1. A computerized method to compress a matrix, the method comprising:
partitioning the matrix into a set of overlapping sub-blocks {mk, k=1, . . . , V};
weighting each sub-block mk by a weight matrix wk to form a weighted sub-block mk*wk, where wk has the same dimension as mk and * denotes element-by-element multiplication, wherein mk*wk has a decomposition
m
k
*
w
k
=
\u2211
i
=
1
N
\u2062
(
k
)
\u2062
\u03c3
i
\u2062
(
k
)
\u2062
u
i
\u2062
(
k
)
\u2062
v
i
\u2032
\u2062
(
k
)
;
and representing each weighted sub-block mk*wk by a set of scalar weights {\u03c3i(k), i=1, . . . , n(k)}, a set of vectors {ui(k), i=1, . . . , n(k)}, and a set of vectors {vi(k), i=1, . . . , n(k)}, where n(k)\u2266N(k).
2. The method as set forth in claim 1, wherein the matrix has elements M(i,j), i=1, . . . , P; j=1, . . . , Q where P and Q are the number of rows and the number of columns, respectively, of the matrix, wherein the weight matrices wk, k=1 . . . , V are such that for any image pixel element M(i,j), the sum of all weight elements in the set of weight matrices wk, k=1, . . . , V multiplying M(i,j) when weighting each sub-block mk by wk is a predetermined value.
3. The method as set forth in claim 2, wherein the predetermined value is unity.
4. The method as set forth in claim 2, wherein for each k, the decomposition
m
k
*
w
k
=
\u2211
i
=
1
N
\u2062
(
k
)
\u2062
\u03c3
i
\u2062
(
k
)
\u2062
u
i
\u2062
(
k
)
\u2062
v
i
\u2032
\u2062
(
k
)
is the singular value decomposition of the weighted sub-block mk*wk.
5. The method as set forth in claim 4, wherein for each index k, n(k) is the smallest index i for which \u03c3i+1(k)<C, where C is a positive constant, the singular values are such that \u03c31(k)\u2267\u03c32(k)\u2267 . . . \u2267\u03c3N(k)(k), and if there is no such smallest integer, then n(k)=N(k).
6. The method as set forth in claim 1, wherein for each k, the decomposition
m
k
*
w
k
=
\u2211
i
=
1
N
\u2062
(
k
)
\u2062
\u03c3
i
\u2062
(
k
)
\u2062
u
i
\u2062
(
k
)
\u2062
v
i
\u2032
\u2062
(
k
)
is the singular value decomposition of the weighted sub-block mk*wk.
7. The method as set forth in claim 6, wherein for each index k, n(k) is the smallest index i for which \u03c3i+1(k)<C, where C is a positive constant, the singular values are such that \u03c31(k)\u2267\u03c32(k)\u2267 . . . \u2267\u03c3N(k)(k), and if there is no such smallest integer, then n(k)=N(k).
8. The method as set forth in claim 6, wherein there is at least one k for which n(k)<N(k).
9. The method as set forth in claim 6, wherein n(k)=min{C,N(k)}, where C is independent of k.
10. An article of manufacture comprising a computer readable medium, the computer readable medium comprising instructions to cause a computer system to:
partition a matrix into a set of overlapping sub-blocks {mk, k=1, . . . , V};
weight each sub-block mk by a weight matrix wk to form a weighted sub-block mk*wk, where wk has the same dimension as mk and * denotes element-by-element multiplication, wherein mk*wk has a decomposition
m
k
*
w
k
=
\u2211
i
=
1
N
\u2062
(
k
)
\u2062
\u03c3
i
\u2062
(
k
)
\u2062
u
i
\u2062
(
k
)
\u2062
v
i
\u2032
\u2062
(
k
)
;
and represent each weighted sub-block mk*wk by a set of scalar weights {\u03c3i(k), i=1, . . . , n(k)}, a set of vectors {ui(k), i=1, . . . , n(k)}, and a set of vectors {vi(k), i=1, . . . , n(k)}, where n(k)\u2266N(k).
11. The method as set forth in claim 10, wherein the matrix has elements M(i,j), i=1, . . . , P; j=1, . . . , Q where P and Q are the number of rows and the number of columns, respectively, of the matrix, wherein the weight matrices wk, k=1, . . . , V are such that for any image pixel element M(i,j), the sum of all weight elements in the set of weight matrices wk, k=1, . . . , V multiplying M(i,j) when weighting each sub-block mk by wk is a predetermined value.
