LAPACK安装指南：工作笔记41

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"LAPACK Working Note 41 是一份针对LAPACK库的安装指南，由Susan Blackford和Jack Dongarra撰写，来自田纳西大学计算机科学系。该文档详细介绍了如何在高性能计算机上安装、测试和评估LAPACK版本3.0。文档包含了针对Unix和非Unix系统的测试包的单独安装步骤，并详细讨论了测试和计时程序的设计。这份工作得到了NSF Grant No. ASC-的支持。" LAPACK（线性代数包）是用于高性能计算的开源软件库，主要处理各种线性代数问题，包括求解线性方程组、特征值问题和奇异值问题等。LAPACK是在BLAS（基础线性代数子程序）库的基础上构建的，提供了更高级别的算法，旨在提高效率和可移植性。安装LAPACK的步骤通常涉及以下几个关键环节： 1. **系统准备**：首先，确保操作系统兼容LAPACK，并安装必要的编译器和依赖库，如Fortran编译器、BLAS库和可能的数学库。 2. **获取源代码**：从官方仓库或镜像站点下载LAPACK的源代码包，通常是压缩文件形式。 3. **解压和配置**：解压缩文件，进入源代码目录，然后运行配置脚本，根据系统环境进行适当设置，例如指定BLAS库的位置。 4. **编译和链接**：执行编译命令，如`make`，将源代码编译成可执行文件和库文件。这个过程可能需要调整编译选项来适应特定的硬件和优化级别。 5. **测试**：LAPACK提供了一套测试程序，用于验证安装是否成功。这些测试涵盖了各种线性代数操作，确保库功能正常工作。 6. **安装**：将编译好的库文件复制到系统库路径，将头文件复制到包含路径，以便其他程序能够找到并使用LAPACK。 7. **非Unix版本**：对于非Unix系统（如Windows），安装步骤可能会有所不同，可能需要使用不同的编译工具链，如Microsoft Visual Studio，或者使用预编译的二进制包。 8. **计时程序**：LAPACK的测试包还包含计时程序，用于评估库函数的执行效率。这有助于用户了解在特定硬件上的性能表现，并可能用于进一步的性能优化。 9. **文档阅读**：指南中的“Revisions Since the First Public Release”部分可能列出了自首次发布以来的更新和修正，这对于保持库的最新状态至关重要。 10. **文件格式和内容概述**：文档可能详细解释了磁带内容的组织结构，方便用户理解和使用提供的测试数据和程序。 LAPACK Working Note 41为用户提供了一个全面的参考，帮助他们在不同环境中成功安装和利用LAPACK，从而在科学研究和工程应用中解决复杂的线性代数问题。

There are also specialized testing and timing versions of ILAENV that will also need to b e

modied.



Testing/timing version of

LAPACK/TESTING/LIN/ilaenv.f



Testing/timing version of

LAPACK/TESTING/EIG/ilaenv.f



Testing/timing version of

LAPACK/TIMING/LIN/ilaenv.f



Testing/timing version of

LAPACK/TIMING/EIG/ilaenv.f

The test program in

LAPACK/INSTALL/tstiee.f

checks an installation architecture to

see if innity arithmetic and NaN arithmetic are IEEE-754 compliant. A warning message

to the user is printed if non-compliance is detected. This same test is p erformed inside the

function ILAENV. If

ILAENV( 10,

:::

)

ILAENV( 11,

:::

)

is issued, then

ILAENV=1

returned to signal IEEE-754 compliance, and

ILAENV=0

if the architecture is non-IEEE-754

compliant.

Toavoid this IEEE test b eing run every time you call

ILAENV( 10,

:::

)

ILAENV(

11,

:::

)

,we suggest that the user hard-co de the setting of

ILAENV=1

ILAENV=0

in the

version of

LAPACK/SRC/ilaenv.f

to be put in his library. As aforementioned, there are also

specialized testing and timing versions of ILAENV that will also need to be mo died.

6.2 Create the BLAS Library

Ideally, a highly optimized version of the BLAS library already exists on your machine.

In this case you can go directly to Section 6.3 to make the BLAS test programs. You

may already have a library containing some of the BLAS, but not all (Level 1 and 2, but

not Level 3, for example). If so, you should use your lo cal version of the BLAS wherever

possible.

a) Go to

LAPACK

and edit the denition of

blaslib

in the le

Makefile

to specify the

data types desired, as in the example in Section 5.3.

