1 @c PSPP - a program for statistical analysis.
2 @c Copyright (C) 2017, 2020, 2021 Free Software Foundation, Inc.
3 @c Permission is granted to copy, distribute and/or modify this document
4 @c under the terms of the GNU Free Documentation License, Version 1.3
5 @c or any later version published by the Free Software Foundation;
6 @c with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
7 @c A copy of the license is included in the section entitled "GNU
8 @c Free Documentation License".
13 Some @pspp{} procedures work with matrices by producing numeric
14 matrices that report results of data analysis, or by consuming
15 matrices as a basis for further analysis. This chapter documents the
16 format of data files that store these matrices and commands for
17 working with them, as well as @pspp{}'s general-purpose facility for
24 A matrix file is an SPSS system file that conforms to the dictionary
25 and case structure described in this section. Procedures that read
26 matrices from files expect them to be in the matrix file format.
27 Procedures that write matrices also use this format.
29 Text files that contain matrices can be converted to matrix file
30 format. @xref{MATRIX DATA}, for a command to read a text file as a
33 A matrix file's dictionary must have the following variables in the
38 Zero or more numeric split variables. These are included by
39 procedures when @cmd{SPLIT FILE} is active. @cmd{MATRIX DATA} assigns
40 split variables format F4.0.
43 @code{ROWTYPE_}, a string variable with width 8. This variable
44 indicates the kind of matrix or vector that a given case represents.
45 The supported row types are listed below.
48 Zero or more numeric factor variables. These are included by
49 procedures that divide data into cells. For within-cell data, factor
50 variables are filled with non-missing values; for pooled data, they
51 are missing. @cmd{MATRIX DATA} assigns factor variables format F4.0.
54 @code{VARNAME_}, a string variable. Matrix data includes one row per
55 continuous variable (see below), naming each continuous variable in
56 order. This column is blank for vector data. @cmd{MATRIX DATA} makes
57 @code{VARNAME_} wide enough for the name of any of the continuous
58 variables, but at least 8 bytes.
61 One or more numeric continuous variables. These are the variables
62 whose data was analyzed to produce the matrices. @cmd{MATRIX DATA}
63 assigns continuous variables format F10.4.
66 Case weights are ignored in matrix files.
69 @anchor{Matrix File Row Types}
71 Matrix files support a fixed set of types of matrix and vector data.
72 The @code{ROWTYPE_} variable in each case of a matrix file indicates
75 The supported matrix row types are listed below. Each type is listed
76 with the keyword that identifies it in @code{ROWTYPE_}. All supported
77 types of matrices are square, meaning that each matrix must include
78 one row per continuous variable, with the @code{VARNAME_} variable
79 indicating each continuous variable in turn in the same order as the
84 Correlation coefficients.
87 Covariance coefficients.
90 General-purpose matrix.
99 The supported vector row types are listed below, along with their
100 associated keyword. Vector row types only require a single row, whose
101 @code{VARNAME_} is blank:
123 Only the row types listed above may appear in matrix files. The
124 @cmd{MATRIX DATA} command, however, accepts the additional row types
125 listed below, which it changes into matrix file row types as part of
126 its conversion process:
133 Synonym for @code{STDDEV}.
136 Accepts a single number from the @code{MATRIX DATA} input and writes
137 it as an @code{N} row with the number replicated across all the
138 continuous variables.
147 VARIABLES=@var{variables}
148 [FILE=@{'@var{file_name}' | INLINE@}
149 [/FORMAT=[@{LIST | FREE@}]
150 [@{UPPER | LOWER | FULL@}]
151 [@{DIAGONAL | NODIAGONAL@}]]
152 [/SPLIT=@var{split_vars}]
153 [/FACTORS=@var{factor_vars}]
156 The following subcommands are only needed when ROWTYPE_ is not
157 specified on the VARIABLES subcommand:
158 [/CONTENTS=@{CORR,COUNT,COV,DFE,MAT,MEAN,MSE,
159 N_MATRIX,N|N_VECTOR,N_SCALAR,PROX,SD|STDDEV@}]
160 [/CELLS=@var{n_cells}]
163 The @cmd{MATRIX DATA} command convert matrices and vectors from text
164 format into the matrix file format (@xref{Matrix Files}) for use by
165 procedures that read matrices. It reads a text file or inline data
166 and outputs to the active file, replacing any data already in the
167 active dataset. The matrix file may then be used by other commands
168 directly from the active file, or it may be written to a @file{.sav}
169 file using the @cmd{SAVE} command.
171 The text data read by @cmd{MATRIX DATA} can be delimited by spaces or
172 commas. A plus or minus sign, except immediately following a @samp{d}
173 or @samp{e}, also begins a new value. Optionally, values may be
174 enclosed in single or double quotes.
176 @cmd{MATRIX DATA} can read the types of matrix and vector data
177 supported in matrix files (@pxref{Matrix File Row Types}).
179 The @subcmd{FILE} subcommand specifies the source of the command's
180 input. To read input from a text file, specify its name in quotes.
181 To supply input inline, omit @subcmd{FILE} or specify @code{INLINE}.
182 Inline data must directly follow @code{MATRIX DATA}, inside @cmd{BEGIN
183 DATA} (@pxref{BEGIN DATA}).
185 @subcmd{VARIABLES} is the only required subcommand. It names the
186 variables present in each input record in the order that they appear.
187 (@cmd{MATRIX DATA} reorders the variables in the matrix file it
188 produces, if needed to fit the matrix file format.) The variable list
189 must include split variables and factor variables, if they are present
190 in the data, in addition to the continuous variables that form matrix
191 rows and columns. It may also include a special variable named
194 Matrix data may include split variables or factor variables or both.
195 List split variables, if any, on the @subcmd{SPLIT} subcommand and
196 factor variables, if any, on the @subcmd{FACTORS} subcommand. Split
197 and factor variables must be numeric. Split and factor variables must
198 also be listed on @subcmd{VARIABLES}, with one exception: if
199 @subcmd{VARIABLES} does not include @code{ROWTYPE_}, then
200 @subcmd{SPLIT} may name a single variable that is not in
201 @subcmd{VARIABLES} (@pxref{MATRIX DATA Example 8}).
203 The @subcmd{FORMAT} subcommand accepts settings to describe the format
207 @item @code{LIST} (default)
209 LIST requires each row to begin at the start of a new input line.
210 FREE allows rows to begin in the middle of a line. Either setting
211 allows a single row to continue across multiple input lines.
213 @item @code{LOWER} (default)
216 With LOWER, only the lower triangle is read from the input data and
217 the upper triangle is mirrored across the main diagonal. UPPER
218 behaves similarly for the upper triangle. FULL reads the entire
221 @item @code{DIAGONAL} (default)
222 @itemx @code{NODIAGONAL}
223 With DIAGONAL, the main diagonal is read from the input data. With
224 NODIAGONAL, which is incompatible with FULL, the main diagonal is not
225 read from the input data but instead set to 1 for correlation matrices
226 and system-missing for others.
229 The @subcmd{N} subcommand is a way to specify the size of the
230 population. It is equivalent to specifying an @code{N} vector with
231 the specified value for each split file.
233 @cmd{MATRIX DATA} supports two different ways to indicate the kinds of
234 matrices and vectors present in the data, depending on whether a
235 variable with the special name @code{ROWTYPE_} is present in
236 @code{VARIABLES}. The following subsections explain @cmd{MATRIX DATA}
237 syntax and behavior in each case.
239 @node MATRIX DATA with ROWTYPE_
240 @subsection With @code{ROWTYPE_}
242 If @code{VARIABLES} includes @code{ROWTYPE_}, each case's
243 @code{ROWTYPE_} indicates the type of data contained in the row.
244 @xref{Matrix File Row Types}, for a list of supported row types.
246 @subsubheading Example 1: Defaults with @code{ROWTYPE_}
247 @anchor{MATRIX DATA Example 1}
249 This example shows a simple use of @cmd{MATRIX DATA} with
250 @code{ROWTYPE_} plus 8 variables named @code{var01} through
253 Because @code{ROWTYPE_} is the first variable in @subcmd{VARIABLES},
254 it appears first on each line. The first three lines in the example
255 data have @code{ROWTYPE_} values of @samp{MEAN}, @samp{SD}, and
256 @samp{N}. These indicate that these lines contain vectors of means,
257 standard deviations, and counts, respectively, for @code{var01}
258 through @code{var08} in order.
260 The remaining 8 lines have a ROWTYPE_ of @samp{CORR} which indicates
261 that the values are correlation coefficients. Each of the lines
262 corresponds to a row in the correlation matrix: the first line is for
263 @code{var01}, the next line for @code{var02}, and so on. The input
264 only contains values for the lower triangle, including the diagonal,
265 since @code{FORMAT=LOWER DIAGONAL} is the default.
267 With @code{ROWTYPE_}, the @code{CONTENTS} subcommand is optional and
268 the @code{CELLS} subcommand may not be used.
272 VARIABLES=ROWTYPE_ var01 TO var08.
274 MEAN 24.3 5.4 69.7 20.1 13.4 2.7 27.9 3.7
275 SD 5.7 1.5 23.5 5.8 2.8 4.5 5.4 1.5
276 N 92 92 92 92 92 92 92 92
280 CORR .36 .31 -.14 1.00
281 CORR .27 .16 -.12 .22 1.00
282 CORR .33 .15 -.17 .24 .21 1.00
283 CORR .50 .29 -.20 .32 .12 .38 1.00
284 CORR .17 .29 -.05 .20 .27 .20 .04 1.00
288 @subsubheading Example 2: @code{FORMAT=UPPER NODIAGONAL}
290 This syntax produces the same matrix file as example 1, but it uses
291 @code{FORMAT=UPPER NODIAGONAL} to specify the upper triangle and omit
292 the diagonal. Because the matrix's @code{ROWTYPE_} is @code{CORR},
293 @pspp{} automatically fills in the diagonal with 1.
297 VARIABLES=ROWTYPE_ var01 TO var08
298 /FORMAT=UPPER NODIAGONAL.
300 MEAN 24.3 5.4 69.7 20.1 13.4 2.7 27.9 3.7
301 SD 5.7 1.5 23.5 5.8 2.8 4.5 5.4 1.5
302 N 92 92 92 92 92 92 92 92
303 CORR .17 .50 -.33 .27 .36 -.22 .18
304 CORR .29 .29 -.20 .32 .12 .38
305 CORR .05 .20 -.15 .16 .21
306 CORR .20 .32 -.17 .12
313 @subsubheading Example 3: @subcmd{N} subcommand
315 This syntax uses the @subcmd{N} subcommand in place of an @code{N}
316 vector. It produces the same matrix file as examples 1 and 2.
320 VARIABLES=ROWTYPE_ var01 TO var08
321 /FORMAT=UPPER NODIAGONAL
324 MEAN 24.3 5.4 69.7 20.1 13.4 2.7 27.9 3.7
325 SD 5.7 1.5 23.5 5.8 2.8 4.5 5.4 1.5
326 CORR .17 .50 -.33 .27 .36 -.22 .18
327 CORR .29 .29 -.20 .32 .12 .38
328 CORR .05 .20 -.15 .16 .21
329 CORR .20 .32 -.17 .12
336 @subsubheading Example 4: Split variables
337 @anchor{MATRIX DATA Example 4}
339 This syntax defines two matrices, using the variable @samp{s1} to
340 distinguish between them. Notice how the order of variables in the
341 input matches their order on @subcmd{VARIABLES}. This example also
342 uses @code{FORMAT=FULL}.