12. The method as set forth in claim 11, wherein the predetermined value is unity.
13. The method as set forth in claim 11, wherein for each k, the decomposition
m
k
*
w
k
=
\u2211
i
=
1
N
\u2062
(
k
)
\u2062
\u03c3
i
\u2062
(
k
)
\u2062
u
i
\u2062
(
k
)
\u2062
v
i
\u2032
\u2062
(
k
)
is the singular value decomposition of the weighted sub-block mk*wk.
14. The method as set forth in claim 13, wherein for each index k, n(k) is the smallest index i for which \u03c3i+1(k)<C, where C is a positive constant, the singular values are such that \u03c31(k)\u2267\u03c32(k)\u2267 . . . \u2267\u03c3N(k)(k), and if there is no such smallest integer, then n(k)=N(k).
15. The article of manufacture as set forth in claim 10, wherein for each k, the decomposition
m
k
*
w
k
=
\u2211
i
=
1
N
\u2062
(
k
)
\u2062
\u03c3
i
\u2062
(
k
)
\u2062
u
i
\u2062
(
k
)
\u2062
v
i
\u2032
\u2062
(
k
)
is the singular value decomposition of the weighted sub-block mk*wk.
16. The article of manufacture as set forth in claim 15, wherein for each index k, n(k) is the smallest index i for which \u03c3i+1(k)<C, where C is a positive constant, the singular values are such that \u03c31(k)\u2267\u03c32(k)\u2267 . . . \u2267\u03c3N(k)(k), and if there is no such smallest integer, then n(k)=N(k).
17. The article of manufacture as set forth in claim 15, wherein there is at least one k for which n(k)<N(k).
18. The article of manufacture as set forth in claim 15, wherein n(k)=min{C,N(k)}, where C is independent of k.
19. A computerized method to compress a matrix, the method comprising:
partitioning the matrix into a set of overlapping sub-blocks {mk, k=1, . . . , V}, where each mk has a decomposition
m
k
=
\u2211
i
=
1
N
\u2062
(
k
)
\u2062
\u03c3
i
\u2062
(
k
)
\u2062
u
i
\u2062
(
k
)
\u2062
v
i
\u2032
\u2062
(
k
)
;
and representing each sub-block mk by a set of scalar weights {\u03c3i(k), i=1, . . . , n(k)}, a set of vectors {ui(k), i=1, . . . , n(k)}, and a set of vectors {vi(k), i=1, . . . , n(k)}, where n(k)\u2266N(k).
20. The method as set forth in claim 19, wherein for each k, the decomposition
m
k
=
\u2211
i
=
1
N
\u2062
(
k
)
\u2062
\u03c3
i
\u2062
(
k
)
\u2062
u
i
\u2062
(
k
)
\u2062
v
i
\u2032
\u2062
(
k
)
is the singular value decomposition of the sub-block mk.
21. The method as set forth in claim 20, wherein for each index k, n(k) is the smallest index i for which \u03c3i+1(k)<C, where C is a positive constant, the singular values are such that \u03c31(k)\u2267\u03c32(k)\u2267 . . . \u2267\u03c3N(k)(k), and if there is no such smallest integer, then n(k)=N(k).
22. The method as set forth in claim 20, wherein there is at least one k for which n(k)<N(k).
23. The method as set forth in claim 20, wherein n(k)=min{C,N(k)}, where C is independent of k.
24. An article of manufacture comprising a computer readable medium, the computer readable medium comprising instructions to cause a computer system to:
partition a matrix into a set of overlapping sub-blocks {mk, k=1, . . . , V}, wherein mk has a decomposition
m
ki
=
\u2211
i
=
1
N
\u2062
(
k
)
\u2062
\u03c3
i
\u2062
(
k
)
\u2062
u
i
\u2062
(
k
)
\u2062
v
i
\u2032
\u2062
(
k
)
;
and represent each sub-block mk by a set of scalar weights {\u03c3i(k), i=1, . . . , n(k)}, a set of vectors {ui(k), i=1, . . . , n(k)}, and a set of vectors {vi(k), k=1, . . . , n(k)}, where n(k)<N(k).