If you already have some of the BLAS, you will need to edit the le

LAPACK/BLAS/SRC/-

Makefile

to comment out the lines dening the BLAS you have.

b) Type

make blaslib

. The make command can be run more than once to add another

data type to the library if necessary.

The BLAS library is created in

LAPACK/blas PLAT.a

, where

PLAT

is the user-dened archi-

tecture sux sp ecied in the le

LAPACK/make.inc

6.3 Run the BLAS Test Programs

Test programs for the Level 1, 2, and 3 BLAS are in the directory

LAPACK/BLAS/TESTING

To compile and run the Level 1, 2, and 3 BLAS test programs, go to

LAPACK

and

type

make blas testing

. The executable les are called

xblat s

xblat d

xblat c

, and

xblat z

, where the (underscore) is replaced by 1, 2, or 3, depending upon the level of

BLAS that it is testing. All executable and output les are created in

LAPACK/BLAS/

.For

the Level 1 BLAS tests, the output le names are

sblat1.out

dblat1.out

cblat1.out

and

zblat1.out

.For the Level 2 and 3 BLAS, the name of the output le is indicated on

the rst line of the input le and is currently dened to b e

SBLAT2.SUMM

for the Level 2

REAL version, and

SBLAT3.SUMM

for the Level 3 REAL version, with similar names for the

other data types.

If the tests using the supplied data les were completed successfully, consider whether

the tests were suciently thorough. For example, on a machine with vector registers, at

least one value of

greater than the length of the vector registers should be used; otherwise,

important parts of the compiled co de may not be exercised by the tests. If the tests were

not successful, either b ecause the program did not nish or the test ratios did not pass

the threshold, you will probably have to nd and correct the problem b efore continuing. If

you have been testing a system-sp ecic BLAS library, try using the Fortran BLAS for the

routines that did not pass the tests. For more details on the BLAS test programs, see [8]

and [6].

6.4 Create the LAPACK Library

a) Go to the directory

LAPACK

and edit the denition of

lapacklib

in the le

Makefile

to specify the data types desired, as in the example in Section 5.3.

b) Type

make lapacklib

. The make command can be run more than once to add

another data type to the library if necessary.

The LAPACK library is created in

LAPACK/lapack

PLAT.a

, where

PLAT

is the user-dened

architecture sux specied in the le

LAPACK/make.inc

6.5 Create the Test Matrix Generator Library

a) Go to the directory

LAPACK

and edit the denition of

tmglib

in the le

Makefile

specify the data types desired, as in the example in Section 5.3.

b) Type

make tmglib

. The make command can b e run more than once to add another

data type to the library if necessary.

The test matrix generator library is created in

LAPACK/tmglib

PLAT.a

, where

PLAT

is the

user-dened architecture sux sp ecied in the le

LAPACK/make.inc

6.6 Run the LAPACK Test Programs

There are two distinct test programs for LAPACK routines in each data type, one for

the linear equation routines and one for the eigensystem routines. In each data typ e, there

is one input le for testing the linear equation routines and seventeen input les for testing

the eigenvalue routines. The input les reside in

LAPACK/TESTING

.For more information

on the test programs and how to mo dify the input les, see Section 7.

If you do not wish to run each of the tests individually,you can go to

LAPACK

, edit the

denition

testing

in the le

Makefile

to sp ecify the data typ es desired, and type

make

testing

. This will compile and run the tests as describ ed in sections 6.6.1 and 6.6.2.

xeigtsts < sgbak.in > sgbak.out

xeigtsts < glm.in > sglm.out

xeigtsts < gqr.in > sgqr.out

xeigtsts < gsv.in > sgsv.out

xeigtsts < lse.in > slse.out

The tests using

xeigtstc

xeigtstd

, and

xeigtstz

also use the input les

nep.in

sep.in

svd.in

glm.in

gqr.in

gsv.in

, and

lse.in

, but the leading `s' in the other

input le names must b e changed to `c', `d', or `z'.

If you encountered failures in this phase of the testing process, please refer to Section 6.8.

6.7 Run the LAPACK Timing Programs

There are two distinct timing programs for LAPACK routines in each data type, one

for the linear equation routines and one for the eigensystem routines. The timing program

for the linear equation routines is also used to time the BLAS. We encourage you to con-

duct these timing exp eriments in REAL and COMPLEX or in DOUBLE PRECISION and

COMPLEX*16; it is not necessary to send timing results in all four data types.

