How to add hot spare on existing Adaptec RAID array using arcconf

Background

Adaptec Raid 7805 hardware raid controller card is installed on a x64 PC. I'd like to run Proxmox VE 8 (flavor of Debian). I failed to run Adaptec MaxView web user interface on Proxmox 8 but the commandline program arcconf works flawlessly on Proxmox.

Total 9x 4TB harddrives are installed on a SAS expander enclosure.

8 drives are to be a member of RAID 10. Remaining 1 drive is to be used as a hot spare.

Potentially booting Proxmox from Adaptec is possible but I decided to boot Proxmox from two onboard SATA SSDs ZFS mirror.

It seems there is no step-by-step guide on this topic on Internet 😀

Setup procedure

 

8 drives RAID 10 array is created using legacy BIOS CTRL-A Adaptec utility before booting OS. Press ctrl-a during computer startup to show Ctrl-a Adaptec utility.

Install Proxmox VE.

Start Proxmox.

Download Adaptec ARCCONF Command Line Utility on Adaptec Raid 7805 storage manager downloads. There are many methods to do this, I downloaded it using Windows PC and send the file to Proxmox PC using Tera term ssh connection, [File][SSH SCP]

Finding channel number and device number of the spare drive

Single Adaptec raid controller is installed. on this case, as far as I know,  controller number is always 1.

Getting device number of the spare drive of raid controller #1:

# ./arcconf getconfig 1

 

Controllers found: 1
----------------------------------------------------------------------
Controller information
----------------------------------------------------------------------
   Controller Status                        : Optimal
   Controller Mode                          : Default/RAID
   Channel description                      : SAS/SATA
   Controller Model                         : Adaptec ASR7805
   Controller Serial Number                 : 3A12130E56E
   Physical Slot                            : 3
   Temperature                              : 73 C/ 163 F (Normal)
   Installed memory                         : 1024 MB
   Copyback                                 : Disabled
   Background consistency check             : Enabled
   Automatic Failover                       : Enabled
   Global task priority                     : High
   Performance Mode                         : Default/Dynamic
   Host bus type                            : PCIe
   Host bus speed                           : 8000 MHz
   Host bus link width                      : 8 bit(s)/link(s)
   Stayawake period                         : Disabled
   Spinup limit internal drives             : 1
   Spinup limit external drives             : 1
   Defunct disk drive count                 : 0
   Logical devices/Failed/Degraded          : 1/0/0
   NCQ status                               : Enabled
   Statistics data collection mode          : Enabled
   --------------------------------------------------------
   Controller Version Information
   --------------------------------------------------------
   BIOS                                     : 7.5-0 (32118)
   Firmware                                 : 7.5-0 (32118)
   Driver                                   : 1.2-1 (50983)
   Boot Flash                               : 7.5-0 (32118)

   --------------------------------------------------------
   Controller Cache Backup Unit Information
   --------------------------------------------------------

    Overall Backup Unit Status              : Ready

         Backup Unit Type                   : AFM-700/700LP
         Non-Volatile Storage Status        : Ready
         Supercap Status                    : Ready

         -----------------------------------
         Supercap Information
         -----------------------------------
         Current Temperature                : 24 deg C
         Threshold Temperature              : 51 deg C
         Life-time Temperature Recorded
         (Min/Max)                          : 8 deg C/ 47 deg C

         Voltage(Present/Max)               : 4918 mV/ 5302 mV
         Life-time Max Voltage Recorded     : 5432 mV

         Current Drawn(Present/Max)         : -9 mA/ 560 mA
         Health                             : 100 percent
         Charge Level                       : 100 percent
         Estimated Life-time                : 5 Years, 0 Month
         Serial Number                      : 3A161D15549

