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+\begin{page}{manpageXXx01}{NAG On-line Documentation: x01}
+\beginscroll
+\begin{verbatim}
+
+
+
+     X01(3NAG)         Foundation Library (12/10/92)         X01(3NAG)
+
+
+
+          X01 -- Mathematical Constants                 Introduction -- X01
+                                    Chapter X01
+                              Mathematical Constants
+
+          1. Scope of the Chapter
+
+          This chapter is concerned with the provision of mathematical
+          constants required by other routines within the Library.
+
+          It should be noted that because of the trivial nature of the
+          routines individual routine documents are not provided.
+
+          2. Background to the Problems
+
+          Some Library routines require mathematical constants to maximum
+          machine precision. These routines call Chapter X01 and thus
+          lessen the number of changes that have to be made between
+          different implementations of the Library.
+
+          3. Recommendations on Choice and Use of Routines
+
+          Although these routines are primarily intended for use by other
+          routines they may be accessed directly by the user:
+
+          Constant           Fortran Specification
+
+          (pi)               DOUBLE PRECISION FUNCTION X01AAF(X)
+                             DOUBLE PRECISION X
+
+          (gamma)            DOUBLE PRECISION FUNCTION X01ABF(X)
+          (Euler constant)   DOUBLE PRECISION X
+
+          The argument X of these routines is a dummy argument.
+
+
+          X01 -- Mathematical Constants                     Contents -- X01
+          Chapter X01
+
+          Mathematical Constants
+
+          X01AAF  (pi)
+
+          X01ABF  Euler's constant, (gamma)
+
+\end{verbatim}
+\endscroll
+\end{page}
+\begin{page}{manpageXXx02}{NAG On-line Documentation: x02}
+\beginscroll
+\begin{verbatim}
+
+
+
+     X02(3NAG)         Foundation Library (12/10/92)         X02(3NAG)
+
+
+
+          X02 -- Machine Constants                      Introduction -- X02
+                                    Chapter X02
+                                 Machine Constants
+
+          1. Scope of the Chapter
+
+          This chapter is concerned with parameters which characterise
+          certain aspects of the computing environment in which the NAG
+          Foundation Library is implemented. They relate primarily to
+          floating-point arithmetic, but also to integer arithmetic and the
+          elementary functions. The values of the parameters vary from one
+          implementation of the Library to another, but within the context
+          of a single implementation they are constants.
+
+          The parameters are intended for use primarily by other routines
+          in the Library, but users of the Library may sometimes need to
+          refer to them directly.
+
+          Each parameter-value is returned by a separate Fortran function.
+          Because of the trivial nature of the functions, individual
+          routine documents are not provided; the necessary details are
+          given in Section 3 of this Introduction.
+
+          2. Background to the Problems
+
+          2.1. Floating-Point Arithmetic
+
+          2.1.1.  A model of floating-point arithmetic
+
+          In order to characterise the important properties of floating-
+          point arithmetic by means of a small number of parameters, NAG
+          uses a simplified model of floating-point arithmetic. The
+          parameters of the model can be chosen to provide a sufficiently
+          close description of the behaviour of actual implementations of
+          floating-point arithmetic, but not, in general, an exact
+          description; actual implementations vary too much in the details
+          of how numbers are represented or arithmetic operations are
+          performed.
+
+          The model is based on that developed by Brown [1], but differs in
+          some respects. The essential features are summarised here.
+
+          The model is characterised by four integer parameters and one
+          logical parameter. The four integer parameters are:
+
+                b  :  the base
+
+                p  :  the precision (i.e. the number of significant base-B
+                      digits)
+
+              e    :  the minimum exponent
+               min
+
+              e    :  the maximum exponent
+               max
+
+          These parameters define a set of numerical values of the form:
+
+                                           e
+                                        f*b
+
+          where the exponent e must lie in the range [e   ,e   ], and the
+                                                       min  max
+          fraction f (also called the mantissa or significand) lies in the
+          range [1/b,1), and may be written:
+
+                                    f=0.f f ...f
+                                         1 2    p
+
+          Thus f is a p-digit fraction to the base b; the f  are the base-b
+                                                           i
+          digits of the fraction: they are integers in the range 0 to b-1,
+          and the leading digit f  must not be zero.
+                                 1
+
+          The set of values so defined (together with zero) are called
+          model numbers. For example, if b=10, p=5, e   =-99 and e   =+99,
+                                                     min          max
+                                                   67
+          then a typical model number is 0.12345*10  .
+
+          The model numbers must obey certain rules for the computed
+          results of the following basic arithmetic operations: addition,
+          subtraction, multiplication, negation, absolute value, and
+          comparisons. The rules depend on the value of the logical
+          parameter ROUNDS.
