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Table 2-1: ALTERA_FP_MATRIX_INV Resource Utilization and Performance for the Stratix IV Device Family
Precision
Matrix
Size
Blocks
Logic usage
Latenc
y
Throug
hput
(kb/s)
Giga
Floatin
g-
Point
Operat
ions
per
Secon
d
(GFLO
PS)
f
MAX
(MHz)
Adapti
ve
Logic
Modul
es
(ALMs)
DSP
Usage
(18 x
18
DSPs)
M9K M144K Memor
y (Bits)
Single
4× 4 2 21159 222 139 — 19919 Pendin
g
Pendin
g
Pendin
g
221
6 × 6 2 59827 574 90 — 15759 Pendin
g
Pendin
g
Pendin
g
170
8 × 8 2 5,538 63 49 — 53,736 2,501 3,987 15.26 332
16 ×
16
4 8,865 95 80 — 138,05
1
11,057 855 30.93 329
32 ×
32
8 15,655 159 193 — 699,16
4
52,625 165 55.12 290
64 ×
64
16 29,940 287 386 22 4,770,3
69
281,50
5
25 83.16 218
ALTERA_FP_MATRIX_INV Functional Description
A matrix inversion function is composed of the following components:
• Cholesky decomposition function.
The Cholesky decomposition function generates a lower triangular matrix.
• Triangular matrix inversion function.
The triangular matrix inversion process then generates the inverse of the lower triangular using
backward substitution.
• Matrix multiplication function.
The matrix multiplier multiplies the transpose of the inverse triangular matrix with the inverse
triangular matrix.
In linear algebra, the Cholesky decomposition states that every positive definite matrix A is decomposed
as A = L×LT
where, L is a lower triangular matrix, and LT denotes the transpose of L.
The property of invertible matrices states that (X×Y)-1 = X-1×Y-1 and the property of transpose states
that (XT )-1 = (X-1)T. Combining these two properties, the following equation represents a derivation of
a matrix inversion using the Cholesky decomposition method:
A-1 = (L×LT)-1
2-2
ALTERA_FP_MATRIX_INV Functional Description
UG-01058
2014.12.19
Altera Corporation
ALTERA_FP_MATRIX_INV IP Core
Send Feedback
- 101 Innovation Drive 1
- San Jose, CA 95134 1
- Contents 2
- About Floating-Point IP Cores 7
- Design Flow 8
- Using the Parameter Editor 10
- File Name Description 12
- Upgrading IP Cores 15
- Related Information 18
- Floating-Point Formats 19
- Special Case Numbers 20
- Non-IEEE-754 Standard Format 21
- Integer bits 22
- Fraction bits 22
- VHDL Component Declaration 24
- VHDL LIBRARY-USE Declaration 24
- ALTERA_FP_MATRIX_INV IP Core 25
- Triangular Matrix Inversion 29
- Matrix Multiplication 29
- Matrix Inversion Operation 29
- Precision Format Numbers 30
- Sample Matrix Data 32
- Matrix Data 33
- ALTERA_FP_MATRIX_INV Signals 34
- ALTERA_FP_MATRIX_MULT IP Core 36
- . . . N-10 . . 38
- . . . N-10 38
- ALTERA_FP_MATRIX_MULT 39
- Parameter Value Description 40
- ALTERA_FP_ACC_CUSTOM IP Core 42
- ALTERA_FP_ACC_CUSTOM Signals 44
- ALTFP_ADD_SUB IP Core 48
- ALTFP_ADD_SUB Signals 51
- ALTFP_ADD_SUB 52
- ALTFP_ADD_SUB Parameters 53
- ALTFP_DIV IP Core 55
- ALTFP_DIV Truth Table 56
- ALTFP_DIV Signals 60
- ALTFP_DIV Parameters 61
- ALTFP_MULT IP Core 63
- Parameters 66
- ALTFP_MULT Signals 67
- ALTFP_SQRT 69
- ALTFP_SQRT Truth Table 70
- ALTFP_SQRT Signals 72
- ALTFP_SQRT Parameters 74
- ALTFP_EXP IP Core 75
- ALTFP_EXP Signals 78
- ALTFP_EXP 79
- ALTFP_EXP Parameters 80
- ALTFP_INV IP Core 81
- ALTFP_INV_SQRT IP Core 87
- ALTFP_INV_SQRT 90
- ALTFP_LOG 93
- ALTFP_ATAN IP Core 99
- ALTFP_ATAN Parameters 100
- Parameter 101
- Type Required Description 101
- ALTFP_SINCOS IP Core 102
- ALTFP_SINCOS Signals 103
- ALTFP_SINCOS Parameters 104
- ALTFP_ABS IP Core 105
- UG-01058 106
- 2014.12.19 106
- ALTFP_ABS Signals 107
- ALTFP_ABS 108
- ALTFP_ABS Parameters 109
- ALTFP_COMPARE IP Core 111
- Format Numbers 112
- ALTFP_COMPARE Signals 113
- ALTFP_COMPARE Parameters 114
- ALTFP_CONVERT IP Core 116
- ALTFP_CONVERT Output Latency 117
- Point Format Numbers 121
- Time Event 122
- ALTFP_CONVERT Signals 123
- ALTFP_CONVERT Parameters 125
- ALTERA_FP_FUNCTIONS IP Core 128
- Function Description 129
- ALTERA_FP_FUNCTIONS Signals 151
- Altera Corporation 152
- Send Feedback 152
- Document Revision History 156
- Date Document 157
- Changes Made 157
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