346 VARIABLES=s1 ROWTYPE_ var01 TO var04
367 @subsubheading Example 5: Factor variables
368 @anchor{MATRIX DATA Example 5}
370 This syntax defines a matrix file that includes a factor variable
371 @samp{f1}. The data includes mean, standard deviation, and count
372 vectors for two values of the factor variable, plus a correlation
373 matrix for pooled data.
377 VARIABLES=ROWTYPE_ f1 var01 TO var04
393 @node MATRIX DATA without ROWTYPE_
394 @subsection Without @code{ROWTYPE_}
396 If @code{VARIABLES} does not contain @code{ROWTYPE_}, the
397 @subcmd{CONTENTS} subcommand defines the row types that appear in the
398 file and their order. If @subcmd{CONTENTS} is omitted,
399 @code{CONTENTS=CORR} is assumed.
401 Factor variables without @code{ROWTYPE_} introduce special
402 requirements, illustrated below in Examples 8 and 9.
404 @subsubheading Example 6: Defaults without @code{ROWTYPE_}
406 This example shows a simple use of @cmd{MATRIX DATA} with 8 variables
407 named @code{var01} through @code{var08}, without @code{ROWTYPE_}.
408 This yields the same matrix file as Example 1 (@pxref{MATRIX DATA
413 VARIABLES=var01 TO var08
414 /CONTENTS=MEAN SD N CORR.
416 24.3 5.4 69.7 20.1 13.4 2.7 27.9 3.7
417 5.7 1.5 23.5 5.8 2.8 4.5 5.4 1.5
418 92 92 92 92 92 92 92 92
423 .27 .16 -.12 .22 1.00
424 .33 .15 -.17 .24 .21 1.00
425 .50 .29 -.20 .32 .12 .38 1.00
426 .17 .29 -.05 .20 .27 .20 .04 1.00
430 @subsubheading Example 7: Split variables with explicit values
432 This syntax defines two matrices, using the variable @code{s1} to
433 distinguish between them. Each line of data begins with @code{s1}.
434 This yields the same matrix file as Example 4 (@pxref{MATRIX DATA
439 VARIABLES=s1 var01 TO var04
442 /CONTENTS=MEAN SD N CORR.
461 @subsubheading Example 8: Split variable with sequential values
462 @anchor{MATRIX DATA Example 8}
464 Like this previous example, this syntax defines two matrices with
465 split variable @code{s1}. In this case, though, @code{s1} is not
466 listed in @subcmd{VARIABLES}, which means that its value does not
467 appear in the data. Instead, @cmd{MATRIX DATA} reads matrix data
468 until the input is exhausted, supplying 1 for the first split, 2 for
469 the second, and so on.
473 VARIABLES=var01 TO var04
476 /CONTENTS=MEAN SD N CORR.
495 @subsubsection Factor variables without @code{ROWTYPE_}
497 Without @subcmd{ROWTYPE_}, factor variables introduce two new wrinkles
498 to @cmd{MATRIX DATA} syntax. First, the @subcmd{CELLS} subcommand
499 must declare the number of combinations of factor variables present in
500 the data. If there is, for example, one factor variable for which the
501 data contains three values, one would write @code{CELLS=3}; if there
502 are two (or more) factor variables for which the data contains five
503 combinations, one would use @code{CELLS=5}; and so on.
505 Second, the @subcmd{CONTENTS} subcommand must distinguish within-cell
506 data from pooled data by enclosing within-cell row types in
507 parentheses. When different within-cell row types for a single factor
508 appear in subsequent lines, enclose the row types in a single set of
509 parentheses; when different factors' values for a given within-cell
510 row type appear in subsequent lines, enclose each row type in
511 individual parentheses.
513 Without @subcmd{ROWTYPE_}, input lines for pooled data do not include
514 factor values, not even as missing values, but input lines for
517 The following examples aim to clarify this syntax.
519 @subsubheading Example 9: Factor variables, grouping within-cell records by factor
521 This syntax defines the same matrix file as Example 5 (@pxref{MATRIX
522 DATA Example 5}), without using @code{ROWTYPE_}. It declares
523 @code{CELLS=2} because the data contains two values (0 and 1) for
524 factor variable @code{f1}. Within-cell vector row types @code{MEAN},
525 @code{SD}, and @code{N} are in a single set of parentheses on
526 @subcmd{CONTENTS} because they are grouped together in subsequent
527 lines for a single factor value. The data lines with the pooled
528 correlation matrix do not have any factor values.
532 VARIABLES=f1 var01 TO var04
535 /CONTENTS=(MEAN SD N) CORR.
550 @subsubheading Example 10: Factor variables, grouping within-cell records by row type
552 This syntax defines the same matrix file as the previous example. The
553 only difference is that the within-cell vector rows are grouped
554 differently: two rows of means (one for each factor), followed by two
555 rows of standard deviations, followed by two rows of counts.
559 VARIABLES=f1 var01 TO var04
562 /CONTENTS=(MEAN) (SD) (N) CORR.
584 [IN(@{@samp{*}|'@var{file}'@})]
585 [OUT(@{@samp{*}|'@var{file}'@})]]
586 [/@{REPLACE,APPEND@}].
589 The @cmd{MCONVERT} command converts matrix data from a correlation
590 matrix and a vector of standard deviations into a covariance matrix,
593 By default, @cmd{MCONVERT} both reads and writes the active file. Use
594 the @cmd{MATRIX} subcommand to specify other files. To read a matrix
595 file, specify its name inside parentheses following @code{IN}. To
596 write a matrix file, specify its name inside parentheses following
597 @code{OUT}. Use @samp{*} to explicitly specify the active file for
600 When @cmd{MCONVERT} reads the input, by default it substitutes a
601 correlation matrix and a vector of standard deviations each time it
602 encounters a covariance matrix, and vice versa. Specify
603 @code{/APPEND} to instead have @cmd{MCONVERT} add the other form of
604 data without removing the existing data. Use @code{/REPLACE} to
605 explicitly request removing the existing data.
607 The @cmd{MCONVERT} command requires its input to be a matrix file.
608 Use @cmd{MATRIX DATA} to convert text input into matrix file format.
609 @xref{MATRIX DATA}, for details.
618 @dots{}@i{matrix commands}@dots{}
623 The following basic matrix commands are supported:
626 @t{COMPUTE} @i{variable}[@t{(}@i{index}[@t{,}@i{index}]@t{)}]@t{=}@i{expression}@t{.}
627 @t{CALL} @i{procedure}@t{(}@i{argument}@t{,} @dots{}).
628 @t{PRINT} [@i{expression}]
629 [@t{/FORMAT}@t{=}@i{format}]
630 [@t{/TITLE}@t{=}@i{title}]
631 [@t{/SPACE}@t{=}@{@t{NEWPAGE} @math{|} @i{n}@}]
632 [@{@t{/RLABELS}@t{=}@i{string}@dots{} @math{|} @t{/RNAMES}@t{=}@i{expression}@}]
633 [@{@t{/CLABELS}@t{=}@i{string}@dots{} @math{|} @t{/CNAMES}@t{=}@i{expression}@}]@t{.}
637 The following matrix commands offer support for flow control:
640 @t{DO IF} @i{expression}@t{.}
641 @dots{}@i{matrix commands}@dots{}
642 [@t{ELSE IF} @i{expression}@t{.}
643 @dots{}@i{matrix commands}@dots{}]@dots{}
645 @dots{}@i{matrix commands}@dots{}]
648 @t{LOOP} [@i{var}@t{=}@i{first} @t{TO} @i{last} [@t{BY} @i{step}]] [@t{IF} @i{expression}]@t{.}
649 @dots{}@i{matrix commands}@dots{}
650 @t{END LOOP} [@t{IF} @i{expression}]@t{.}
656 The following matrix commands support matrix input and output:
659 @t{READ} @i{variable}[@t{(}@i{index}[@t{,}@i{index}]@t{)}]
660 [@t{/FILE}@t{=}@i{file}]
661 @t{/FIELD}@t{=}@i{first} @t{TO} @i{last} [@t{BY} @i{width}]
662 [@t{/FORMAT}@t{=}@i{format}]
663 [@t{/SIZE}@t{=}@i{expression}]
664 [@t{/MODE}@t{=}@{@t{RECTANGULAR} @math{|} @t{SYMMETRIC}@}]
666 @t{WRITE} @i{expression}
667 [@t{/OUTFILE}@t{=}@i{file}]
668 @t{/FIELD}@t{=}@i{first} @t{TO} @i{last} [@t{BY} @i{width}]
669 [@t{/MODE}@t{=}@{@t{RECTANGULAR} @math{|} @t{TRIANGULAR}@}]
671 [@t{/FORMAT}@t{=}@i{format}]@t{.}
672 @t{GET} @i{variable}[@t{(}@i{index}[@t{,}@i{index}]@t{)}]
673 [@t{/FILE}@t{=}@{@i{file} @math{|} @t{*}@}]
674 [@t{/VARIABLES}@t{=}@i{variable}@dots{}]
675 [@t{/NAMES}@t{=}@i{expression}]
676 [@t{/MISSING}@t{=}@{@t{ACCEPT} @math{|} @t{OMIT} @math{|} @i{number}@}]
677 [@t{/SYSMIS}@t{=}@{@t{OMIT} @math{|} @i{number}@}]@t{.}
678 @t{SAVE} @i{expression}
679 [@t{/OUTFILE}@t{=}@{@i{file} @math{|} @t{*}@}]
680 [@t{/VARIABLES}@t{=}@i{variable}@dots{}]
681 [@t{/NAMES}@t{=}@i{expression}]
682 [@t{/STRINGS}@t{=}@i{variable}@dots{}]@t{.}
683 @t{MGET} [@t{/FILE}@t{=}@i{file}]
684 [@t{/TYPE}@t{=}@{@t{COV} @math{|} @t{CORR} @math{|} @t{MEAN} @math{|} @t{STDDEV} @math{|} @t{N} @math{|} @t{COUNT}@}]@t{.}
685 @t{MSAVE} @i{expression}
686 @t{/TYPE}@t{=}@{@t{COV} @math{|} @t{CORR} @math{|} @t{MEAN} @math{|} @t{STDDEV} @math{|} @t{N} @math{|} @t{COUNT}@}
687 [@t{/OUTFILE}@t{=}@i{file}]
688 [@t{/VARIABLES}@t{=}@i{variable}@dots{}]
689 [@t{/SNAMES}@t{=}@i{variable}@dots{}]
690 [@t{/SPLIT}@t{=}@i{expression}]
691 [@t{/FNAMES}@t{=}@i{variable}@dots{}]
692 [@t{/FACTOR}@t{=}@i{expression}]@t{.}
696 The following matrix commands provide additional support:
699 @t{DISPLAY} [@{@t{DICTIONARY} @math{|} @t{STATUS}@}]@t{.}
700 @t{RELEASE} @i{variable}@dots{}@t{.}
703 @code{MATRIX} and @code{END MATRIX} enclose a special @pspp{}
704 sub-language, called the matrix language. The matrix language does
705 not require an active dataset to be defined and only a few of the
706 matrix language commands work with any datasets that are defined.