+
+          If ROUNDS is true, then the computed result must be the nearest
+          model number to the exact result (assuming that overflow or
+          underflow does not occur); if the exact result is midway between
+          two model numbers, then it may be rounded either way.
+
+          If ROUNDS is false, then: if the exact result is a model number,
+          the computed result must be equal to the exact result; otherwise,
+          the computed result may be either of the adjacent model numbers
+          on either side of the exact result.
+
+          For division and square root, this latter rule is further relaxed
+          (regardless of the value of ROUNDS): the computed result may also
+          be one of the next adjacent model numbers on either side of the
+          permitted values just stated.
+
+          On some machines, the full set of representable floating-point
+          numbers conforms to the rules of the model with appropriate
+          values of b, p, e   , e    and ROUNDS. For example, for machines
+                           min   max
+          with IEEE arithmetic, in double precision:
+
+              b    =  2
+
+              p    =  53
+
+              e    =-1021
+               min
+
+              e    =1024 and ROUNDS is true.
+               max
+
+          For other machines, values of the model parameters must be chosen
+          which define a large subset of the representable numbers;
+          typically it may be necessary to decrease p by 1 (in which case
+          ROUNDS is always set to false), or to increase e    or decrease
+                                                          min
+          e    by a little bit. There are additional rules to ensure that
+           max
+          arithmetic operations on those representable numbers which are
+          not model numbers, are consistent with arithmetic on model
+          numbers.
+
+          (Note: the model used here differs from that described in Brown
+          [1] in the following respects: square-root is treated, like
+          division, as a weakly supported operator; and the logical
+          parameter ROUNDS has been introduced to take account of machines
+          with good rounding.)
+
+          2.1.2.  Derived parameters of floating-point arithmetic
+
+          Most numerical algorithms require access, not to the basic
+          parameters of the model, but to certain derived values, of which
+          the most important are:
+
+                                   (1)  1-p
+          the machine precision =  (-)*b    if ROUNDS is true,
+          (epsilon):               (2)
+
+                                    1-p
+                                =  b    otherwise (but see Note below).
+
+                                    e   -1
+                                     min
+          the smallest positive =  b
+          model number:
+
+                                            e
+                                       -p    max
+          the largest positive  =  (1-b  )*b
+          model number:
+
+          Note: this value is increased very slightly in some
+          implementations to ensure that the computed result of 1+(epsilon)
+          or 1-(epsilon) differs from 1. For example in IEEE binary single
+                                                    -24  -47
+          precision arithmetic the value is set to 2   +2   .
+
+          Two additional derived values are used in the NAG Foundation
+          Library. Their definitions depend not only on the properties of
+          the basic arithmetic operations just considered, but also on
+          properties of some of the elementary functions. We define the
+          safe range parameter to be the smallest positive model number z
+          such that for any x in the range [z,1/z] the following can be
+          computed without undue loss of accuracy, overflow, underflow or
+          other error:
+
+              -x
+
+              1/x
+
+              -1/x
+
+              SQRT(x)
+
+              LOG(x)
+
+              EXP(LOG(x))
+
+              y**(LOG(x)/LOG(y)) for any y
+
+          In a similar fashion we define the safe range parameter for
+          complex arithmetic as the smallest positive model number z such
+          that for any x in the range [z,1/z] the following can be computed
+          without any undue loss of accuracy, overflow, underflow or other
+          error:
+
+              -w
+
+              1/w
+
+              -1/w
+
+              SQRT(w)
+
+              LOG(w)
+
+              EXP(LOG(w))
+
+              y**(LOG(w)/LOG(y)) for any y
+
+              ABS(w)
+
+          where w is any of x, ix, x+ix, 1/x, i/x, 1/x+i/x, and i is the
+          square root of -1.
+
+          This parameter was introduced to take account of the quality of
+          complex arithmetic on the machine. On machines with well
+          implemented complex arithmetic, its value will differ from that
+          of the real safe range parameter by a small multiplying factor
+          less than 10. For poorly implemented complex arithmetic this
+          factor may be larger by many orders of magnitude.
+
+          2.2. Other Aspects of the Computing Environment
+
+          No attempt has been made to characterise comprehensively any
+          other aspects of the computing environment. The other functions
+          in this chapter provide specific information that is occasionally
+          required by routines in the Library.
+
+          2.3. References
+
+          [1]   Brown W S (1981) A Simple but Realistic Model of Floating-
+                point Computation. ACM Trans. Math. Softw. 7 445--480.
+
+          3. Recommendations on Choice and Use of Routines
+
+          3.1. Parameters of Floating-point Arithmetic
+
+          DOUBLE PRECISION FUNCTION returns the machine precision i.e.