----------------------------------------------------------------------
Logical device information
----------------------------------------------------------------------
Logical device number 0
   Logical device name                      : Raid10
   Block Size of member drives              : 512 Bytes
   RAID level                               : 10
   Status of logical device                 : Optimal
   Size                                     : 15257590 MB
   Parity space                             : 15257600 MB
   Stripe-unit size                         : 256 KB
   Read-cache setting                       : Enabled
   Read-cache status                        : On
   Write-cache setting                      : On when protected by battery/ZMM
   Write-cache status                       : On
   Partitioned                              : No
   Protected by Hot-Spare                   : No
   Bootable                                 : Yes
   Failed stripes                           : No
   Power settings                           : Enabled
   Slow down after(Minutes)                 : 30m
   Power off after(Minutes)                 : 1h
   Verify after(Hours)                      : 24h
   Power State                              : Active
   --------------------------------------------------------
   Logical device segment information
   --------------------------------------------------------
   Group 0, Segment 0                       : Present (Controller:1,Enclosure:0,Slot:12)      WD-WCC7K1XV444P
   Group 0, Segment 1                       : Present (Controller:1,Enclosure:0,Slot:16)      WD-WCC7K4SLFCLU
   Group 1, Segment 0                       : Present (Controller:1,Enclosure:0,Slot:17)      WD-WCC7K6FVPTR7
   Group 1, Segment 1                       : Present (Controller:1,Enclosure:0,Slot:18)      WD-WCC7K2LJ0YF3
   Group 2, Segment 0                       : Present (Controller:1,Enclosure:0,Slot:19)      WD-WCC7K2NH509H
   Group 2, Segment 1                       : Present (Controller:1,Enclosure:0,Slot:20)             ZGY58L8C
   Group 3, Segment 0                       : Present (Controller:1,Enclosure:0,Slot:21)      WD-WCC7K4FJFJJY
   Group 3, Segment 1                       : Present (Controller:1,Enclosure:0,Slot:22)      WD-WCC7K1NE95P4