707 Each instance of @code{MATRIX}@dots{}@code{END MATRIX} is a separate
708 program whose state is independent of any instance, so that variables
709 declared within a matrix program are forgotten at its end.
711 The matrix language works with matrices, where a @dfn{matrix} is a
712 rectangular array of real numbers. An @math{@var{n}@times{}@var{m}}
713 matrix has @var{n} rows and @var{m} columns. Some special cases are
714 important: a @math{@var{n}@times{}1} matrix is a @dfn{column vector},
715 a @math{1@times{}@var{n}} is a @dfn{row vector}, and a
716 @math{1@times{}1} matrix is a @dfn{scalar}.
718 The matrix language also has limited support for matrices that contain
719 8-byte strings instead of numbers. Strings longer than 8 bytes are
720 truncated, and shorter strings are padded with spaces. String
721 matrices are mainly useful for labeling rows and columns when printing
722 numerical matrices with the @code{MATRIX PRINT} command. Arithmetic
723 operations on string matrices will not produce useful results. The
724 user should not mix strings and numbers within a matrix.
726 The matrix language does not work with cases. A variable in the
727 matrix language represents a single matrix.
729 The matrix language does not support missing values.
731 @code{MATRIX} is a procedure, so it cannot be enclosed inside @code{DO
732 IF}, @code{LOOP}, etc.
734 Macros may be used within a matrix program, and macros may expand to
735 include entire matrix programs. The @code{DEFINE} command may not
736 appear within a matrix program. @xref{DEFINE}, for more information
739 The following sections describe the details of the matrix language:
740 first, the syntax of matrix expressions, then each of the supported
741 commands. The @code{COMMENT} command (@pxref{COMMENT}) is also
744 @node Matrix Expressions
745 @subsection Matrix Expressions
747 Many matrix commands use expressions. A matrix expression may use the
748 following operators, listed in descending order of operator
749 precedence. Within a single level, operators associate from left to
754 Function call @t{()} and matrix construction @t{@{@}}
760 Unary @t{+} and @t{-}
763 Integer sequence @t{:}
766 Exponentiation @t{**} and @t{&**}
769 Multiplication @t{*} and @t{&*}, and division @t{/} and @t{&/}
772 Addition @t{+} and subtraction @t{-}
775 Relational @t{< <= = >= > <>}
784 Logical @t{OR} and @t{XOR}
787 @xref{Matrix Functions}, for the available matrix functions. The
788 remaining operators are described in more detail below.
790 @cindex restricted expressions
791 Expressions appear in the matrix language in some contexts where there
792 would be ambiguity whether @samp{/} is an operator or a separator
793 between subcommands. In these contexts, only the operators with
794 higher precedence than @samp{/} are allowed outside parentheses.
795 Later sections call these @dfn{restricted expressions}.
797 @node Matrix Construction Operator
798 @subsubsection Matrix Construction Operator @t{@{@}}
800 Use the @t{@{}@t{@}} operator to construct matrices. Within
801 the curly braces, commas separate elements within a row and semicolons
802 separate rows. The following examples show a @math{2@times{}3}
803 matrix, a @math{1@times{}4} row vector, a @math{3@times{}1} column
804 vector, and a scalar.
806 @multitable @columnfractions .4 .05 .4
807 @item @t{@{1, 2, 3; 4, 5, 6@}}
811 @t{[1 2 3] @* [4 5 6]}
814 @math{\left(\matrix{1 & 2 & 3 \cr 4 & 5 & 6}\right)}
817 @item @t{@{3.14, 6.28, 9.24, 12.57@}}
821 [3.14 6.28 9.42 12.57]
824 @math{(\matrix{3.14 & 6.28 & 9.42 & 12.57})}
827 @item @t{@{1.41; 1.73; 2@}}
831 @t{[1.41] @* [1.73] @* [2.00]}
834 @math{(\matrix{1.41 & 1.73 & 2.00})}
842 Curly braces are not limited to holding numeric literals. They can
843 contain calculations, and they can paste together matrices and vectors
844 in any way as long as the result is rectangular. For example, if
845 @samp{m} is matrix @code{@{1, 2; 3, 4@}}, @samp{r} is row vector
846 @code{@{5, 6@}}, and @samp{c} is column vector @code{@{7, 8@}}, then
847 curly braces can be used as follows:
849 @multitable @columnfractions .4 .05 .4
850 @item @t{@{m, c; r, 10@}}
854 @t{[1 2 7] @* [3 4 8] @* [5 6 10]}
857 @math{\left(\matrix{1 & 2 & 7 \cr 3 & 4 & 8 \cr 5 & 6 & 10}\right)}
860 @item @t{@{c, 2 * c, T(r)@}}
864 @t{[7 14 5] @* [8 16 6]}
867 @math{\left(\matrix{7 & 14 & 5 \cr 8 & 16 & 6}\right)}
871 The final example above uses the transposition function @code{T}.
873 @node Matrix Sequence Operator
874 @subsubsection Integer Sequence Operator @samp{:}
876 The syntax @code{@var{first}:@var{last}:@var{step}} yields a row
877 vector of consecutive integers from @var{first} to @var{last} counting
878 by @var{step}. The final @code{:@var{step}} is optional and
879 defaults to 1 when omitted.
881 Each of @var{first}, @var{last}, and @var{step} must be a scalar and
882 should be an integer (any fractional part is discarded). Because
883 @samp{:} has a high precedence, operands other than numeric literals
884 must usually be parenthesized.
886 When @var{step} is positive (or omitted) and @math{@var{end} <
887 @var{start}}, or if @var{step} is negative and @math{@var{end} >
888 @var{start}}, then the result is an empty matrix. If @var{step} is 0,
889 then @pspp{} reports an error.
891 Here are some examples:
893 @multitable @columnfractions .4 .05 .4
894 @item @t{1:6} @tab @result{} @tab @t{@{1, 2, 3, 4, 5, 6@}}
895 @item @t{1:6:2} @tab @result{} @tab @t{@{1, 3, 5@}}
896 @item @t{-1:-5:-1} @tab @result{} @tab @t{@{-1, -2, -3, -4, -5@}}
897 @item @t{-1:-5} @tab @result{} @tab @t{@{@}}
898 @item @t{2:1:0} @tab @result{} @tab (error)
901 @node Matrix Index Operator
902 @subsubsection Index Operator @code{()}
904 The result of the submatrix or indexing operator, written
905 @code{@var{m}(@var{rindex}, @var{cindex})}, contains the rows of
906 @var{m} whose indexes are given in vector @var{rindex} and the columns
907 whose indexes are given in vector @var{cindex}.
909 In the simplest case, if @var{rindex} and @var{cindex} are both
910 scalars, the result is also a scalar:
912 @multitable @columnfractions .4 .05 .4
913 @item @t{@{10, 20; 30, 40@}(1, 1)} @tab @result{} @tab @t{10}
914 @item @t{@{10, 20; 30, 40@}(1, 2)} @tab @result{} @tab @t{20}
915 @item @t{@{10, 20; 30, 40@}(2, 1)} @tab @result{} @tab @t{30}
916 @item @t{@{10, 20; 30, 40@}(2, 2)} @tab @result{} @tab @t{40}
919 If the index arguments have multiple elements, then the result
920 includes multiple rows or columns:
922 @multitable @columnfractions .4 .05 .4
923 @item @t{@{10, 20; 30, 40@}(1:2, 1)} @tab @result{} @tab @t{@{10; 30@}}
924 @item @t{@{10, 20; 30, 40@}(2, 1:2)} @tab @result{} @tab @t{@{30, 40@}}
925 @item @t{@{10, 20; 30, 40@}(1:2, 1:2)} @tab @result{} @tab @t{@{10, 20; 30, 40@}}
928 The special argument @samp{:} may stand in for all the rows or columns
929 in the matrix being indexed, like this:
931 @multitable @columnfractions .4 .05 .4
932 @item @t{@{10, 20; 30, 40@}(:, 1)} @tab @result{} @tab @t{@{10; 30@}}
933 @item @t{@{10, 20; 30, 40@}(2, :)} @tab @result{} @tab @t{@{30, 40@}}
934 @item @t{@{10, 20; 30, 40@}(:, :)} @tab @result{} @tab @t{@{10, 20; 30, 40@}}
937 The index arguments do not have to be in order, and they may contain
938 repeated values, like this:
940 @multitable @columnfractions .4 .05 .4
941 @item @t{@{10, 20; 30, 40@}(@{2, 1@}, 1)} @tab @result{} @tab @t{@{30; 10@}}
942 @item @t{@{10, 20; 30, 40@}(2, @{2; 2; 1@})} @tab @result{} @tab @t{@{40, 40, 30@}}
943 @item @t{@{10, 20; 30, 40@}(2:1:-1, :)} @tab @result{} @tab @t{@{30, 40; 10, 20@}}
946 When the matrix being indexed is a row or column vector, only a single
947 index argument is needed, like this:
949 @multitable @columnfractions .4 .05 .4
950 @item @t{@{11, 12, 13, 14, 15@}(2:4)} @tab @result{} @tab @t{@{12, 13, 14@}}
951 @item @t{@{11; 12; 13; 14; 15@}(2:4)} @tab @result{} @tab @t{@{12; 13; 14@}}
954 When an index is not an integer, @pspp{} discards the fractional part.
955 It is an error for an index to be less than 1 or greater than the
956 number of rows or columns:
958 @multitable @columnfractions .4 .05 .4
959 @item @t{@{11, 12, 13, 14@}(@{2.5, 4.6@})} @tab @result{} @tab @t{@{12, 14@}}
960 @item @t{@{11; 12; 13; 14@}(0)} @tab @result{} @tab (error)
963 @node Matrix Unary Operators
964 @subsubsection Unary Operators
966 The unary operators take a single operand of any dimensions and
967 operate on each of its elements independently. The unary operators
972 Inverts the sign of each element.
978 Logical inversion: each positive value becomes 0 and each zero or
979 negative value becomes 1.
984 @multitable @columnfractions .4 .05 .4
985 @item @t{-@{1, -2; 3, -4@}} @tab @result{} @tab @t{@{-1, 2; -3, 4@}}
986 @item @t{+@{1, -2; 3, -4@}} @tab @result{} @tab @t{@{1, -2; 3, -4@}}
987 @item @t{NOT @{1, 0; -1, 1@}} @tab @result{} @tab @t{@{0, 1; 1, 0@}}
990 @node Matrix Elementwise Binary Operators
991 @subsubsection Elementwise Binary Operators
993 The elementwise binary operators require their operands to be matrices
994 with the same dimensions. Alternatively, if one operand is a scalar,
995 then its value is treated as if it were duplicated to the dimensions
996 of the other operand. The result is a matrix of the same size as the
997 operands, in which each element is the result of the applying the
998 operator to the corresponding elements of the operands.
1000 The elementwise binary operators are listed below.
1004 The arithmetic operators, for familiar arithmetic operations:
1014 Multiplication, if one operand is a scalar. (Otherwise this is matrix
1015 multiplication, described below.)