+          X02AJF()                  (1)  1-p                       1-p
+                                    (-)*b    if ROUNDS is true or b
+                                    (2)
+                                    otherwise (or a value very slightly
+                                    larger than this, see Section 2.1.2)
+
+          DOUBLE PRECISION FUNCTION returns the smallest positive model
+          X02AKF()                               e   -1
+                                                  min
+                                    number i.e. b
+
+          DOUBLE PRECISION FUNCTION returns the largest positive model
+          X02ALF()                                       e
+                                                    -p    max
+                                    number i.e. (1-b  )*b
+
+
+          DOUBLE PRECISION FUNCTION returns the safe range parameter as
+          X02AMF()                  defined in Section 2.1.2
+
+          DOUBLE PRECISION FUNCTION returns the safe range parameter for
+          X02ANF()                  complex arithmetic as defined in
+                                    Section 2.1.2
+
+          INTEGER FUNCTION X02BHF() returns the model parameter b
+
+          INTEGER FUNCTION X02BJF() returns the model parameter p
+
+          INTEGER FUNCTION X02BKF() returns the model parameter e
+                                                                 min
+
+          INTEGER FUNCTION X02BLF() returns the model parameter e
+                                                                 max
+
+          LOGICAL FUNCTION X02DJF() returns the model parameter ROUNDS
+
+          3.2. Parameters of Other Aspects of the Computing Environment
+
+          DOUBLE PRECISION FUNCTION returns the largest positive real
+          X02AHF(X)                 argument for which the SIN and COS
+          DOUBLE PRECISION X        routines return a result with some
+                                    meaningful accuracy
+
+          INTEGER FUNCTION X02BBF   returns the largest positive integer
+          (X)                       value
+          DOUBLE PRECISION X
+
+          INTEGER FUNCTION X02BEF   returns the maximum number of decimal
+          (X)                       digits which can be accurately
+          DOUBLE PRECISION X        represented over the whole range of
+                                    floating-point numbers
+
+          The argument X of these routines is a dummy argument.
+
+          4. Example Program Text
+
+          The example program simply prints the values of all the functions
+          in Chapter X02. Obviously the results will vary from one
+          implementation of the Library to another.
+
+
+          X02 -- Machine Constants                          Contents -- X02
+          Chapter X02
+
+          Machine Constants
+
+          X02AHF  Largest permissible argument for SIN and COS
+
+          X02AJF  Machine precision
+
+          X02AKF  Smallest positive model number
+
+          X02ALF  Largest positive model number
+
+          X02AMF  Safe range of floating-point arithmetic
+
+          X02ANF  Safe range of complex floating-point arithmetic
+
+          X02BBF  Largest representable integer
+
+          X02BEF  Maximum number of decimal digits that can be represented
+
+          X02BHF  Parameter of floating-point arithmetic model, b
+
+          X02BJF  Parameter of floating-point arithmetic model, p
+
+          X02BKF  Parameter of floating-point arithmetic model, e
+                                                                 min
+
+          X02BLF  Parameter of floating-point arithmetic model, e
+                                                                 max
+
+          X02DJF  Parameter of floating-point arithmetic model, ROUNDS
+
+\end{verbatim}
+\endscroll
+\end{page}
+\begin{page}{manpageXXx04}{NAG On-line Documentation: x04}
+\beginscroll
+\begin{verbatim}
+
+
+
+     X04(3NAG)         Foundation Library (12/10/92)         X04(3NAG)
+
+
+
+          X04 -- Input/Output Utilities                 Introduction -- X04
+                                    Chapter X04
+                              Input/Output Utilities
+
+          1. Scope of the Chapter
+
+          This chapter contains utility routines concerned with input and
+          output to or from an external file.
+
+          2. Background to the Problems
+
+          2.1. Output from NAG Foundation Library Routines
+
+          Output from NAG Foundation Library routines to an external file
+          falls into two categories:
+
+          (a)   Error messages which are always associated with an error
+                exit from a routine, that is, with a non-zero value of
+                IFAIL as specified in Section 6 of the routine document.
+
+          (b)   Advisory messages which include output of final results,
+                output of intermediate results to monitor the course of a
+                computation, and various warning or informative messages.
+
+          Each category of output is written to its own Fortran output unit
+          - the  error message unit  or the  advisory message unit. In
+          practice these may be the same unit number. Default unit numbers
+          are provided for each implementation of the Library (see the
+          Users' Note); they may be changed by users. Output of error
+          messages may be controlled by the setting of IFAIL (see the
+          Essential Introduction). Output of advisory messages may usually
+          be controlled by the setting of some other parameter (e.g.
+          MSGLVL) (or in some routines also by IFAIL). An alternative
+          mechanism for completely suppressing output is to set the
+          relevant unit number < 0.