Two sets of input les are provided, a small set and a large set. The small data sets are

appropriate for a standard workstation or other non-vector machine. The large data sets

are appropriate for supercomputers, vector computers, and high-p erformance workstations.

We are mainly interested in results from the large data sets, and it is not necessary to run

both the large and small sets. The values of N in the large data sets are ab out ve times

larger than those in the small data set, and the large data sets use additional values for

parameters such as the blo ck size NB and the leading array dimension LDA. Small data

sets are indicated bylower case names, suchas

stime.in

, and large data sets are indicated

by upp er case names, suchas

STIME.in

. Except as noted, the leading `s' (or `S') in the

input le name must b e replaced by `d', `c', or `z' (`D', `C', or `Z') for the other data types.

We encourage you to obtain timing results with the large data sets, as this allows us to

compare dierent machines. If this would taketoomuch time, suggestions for paring back

the large data sets are given in the instructions below. We also encourage you to exp eriment

with these timing programs and send us anyinteresting results, such as results for larger

problems or for a wider range of blo ck sizes. The main programs are dimensioned for the

large data sets, so the parameters in the main program mayhave to b e reduced in order

to run the small data sets on a small machine, or increased to run experiments with larger

problems.

The minimum time each subroutine will b e timed is set to 0.0 in the large data les

and to 0.05 in the small data les, and on many machines this value should b e increased.

If the timing interval is not long enough, the time for the subroutine after subtracting the

overhead maybe very small or zero, resulting in megaop rates that are very large or zero.

(Toavoid division by zero, the megaop rate is set to zero if the time is less than or equal to

zero.) The minimum time that should b e used depends on the machine and the resolution

of the clock.

For more information on the timing programs and how to mo dify the input les, see

Section 8.

If you do not wish to run each of the timings individuall y,you can go to

LAPACK

, edit

the denition

timing

in the le

Makefile

to specify the data types desired, and type

make

timing

. This will compile and run the timings for the linear equation routines and the

eigensystem routines (see Sections 6.7.1 and 6.7.3).

If you encounter failures in any phase of the timing process, please feel free to contact

the authors as directed in Section 6.8.

Please note that the BLAS timing runs will still need to be run as instructed in 6.7.2.

6.7.1 Timing the Linear Equations Routines

The linear equation timing program is found in

LAPACK/TIMING/LIN

and the input les

are in

LAPACK/TIMING

. Three input les are provided in each data typ e for timing the

linear equation routines, one for square matrices, one for band matrices, and one for rect-

angular matrices. The small data sets for the REAL version are

stime.in

sband.in

, and

stime2.in

, respectively, and the large data sets are

STIME.in

SBAND.in

, and

STIME2.in

The timing program for the least squares routines uses sp ecial instrumented versions of

the LAPACK routines to time individual sections of the co de. The rst step in compiling

the timing program is therefore to make a library of the instrumented routines.

a) To make a library of the instrumented LAPACK routines, rst go to

LAPACK/TIMING/LIN/LINSRC

and type

make

followed by the data typ es desired, as

in the examples of Section 5.3.

The library of instrumented co de is created in

LAPACK/TIMING/LIN/linsrc PLAT.a

where

PLAT

is the user-dened architecture sux specied in the le

LAPACK/make.inc

b) To make the linear equation timing programs, go to

LAPACK/TIMING/LIN

and type

make

followed by the data types desired, as in the examples in Section 5.3. The

executable les are called

xlintims

xlintimc

xlintimd

, and

xlintimz

and are

created in

LAPACK/TIMING

c) Go to

LAPACK/TIMING

and makeany necessary mo dications to the input les. You

may need to set the minimum time a subroutine will b e timed to a p ositivevalue, or to

restrict the size of the tests if you are using a computer with p erformance in between

that of a workstation and that of a supercomputer. The computational requirements

can be cut in half by using only one value of LDA. If it is necessary to also reduce the

matrix sizes or the values of the blocksize, corresp onding changes should b e made to

the BLAS input les (see Section 6.7.2).

d) Run the programs for each data type you are using. For the REAL version, the

commands for the small data sets are

xlintims < stime.in > stime.out

xlintims < sband.in > sband.out

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