1017 @item @code{/} or @code{&/}
1028 The relational operators, whose results are 1 when a comparison is
1029 true and 0 when it is false:
1032 @item @code{<} or @code{LT}
1035 @item @code{<=} or @code{LE}
1038 @item @code{=} or @code{EQ}
1041 @item @code{>} or @code{GT}
1044 @item @code{>=} or @code{GE}
1045 Greater than or equal.
1047 @item @code{<>} or @code{~=} or @code{NE}
1052 The logical operators, which treat positive operands as true and
1053 nonpositive operands as false. They yield 0 for false and 1 for true:
1057 True if both operands are true.
1060 True if at least one operand is true.
1063 True if exactly one operand is true.
1069 @multitable @columnfractions .4 .05 .4
1070 @item @t{1 + 2} @tab @result{} @tab @t{3}
1071 @item @t{1 + @{3; 4@}} @tab @result{} @tab @t{@{4; 5@}}
1072 @item @t{@{66, 77; 88, 99@} + 5} @tab @result{} @tab @t{@{71, 82; 93, 104@}}
1073 @item @t{@{4, 8; 3, 7@} + @{1, 0; 5, 2@}} @tab @result{} @tab @t{@{5, 8; 8, 9@}}
1074 @item @t{@{1, 2; 3, 4@} < @{4, 3; 2, 1@}} @tab @result{} @tab @t{@{1, 1; 0, 0@}}
1075 @item @t{@{1, 3; 2, 4@} >= 3} @tab @result{} @tab @t{@{0, 1; 0, 1@}}
1076 @item @t{@{0, 0; 1, 1@} AND @{0, 1; 0, 1@}} @tab @result{} @tab @t{@{0, 0; 0, 1@}}
1079 @node Matrix Multiplication Operator
1080 @subsubsection Matrix Multiplication Operator @samp{*}
1082 If @code{A} is an @math{@var{m}@times{}@var{n}} matrix and @code{B} is
1083 an @math{@var{n}@times{}@var{p}} matrix, then @code{A*B} is the
1084 @math{@var{m}@times{}@var{p}} matrix multiplication product @code{C}.
1085 @pspp{} reports an error if the number of columns in @code{A} differs
1086 from the number of rows in @code{B}.
1088 The @code{*} operator performs elementwise multiplication (see above)
1089 if one of its operands is a scalar.
1091 No built-in operator yields the inverse of matrix multiplication.
1092 Instead, multiply by the result of @code{INV} or @code{GINV}.
1096 @multitable @columnfractions .4 .05 .4
1097 @item @t{@{1, 2, 3@} * @{4; 5; 6@}} @tab @result{} @tab @t{32}
1098 @item @t{@{4; 5; 6@} * @{1, 2, 3@}} @tab @result{} @tab @t{@{4,@w{ } 8, 12; @*@w{ }5, 10, 15; @*@w{ }6, 12, 18@}}
1101 @node Matrix Exponentiation Operator
1102 @subsubsection Matrix Exponentiation Operator @code{**}
1104 The result of @code{A**B} is defined as follows when @code{A} is a
1105 square matrix and @code{B} is an integer scalar:
1109 For @code{B > 0}, @code{A**B} is @code{A*@dots{}*A}, where there are
1110 @code{B} @samp{A}s. (@pspp{} implements this efficiently for large
1111 @code{B}, using exponentiation by squaring.)
1114 For @code{B < 0}, @code{A**B} is @code{INV(A**(-B))}.
1117 For @code{B = 0}, @code{A**B} is the identity matrix.
1121 @pspp{} reports an error if @code{A} is not square or @code{B} is not
1126 @multitable @columnfractions .4 .05 .4
1127 @item @t{@{2, 5; 1, 4@}**3} @tab @result{} @tab @t{@{48, 165; 33, 114@}}
1128 @item @t{@{2, 5; 1, 4@}**0} @tab @result{} @tab @t{@{1, 0; 0, 1@}}
1129 @item @t{10*@{4, 7; 2, 6@}**-1} @tab @result{} @tab @t{@{6, -7; -2, 4@}}
1132 @node Matrix Functions
1133 @subsection Matrix Functions
1135 The matrix language support numerous functions in multiple categories.
1136 The following subsections document each of the currently supported
1137 functions. The first letter of each parameter's name indicate the
1138 required argument type:
1145 A nonnegative integer scalar. (Non-integers are accepted and silently
1146 rounded down to the nearest integer.)
1149 A row or column vector.
1155 @node Matrix Elementwise Functions
1156 @subsubsection Elementwise Functions
1158 These functions act on each element of their argument independently,
1159 like the elementwise operators (@pxref{Matrix Elementwise Binary
1162 @deffn {Matrix Function} ABS (@var{M})
1163 Takes the absolute value of each element of @var{M}.
1165 @t{ABS(@{-1, 2; -3, 0@}) @result{} @{1, 2; 3, 0@}}
1168 @deffn {Matrix Function} ARSIN (@var{M})
1169 @deffnx {Matrix Function} ARTAN (@var{M})
1170 Computes the inverse sine or tangent, respectively, of each element in
1171 @var{M}. The results are in radians, between @math{-\pi/2} and
1172 @math{+\pi/2}, inclusive.
1174 The value of @math{\pi} can be computed as @code{4*ARTAN(1)}.
1176 @t{ARSIN(@{-1, 0, 1@}) @result{} @{-1.57, 0, 1.57@}} (approximately)
1178 @t{ARTAN(@{-5, -1, 1, 5@}) @result{} @{-1.37, -.79, .79, 1.37@}} (approximately)
1181 @deffn {Matrix Function} COS (@var{M})
1182 @deffnx {Matrix Function} SIN (@var{M})
1183 Computes the cosine or sine, respectively, of each element in @var{M},
1184 which must be in radians.
1186 @t{COS(@{0.785, 1.57; 3.14, 1.57 + 3.14@}) @result{} @{.71, 0; -1, 0@}} (approximately)
1189 @deffn {Matrix Function} EXP (@var{M})
1190 Computes @math{e^x} for each element @var{x} in @var{M}.
1192 @t{EXP(@{2, 3; 4, 5@}) @result{} @{7.39, 20.09; 54.6, 148.4@}} (approximately)
1195 @deffn {Matrix Function} LG10 (@var{M})
1196 @deffnx {Matrix Function} LN (@var{M})
1197 Takes the logarithm with base 10 or base @math{e}, respectively, of
1198 each element in @var{M}.
1200 @t{LG10(@{1, 10, 100, 1000@}) @result{} @{0, 1, 2, 3@}} @*
1201 @t{LG10(0) @result{}} (error)
1203 @t{LN(@{EXP(1), 1, 2, 3, 4@}) @result{} @{1, 0, .69, 1.1, 1.39@}} (approximately) @*
1204 @t{LN(0) @result{}} (error)
1207 @deffn {Matrix Function} MOD (@var{M}, @var{s})
1208 Takes each element in @var{M} modulo nonzero scalar value @var{s},
1209 that is, the remainder of division by @var{s}. The sign of the result
1210 is the same as the sign of the dividend.
1212 @t{MOD(@{5, 4, 3, 2, 1, 0@}, 3) @result{} @{2, 1, 0, 2, 1, 0@}} @*
1213 @t{MOD(@{5, 4, 3, 2, 1, 0@}, -3) @result{} @{2, 1, 0, 2, 1, 0@}} @*
1214 @t{MOD(@{-5, -4, -3, -2, -1, 0@}, 3) @result{} @{-2, -1, 0, -2, -1, 0@}} @*
1215 @t{MOD(@{-5, -4, -3, -2, -1, 0@}, -3) @result{} @{-2, -1, 0, -2, -1, 0@}} @*
1216 @t{MOD(@{5, 4, 3, 2, 1, 0@}, 1.5) @result{} @{.5, 1.0, .0, .5, 1.0, .0@}} @*
1217 @t{MOD(@{5, 4, 3, 2, 1, 0@}, 0) @result{}} (error)
1220 @deffn {Matrix Function} RND (@var{M})
1221 @deffnx {Matrix Function} TRUNC (@var{M})
1222 Rounds each element of @var{M} to an integer. @code{RND} rounds to
1223 the nearest integer, with halves rounded to even integers, and
1224 @code{TRUNC} rounds toward zero.
1226 @t{RND(@{-1.6, -1.5, -1.4@}) @result{} @{-2, -2, -1@}} @*
1227 @t{RND(@{-.6, -.5, -.4@}) @result{} @{-1, 0, 0@}} @*
1228 @t{RND(@{.4, .5, .6@} @result{} @{0, 0, 1@}} @*
1229 @t{RND(@{1.4, 1.5, 1.6@}) @result{} @{1, 2, 2@}}
1231 @t{TRUNC(@{-1.6, -1.5, -1.4@}) @result{} @{-1, -1, -1@}} @*
1232 @t{TRUNC(@{-.6, -.5, -.4@}) @result{} @{0, 0, 0@}} @*
1233 @t{TRUNC(@{.4, .5, .6@} @result{} @{0, 0, 0@}} @*
1234 @t{TRUNC(@{1.4, 1.5, 1.6@}) @result{} @{1, 1, 1@}}
1237 @deffn {Matrix Function} SQRT (@var{M})
1238 Takes the square root of each element of @var{M}, which must not be
1241 @t{SQRT(@{0, 1, 2, 4, 9, 81@}) @result{} @{0, 1, 1.41, 2, 3, 9@}} (approximately) @*
1242 @t{SQRT(-1) @result{}} (error)
1245 @node Matrix Logical Functions
1246 @subsubsection Logical Functions
1248 @deffn {Matrix Function} ALL (@var{M})
1249 Returns a scalar with value 1 if all of the elements in @var{M} are
1250 nonzero, or 0 if at least one element is zero.
1252 @t{ALL(@{1, 2, 3@} < @{2, 3, 4@}) @result{} 1} @*
1253 @t{ALL(@{2, 2, 3@} < @{2, 3, 4@}) @result{} 0} @*
1254 @t{ALL(@{2, 3, 3@} < @{2, 3, 4@}) @result{} 0} @*
1255 @t{ALL(@{2, 3, 4@} < @{2, 3, 4@}) @result{} 0}
1258 @deffn {Matrix Function} ANY (@var{M})
1259 Returns a scalar with value 1 if any of the elements in @var{M} is
1260 nonzero, or 0 if all of them are zero.
1262 @t{ANY(@{1, 2, 3@} < @{2, 3, 4@}) @result{} 1} @*
1263 @t{ANY(@{2, 2, 3@} < @{2, 3, 4@}) @result{} 1} @*
1264 @t{ANY(@{2, 3, 3@} < @{2, 3, 4@}) @result{} 1} @*
1265 @t{ANY(@{2, 3, 4@} < @{2, 3, 4@}) @result{} 0}
1268 @node Matrix Construction Functions
1269 @subsubsection Matrix Construction Functions
1271 @deffn {Matrix Function} BLOCK (@var{M1}, @dots{}, @var{Mn})
1272 Returns a block diagonal matrix with as many rows as the sum of its
1273 arguments' row counts and as many columns as the sum of their columns.