+
+          For further information about error and advisory messages, see
+          Chapter P01.
+
+          2.2. Matrix Printing Routines
+
+          Routines are provided to allow formatted output of general
+          rectangular or triangular matrices stored in a two-dimensional
+          array (real and complex data types).
+
+          All output is directed to the unit number for output of advisory
+          messages, which may be altered by a call to X04ABF.
+
+          3. Recommendations on Choice and Use of Routines
+
+          Apart from the obvious utility of the matrix printing routines,
+          users of the Library may need to call routines in Chapter X04 for
+          the following purposes:
+
+               if the default unit number for error messages (given in the
+               Users' Note for your implementation) is not satisfactory,
+               it may be changed to a new value NERR by the statement
+
+                     CALL X04AAF(1,NERR)
+
+               Similarly the unit number for advisory messages may be
+               changed to a new value NADV by the statement
+
+                     CALL X04ABF(1,NADV)
+
+          4. Index
+
+          Accessing unit number:
+               of advisory message unit                              X04ABF
+               of error message unit                                 X04AAF
+          Printing matrices:
+               general complex matrix                                X04DAF
+               general real matrix                                   X04CAF
+
+
+
+          X04 -- Input/Output Utilities                     Contents -- X04
+          Chapter X04
+
+          Input/Output Utilities
+
+          X04AAF  Return or set unit number for error messages
+
+          X04ABF  Return or set unit number for advisory messages
+
+          X04CAF  Print a real general matrix
+
+          X04DAF  Print a complex general matrix
+
+\end{verbatim}
+\endscroll
+\end{page}
+\begin{page}{manpageXXx04aaf}{NAG On-line Documentation: x04aaf}
+\beginscroll
+\begin{verbatim}
+
+
+
+     X04AAF(3NAG)      Foundation Library (12/10/92)      X04AAF(3NAG)
+
+
+
+          X04 -- Input/Output Utilities                              X04AAF
+                  X04AAF -- NAG Foundation Library Routine Document
+
+          Note: Before using this routine, please read the Users' Note for
+          your implementation to check implementation-dependent details.
+          The symbol (*) after a NAG routine name denotes a routine that is
+          not included in the Foundation Library.
+
+          1. Purpose
+
+          X04AAF returns the value of the current error message unit
+          number, or sets the current error message unit number to a new
+          value.
+
+          2. Specification
+
+                 SUBROUTINE X04AAF (IFLAG, NERR)
+                 INTEGER          IFLAG, NERR
+
+          3. Description
+
+          This routine enables those library routines which output error
+          messages, to determine the number of the output unit to which the
+          error messages are to be sent; in this case X04AAF is called with
+          IFLAG = 0. X04AAF may also be called with IFLAG = 1 to set the
+          unit number to a specified value. Otherwise a default value
+          (stated in the Users' Note for your implementation) is returned.
+
+          Records written to this output unit by other library routines are
+          at most 80 characters long (including a line-printer carriage
+          control character).
+
+          Note that if the unit number is set < 0, no messages will be
+          output.
+
+          4. References
+
+          None.
+
+          5. Parameters
+
+           1:  IFLAG -- INTEGER                                       Input
+               On entry: the action to be taken (see NERR). Constraint:
+               IFLAG = 0 or 1.
+
+           2:  NERR -- INTEGER                                 Input/Output
+               On entry:
+                    if IFLAG = 0, NERR need not be set;
+
+                    if IFLAG = 1, NERR must specify the new error message
+                    unit number.
+               On exit:
+                    if IFLAG = 0, NERR is set to the current error message
+                    unit number,
+
+                    if IFLAG = 1, NERR is unchanged.
+               Note that Fortran unit numbers must be positive or zero. If
+               NERR is set < 0, output of error messages is totally
+               suppressed.
+
+          6. Error Indicators and Warnings
+
+          None.
+
+          7. Accuracy
+
+          Not applicable.
+
+          8. Further Comments
+
+          The time taken by the routine is negligible.
+
+          9. Example
+
+          In this example X04AAF is called by the user's main program to
+          make the error message from the routine DUMMY appear on the same
+          unit as the rest of the output (unit 6). Normally a NAG
+          Foundation Library routine with an IFAIL parameter (see Essential
+          Introduction) would take the place of DUMMY.
+
+          The example program is not reproduced here. The source code for
+          all example programs is distributed with the NAG Foundation
+          Library software and should be available on-line.
