcr
120.00
…
…
…
1999q01
vcr
360.00
1998q04
vcr
370.00
…
…
…
Time Series Calculation (3)
Compute the ratio of current period sales of each product to sales a
year ago, quarter ago and a month ago.
For each row, we use the reference Model to find 3 other rows.
Sales cube: prod sales per y, q, m
t
product
sales
r_y_ago
r_q_ago
a_m_ago
1999m01
vcr
100.00
0.050
0.280
0.830
1999m02
vcr
120.00
0.055
0.330
…
…
…
…
1999q01
vcr
360.00
0.160
0.970
null
1998q04
vcr
370.00
…
…
…
Time Series Calculation (3)
Compute the ratio of current period sales of each product to sales a
year ago, quarter ago and a month ago.
For each row, we use the reference Model to find 3 other rows.
Sales cube: prod sales per y, q, m
t
product
sales
r_y_ago
r_q_ago
a_m_ago
1999m01
vcr
100.00
0.050
0.280
0.830
1999m02
vcr
120.00
0.055
0.330
...
…
…
…
1999q01
vcr
360.00
0.160
0.970
null
1998q04
vcr
370.00
…
…
null
…
…
…
Recursive Model Solving: Ledger
(1)
In my ledger, I have accounts: Net income, Interest, Taxes, etc.
•I want to have 30 % of my Net income as Interest (F1)
•My Net income is Salary minus Interest, minus Tax (F2)
•Taxes are 38% of Gross (salary–interest) and 28% of Capital_gain (F3)
SELECT account, b FROM ledger
MODEL IGNORE NAV DIMENSION (account) MEASURES (balance b)
RULES ITERATE (..) UNTIL ..
(
b[‘interest’] = b[‘net’] * 0.30, --F1
b[‘net’] = b[‘salary’] – b[‘interest’] – b[‘tax’], --F2
b[‘tax’] = (b[‘salary’] – b[‘interest’]) * 0.38 + b[‘capital_gain’] *0.28 --F3
)
Recursive Model Solving: Ledger
(1)
In my ledger, I have accounts: Net income, Interest, Taxes, etc.
•I want to have 30 % of my Net income as Interest (F1)
•My Net income is Salary minus Interest, minus Tax (F2)
•Taxes are 38% of Gross (salary–interest) and 28% of Capital_gain (F3)
SELECT account, b FROM ledger
MODEL IGNORE NAV DIMENSION (account) MEASURES (balance b)
RULES ITERATE (..) UNTIL ..
(
b[‘interest’] = b[‘net’] * 0.30, --F1
b[‘net’] = b[‘salary’] – b[‘interest’] – b[‘tax’],
--F2
b[‘tax’] = (b[‘salary’] – b[‘interest’]) * 0.38 + b[‘capital_gain’] *0.28
--F3
)
net
F1
interest
interest
F2
tax
F3
two cycles in the formulas
Recursive Model Solving: Ledger
(2)
In my ledger, I know Salary & Capital_gains. What are my
Net income, Interest expense & Taxes?
SELECT account, b FROM ledger
MODEL IGNORE NAV DIMENSION BY (account) MEASURES (balance b)
RULES ITERATE (10000) UNTIL (ABS(b[‘net’] - PREVIOUS(b[‘net’])) < 0.01)
(
b[‘interest’] = b[‘net’] * 0.30,
b[‘net’] = b[‘salary’] – b[‘interest’] – b[‘tax’],
b[‘tax’] = (b[‘salary’] – b[‘interest’]) * 0.38 + b[‘capital_gain’] *0.28
)
Input Ledger
Account
salary
capital_gains
net
tax
interest
Balance
100,000
15,000
0
0
0
Output
Iterate till accuracy of .01
after 1st iteration
Account
salary
capital_gains
net
tax
interest
Balance
100,000
15,000
100,000
42,220
30,000
Recursive Model Solving: Ledger
(2)
In
my ledger, I know Salary & Capital_gains. What is my Net & Taxes?
SELECT account, b FROM ledger
MODEL IGNORE NAV DIMENSION BY (account) MEASURES (balance b)
RULES ITERATE (10000) UNTIL (ABS(b[‘net’] - PREVIOUS(b[‘net’])) < 0.01)
(
b[‘interest’] = b[‘net’] * 0.30,
b[‘net’] = b[‘salary’] – b[‘interest’] – b[‘tax’],
b[‘tax’] = (b[‘salary’] – b[‘interest’]) * 0.38 + b[‘capital_gain’] *0.28
)
Input Ledger
Account
salary
capital_gains
net
tax
interest
Balance
100,000
15,000
0
0
0
Output
Iterate till accuracy of .01
after 2nd iteration
Account
salary
capital_gains
net
tax
interest
Balance
100,000
15,000
27,800
30,800
8,340
Recursive Model Solving: Ledger
(2)
In
my ledger, I know Salary & Capital_gains. What is my Net & Taxes?
SELECT account, b FROM ledger
MODEL IGNORE NAV DIMENSION BY (account) MEASURES (balance b)
RULES ITERATE (10000) UNTIL (ABS(b[‘net’] - PREVIOUS(b[‘net’])) < 0.01)
(
b[‘interest’] = b[‘net’] * 0.30,
b[‘net’] = b[‘salary’] – b[‘interest’] – b[‘tax’],
b[‘tax’] = (b[‘salary’] – b[‘interest’]) * 0.38 + b[‘capital_gain’] *0.28
)
Input Ledger
Account
salary
capital_gains
net
tax
interest
Balance
100,000
15,000
0
0
0
Output
Iterate till accuracy of .01
after reaching accuracy
(26 iterations)
Account
salary
capital_gains
net
tax
interest
Balance
100,000
15,000
48,735
36,644
14,620
Financial Functions: NPV
NPV – net present value of a series of periodic cash flows. 