1274 Each argument matrix is placed along the main diagonal of the result,
1275 and all other elements are zero.
1278 @t{BLOCK(@{1, 2; 3, 4@}, 5, @{7; 8; 9@}, @{10, 11@}) @result{}
1289 @deffn {Matrix Function} IDENT (@var{n})
1290 @deffnx {Matrix Function} IDENT (@var{nr}, @var{nc})
1291 Returns an identity matrix, whose main diagonal elements are one and
1292 whose other elements are zero. The returned matrix has @var{n} rows
1293 and columns or @var{nr} rows and @var{nc} columns, respectively.
1296 @t{IDENT(1) @result{} 1
1300 IDENT(3, 5) @result{}
1304 IDENT(5, 3) @result{}
1313 @deffn {Matrix Function} MAGIC (@var{n})
1314 Returns an @math{@var{n}@times{}@var{n}} matrix that contains each of
1315 the integers @math{1@dots{}@var{n}} once, in which each column, each
1316 row, and each diagonal sums to @math{n(n^2+1)/2}. There are many
1317 magic squares with given dimensions, but this function always returns
1318 the same one for a given value of @var{n}.
1320 @t{MAGIC(3) @result{} @{8, 1, 6; 3, 5, 7; 4, 9, 2@}} @*
1321 @t{MAGIC(4) @result{} @{1, 5, 12, 16; 15, 11, 6, 2; 14, 8, 9, 3; 4, 10, 7, 13@}}
1324 @deffn {Matrix Function} MAKE (@var{nr}, @var{nc}, @var{s})
1325 Returns an @math{@var{nr}@times{}@var{nc}} matrix whose elements are
1328 @t{MAKE(1, 2, 3) @result{} @{3, 3@}} @*
1329 @t{MAKE(2, 1, 4) @result{} @{4; 4@}} @*
1330 @t{MAKE(2, 3, 5) @result{} @{5, 5, 5; 5, 5, 5@}}
1333 @deffn {Matrix Function} MDIAG (@var{V})
1334 @anchor{MDIAG} Given @var{n}-element vector @var{V}, returns a
1335 @math{@var{n}@times{}@var{n}} matrix whose main diagonal is copied
1336 from @var{V}. The other elements in the returned vector are zero.
1338 Use @code{CALL SETDIAG} (@pxref{CALL SETDIAG}) to replace the main
1339 diagonal of a matrix in-place.
1342 @t{MDIAG(@{1, 2, 3, 4@}) @result{}
1350 @deffn {Matrix Function} RESHAPE (@var{M}, @var{nr}, @var{nc})
1351 Returns an @math{@var{nr}@times{}@var{nc}} matrix whose elements come
1352 from @var{M}, which must have the same number of elements as the new
1353 matrix, copying elements from @var{M} to the new matrix row by row.
1356 @t{RESHAPE(1:12, 1, 12) @result{}
1357 1 2 3 4 5 6 7 8 9 10 11 12
1358 RESHAPE(1:12, 2, 6) @result{}
1361 RESHAPE(1:12, 3, 4) @result{}
1365 RESHAPE(1:12, 4, 3) @result{}
1373 @deffn {Matrix Function} T (@var{M})
1374 @deffnx {Matrix Function} TRANSPOS (@var{M})
1375 Returns @var{M} with rows exchanged for columns.
1377 @t{T(@{1, 2, 3@}) @result{} @{1; 2; 3@}} @*
1378 @t{T(@{1; 2; 3@}) @result{} @{1, 2, 3@}}
1381 @deffn {Matrix Function} UNIFORM (@var{nr}, @var{nc})
1382 Returns a @math{@var{nr}@times{}@var{nc}} matrix in which each element
1383 is randomly chosen from a uniform distribution of real numbers between
1384 0 and 1. Random number generation honors the current seed setting
1387 The following example shows one possible output, but of course every
1388 result will be different (given different seeds):
1391 @t{UNIFORM(4, 5)*10 @result{}
1392 7.71 2.99 .21 4.95 6.34
1393 4.43 7.49 8.32 4.99 5.83
1394 2.25 .25 1.98 7.09 7.61
1395 2.66 1.69 2.64 .88 1.50}
1399 @node Matrix Minimum and Maximum and Sum Functions
1400 @subsubsection Minimum, Maximum, and Sum Functions
1402 @deffn {Matrix Function} CMIN (@var{M})
1403 @deffnx {Matrix Function} CMAX (@var{M})
1404 @deffnx {Matrix Function} CSUM (@var{M})
1405 @deffnx {Matrix Function} CSSQ (@var{M})
1406 Returns a row vector with the same number of columns as @var{M}, in
1407 which each element is the minimum, maximum, sum, or sum of squares,
1408 respectively, of the elements in the same column of @var{M}.
1410 @t{CMIN(@{1, 2, 3; 4, 5, 6; 7, 8, 9@} @result{} @{1, 2, 3@}} @*
1411 @t{CMAX(@{1, 2, 3; 4, 5, 6; 7, 8, 9@} @result{} @{7, 8, 9@}} @*
1412 @t{CSUM(@{1, 2, 3; 4, 5, 6; 7, 8, 9@} @result{} @{12, 15, 18@}} @*
1413 @t{CSSQ(@{1, 2, 3; 4, 5, 6; 7, 8, 9@} @result{} @{66, 93, 126@}}
1416 @deffn {Matrix Function} MMIN (@var{M})
1417 @deffnx {Matrix Function} MMAX (@var{M})
1418 @deffnx {Matrix Function} MSUM (@var{M})
1419 @deffnx {Matrix Function} MSSQ (@var{M})
1420 Returns the minimum, maximum, sum, or sum of squares, respectively, of
1421 the elements of @var{M}.
1423 @t{MMIN(@{1, 2, 3; 4, 5, 6; 7, 8, 9@} @result{} 1} @*
1424 @t{MMAX(@{1, 2, 3; 4, 5, 6; 7, 8, 9@} @result{} 9} @*
1425 @t{MSUM(@{1, 2, 3; 4, 5, 6; 7, 8, 9@} @result{} 45} @*
1426 @t{MSSQ(@{1, 2, 3; 4, 5, 6; 7, 8, 9@} @result{} 285}
1429 @deffn {Matrix Function} RMIN (@var{M})
1430 @deffnx {Matrix Function} RMAX (@var{M})
1431 @deffnx {Matrix Function} RSUM (@var{M})
1432 @deffnx {Matrix Function} RSSQ (@var{M})
1433 Returns a column vector with the same number of rows as @var{M}, in
1434 which each element is the minimum, maximum, sum, or sum of squares,
1435 respectively, of the elements in the same row of @var{M}.
1437 @t{RMIN(@{1, 2, 3; 4, 5, 6; 7, 8, 9@} @result{} @{1; 4; 7@}} @*
1438 @t{RMAX(@{1, 2, 3; 4, 5, 6; 7, 8, 9@} @result{} @{3; 6; 9@}} @*
1439 @t{RSUM(@{1, 2, 3; 4, 5, 6; 7, 8, 9@} @result{} @{6; 15; 24@}} @*
1440 @t{RSSQ(@{1, 2, 3; 4, 5, 6; 7, 8, 9@} @result{} @{14; 77; 194@}}
1443 @deffn {Matrix Function} SSCP (@var{M})
1444 Returns @math{@var{M}^T @times{} @var{M}}.
1446 @t{SSCP(@{1, 2, 3; 4, 5, 6@}) @result{} @{17, 22, 27; 22, 29, 36; 27, 36, 45@}}
1449 @deffn {Matrix Function} TRACE (@var{M})
1450 Returns the sum of the elements along @var{M}'s main diagonal,
1451 equivalent to @code{MSUM(DIAG(@var{M}))}.
1453 @t{TRACE(MDIAG(1:5)) @result{} 15}
1456 @node Matrix Property Functions
1457 @subsubsection Matrix Property Functions
1459 @deffn {Matrix Function} NROW (@var{M})
1460 @deffnx {Matrix Function} NCOL (@var{M})
1461 Returns the number of row or columns, respectively, in @var{M}.
1464 @t{NROW(@{1, 0; -2, -3; 3, 3@}) @result{} 3
1465 NROW(1:5) @result{} 1
1467 NCOL(@{1, 0; -2, -3; 3, 3@}) @result{} 2
1468 NCOL(1:5) @result{} 5}
1472 @deffn {Matrix Function} DIAG (@var{M})
1473 Returns a column vector containing a copy of @var{M}'s main diagonal.
1474 The vector's length is the lesser of @code{NCOL(@var{M})} and
1475 @code{NROW(@var{M})}.
1477 @t{DIAG(@{1, 0; -2, -3; 3, 3@}) @result{} @{1; -3@}}
1480 @node Matrix Rank Ordering Functions
1481 @subsubsection Matrix Rank Ordering Functions
1483 The @code{GRADE} and @code{RANK} functions each take a matrix @var{M}
1484 and return a matrix @var{r} with the same dimensions. Each element in
1485 @var{r} ranges between 1 and the number of elements @var{n} in
1486 @var{M}, inclusive. When the elements in @var{M} all have unique
1487 values, both of these functions yield the same results: the smallest
1488 element in @var{M} corresponds to value 1 in @var{r}, the next
1489 smallest to 2, and so on, up to the largest to @var{n}. When multiple
1490 elements in @var{M} have the same value, these functions use different
1491 rules for handling the ties.
1493 @deffn {Matrix Function} GRADE (@var{M})
1494 Returns a ranking of @var{M}, turning duplicate values into sequential
1495 ranks. The returned matrix always contains each of the integers 1
1496 through the number of elements in the matrix exactly once.
1498 @t{GRADE(@{1, 0, 3; 3, 1, 2; 3, 0, 5@})} @result{} @t{@{3, 1, 6; 7, 4, 5; 8, 2, 9@}}
1501 @deffn {Matrix Function} RNKORDER (@var{M})
1502 Returns a ranking of @var{M}, turning duplicate values into the mean
1503 of their sequential ranks.
1505 @t{RNKORDER(@{1, 0, 3; 3, 1, 2; 3, 0, 5@})} @*@w{ }@result{} @t{@{3.5, 1.5, 7; 7, 3.5, 5; 7, 1.5, 9@}}
1509 One may use @code{GRADE} to sort a vector:
1512 COMPUTE v(GRADE(v))=v. /* Sort v in ascending order.
1513 COMPUTE v(GRADE(-v))=v. /* Sort v in descending order.
1516 @node Matrix Algebra Functions
1517 @subsubsection Matrix Algebra Functions
1519 @deffn {Matrix Function} CHOL (@var{M})
1520 Matrix @var{M} must be an @math{@var{n}@times{}@var{n}} symmetric
1521 positive-definite matrix. Returns an @math{@var{n}@times{}@var{n}}
1522 matrix @var{B} such that @math{@var{B}^T@times{}@var{B}=@var{M}}.
1525 @t{CHOL(@{4, 12, -16; 12, 37, -43; -16, -43, 98@}) @result{}
1532 @deffn {Matrix Function} DESIGN (@var{M})
1533 Returns a design matrix for @var{M}. The design matrix has the same
1534 number of rows as @var{M}. Each column @var{c} in @var{M}, from left
1535 to right, yields a group of columns in the output. For each unique
1536 value @var{v} in @var{c}, from top to bottom, add a column to the
1537 output in which @var{v} becomes 1 and other values become 0.