+\end{verbatim}
+\endscroll
+\end{page}
+\begin{page}{manpageXXx04abf}{NAG On-line Documentation: x04abf}
+\beginscroll
+\begin{verbatim}
+
+
+
+     X04ABF(3NAG)      Foundation Library (12/10/92)      X04ABF(3NAG)
+
+
+
+          X04 -- Input/Output Utilities                              X04ABF
+                  X04ABF -- NAG Foundation Library Routine Document
+
+          Note: Before using this routine, please read the Users' Note for
+          your implementation to check implementation-dependent details.
+          The symbol (*) after a NAG routine name denotes a routine that is
+          not included in the Foundation Library.
+
+          1. Purpose
+
+          X04ABF returns the value of the current advisory message unit
+          number, or sets the current advisory message unit number to a new
+          value.
+
+          2. Specification
+
+                 SUBROUTINE X04ABF (IFLAG, NADV)
+                 INTEGER          IFLAG, NADV
+
+          3. Description
+
+          This routine enables those library routines which output advisory
+          messages, to determine the number of the output unit to which the
+          advisory messages are to be sent; in this case X04ABF is called
+          with IFLAG = 0. X04ABF may also be called with IFLAG = 1 to set
+          the unit number to a specified value. Otherwise a default value
+          (stated in the User's Note for your implementation) is returned.
+
+          Records written to this output unit by other library routines are
+          at most 120 characters long (including a line-printer carriage
+          control character), unless those library routines allow users to
+          specify longer records.
+
+          Note that if the unit number is set < 0, no messages will be
+          output.
+
+          4. References
+
+          None.
+
+          5. Parameters
+
+           1:  IFLAG -- INTEGER                                       Input
+               On entry: the action to be taken (see NADV). Constraint:
+               IFLAG = 0 or 1.
+
+           2:  NADV -- INTEGER                                 Input/Output
+               On entry:
+                    if IFLAG = 0, NADV need not be set;
+
+                    if IFLAG = 1, NADV must specify the new advisory
+                    message unit number.
+               On exit:
+                    if IFLAG = 0, NADV is set to the current advisory
+                    message unit number;
+
+                    if IFLAG = 1, NADV is unchanged.
+               Note that Fortran unit numbers must be positive or zero. If
+               NADV is set < 0, output of advisory messages is totally
+               suppressed.
+
+          6. Error Indicators and Warnings
+
+          None.
+
+          7. Accuracy
+
+          Not applicable.
+
+          8. Further Comments
+
+          The time taken by this routine is negligible.
+
+          9. Example
+
+          In this example X04ABF is called by the user's main program to
+          make the advisory message from the routine DUMMY appear on the
+          same unit as the rest of the output (unit 6). Normally a NAG
+          Foundation Library routine with an IFAIL parameter (see Essential
+          Introduction) would take the place of DUMMY.
+
+          The example program is not reproduced here. The source code for
+          all example programs is distributed with the NAG Foundation
+          Library software and should be available on-line.
+\end{verbatim}
+\endscroll
+\end{page}
+\begin{page}{manpageXXx04caf}{NAG On-line Documentation: x04caf}
+\beginscroll
+\begin{verbatim}
+
+
+
+     X04CAF(3NAG)      Foundation Library (12/10/92)      X04CAF(3NAG)
+
+
+
+          X04 -- Input/Output Utilities                              X04CAF
+                  X04CAF -- NAG Foundation Library Routine Document
+
+          Note: Before using this routine, please read the Users' Note for
+          your implementation to check implementation-dependent details.
+          The symbol (*) after a NAG routine name denotes a routine that is
+          not included in the Foundation Library.
+
+          1. Purpose
+
+          X04CAF is an easy-to-use routine to print a real matrix stored in
+          a two-dimensional array.
+
+          2. Specification
+
+                 SUBROUTINE X04CAF (MATRIX, DIAG, M, N, A, LDA, TITLE,
+                1                   IFAIL)
+                 INTEGER          M, N, LDA, IFAIL
+                 DOUBLE PRECISION A(LDA,*)
+                 CHARACTER*1      MATRIX, DIAG
+                 CHARACTER*(*)    TITLE
+
+          3. Description
+
+          X04CAF prints a real matrix. It is an easy-to-use driver for
+          X04CBF(*). The routine uses default values for the format in
+          which numbers are printed, for labelling the rows and columns,
+          and for output record length.
+
+          X04CAF will choose a format code such that numbers will be
+          printed with either an F8.4, F11.4 or a 1PE13.4 format. The F8.4
+          code is chosen if the sizes of all the matrix elements to be
+          printed lie between 0.001 and 1.0. The F11.4 code is chosen if
+          the sizes of all the matrix elements to be printed lie between 0.
+          001 and 9999.9999. Otherwise the 1PE13.4 code is chosen.
+
+          The matrix is printed with integer row and column labels, and
+          with a maximum record length of 80.
+
+          The matrix is output to the unit defined by X04ABF.