----------------------------------------------------------------------
Physical Device information
----------------------------------------------------------------------
      Device #0
         Device is a Hard drive
         State                              : Online
         Block Size                         : 512 Bytes
         Supported                          : Yes
         Transfer Speed                     : SATA 6.0 Gb/s
         Reported Channel,Device(T:L)       : 0,44(44:0)
         Reported Location                  : Enclosure 0, Slot 12
                  Reported ESD(T:L)                  : 2,0(0:0)
         Vendor                             : ATA
         Model                              : WDC WD40EZRZ-00G
         Firmware                           : 80.00A80
         Serial number                      : WD-WCC7K1XV444P
         World-wide name                    : 50014EE267ADB7A7
         Reserved Size                      : 1072920 KB
         Used Size                          : 3814400 MB
         Unused Size                        : 64 KB
         Total Size                         : 3815447 MB
         Write Cache                        : Enabled (write-back)
         FRU                                : None
         S.M.A.R.T.                         : No
         S.M.A.R.T. warnings                : 0
         Power State                        : Full rpm
         Supported Power States             : Full rpm,Powered off
         SSD                                : No
         NCQ status                         : Enabled
      Device #1
         Device is a Hard drive
         State                              : Raw (Pass Through)
         Block Size                         : 512 Bytes
         Supported                          : Yes
         Transfer Speed                     : SATA 6.0 Gb/s
         Reported Channel,Device(T:L)       : 0,45(45:0)
         Reported Location                  : Enclosure 0, Slot 13
         Reported ESD(T:L)                  : 2,0(0:0)
         Vendor                             : ATA
         Model                              : TOSHIBA MN08ACA1
         Firmware                           : 0601
         Serial number                      : Y1N0A0CXFW4G
         World-wide name                    : 5000039B48DAC90B
         Reserved Size                      : 0 KB
         Used Size                          : 0 MB
         Unused Size                        : 15259648 MB
         Total Size                         : 15259648 MB
         Write Cache                        : Enabled (write-back)
         FRU                                : None
         S.M.A.R.T.                         : No
         S.M.A.R.T. warnings                : 0
         Power State                        : Full rpm
         Supported Power States             : Full rpm,Powered off,Reduced rpm
         SSD                                : No
         NCQ status                         : Enabled
      Device #2
         Device is a Hard drive
         State                              : Online
         Block Size                         : 512 Bytes
         Supported                          : Yes
         Transfer Speed                     : SATA 6.0 Gb/s
         Reported Channel,Device(T:L)       : 0,48(48:0)
         Reported Location                  : Enclosure 0, Slot 16
         Reported ESD(T:L)                  : 2,0(0:0)
         Vendor                             : ATA
         Model                              : WDC WD40EZRZ-00G
        Firmware                           : 80.00A80
         Serial number                      : WD-WCC7K4SLFCLU
         World-wide name                    : 50014EE267ADC550
         Reserved Size                      : 1072920 KB
         Used Size                          : 3814400 MB
         Unused Size                        : 64 KB
         Total Size                         : 3815447 MB
         Write Cache                        : Enabled (write-back)
         FRU                                : None
         S.M.A.R.T.                         : No
         S.M.A.R.T. warnings                : 0
         Power State                        : Full rpm
         Supported Power States             : Full rpm,Powered off
         SSD                                : No
         NCQ status                         : Enabled
      Device #3
         Device is a Hard drive
         State                              : Online
         Block Size                         : 512 Bytes
         Supported                          : Yes
         Transfer Speed                     : SATA 6.0 Gb/s
         Reported Channel,Device(T:L)       : 0,49(49:0)
         Reported Location                  : Enclosure 0, Slot 17
         Reported ESD(T:L)                  : 2,0(0:0)
         Vendor                             : ATA
         Model                              : WDC WD40EZRZ-00G
         Firmware                           : 80.00A80
         Serial number                      : WD-WCC7K6FVPTR7
         World-wide name                    : 50014EE2BD01B094
         Reserved Size                      : 1072920 KB
         Used Size                          : 3814400 MB
         Unused Size                        : 64 KB
         Total Size                         : 3815447 MB
         Write Cache                        : Enabled (write-back)
         FRU                                : None
         S.M.A.R.T.                         : No
         S.M.A.R.T. warnings                : 0
         Power State                        : Full rpm
         Supported Power States             : Full rpm,Powered off
         SSD                                : No
         NCQ status                         : Enabled
      Device #4
         Device is a Hard drive
         State                              : Online
         Block Size                         : 512 Bytes
         Supported                          : Yes
         Transfer Speed                     : SATA 6.0 Gb/s
         Reported Channel,Device(T:L)       : 0,50(50:0)
         Reported Location                  : Enclosure 0, Slot 18
         Reported ESD(T:L)                  : 2,0(0:0)
         Vendor                             : ATA
         Model                              : WDC WD40EZRZ-00G
         Firmware                           : 80.00A80
         Serial number                      : WD-WCC7K2LJ0YF3
:        World-wide name                    : 50014EE212569CFA
         Reserved Size                      : 1072920 KB
         Used Size                          : 3814400 MB
         Unused Size                        : 64 KB
         Total Size                         : 3815447 MB
         Write Cache                        : Enabled (write-back)
         FRU                                : None
         S.M.A.R.T.                         : No
         S.M.A.R.T. warnings                : 0
         Power State                        : Full rpm
         Supported Power States             : Full rpm,Powered off
         SSD                                : No
         NCQ status                         : Enabled
      Device #5
         Device is a Hard drive
         State                              : Online
         Block Size                         : 512 Bytes
         Supported                          : Yes
         Transfer Speed                     : SATA 6.0 Gb/s
         Reported Channel,Device(T:L)       : 0,51(51:0)
         Reported Location                  : Enclosure 0, Slot 19