1539 @pspp{} issues a warning if a column only contains a single unique value.
1542 @t{DESIGN(@{1; 2; 3@}) @result{} @{1, 0, 0; 0, 1, 0; 0, 0, 1@}}
1543 @t{DESIGN(@{5; 8; 5@}) @result{} @{1, 0; 0, 1; 1, 0@}}
1544 @t{DESIGN(@{1, 5; 2, 8; 3, 5@})}
1545 @result{} @t{@{1, 0, 0, 1, 0; 0, 1, 0, 0, 1; 0, 0, 1, 1, 0@}}
1546 @t{DESIGN(@{5; 5; 5@})} @result{} (warning)
1550 @deffn {Matrix Function} DET (@var{M})
1551 Returns the determinant of square matrix @var{M}.
1554 @deffn {Matrix Function} EVAL (@var{M})
1556 Returns a column vector containing the eigenvalues of symmetric matrix
1557 @var{M}, sorted in ascending order.
1559 Use @code{CALL EIGEN} (@pxref{CALL EIGEN}) to compute eigenvalues and
1560 eigenvectors of a matrix.
1563 @deffn {Matrix Function} GINV (@var{M})
1564 Returns the @math{@var{k}@times{}@var{n}} matrix @var{A} that is the
1565 @dfn{generalized inverse} of @math{@var{n}@times{}@var{k}} matrix
1566 @var{M}, defined such that
1567 @math{@var{M}@times{}@var{A}@times{}@var{M}=@var{M}} and
1568 @math{@var{A}@times{}@var{M}@times{}@var{A}=@var{A}}.
1572 @deffn {Matrix Function} GSCH (@var{M})
1573 @var{M} must be a @math{@var{n}@times{}@var{m}} matrix, @math{@var{m}
1574 @geq{} @var{n}}, with rank @var{n}. Returns an
1575 @math{@var{n}@times{}@var{n}} orthonormal basis for @var{M}, obtained
1576 using the Gram-Schmidt process.
1579 @deffn {Matrix Function} INV (@var{M})
1580 Returns the @math{@var{n}@times{}@var{n}} matrix @var{A} that is the
1581 inverse of @math{@var{n}@times{}@var{n}} matrix @var{M}, defined such
1582 that @math{@var{M}@times{}@var{A} = @var{A}@times{}@var{M} = I}, where
1583 @var{I} is the identity matrix. @var{M} must not be singular, that
1584 is, @math{\det(@var{M}) @ne{} 0}.
1587 @deffn {Matrix Function} KRONEKER (@var{Ma}, @var{Mb})
1588 Returns the @math{@var{pm}@times{}@var{qn}} matrix @var{P} that is the
1589 @dfn{Kroneker product} of @math{@var{m}@times{}@var{n}} matrix
1590 @var{Ma} and @math{@var{p}@times{}@var{q}} matrix @var{Mb}. One may
1591 view @var{P} as the concatenation of multiple
1592 @math{@var{p}@times{}@var{q}} blocks, each of which is the scalar
1593 product of @var{Mb} by a different element of @var{Ma}. For example,
1594 when @code{A} is a @math{2@times{}2} matrix, @code{KRONEKER(A, B)} is
1595 equivalent to @code{@{A(1,1)*B, A(1,2)*B; A(2,1)*B, A(2,2)*B@}}.
1598 @deffn {Matrix Function} RANK (@var{M})
1599 Returns the rank of matrix @var{M}, a integer scalar whose value is
1600 the dimension of the vector space spanned by its columns or,
1601 equivalently, by its rows.
1604 @deffn {Matrix Function} SOLVE (@var{Ma}, @var{Mb})
1605 @var{Ma} must be an @math{@var{n}@times{}@var{n}} matrix, with
1606 @math{\det(@var{Ma}) @ne{} 0}, and @var{Mb} an
1607 @math{@var{n}@times{}@var{k}} matrix. Returns an
1608 @math{@var{n}@times{}@var{k}} matrix @var{X} such that @math{@var{Ma}
1609 @times{} @var{X} = @var{Mb}}.
1612 @deffn {Matrix Function} SVAL (@var{M})
1615 Given @math{@var{n}@times{}@var{k}} matrix @var{M}, returns a
1616 @math{\min(@var{n},@var{k})}-element column vector containing the
1617 singular values of @var{M} in descending order.
1619 Use @code{CALL SVD} (@pxref{CALL SVD}) to compute the full singular
1620 value decomposition of a matrix.
1623 @deffn {Matrix Function} SWEEP (@var{M}, @var{nk})
1624 Given @math{@var{r}@times{}@var{c}} matrix @var{M} and integer scalar
1625 @math{k = @var{nk}} such that @math{1 @leq{} k @leq{}
1626 \min(@var{r},@var{c})}, returns the @math{@var{r}@times{}@var{c}}
1627 sweep matrix @var{A}.
1629 If @math{@var{M}_{kk} @ne{} 0}, then:
1632 @math{@var{A}_{kk} = 1/@var{M}_{kk}},
1633 @math{@var{A}_{ik} = -@var{M}_{ik}/@var{M}_{kk} @r{for} i @ne{} k},
1634 @math{@var{A}_{kj} = @var{M}_{kj}/@var{M}_{kk} @r{for} j @ne{} k, @r{and}}
1635 @math{@var{A}_{ij} = @var{M}_{ij} - (@var{M}_{ik} * @var{M}_{kj}) / @var{M}_{kk} @r{for} i @ne{} k @r{and} j @ne{} k}.
1638 If @math{@var{M}_{kk} = 0}, then:
1641 @math{@var{A}_{ik} = @var{A}_{ki} = 0 @r{and}}
1642 @math{@var{A}_{ij} = @var{M}_{ij}, @r{for} i @ne{} k @r{and} j @ne{} k}.
1649 @deffn {Matrix Function} EOF (@var{file})
1650 @anchor{EOF Matrix Function}
1652 Given a file handle or file name @var{file}, returns an integer scalar
1653 that indicates whether the last record in the file has been read.
1654 Determining this requires attempting reading past the current record,
1655 which means that @code{REREAD} on the next @code{READ} command
1656 following @code{EOF} on the same file will be ineffective.
1659 @node Matrix COMPUTE Command
1660 @subsection The @code{COMPUTE} Command
1663 @t{COMPUTE} @i{variable}[@t{(}@i{index}[@t{,}@i{index}]@t{)}]@t{=}@i{expression}@t{.}
1666 The @code{COMPUTE} command evaluates an expression and assigns the
1667 result to a variable or a submatrix of a variable. Assigning to a
1668 submatrix uses the same syntax as the index operator (@pxref{Matrix
1671 @node Matrix CALL command
1672 @subsection The @code{CALL} Command
1674 A matrix function returns a single result. The @code{CALL} command
1675 implements procedures, which take a similar syntactic form to
1676 functions but yield results by modifying their arguments rather than
1679 Output arguments to a @code{CALL} procedure must be a single variable
1682 The following procedures are implemented via @code{CALL} to allow them
1683 to return multiple results. For these procedures, the output
1684 arguments need not name existing variables; if they do, then their
1685 previous values are replaced:
1688 @item @t{CALL EIGEN(@var{M}, @var{evec}, @var{eval})}
1691 Computes the eigenvalues and eigenvector of symmetric
1692 @math{@var{n}@times{}@var{n}} matrix @var{M}. Assigns the
1693 eigenvectors of @var{M} to the columns of
1694 @math{@var{n}@times{}@var{n}} matrix @var{evec} and the eigenvalues in
1695 descending order to @var{n}-element column vector @var{eval}.
1697 Use the @code{EVAL} function (@pxref{EVAL}) to compute just the
1698 eigenvalues of a symmetric matrix.
1700 @item @t{CALL SVD(@var{M}, @var{U}, @var{S}, @var{V})}
1703 Computes the singular value decomposition of
1704 @math{@var{n}@times{}@var{k}} matrix @var{M}, assigning @var{S} a
1705 @math{@var{n}@times{}@var{k}} diagonal matrix and to @var{U} and
1706 @var{V} unitary @math{@var{k}@times{}@var{k}} matrices such that
1707 @math{@var{M} = @var{U}@times{}@var{S}@times{}@var{V}^T}. The main
1708 diagonal of @var{Q} contains the singular values of @var{M}.
1710 Use the @code{SVAL} function (@pxref{SVAL}) to compute just the
1711 singular values of a matrix.
1714 The final procedure is implemented via @code{CALL} to allow it to
1715 modify a matrix instead of returning a modified version. For this
1716 procedure, the output argument must name an existing variable.
1719 @item @t{CALL SETDIAG(@var{M}, @var{V})}
1720 @anchor{CALL SETDIAG}
1722 Replaces the main diagonal of @math{@var{n}@times{}@var{p}} matrix
1723 @var{M} by the contents of @var{k}-element vector @var{V}. If
1724 @math{@var{k} = 1}, so that @var{V} is a scalar, replaces all of the
1725 diagonal elements of @var{M} by @var{V}. If @math{@var{k} <
1726 \min(@var{n},@var{p})}, only the upper @var{k} diagonal elements are
1727 replaced; if @math{@var{k} > \min(@var{n},@var{p})}, then the
1728 extra elements of @var{V} are ignored.
1730 Use the @code{MDIAG} function (@pxref{MDIAG}) to construct a new
1731 matrix with a specified main diagonal.
1734 @node Matrix PRINT Command
1735 @subsection The @code{PRINT} Command
1738 @t{PRINT} [@i{expression}]
1739 [@t{/FORMAT}@t{=}@i{format}]
1740 [@t{/TITLE}@t{=}@i{title}]
1741 [@t{/SPACE}@t{=}@{@t{NEWPAGE} @math{|} @i{n}@}]
1742 [@{@t{/RLABELS}@t{=}@i{string}@dots{} @math{|} @t{/RNAMES}@t{=}@i{expression}@}]
1743 [@{@t{/CLABELS}@t{=}@i{string}@dots{} @math{|} @t{/CNAMES}@t{=}@i{expression}@}]@t{.}
1746 The @code{PRINT} command is commonly used to display a matrix. It
1747 evaluates the restricted @var{expression}, if present, and outputs it
1748 either as text or a pivot table, depending on the setting of
1749 @code{MDISPLAY} (@pxref{SET MDISPLAY}).
1751 Use the @code{FORMAT} subcommand to specify a format, such as
1752 @code{F8.2}, for displaying the matrix elements. @code{FORMAT} is
1753 optional for numerical matrices. When it is omitted, @pspp{} chooses
1754 how to format entries automatically using @var{m}, the magnitude of
1755 the largest-magnitude element in the matrix to be displayed:
1759 If the matrix's elements are all integers, then, if possible, @pspp{}
1760 chooses the narrowest @code{F} format with width 12 or less that fits
1761 @var{m} plus a sign.