+
+          4. References
+
+          None.
+
+          5. Parameters
+
+           1:  MATRIX -- CHARACTER*1                                  Input
+               On entry: indicates the part of the matrix to be printed, as
+               follows:
+
+               MATRIX = 'G' (General), the whole of the rectangular matrix.
+
+               MATRIX = 'L' (Lower), the lower triangle of the matrix, or
+               the lower trapezium if the matrix has more rows than
+               columns.
+
+               MATRIX = 'U' (Upper), the upper triangle of the matrix, or
+               the upper trapezium if the matrix has more columns than
+               rows. Constraint: MATRIX must be one of 'G', 'L' or 'U'.
+
+           2:  DIAG -- CHARACTER*1                                    Input
+               On entry: unless MATRIX = 'G', DIAG must specify whether the
+               diagonal elements of the matrix are to be printed, as
+               follows:
+
+               DIAG = 'B' (Blank), the diagonal elements of the matrix are
+               not referenced and not printed.
+
+               DIAG = 'U' (Unit diagonal), the diagonal elements of the
+               matrix are not referenced, but are assumed all to be unity,
+               and are printed as such.
+
+               DIAG = 'N' (Non-unit diagonal), the diagonal elements of the
+               matrix are referenced and printed.
+
+               If MATRIX = 'G', then DIAG need not be set. Constraint: If
+               MATRIX /= 'G', then DIAG must be one of 'B', 'U' or 'N'.
+
+           3:  M -- INTEGER                                           Input
+
+           4:  N -- INTEGER                                           Input
+               On entry: the number of rows and columns of the matrix,
+               respectively, to be printed.
+
+               If either of M or N is less than 1, X04CAF will exit
+               immediately after printing TITLE; no row or column labels
+               are printed.
+
+           5:  A(LDA,*) -- DOUBLE PRECISION array                     Input
+               Note: the second dimension of the array A must be at least
+               max(1,N).
+               On entry: the matrix to be printed. Only the elements that
+               will be referred to, as specified by parameters MATRIX and
+               DIAG, need be set.
+
+           6:  LDA -- INTEGER                                         Input
+               On entry:
+               the first dimension of the array A as declared in the
+               (sub)program from which X04CAF is called.
+               Constraint: LDA >= M.
+
+           7:  TITLE -- CHARACTER*(*)                                 Input
+               On entry: a title to be printed above the matrix. If TITLE =
+               ' ', no title (and no blank line) will be printed.
+
+               If TITLE contains more than 80 characters, the contents of
+               TITLE will be wrapped onto more than one line, with the
+               break after 80 characters.
+
+               Any trailing blank characters in TITLE are ignored.
+
+           8:  IFAIL -- INTEGER                                Input/Output
+               On entry: IFAIL must be set to 0, -1 or 1. For users not
+               familiar with this parameter (described in the Essential
+               Introduction) the recommended value is 0.
+
+               On exit: IFAIL = 0 unless the routine detects an error (see
+               Section 6).
+
+          6. Error Indicators and Warnings
+
+          Errors detected by the routine:
+
+          If on entry IFAIL = 0 or -1, explanatory error messages are
+          output on the current error message unit (as defined by X04AAF).
+
+          IFAIL= 1
+               On entry MATRIX /= 'G', 'L' or 'U'.
+
+          IFAIL= 2
+               On entry MATRIX = 'L' or 'U', but DIAG /= 'N', 'U' or 'B'.
+
+          IFAIL= 3
+               On entry LDA < M.
+
+          7. Accuracy
+
+          Not applicable.
+
+          8. Further Comments
+
+          A call to X04CAF is equivalent to a call to X04CBF(*) with the
+          following argument values:
+
+
+                NCOLS = 80
+                INDENT = 0
+                LABROW = 'I'
+                LABCOL = 'I'
+                FORMAT = ' '
+
+
+          9. Example
+
+          This example program calls X04CAF twice, first to print a 3 by 5
+          rectangular matrix, and then to print a 5 by 5 lower triangular
+          matrix.
+
+          The example program is not reproduced here. The source code for
+          all example programs is distributed with the NAG Foundation
+          Library software and should be available on-line.
+
+\end{verbatim}
+\endscroll
+\end{page}
+\begin{page}{manpageXXx04daf}{NAG On-line Documentation: x04daf}
+\beginscroll
+\begin{verbatim}
+
+
+
+     X04DAF(3NAG)      Foundation Library (12/10/92)      X04DAF(3NAG)
+
+
+
+          X04 -- Input/Output Utilities                              X04DAF
+                  X04DAF -- NAG Foundation Library Routine Document
+
+          Note: Before using this routine, please read the Users' Note for
+          your implementation to check implementation-dependent details.