25. The article of manufacture as set forth in claim 24, wherein for each k, the decomposition
m
k
=
\u2211
i
=
1
N
\u2062
(
k
)
\u2062
\u03c3
i
\u2062
(
k
)
\u2062
u
i
\u2062
(
k
)
\u2062
v
i
\u2032
\u2062
(
k
)
is the singular value decomposition of the sub-block mk.
26. The article of manufacture as set forth in claim 25, wherein for each index k, n(k) is the smallest index i for which \u03c3i+1(k)<C, where C is a positive constant, the singular values are such that \u03c31(k)\u2267\u03c32(k)\u2267 . . . \u2267\u03c3N(k)(k), and if there is no such smallest integer, then n(k)=N(k).
27. The article of manufacture as set forth in claim 25, wherein there is at least one k for which n(k)<N(k).
28. The article of manufacture as set forth in claim 25, wherein n(k)=min{C,N(k)}, where C is independent of k.
29. A method computerized to synthesize a matrix {circumflex over (M)}, the method comprising:
receiving families of sets comprising:
a family of sets of scalar weights {{\u03c3i(k), i=1, . . . , n(k)}, k=1, . . . , V};
a family of sets of vectors {{ui(k), i=1, . . . , n(k)}, k=1, . . . , V}; and
a family of sets of vectors {{vi(k), i=1, . . . , n(k)}, k=1, . . . , V};
forming weighted vector outer products and summing to provide {circumflex over (m)}k, k=1, . . . , V where
m
^
k
=
\u2211
i
=
1
n
\u2062
(
k
)
\u2062
\u03c3
i
\u2062
(
k
)
\u2062
u
i
\u2062
(
k
)
\u2062
v
i
\u2032
\u2062
(
k
)
;
and overlaying {circumflex over (m)}k for k=1, . . . , V and summing to provide the synthesized matrix {circumflex over (M)}.
30. An article of manufacture comprising a readable computer medium, the readable computer medium comprising instructions to cause a computer system to synthesize a matrix {circumflex over (M)} by
receiving families of sets comprising:
a family of sets of scalar weights {{\u03c3i(k), i=1, . . . , n(k)}, k=1, . . . , V};
a family of sets of vectors {{ui(k), i=1, . . . , n(k)}, k=1, . . . , V}; and
a family of sets of vectors {{vi(k), i=1, . . . , n(k)}, k=1, . . . , V};
forming weighted vector outer products and summing to provide {circumflex over (m)}k, k=1, . . . , V where
m
^
k
=
\u2211
i
=
1
n
\u2062
(
k
)
\u2062
\u03c3
i
\u2062
(
k
)
\u2062
u
i
\u2062
(
k
)
\u2062
v
i
\u2032
\u2062
(
k
)
;
and overlaying {circumflex over (m)}k for k=1, . . . , V and summing to provide the synthesized matrix {circumflex over (M)}.
31. A computerized method to synthesize a {circumflex over (M)}, the method comprising:
receiving families of sets comprising:
a family of sets of scalar weights {{\u03c3i(k), i=1, . . . , n(k), k}, k=1, . . . , V};
a family of sets of vectors {{ui(k), i=1, . . . , n(k)}, k=1, . . . , V}; and
a family of sets of vectors {{vi(k), i=1, . . . , n(k)}, k=1, . . . , V};
forming weighted vector outer products and summing to provide {circumflex over (m)}k, k=1, . . . , V where
m
^
k
=
\u2211
i
=
1
n
\u2062
(
k
)
\u2062
\u03c3
i
\u2062
(
k
)
\u2062
u
i
\u2062
(
k
)
\u2062
v
i
\u2032
\u2062
(
k
)
;
weighting each {circumflex over (m)}k by a weight matrix wk to form {circumflex over (m)}k*wk where * denotes element-by-element multiplication; and
overlaying {circumflex over (m)}k*wk for k=1, . . . , V and summing to provide the synthesized matrix {circumflex over (M)}.