1764 Otherwise, if @math{@var{m} @geq{} 10^9} or @math{@var{m} @leq{}
1765 10^{-4}}, @pspp{} scales all of the numbers in the matrix by
1766 @math{10^x}, where @var{x} is the exponent used when @var{m} is
1767 displayed in scientific notation, and displays the scaled value in
1768 format @code{F13.10}. @pspp{} adds a note to the output to indicate
1772 Otherwise, @pspp{} displays the value, without scaling, in format
1776 The optional @code{TITLE} subcommand specifies a title for the output
1777 text or table, as a quoted string. When it is omitted, the syntax of
1778 the matrix expression is used as the title.
1780 Use the @code{SPACE} subcommand to request extra space above the
1781 matrix output. With a numerical argument, it adds the specified
1782 number of lines of blank space above the matrix. With @code{NEWPAGE}
1783 as an argument, it prints the matrix at the top of a new page. The
1784 @code{SPACE} subcommand has no effect when a matrix is output as a
1787 The @code{RLABELS} and @code{RNAMES} subcommands, which are mutually
1788 exclusive, can supply a label to accompany each row in the output.
1789 With @code{RLABELS}, specify the labels as comma-separated strings or
1790 other tokens. With @code{RNAMES}, specify a single expression that
1791 evaluates to a vector of strings. Either way, if there are more
1792 labels than rows, the extra labels are ignored, and if there are more
1793 rows than labels, the extra rows are unlabeled. For output to a pivot
1794 table with @code{RLABELS}, the labels can be any length; otherwise,
1795 the labels are truncated to 8 bytes.
1797 The @code{CLABELS} and @code{CNAMES} subcommands work for labeling
1798 columns as @code{RLABELS} and @code{RNAMES} do for labeling rows.
1800 @subsubheading Text Output
1802 When the @var{expression} is omitted, @code{PRINT} does not output a
1803 matrix. Instead, it outputs only the text specified on @code{TITLE},
1804 if any, preceded by any space specified on the @code{SPACE}
1805 subcommand, if any. Any other subcommands are ignored, and the
1806 command acts as if @code{MDISPLAY} is set to @code{TEXT} regardless of
1809 @node Matrix DO IF Command
1810 @subsection The @code{DO IF} Command
1813 @t{DO IF} @i{expression}@t{.}
1814 @dots{}@i{matrix commands}@dots{}
1815 [@t{ELSE IF} @i{expression}@t{.}
1816 @dots{}@i{matrix commands}@dots{}]@dots{}
1818 @dots{}@i{matrix commands}@dots{}]
1822 A @code{DO IF} command evaluates its expression argument. If the
1823 @code{DO IF} expression evaluates to true, then @pspp{} executes the
1824 associated commands. Otherwise, @pspp{} evaluates the expression on
1825 each @code{ELSE IF} clause (if any) in order, and executes the
1826 commands associated with the first one that yields a true value.
1827 Finally, if the @code{DO IF} and all the @code{ELSE IF} expressions
1828 all evaluate to false, @pspp{} executes the commands following the
1829 @code{ELSE} clause (if any).
1831 Each expression on @code{DO IF} and @code{ELSE IF} must evaluate to a
1832 scalar. Positive scalars are considered to be true, and scalars that
1833 are zero or negative are considered to be false.
1835 @node Matrix LOOP and BREAK Commands
1836 @subsection The @code{LOOP} and @code{BREAK} Commands
1839 @t{LOOP} [@i{var}@t{=}@i{first} @t{TO} @i{last} [@t{BY} @i{step}]] [@t{IF} @i{expression}]@t{.}
1840 @dots{}@i{matrix commands}@dots{}
1841 @t{END LOOP} [@t{IF} @i{expression}]@t{.}
1846 The @code{LOOP} command executes a nested group of matrix commands,
1847 called the loop's @dfn{body}, repeatedly. It has three optional
1848 clauses that control how many times the loop body executes.
1849 Regardless of these clauses, the global @code{MXLOOPS} setting, which
1850 defaults to 40, also limits the number of iterations of a loop. To
1851 iterate more times, raise the maximum with @code{SET MXLOOPS} outside
1852 of the @code{MATRIX} command (@pxref{SET MXLOOPS}).
1854 The optional index clause causes @var{var} to be assigned successive
1855 values on each trip through the loop: first @var{first}, then
1856 @math{@var{first} + @var{step}}, then @math{@var{first} + 2 @times{}
1857 @var{step}}, and so on. The loop ends when @math{@var{var} >
1858 @var{last}}, for positive @var{step}, or @math{@var{var} <
1859 @var{last}}, for negative @var{step}. If @var{step} is not specified,
1860 it defaults to 1. All the index clause expressions must evaluate to
1861 scalars, and non-integers are rounded toward zero. If @var{step}
1862 evaluates as zero (or rounds to zero), then the loop body never
1865 The optional @code{IF} on @code{LOOP} is evaluated before each
1866 iteration through the loop body. If its expression, which must
1867 evaluate to a scalar, is zero or negative, then the loop terminates
1868 without executing the loop body.
1870 The optional @code{IF} on @code{END LOOP} is evaluated after each
1871 iteration through the loop body. If its expression, which must
1872 evaluate to a scalar, is zero or negative, then the loop terminates.
1874 The @code{BREAK} command may be used inside a loop body, ordinarily
1875 within a @code{DO IF} command. If it is executed, then the loop
1876 terminates immediately, jumping to the command just following
1877 @code{END LOOP}. When multiple @code{LOOP} commands nest,
1878 @code{BREAK} terminates the innermost loop.
1880 @node Matrix READ and WRITE Commands
1881 @subsection The @code{READ} and @code{WRITE} Commands
1883 The @code{READ} and @code{WRITE} commands perform matrix input and
1884 output with text files. They share the following syntax for
1885 specifying how data is divided among input lines:
1888 @t{/FIELD}@t{=}@i{first} @t{TO} @i{last} [@t{BY} @i{width}]
1889 [@t{/FORMAT}@t{=}@i{format}]
1892 Both commands require the @code{FIELD} subcommand. It specifies the
1893 range of columns, from @var{first} to @var{last}, inclusive, that the
1894 data occupies on each line of the file. The leftmost column is column
1895 1. The columns must be literal numbers, not expressions. To use
1896 entire lines, even if they might be very long, specify a column range
1897 such as @code{1 TO 100000}.
1899 The @code{FORMAT} subcommand is optional for numerical matrices. For
1900 string matrix input and output, specify an @code{A} format. In
1901 addition to @code{FORMAT}, the optional @code{BY} specification on
1902 @code{FIELD} determine the meaning of each text line:
1906 Without @code{BY} and @code{FORMAT}, the numbers in the text file are
1907 in @code{F} format separated by spaces or commas. For @code{WRITE},
1908 @pspp{} uses as many digits of precision needed to represent the
1909 numbers in the matrix
1912 With @code{BY @i{width}}, the input area is divided into fixed-width
1913 fields with the given @i{width}. The input area must be a multiple of
1914 @i{width} columns wide. Numbers are read or written as
1915 @code{F@i{width}.0} format.
1918 With @code{FORMAT=@i{count}F}, the input area is divided into
1919 @i{count} equal-width fields per line. The input area must be a
1920 multiple of @i{count} columns wide. Another format type may be
1921 substituted for @code{F}.
1924 @code{FORMAT=F@i{w}.@i{d}} divides the input area into fixed-width
1925 fields with width @i{w}. The input area must be a multiple of @i{w}
1926 columns wide. Another format type may be substituted for @code{F}.
1929 If @code{BY} and @code{FORMAT} are both used, then they must agree on
1933 @node Matrix READ Command
1934 @subsubsection The @code{READ} Command
1937 @t{READ} @i{variable}[@t{(}@i{index}[@t{,}@i{index}]@t{)}]
1938 [@t{/FILE}@t{=}@i{file}]
1939 @t{/FIELD}@t{=}@i{first} @t{TO} @i{last} [@t{BY} @i{width}]
1940 [@t{/FORMAT}@t{=}@i{format}]
1941 [@t{/SIZE}@t{=}@i{expression}]
1942 [@t{/MODE}@t{=}@{@t{RECTANGULAR} @math{|} @t{SYMMETRIC}@}]
1946 The @code{READ} command reads from a text file into a matrix variable.
1947 Specify the target variable just after the command name, either just a
1948 variable name to create or replace an entire variable, or a variable
1949 name followed by an indexing expression to replace a submatrix of an
1952 The @code{FILE} subcommand is required in the first @code{READ}
1953 command that appears within @code{MATRIX}. It specifies the text file
1954 to be read, either as a file name in quotes or a file handle
1955 previously declared on @code{FILE HANDLE} (@pxref{FILE HANDLE}).
1956 Later @code{READ} commands (in syntax order) use the previous
1957 referenced file if @code{FILE} is omitted.
1959 The @code{FIELD} and @code{FORMAT} subcommands specify how input lines
1960 are interpreted. @xref{Matrix READ and WRITE Commands}, for details.
1962 The @code{SIZE} subcommand is required for reading into an entire
1963 variable. Its restricted expression argument should evaluate to a
1964 2-element vector @code{@{@var{n},@w{ }@var{m}@}} or
1965 @code{@{@var{n};@w{ }@var{m}@}}, which indicates a
1966 @math{@var{n}@times{}@var{m}} matrix destination. A scalar @var{n} is
1967 also allowed and indicates a @math{@var{n}@times{}1} column vector
1968 destination. When the destination is a submatrix, @code{SIZE} is
1969 optional, and if it is present then it must match the size of the
1972 By default, or with @code{MODE=RECTANGULAR}, the command reads an
1973 entry for every row and column. With @code{MODE=SYMMETRIC}, the
1974 command reads only the entries on and below the matrix's main
1975 diagonal, and copies the entries above the main diagonal from the
1976 corresponding symmetric entries below it. Only square matrices
1977 may use @code{MODE=SYMMETRIC}.
1979 Ordinarily, each @code{READ} command starts from a new line in the
1980 text file. Specify the @code{REREAD} subcommand to instead start from
1981 the last line read by the previous @code{READ} command. This has no
1982 effect for the first @code{READ} command to read from a particular
1983 file. It is also ineffective just after a command that uses the
1984 @code{EOF} matrix function (@pxref{EOF Matrix Function}) on a
1985 particular file, because @code{EOF} has to try to read the next line
1986 from the file to determine whether the file contains more input.
1988 @node Matrix WRITE Command
1989 @subsubsection The @code{WRITE} Command
1992 @t{WRITE} @i{expression}
1993 [@t{/OUTFILE}@t{=}@i{file}]
1994 @t{/FIELD}@t{=}@i{first} @t{TO} @i{last} [@t{BY} @i{width}]
1995 [@t{/FORMAT}@t{=}@i{format}]
1996 [@t{/MODE}@t{=}@{@t{RECTANGULAR} @math{|} @t{TRIANGULAR}@}]
2000 The @code{WRITE} command evaluates @i{expression} and writes it to a
2001 text file in a specified format. Write the expression to evaluate
2002 just after the command name.
2004 The @code{OUTFILE} subcommand is required in the first @code{WRITE}
2005 command that appears within @code{MATRIX}. It specifies the text file
2006 to be written, either as a file name in quotes or a file handle
2007 previously declared on @code{FILE HANDLE} (@pxref{FILE HANDLE}).