         Reported ESD(T:L)                  : 2,0(0:0)
         Vendor                             : ATA
         Model                              : WDC WD40EZRZ-00G
         Firmware                           : 80.00A80
         Serial number                      : WD-WCC7K2NH509H
         World-wide name                    : 50014EE2125694D1
         Reserved Size                      : 1072920 KB
         Used Size                          : 3814400 MB
         Unused Size                        : 64 KB
         Total Size                         : 3815447 MB
         Write Cache                        : Enabled (write-back)
         FRU                                : None
         S.M.A.R.T.                         : No
         S.M.A.R.T. warnings                : 0
         Power State                        : Full rpm
         Supported Power States             : Full rpm,Powered off
         SSD                                : No
         NCQ status                         : Enabled
      Device #6
         Device is a Hard drive
         State                              : Online
         Block Size                         : 512 Bytes
         Supported                          : Yes
         Transfer Speed                     : SATA 6.0 Gb/s
         Reported Channel,Device(T:L)       : 0,52(52:0)
         Reported Location                  : Enclosure 0, Slot 20
         Reported ESD(T:L)                  : 2,0(0:0)
         Vendor                             : ATA
         Model                              : ST4000VN008-2DR1
         Firmware                           : SC60
         Serial number                      : ZGY58L8C
         World-wide name                    : 5000C500B68A16CF
         Reserved Size                      : 1072920 KB
        Used Size                          : 3814400 MB
         Unused Size                        : 64 KB
         Total Size                         : 3815447 MB
         Write Cache                        : Enabled (write-back)
         FRU                                : None
         S.M.A.R.T.                         : No
         S.M.A.R.T. warnings                : 0
         Power State                        : Full rpm
         Supported Power States             : Full rpm,Powered off,Reduced rpm
         SSD                                : No
         NCQ status                         : Enabled
      Device #7
         Device is a Hard drive
         State                              : Online
         Block Size                         : 512 Bytes
         Supported                          : Yes
         Transfer Speed                     : SATA 6.0 Gb/s
         Reported Channel,Device(T:L)       : 0,53(53:0)
         Reported Location                  : Enclosure 0, Slot 21
         Reported ESD(T:L)                  : 2,0(0:0)
         Vendor                             : ATA
         Model                              : WDC WD40EZRZ-00G
         Firmware                           : 80.00A80
         Serial number                      : WD-WCC7K4FJFJJY
         World-wide name                    : 50014EE21256970B
         Reserved Size                      : 1072920 KB
         Used Size                          : 3814400 MB
         Unused Size                        : 64 KB
         Total Size                         : 3815447 MB
         Write Cache                        : Enabled (write-back)
         FRU                                : None
         S.M.A.R.T.                         : No
         S.M.A.R.T. warnings                : 0
         Power State                        : Full rpm
         Supported Power States             : Full rpm,Powered off
         SSD                                : No
         NCQ status                         : Enabled
      Device #8
         Device is a Hard drive
         State                              : Online
         Block Size                         : 512 Bytes
         Supported                          : Yes
         Transfer Speed                     : SATA 6.0 Gb/s
         Reported Channel,Device(T:L)       : 0,54(54:0)
         Reported Location                  : Enclosure 0, Slot 22
         Reported ESD(T:L)                  : 2,0(0:0)
         Vendor                             : ATA
         Model                              : WDC WD40EZRZ-00G
         Firmware                           : 80.00A80
         Serial number                      : WD-WCC7K1NE95P4
         World-wide name                    : 50014EE212587634
         Reserved Size                      : 1072920 KB
         Used Size                          : 3814400 MB
         Unused Size                        : 64 KB
         Total Size                         : 3815447 MB
         Write Cache                        : Enabled (write-back)
         FRU                                : None
         S.M.A.R.T.                         : No
         S.M.A.R.T. warnings                : 0
         Power State                        : Full rpm
         Supported Power States             : Full rpm,Powered off
         SSD                                : No
         NCQ status                         : Enabled
      Device #9
         Device is a Hard drive
         State                              : Ready
         Block Size                         : 512 Bytes
         Supported                          : Yes
         Transfer Speed                     : SATA 6.0 Gb/s
         Reported Channel,Device(T:L)       : 0,55(55:0)
         Reported Location                  : Enclosure 0, Slot 23
         Reported ESD(T:L)                  : 2,0(0:0)
         Vendor                             : ATA
         Model                              : WDC WD40EZRZ-00G
         Firmware                           : 80.00A80
         Serial number                      : WD-WCC7K1YK8283
         World-wide name                    : 50014EE2BD039777
         Reserved Size                      : 1072920 KB
         Used Size                          : 0 MB
         Unused Size                        : 3814400 MB
         Total Size                         : 3815447 MB
         Write Cache                        : Enabled (write-back)
         FRU                                : None
         S.M.A.R.T.                         : No
         S.M.A.R.T. warnings                : 0
         Power State                        : Full rpm
         Supported Power States             : Full rpm,Powered off
         SSD                                : No
         NCQ status                         : Enabled
      Device #10
         Device is an Enclosure services device
         Reported Channel,Device(T:L)       : 2,0(0:0)
         Enclosure ID                       : 0
         Type                               : SES2
         Vendor                             : ADAPTEC
         Model                              : AEC-82885T
         Firmware                           : B059
         Status of Enclosure services device
            Fan 1 status                    : 0 rpm (Not supported)
            Fan 2 status                    : 0 rpm (Not supported)
            Fan 3 status                    : 0 rpm (Not supported)
            Fan 4 status                    : 0 rpm (Not supported)
            Power supply 1 status           : Optimal
            Power supply 2 status           : Optimal
            Temperature Sensor Status 1     : Unknown
            Temperature Sensor Status 2     : Unknown
            Speaker status                  : Off