+          The symbol (*) after a NAG routine name denotes a routine that is
+          not included in the Foundation Library.
+
+          1. Purpose
+
+          X04DAF is an easy-to-use routine to print a complex matrix stored
+          in a two-dimensional array.
+
+          2. Specification
+
+                 SUBROUTINE X04DAF (MATRIX, DIAG, M, N, A, LDA, TITLE,
+                1                   IFAIL)
+                 INTEGER              M, N, LDA, IFAIL
+                 COMPLEX(KIND(1.0D0)) A(LDA,*)
+                 CHARACTER*1          MATRIX, DIAG
+                 CHARACTER*(*)        TITLE
+
+          3. Description
+
+          X04DAF prints a complex matrix. It is an easy-to-use driver for
+          X04DBF(*). The routine uses default values for the format in
+          which numbers are printed, for labelling the rows and columns,
+          and for output record length.
+
+          X04DAF will choose a format code such that numbers will be
+          printed with either an F8.4, F11.4 or a 1PE13.4 format. The F8.4
+          code is chosen if the sizes of all the matrix elements to be
+          printed lie between 0.001 and 1.0. The F11.4 code is chosen if
+          the sizes of all the matrix elements to be printed lie between 0.
+          001 and 9999.9999. Otherwise the 1PE13.4 code is chosen. The
+          chosen code is used to print each complex element of the matrix
+          with the real part above the imaginary part.
+
+          The matrix is printed with integer row and column labels, and
+          with a maximum record length of 80.
+
+          The matrix is output to the unit defined by X04ABF.
+
+          4. References
+
+          None.
+
+          5. Parameters
+
+           1:  MATRIX -- CHARACTER*1                                  Input
+               On entry: indicates the part of the matrix to be printed, as
+               follows:
+
+               MATRIX = 'G' (General), the whole of the rectangular matrix.
+
+               MATRIX = 'L' (Lower), the lower triangle of the matrix, or
+               the lower trapezium if the matrix has more rows than
+               columns.
+
+               MATRIX = 'U' (Upper), the upper triangle of the matrix, or
+               the upper trapezium if the matrix has more columns than
+               rows. Constraint: MATRIX must be one of 'G', 'L' or 'U'.
+
+           2:  DIAG -- CHARACTER*1                                    Input
+               On entry: unless MATRIX = 'G', DIAG must specify whether the
+               diagonal elements of the matrix are to be printed, as
+               follows:
+
+               DIAG = 'B' (Blank), the diagonal elements of the matrix are
+               not referenced and not printed.
+
+               DIAG = 'U' (Unit diagonal), the diagonal elements of the
+               matrix are not referenced, but are assumed all to be unity,
+               and are printed as such.
+
+               DIAG = 'N' (Non-unit diagonal), the diagonal elements of the
+               matrix are referenced and printed.
+
+               If MATRIX = 'G', then DIAG need not be set. Constraint: If
+               MATRIX /= 'G', then DIAG must be one of 'B', 'U' or 'N'.
+
+           3:  M -- INTEGER                                           Input
+
+           4:  N -- INTEGER                                           Input
+               On entry: the number of rows and columns of the matrix,
+               respectively, to be printed.
+
+               If either of M or N is less than 1, X04DAF will exit
+               immediately after printing TITLE; no row or column labels
+               are printed.
+
+           5:  A(LDA,*) -- COMPLEX(KIND(1.0D)) array                  Input
+               Note: the second dimension of the array A must be at least
+               max(1,N).
+               On entry: the matrix to be printed. Only the elements that
+               will be referred to, as specified by parameters MATRIX and
+               DIAG, need be set.
+
+           6:  LDA -- INTEGER                                         Input
+               On entry:
+               the first dimension of the array A as declared in the
+               (sub)program from which X04DAF is called.
+               Constraint: LDA >= M.
+
+           7:  TITLE -- CHARACTER*(*)                                 Input
+
+               On entry: a title to be printed above the matrix. If TITLE =
+               ' ', no title (and no blank line) will be printed.
+
+               If TITLE contains more than 80 characters, the contents of
+               TITLE will be wrapped onto more than one line, with the
+               break after 80 characters.
+
+               Any trailing blank characters in TITLE are ignored.
+
+           8:  IFAIL -- INTEGER                                Input/Output
+               On entry: IFAIL must be set to 0, -1 or 1. For users not
+               familiar with this parameter (described in the Essential
+               Introduction) the recommended value is 0.
+
+               On exit: IFAIL = 0 unless the routine detects an error (see
+               Section 6).
+
+          6. Error Indicators and Warnings
+
+          Errors detected by the routine:
+
+          If on entry IFAIL = 0 or -1, explanatory error messages are
+          output on the current error message unit (as defined by X04AAF).