2008 Later @code{WRITE} commands (in syntax order) use the previous
2009 referenced file if @code{FILE} is omitted.
2011 The @code{FIELD} and @code{FORMAT} subcommands specify how output
2012 lines are formed. @xref{Matrix READ and WRITE Commands}, for details.
2014 By default, or with @code{MODE=RECTANGULAR}, the command writes an
2015 entry for every row and column. With @code{MODE=TRIANGULAR}, the
2016 command writes only the entries on and below the matrix's main
2017 diagonal. Entries above the diagonal are not written. Only square
2018 matrices may be written with @code{MODE=TRIANGULAR}.
2020 Ordinarily, each @code{WRITE} command starts a new line in the output
2021 file. With @code{HOLD}, the next @code{WRITE} command will write to
2022 the same line as the current one. This can be useful to write more
2023 than one matrix on a single output line.
2025 @node Matrix GET Command
2026 @subsection The @code{GET} Command
2029 @t{GET} @i{variable}[@t{(}@i{index}[@t{,}@i{index}]@t{)}]
2030 [@t{/FILE}@t{=}@{@i{file} @math{|} @t{*}@}]
2031 [@t{/VARIABLES}@t{=}@i{variable}@dots{}]
2032 [@t{/NAMES}@t{=}@i{variable}]
2033 [@t{/MISSING}@t{=}@{@t{ACCEPT} @math{|} @t{OMIT} @math{|} @i{number}@}]
2034 [@t{/SYSMIS}@t{=}@{@t{OMIT} @math{|} @i{number}@}]@t{.}
2037 The @code{READ} command reads numeric data from an SPSS system file,
2038 SPSS/PC+ system file, or SPSS portable file into a matrix variable or
2043 To read data into a variable, specify just its name following
2044 @code{GET}. The variable need not already exist; if it does, it is
2045 replaced. The variable will have as many columns as there are
2046 variables specified on the @code{VARIABLES} subcommand and as many
2047 rows as there are cases in the input file.
2050 To read data into a submatrix, specify the name of an existing
2051 variable, followed by an indexing expression, just after @code{GET}.
2052 The submatrix must have as many columns as variables specified on
2053 @code{VARIABLES} and as many rows as cases in the input file.
2056 Specify the name or handle of the file to be read on @code{FILE}. Use
2057 @samp{*}, or simply omit the @code{FILE} subcommand, to read from the
2058 active file. Reading from the active file is only permitted if it was
2059 already defined outside @code{MATRIX}.
2061 List the variables to be read as columns in the matrix on the
2062 @code{VARIABLES} subcommand. The list can use @code{TO} for
2063 collections of variables or @code{ALL} for all variables. If
2064 @code{VARIABLES} is omitted, all variables are read. Only numeric
2065 variables may be read.
2067 If a variable is named on @code{NAMES}, then the names of the
2068 variables read as data columns are stored in a string vector within
2069 the given name, replacing any existing matrix variable with that name.
2070 Variable names are truncated to 8 bytes.
2072 The @code{MISSING} and @code{SYSMIS} subcommands control the treatment
2073 of missing values in the input file. By default, any user- or
2074 system-missing data in the variables being read from the input causes
2075 an error that prevents @code{GET} from executing. To accept missing
2076 values, specify one of the following settings on @code{MISSING}:
2080 Accept user-missing values with no change. By default, system-missing
2081 values still yield an error. Use the @code{SYSMIS} subcommand to
2082 change this treatment:
2086 Skip any case that contains a system-missing value.
2089 Recode the system-missing value to @i{number}.
2093 Skip any case that contains any user- or system-missing value.
2096 Recode all user- and system-missing values to @i{number}.
2099 The @code{SYSMIS} subcommand has an effect only with
2100 @code{MISSING=ACCEPT}.
2102 @node Matrix SAVE Command
2103 @subsection The @code{SAVE} Command
2106 @t{SAVE} @i{expression}
2107 [@t{/OUTFILE}@t{=}@{@i{file} @math{|} @t{*}@}]
2108 [@t{/VARIABLES}@t{=}@i{variable}@dots{}]
2109 [@t{/NAMES}@t{=}@i{expression}]
2110 [@t{/STRINGS}@t{=}@i{variable}@dots{}]@t{.}
2113 The @code{SAVE} matrix command evaluates @i{expression} and writes the
2114 resulting matrix to an SPSS system file. In the system file, each
2115 matrix row becomes a case and each column becomes a variable.
2117 Specify the name or handle of the SPSS system file on the
2118 @code{OUTFILE} subcommand, or @samp{*} to write the output as the new
2119 active file. The @code{OUTFILE} subcommand is required on the first
2120 @code{SAVE} command, in syntax order, within @code{MATRIX}. For
2121 @code{SAVE} commands after the first, the default output file is the
2122 same as the previous.
2124 When multiple @code{SAVE} commands write to one destination within a
2125 single @code{MATRIX}, the later commands append to the same output
2126 file. All the matrices written to the file must have the same number
2127 of columns. The @code{VARIABLES}, @code{NAMES}, and @code{STRINGS}
2128 subcommands are honored only for the first @code{SAVE} command that
2129 writes to a given file.
2131 By default, @code{SAVE} names the variables in the output file
2132 @code{COL1} through @code{COL@i{n}}. Use @code{VARIABLES} or
2133 @code{NAMES} to give the variables meaningful names. The
2134 @code{VARIABLES} subcommand accepts a comma-separated list of variable
2135 names. Its alternative, @code{NAMES}, instead accepts an expression
2136 that must evaluate to a row or column string vector of names. The
2137 number of names need not exactly match the number of columns in the
2138 matrix to be written: extra names are ignored; extra columns use
2141 By default, @code{SAVE} assumes that the matrix to be written is all
2142 numeric. To write string columns, specify a comma-separated list of
2143 the string columns' variable names on @code{STRINGS}.
2145 @node Matrix MGET Command
2146 @subsection The @code{MGET} Command
2149 @t{MGET} [@t{/FILE}@t{=}@i{file}]
2150 [@t{/TYPE}@t{=}@{@t{COV} @math{|} @t{CORR} @math{|} @t{MEAN} @math{|} @t{STDDEV} @math{|} @t{N} @math{|} @t{COUNT}@}]@t{.}
2153 The @code{MGET} command reads the data from a matrix file
2154 (@pxref{Matrix Files}) into matrix variables. Specify the name or
2155 handle of the matrix file to be read on the @code{FILE} subcommand; if
2156 it is omitted, then the command reads the active file.
2158 By default, @code{MGET} reads all of the data from the matrix file.
2159 Specify a space-delimited list of matrix types @code{TYPE} to limit the
2160 kinds of data to the one specified:
2167 Correlation coefficient matrix.
2173 Vector of standard deviations.
2176 Vector of case counts.
2182 @code{MGET} reads the entire matrix file and automatically names,
2183 creates, and populates matrix variables using its contents. It
2184 constructs the name of each variable by concatenating the following:
2188 A 2-character prefix that identifies the type of the matrix:
2195 Correlation coefficient matrix.
2201 Vector of standard deviations.
2204 Vector of case counts.
2211 If the matrix file has factor variables, @code{F@i{n}}, where @i{n}
2212 is a number identifying a group of factors: @code{F1} for the first
2213 group, @code{F2} for the second, and so on.
2216 If the matrix file has split file variables, @code{S@i{n}}, where
2217 @i{n} is a number identifying a split group: @code{S1} for the first
2218 group, @code{S2} for the second, and so on.
2221 If @code{MGET} chooses the name of an existing variable, it issues a
2222 warning and does not change the variable.
2224 @node Matrix MSAVE Command
2225 @subsection The @code{MSAVE} Command
2228 @t{MSAVE} @i{expression}
2229 @t{/TYPE}@t{=}@{@t{COV} @math{|} @t{CORR} @math{|} @t{MEAN} @math{|} @t{STDDEV} @math{|} @t{N} @math{|} @t{COUNT}@}
2230 [@t{/FACTOR}@t{=}@i{expression}]
2231 [@t{/SPLIT}@t{=}@i{expression}]
2232 [@t{/OUTFILE}@t{=}@i{file}]
2233 [@t{/VARIABLES}@t{=}@i{variable}@dots{}]
2234 [@t{/SNAMES}@t{=}@i{variable}@dots{}]
2235 [@t{/FNAMES}@t{=}@i{variable}@dots{}]@t{.}
2238 The @code{MSAVE} command evaluates the @i{expression} specifies just
2239 after the command name, and writes the resulting matrix to a matrix
2240 file (@pxref{Matrix Files}).
2242 The @code{TYPE} subcommand is required. It specifies the
2243 @code{ROWTYPE_} to write along with this matrix.
2245 The @code{FACTOR} and @code{SPLIT} subcommands are required if and
2246 only if the matrix file has factor or split variables, respectively.
2247 Each one takes an expression that must evaluate to a vector with the
2248 same number of entries as the matrix has factor or split variables,
2249 respectively. Each @code{MSAVE} only writes data for a single
2250 combination of factor and split variables, so many @code{MSAVE}
2251 commands (or one inside a loop) may be needed to write a complete set.
2253 The remaining @code{MSAVE} subcommands define the format of the matrix
2254 file. All of the @code{MSAVE} commands within a given matrix program
2255 write to the same matrix file, so these subcommands are only
2256 meaningful on the first @code{MSAVE} command within a matrix program.
2257 (If they are given again on later @code{MSAVE} commands, then they
2258 must have the same values as on the first.)
2260 The @code{OUTFILE} subcommand specifies the name or handle of the
2261 matrix file to be written. Output must go to an external file, not a
2262 data set or the active file.
2264 The @code{VARIABLES} subcommand specifies a comma-separated list of
2265 the names of the continuous variables to be written to the matrix
2266 file. The @code{TO} keyword can be used to define variables named
2267 with consecutive integer suffixes. These names become column names
2268 and names that appear in @code{VARNAME_} in the matrix file.
2269 @code{ROWTYPE_} and @code{VARNAME_} are not allowed on
2270 @code{VARIABLES}. If @code{VARIABLES} is omitted, then @pspp{} uses
2271 the names @code{COL1}, @code{COL2}, and so on.
2273 The @code{FNAMES} subcommand may be used to supply a comma-separated
2274 list of factor variable names. The default names are @code{FAC1},
2275 @code{FAC2}, and so on.
2277 The @code{SNAMES} subcommand can supply a comma-separated list of
2278 split variable names. The default names are @code{SPL1}, @code{SPL2},
2281 @node Matrix DISPLAY Command
2282 @subsection The @code{DISPLAY} Command
2285 @t{DISPLAY} [@{@t{DICTIONARY} @math{|} @t{STATUS}@}]@t{.}
2288 The @code{DISPLAY} command makes @pspp{} display a table with the name
2289 and dimensions of each matrix variable. The @code{DICTIONARY} and
2290 @code{STATUS} keywords are accepted but have no effect.
2292 @node Matrix RELEASE Command
2293 @subsection The @code{RELEASE} Command
2296 @t{RELEASE} @i{variable}@dots{}@t{.}
2299 The @code{RELEASE} command accepts a comma-separated list of matrix
2300 variable names. It deletes each variable and releases the memory
2303 The @code{END MATRIX} command releases all matrix variables.