Command completed successfully.

Found the spare drive is 

• Device 9 
• CHANNEL# 0
• DEVICE# 55

The report above is lengthy and a bit confusing but device number we need is 55.

RAID 10 array logical device number LD# is 0

ASR-7805 raid CONTROLLER# is 1

 

Executing hot spare adding command

 

Hot spare adding command syntax is 

# ./arcconf setstate CONTROLLER# device CHANNEL# DEVICE# hsp logicaldrive LD#

 

Therefore,

# ./arcconf setstate 1 device 0 55 hsp logicaldrive 0
Controllers found: 1

Command completed successfully.

 

Hot spare drive is successfully added onto the RAID 10 array.

 

 

 

How to run HMA single image super resolution on Windows 11 computer

Prerequisites

Windows 11 PC with 64GB+ memory

Nvidia GPU with 24GB+ VRAM

Setup HMA

Install Cuda 11.8.0 https://developer.nvidia.com/cuda-toolkit-archive
Install cudnn 9.4.0 https://developer.nvidia.com/cudnn-archive

Install miniforge https://github.com/conda-forge/miniforge/releases/download/24.7.1-0/Miniforge3-24.7.1-0-Windows-x86_64.exe

Download HMA zip from https://github.com/korouuuuu/HMA 

   press code → Download ZIP onto C:\work\HMA

Fix bug of C:\work\HMA\hma\data\paired_imagenet_dataset.py according to https://github.com/korouuuuu/HMA/pull/5/files

Run Miniforge prompt and type following commands

conda update -y -n base -c defaults conda

conda update -y --all

cd C:\work\HMA

conda create -y -n HMA python=3.9

conda activate HMA

conda install -y pytorch==2.0.1 torchvision==0.15.2 torchaudio==2.0.2 pytorch-cuda=11.8 -c pytorch -c nvidia

 pip install "numpy==1.23.0" "ipython==7.21.0" "opencv-python==4.5.4.58" "einops==0.4.1"

pip install -r requirements.txt

python setup.py develop

          

Download pretrained model file HMA_SRx2_pretrain.pth from

https://drive.google.com/drive/folders/13Bxt_BXtWgwwcO7tjfoL6zYZAUY1v3zi

Save it as

C:\work\HMA\experiments\pretrained_models\HMA_SRx2_pretrain.pth

Dataset preparation

(Dataset used is https://github.com/XPixelGroup/BasicSR/blob/master/docs/DatasetPreparation.md )

Download Set5 Set14 BSD100 Urban100 MANGA109

from https://drive.google.com/drive/folders/1gt5eT293esqY0yr1Anbm36EdnxWW_5oH

Unzip and arrange Set5 Set14 directories as

C:\work\HMA\datasets\Set5\LRbicx2

C:\work\HMA\datasets\Set5\GTmod2 (renamed from GTmod12)

C:\work\HMA\datasets\Set14\LRbicx2

C:\work\HMA\datasets\Set14\GTmod2( renamed from GTmod12)

Edit C:\work\HMA\options\test\HMA_SRx2.yml to delete test_3 test_4 test_5, leave Set5 Set14 as it is

Run test

On the Miniforge prompt

conda activate HMA

python hma/test.py -opt options/test/HMA_SRx2.yml

Suprer-esolution result images are written onto C:\work\HMA\results\HMA_test_X2\visualization

How to run RealBasicVSR on Windows 11

Prerequisites

Windows 11 PC with 64GB+ memory

Nvidia GPU with 12GB+ VRAM

mp4 video file of short duration (30 seconds or less) as input.mp4

Setup and run RealBasicVSR

Install Cuda 11.8.0 https://developer.nvidia.com/cuda-toolkit-archive
Install cudnn 9.4.0 https://developer.nvidia.com/cudnn-archive

Install miniforge https://github.com/conda-forge/miniforge/releases/download/24.7.1-0/Miniforge3-24.7.1-0-Windows-x86_64.exe

Install Visual Studio 2022 Professional
add C:\Program Files\Microsoft Visual Studio\2022\Professional\VC\Tools\MSVC\14.41.34120\bin\Hostx64\x64 to environment PATH
(I think it is possible to use Visual Studio 2022 Community edition instead)

Run Miniforge prompt and type following commands

conda update -y -n base -c defaults conda
conda update -y --all

conda env remove -y -n realbasicvsr

conda create -y -n realbasicvsr python=3.9

conda activate  realbasicvsr 

conda install -y pytorch==2.0.1 torchvision==0.15.2 torchaudio==2.0.2 pytorch-cuda=11.8 -c pytorch -c nvidia
conda install -y fsspec==2024.9.0 openmim==0.3.7 ninja==1.12.1 albumentations==1.4.14

mim install mmcv==2.1
mim install mmengine==0.10.4
mim install mmagic==1.2.0
conda install -y numpy==1.26
conda install -y platformdirs==4.3.2
conda install -y diffusers==0.28

Download mmagic=1.2.0 as zip https://github.com/open-mmlab/mmagic/archive/refs/tags/v1.2.0.zip
extract it
cd mmagic-1.2.0

python demo/mmagic_inference_demo.py --model-name real_basicvsr --video ./input.mp4 --result-out-dir ./out/out.mp4


It runs. The result is not convincing. Maybe something is wrong.