Cash_Flow table
year
i
prod
amoun
t
1999
0
vcr
100.00
2000
1
vcr
12.00
2001
2
vcr
10.00
2002
3
vcr
20.00
1999
0
dvd
200.00
2000
1
dvd
22.00
2001
2
dvd
12.00
npv
values
i
(1  rate) i
amount
i
(1  rate) i
Financial Functions: NPV
NPV – net present value of a series of periodic cash flows. 

values
i
amount
i
(1  rate) i
(1  rate) i
Cash_Flow table
year
i
prod
amoun
t
1999
0
vcr
100.00
2000
1
vcr
12.00
2001
2
vcr
10.00
2002
3
vcr
20.00
1999
0
dvd
200.00
2000
1
dvd
22.00
2001
2
dvd
12.00
npv
amount[1]/power(1+rate,1) + npv[1-1]
Financial Functions: NPV
NPV – net present value of a series of periodic cash flows. 

values
i
amount
i
(1  rate) i
(1  rate) i
Cash_Flow table
year
i
prod
amoun
t
1999
0
vcr
100.00
2000
1
vcr
12.00
2001
2
vcr
10.00
2002
3
vcr
20.00
1999
0
dvd
200.00
2000
1
dvd
22.00
2001
2
dvd
12.00
2002
3
dvd
14.00
npv
amount[2]/power(1+rate,2) + npv[2-1]
Financial Functions: NPV
NPV – net present value of a series of periodic cash flows. 

values
i
amount
i
(1  rate) i
(1  rate) i
Cash_Flow table
year
i
prod
amoun
t
1999
0
vcr
100.00
2000
1
vcr
12.00
2001
2
vcr
10.00
2002
3
vcr
20.00
1999
0
dvd
200.00
2000
1
dvd
22.00
2001
2
dvd
12.00
npv
amount[3]/power(1+rate,3) + npv[3-1]
Financial Functions: NPV
NPV – net present value of a series of periodic cash flows. 

values
i
amount
i
(1  rate) i
(1  rate) i
Cash_Flow table
year
i
prod
amoun
t
1999
0
vcr
100.00
2000
1
vcr
12.00
2001
2
vcr
10.00
2002
3
vcr
20.00
1999
0
dvd
200.00
2000
1
dvd
22.00
2001
2
dvd
12.00
2002
3
dvd
14.00
npv
amount[i]/power(1+rate, i) + npv[i-1]
npv[ANY] ORDER BY i
= amount[ CV(i) ] / power(1+rate, CV(i))
+ npv[CV(i) – 1]
Financial Functions: NPV (2)
NPV – Net present value of a series of
periodic cash flows.

amount
i
(1  rate) i
Cash_Flow table and npv for rate = 0.14
year
i
prod
amoun
t
npv
1999
0
vcr
100.00
100.00
2000
1
vcr
12.00
-89.47
2001
2
vcr
10.00
-81.78
2002
3
vcr
20.00
-68.28
1999
0
dvd
200.00
200.00
2000
1
dvd
22.00
180.70
2001
2
dvd
12.00
171.47
SELECT year, i, prod, amount, npv
FROM cash_flow
MODEL PARTITION BY (prod)
DIMENSION BY (i)
MEASURES
(amount, 0 npv, year)
RULES
(
npv[ 0] = amount[0],
npv[i !=0] ORDER BY i
= amount[ CV() ] /
POWER(1.14, CV() ) +
npv[CV() - 1]
)
SQL Model
Performance
SQL Model – Time Series
Earlier example: ratio of sales to year, quarter and month ago
SELECT product, sales, r_y_ago, r_q_ago, r_m_ago
FROM sales_cube
MODEL REFERENCE r ON (SELECT * from time)
DIMENSION BY (t) MEASURES (y_ago, q_ago, m_ago)
MAIN PARTITION BY (product) DIMENSION BY (t)
MEASURES (sales, 0 r_y_ago, 0 r_q_ago, 0 r_m_ago)
RULES
(
r_y_ago[ANY] = s[CV(t)] / s[ y_ago[CV(t)] ],
-- year ago
r_q_ago[ANY] = s[CV(t)] / s[ q_ago[CV(t)] ], -- quarter ago
r_m_ago[ANY] = s[CV(t)] / s[ m_ago[CV(t)] ] -- month ago
);
• ANSI SQL version needs outer join for each formula plus a join for
reference model.
• N formulas, M reference models  N+M joins  4 joins in this example:
sales_cube  time  sales_cube  sales_cube  sales_cube
SQL Model vs. ANSI Joins
400
ANSI joins
350
300
250
200
SQL Model
150
100
50
Number of rules or joins
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Summary
 New facility for spreadsheet-like computations in SQL
 High Performance
–
–
–
Replaces multiple joins, unions
Scalable in size and parallel processing
Powerful optimizations
 Collaborative analysis
 Move external processing such as spreadsheets into
RDBMs for manageability and consolidation
Next Steps….
 Demonstration at Oracle DEMOgrounds
–
–
Exhibit hall, Booth 1326, Database Area
Monday: 5:00 PM - 8:00, Tuesday: 10:30 - 1:00, 3:00 6:00,
Wednesday: 11:00 - 4:30, Thursday: 10:30 - 2:00
 Hands-on Lab
–
–
–
Marriott Hotel - Golden Gate B1
Lab Section: Use Information from your Data Warehouse
Lesson 1: Using the SQL Model clause
Monday: 10:30 - 5:00, Tuesday: 8:30 - 12:30, 3:00 5:00,
Wednesday: 8:30 - 4:30, Thursday: 8:30 - 2:30
Reminder –
please complete the
OracleWorld online session
survey
Thank you.
Q U E S T I O N S
A N S W E R S