32. An article of manufacture comprising a computer readable medium, the computer readable medium comprising instructions to cause a computer system to synthesize a matrix {circumflex over (M)} by
receiving families of sets comprising:
a family of sets of scalar weights {{\u03c3i(k), i=1, . . . , n(k)}, k=1, . . . , V};
a family of sets of vectors {{ui(k), i=1, . . . , n(k)}, k=1, . . . , V}; and
a family of sets of vectors {{vi(k), i=1, . . . , n(k)}, k=1, . . . , V};
forming weighted vector outer products and summing to provide {circumflex over (m)}k, k=1, . . . , V where
m
^
k
=
\u2211
i
=
1
n
\u2062
(
k
)
\u2062
\u03c3
i
\u2062
(
k
)
\u2062
u
i
\u2062
(
k
)
\u2062
v
i
\u2032
\u2062
(
k
)
;
weighting each {circumflex over (m)} by a weight matrix wk to form {circumflex over (m)}k*wk where * denotes element-by-element multiplication; and
overlaying {circumflex over (m)}k*wk for k=1, . . . , V and summing to provide the synthesized matrix {circumflex over (M)}.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A method of packaging a plurality of repeating commands for device command word (DCW) processing in a computer environment having an IO link handling complex instruction chains for a processing operation, the method comprising:
packaging locate record information into DCW prefix parameter data,
the locate record information including an intent count argument; and
embedding the plurality of repeating commands as a truncated concatenation to the locate record information, the plurality of repeating commands identified by redefining the intent count argument for the plurality of repeating commands as a repeat count argument using a flag argument incorporated into the locate record information, the repeat count argument indicating a number of times for a control unit in the computer environment to execute the plurality of repeating commands,
wherein embedding the plurality of repeating commands as a truncated concatenation to the locate record information further includes embedding a channel control word (CCW) parameter in the locate record information to specify which command the plurality of repeating commands will repeat.
2. The method of claim 1, further including specifying a locate record domain for the plurality of repeating commands in the DCW prefix parameter data.
3. The method of claim 1, wherein the repeat count argument is defined as one of a one-byte value and a one-bit value.
4. The method of claim 1, wherein the flag argument is defined as one of a one-byte value and a one-bit value.
5. The method of claim 1, wherein the plurality of repeating commands are one of a read system command, a write system command, and a search command.
6. A system of packaging a plurality of repeating commands for device command word (DCW) processing in a computer environment having an IO link handling complex instruction chains for a processing operation, the system comprising:
an initiator processor in communication with a control unit in the computer environment, the initiator processor adapted for:
packaging locate record information into DCW prefix parameter data, the locate record information including an intent count argument, and embedding the plurality of repeating commands as a truncated concatenation to the locate record information, the plurality of repeating commands identified by redefining the intent count argument for the plurality of repeating commands as a repeat count argument using a flag argument incorporated into the locate record information, the repeat count argument indicating a number of times for a control unit in the computer environment to execute the plurality of repeating commands,
wherein the initiator processor is further adapted for embedding a channel control word (CCW) parameter in the locate record information to specify which command the plurality of repeating commands will repeat.
7. The system of claim 6, wherein the initiator processor is further adapted for specifying a locate record domain for the plurality of repeating commands in the DCW prefix parameter data.
8. The system of claim 6, wherein the repeat count argument is defined as one of a one-byte value and a one-bit value.
9. The system of claim 6, wherein the flag argument is defined as one of a one-byte value and a one-bit value.
10. The system of claim 6, wherein the plurality of repeating commands are one of a read system command, a write system command, and a search command.
11. A computer program product for packaging a plurality of repeating commands for device command word (DCW) processing in a computer environment having an IO link handling complex instruction chains for a processing operation, the computer program product comprising a computer-readable non-transitory storage medium having computer-readable program code portions stored therein, the computer-readable program code portions comprising:
a first executable portion for packaging locate record information into DCW prefix parameter data, the locate record information including an intent count argument;
a second executable portion for embedding the plurality of repeating commands as a truncated concatenation to the locate record information, the plurality of repeating commands identified by redefining the intent count argument for the plurality of repeating commands as a repeat count argument using a flag argument incorporated into the locate record information, the repeat count argument indicating a number of times for a control unit in the computer environment to execute the plurality of repeating commands; and
a third executable portion for embedding a channel control word (CCW) parameter in the locate record information to specify which command the plurality of repeating commands will repeat.
12. The computer program product of claim 11, further including a third executable portion for specifying a locate record domain for the plurality of repeating commands in the DCW prefix parameter data.
13. The computer program product of claim 11, wherein the repeat count argument is defined as one of a one-byte value and a one-bit value.
14. The computer program product of claim 11, wherein the flag argument is defined as one of a one-byte value and a one-bit value.
15. The computer program product of claim 11, wherein the plurality of repeating commands are one of a read system command, a write system command, and a search command.