Hilbert Matrix 20x20 LDLT decomposition

 The following is LDLT decomposition of 20x20 Hilbert Matrix. The diagonal matrix contains very small number.

It seems Firefox render this page correctly.

$\mathrm{Hilbert\; Matrix\; H}=\left[\begin{array}{cccccccccccccccccccc}1& \frac{1}{2}& \frac{1}{3}& \frac{1}{4}& \frac{1}{5}& \frac{1}{6}& \frac{1}{7}& \frac{1}{8}& \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}\\ \frac{1}{2}& \frac{1}{3}& \frac{1}{4}& \frac{1}{5}& \frac{1}{6}& \frac{1}{7}& \frac{1}{8}& \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}\\ \frac{1}{3}& \frac{1}{4}& \frac{1}{5}& \frac{1}{6}& \frac{1}{7}& \frac{1}{8}& \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}\\ \frac{1}{4}& \frac{1}{5}& \frac{1}{6}& \frac{1}{7}& \frac{1}{8}& \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}\\ \frac{1}{5}& \frac{1}{6}& \frac{1}{7}& \frac{1}{8}& \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}\\ \frac{1}{6}& \frac{1}{7}& \frac{1}{8}& \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}\\ \frac{1}{7}& \frac{1}{8}& \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}\\ \frac{1}{8}& \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}\\ \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}\\ \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}\\ \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}\\ \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}\\ \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}& \frac{1}{32}\\ \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}& \frac{1}{32}& \frac{1}{33}\\ \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}& \frac{1}{32}& \frac{1}{33}& \frac{1}{34}\\ \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}& \frac{1}{32}& \frac{1}{33}& \frac{1}{34}& \frac{1}{35}\\ \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}& \frac{1}{32}& \frac{1}{33}& \frac{1}{34}& \frac{1}{35}& \frac{1}{36}\\ \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}& \frac{1}{32}& \frac{1}{33}& \frac{1}{34}& \frac{1}{35}& \frac{1}{36}& \frac{1}{37}\\ \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}& \frac{1}{32}& \frac{1}{33}& \frac{1}{34}& \frac{1}{35}& \frac{1}{36}& \frac{1}{37}& \frac{1}{38}\\ \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}& \frac{1}{32}& \frac{1}{33}& \frac{1}{34}& \frac{1}{35}& \frac{1}{36}& \frac{1}{37}& \frac{1}{38}& \frac{1}{39}\end{array}\right]$

$L=\left[\begin{array}{cccccccccccccccccccc}1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{2}& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{3}& 1& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{4}& \frac{9}{10}& \frac{3}{2}& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{5}& \frac{4}{5}& \frac{12}{7}& 2& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{6}& \frac{5}{7}& \frac{25}{14}& \frac{25}{9}& \frac{5}{2}& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{7}& \frac{9}{14}& \frac{25}{14}& \frac{10}{3}& \frac{45}{11}& 3& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{8}& \frac{7}{12}& \frac{7}{4}& \frac{245}{66}& \frac{245}{44}& \frac{147}{26}& \frac{7}{2}& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{9}& \frac{8}{15}& \frac{56}{33}& \frac{392}{99}& \frac{980}{143}& \frac{112}{13}& \frac{112}{15}& 4& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{10}& \frac{27}{55}& \frac{18}{11}& \frac{588}{143}& \frac{1134}{143}& \frac{756}{65}& \frac{63}{5}& \frac{162}{17}& \frac{9}{2}& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{11}& \frac{5}{11}& \frac{225}{143}& \frac{600}{143}& \frac{1260}{143}& \frac{189}{13}& \frac{315}{17}& \frac{300}{17}& \frac{225}{19}& 5& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{12}& \frac{11}{26}& \frac{275}{182}& \frac{55}{13}& \frac{495}{52}& \frac{7623}{442}& \frac{847}{34}& \frac{9075}{323}& \frac{1815}{76}& \frac{605}{42}& \frac{11}{2}& 1& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{13}& \frac{36}{91}& \frac{132}{91}& \frac{55}{13}& \frac{4455}{442}& \frac{4356}{221}& \frac{10164}{323}& \frac{13068}{323}& \frac{5445}{133}& \frac{220}{7}& \frac{396}{23}& 6& 1& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{14}& \frac{13}{35}& \frac{39}{28}& \frac{143}{34}& \frac{715}{68}& \frac{14157}{646}& \frac{61347}{1615}& \frac{122694}{2261}& \frac{16731}{266}& \frac{9295}{161}& \frac{1859}{46}& \frac{507}{25}& \frac{13}{2}& 1& 0& 0& 0& 0& 0& 0\\ \frac{1}{15}& \frac{7}{20}& \frac{91}{68}& \frac{637}{153}& \frac{7007}{646}& \frac{77077}{3230}& \frac{143143}{3230}& \frac{22308}{323}& \frac{39039}{437}& \frac{13013}{138}& \frac{91091}{1150}& \frac{1274}{25}& \frac{637}{27}& 7& 1& 0& 0& 0& 0& 0\\ \frac{1}{16}& \frac{45}{136}& \frac{175}{136}& \frac{15925}{3876}& \frac{28665}{2584}& \frac{33033}{1292}& \frac{65065}{1292}& \frac{1254825}{14858}& \frac{418275}{3496}& \frac{13013}{92}& \frac{63063}{460}& \frac{637}{6}& \frac{2275}{36}& \frac{1575}{58}& \frac{15}{2}& 1& 0& 0& 0& 0\\ \frac{1}{17}& \frac{16}{51}& \frac{400}{323}& \frac{3920}{969}& \frac{3640}{323}& \frac{8736}{323}& \frac{416416}{7429}& \frac{743600}{7429}& \frac{66924}{437}& \frac{4576}{23}& \frac{224224}{1035}& \frac{2912}{15}& \frac{36400}{261}& \frac{2240}{29}& \frac{960}{31}& 8& 1& 0& 0& 0\\ \frac{1}{18}& \frac{17}{57}& \frac{68}{57}& \frac{680}{171}& \frac{2380}{209}& \frac{12376}{437}& \frac{80444}{1311}& \frac{252824}{2185}& \frac{82654}{437}& \frac{165308}{621}& \frac{330616}{1035}& \frac{420784}{1305}& \frac{210392}{783}& \frac{161840}{899}& \frac{2890}{31}& \frac{1156}{33}& \frac{17}{2}& 1& 0& 0\\ \frac{1}{19}& \frac{27}{95}& \frac{153}{133}& \frac{816}{209}& \frac{55080}{4807}& \frac{12852}{437}& \frac{723996}{10925}& \frac{286416}{2185}& \frac{495924}{2185}& \frac{165308}{483}& \frac{1487772}{3335}& \frac{360672}{725}& \frac{420784}{899}& \frac{327726}{899}& \frac{78030}{341}& \frac{1224}{11}& \frac{1377}{35}& 9& 1& 0\\ \frac{1}{20}& \frac{19}{70}& \frac{171}{154}& \frac{969}{253}& \frac{2907}{253}& \frac{17442}{575}& \frac{40698}{575}& \frac{16796}{115}& \frac{214149}{805}& \frac{29838094}{70035}& \frac{29838094}{50025}& \frac{16275324}{22475}& \frac{1356277}{1798}& \frac{6572727}{9889}& \frac{165699}{341}& \frac{110466}{385}& \frac{18411}{140}& \frac{3249}{74}& \frac{19}{2}& 1\end{array}\right]$

$D=\left[\begin{array}{cccccccccccccccccccc}1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& \frac{1}{12}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& \frac{1}{180}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& \frac{1}{2800}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& \frac{1}{44100}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& \frac{1}{698544}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& \frac{1}{11099088}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& \frac{1}{176679360}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{2815827300}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{44914183600}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{716830370256}& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{11445589052352}& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{182811491808400}& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{2920656969720000}& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{46670906271240000}& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{745904795339462400}& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{11922821963004219300}& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{190600129650794094000}& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{3047248986392325330000}& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{48722219250572027160000}\end{array}\right]$

$\mathrm{Hilbert\; Matrix\; H}=LD{L}^{\mathrm{T}}$