+
+          IFAIL= 1
+               On entry MATRIX /= 'G', 'L' or 'U'.
+
+          IFAIL= 2
+               On entry MATRIX = 'L' or 'U', but DIAG /= 'N', 'U' or 'B'.
+
+          IFAIL= 3
+               On entry LDA < M.
+
+          7. Accuracy
+
+          Not applicable.
+
+          8. Further Comments
+
+          A call to X04DAF is equivalent to a call to X04DBF(*) with the
+          following argument values:
+
+
+                NCOLS = 80
+                INDENT = 0
+                LABROW = 'I'
+                LABCOL = 'I'
+                FORMAT = ' '
+                USEFRM = 'A'
+
+
+          9. Example
+
+          This example program calls X04DAF twice, first to print a 4 by 3
+          rectangular matrix, and then to print a 4 by 4 lower triangular
+          matrix.
+
+          The example program is not reproduced here. The source code for
+          all example programs is distributed with the NAG Foundation
+          Library software and should be available on-line.
+
+
+\end{verbatim}
+\endscroll
+\end{page}
+\begin{page}{manpageXXx05}{NAG On-line Documentation: x05}
+\beginscroll
+\begin{verbatim}
+
+
+
+     X05(3NAG)         Foundation Library (12/10/92)         X05(3NAG)
+
+
+
+          X05 -- Date and Time Utilities                Introduction -- X05
+                                    Chapter X05
+                              Date and Time Utilities
+
+          1. Scope of the Chapter
+
+          This chapter provides routines to obtain the current real time,
+          and the amount of processor time used.
+
+          2. Background to the Problems
+
+          2.1. Real Time
+
+          Routines are provided to obtain the current time in two different
+          formats, and to compare two such times.
+
+          2.2. Processor Time
+
+          A routine is provided to return the current amount of processor
+          time used. This allows the timing of a particular routine or
+          section of code.
+
+          3. Recommendations on Choice and Use of Routines
+
+          X05AAF     returns the current date/time in integer format.
+
+          X05ABF     converts from integer to character string date/time.
+
+          X05ACF     compares two date/time character strings.
+
+          X05BAF     returns the amount of processor time used.
+
+
+          X05 -- Date and Time Utilities                    Contents -- X05
+          Chapter X05
+
+          Date and Time Utilities
+
+          X05AAF  Return date and time as an array of integers
+
+          X05ABF  Convert array of integers representing date and time to
+                  character string
+
+          X05ACF  Compare two character strings representing date and time
+
+          X05BAF  Return the CPU time
+
+\end{verbatim}
+\endscroll
+\end{page}
+\begin{page}{manpageXXx05aaf}{NAG On-line Documentation: x05aaf}
+\beginscroll
+\begin{verbatim}
+
+
+
+     X05AAF(3NAG)      Foundation Library (12/10/92)      X05AAF(3NAG)
+
+
+
+          X05 -- Date and Time Utilities                             X05AAF
+                  X05AAF -- NAG Foundation Library Routine Document
+
+          Note: Before using this routine, please read the Users' Note for
+          your implementation to check implementation-dependent details.
+          The symbol (*) after a NAG routine name denotes a routine that is
+          not included in the Foundation Library.
+
+          1. Purpose
+
+          X05AAF returns the current date and time.
+
+          2. Specification
+
+                 SUBROUTINE X05AAF (ITIME)
+                 INTEGER          ITIME(7)
+
+          3. Description
+
+          X05AAF returns the current date and time as a set of seven
+          integers.
+
+          4. References
+
+          None.
+
+          5. Parameters
+
+           1:  ITIME(7) -- INTEGER array                             Output
+               On exit: the current date and time, as follows:
+
+               ITIME(1) contains the current year.
+
+               ITIME(2) contains the current month, in the range 1--12.
+
+               ITIME(3) contains the current day, in the range 1--31.
+
+               ITIME(4) contains the current hour, in the range 0--23.
+
+               ITIME(5) contains the current minute, in the range 0--59.
+
+               ITIME(6) contains the current second, in the range 0--59.
+
+               ITIME(7) contains the current millisecond, in the range 0--
+               999.
+
+          6. Error Indicators and Warnings
+
+          None.
+
+          7. Accuracy
+
+          The accuracy of this routine depends on the accuracy of the host
+          machine. In particular, on some machines it may not be possible
+          to return a value for the current millisecond, for example. In
+          this case, the value returned will be zero.
+
+          8. Further Comments
+
+          None.
+
+          9. Example
+
+          This program prints out the vector ITIME after a call to X05AAF.
+
+          The example program is not reproduced here. The source code for
+          all example programs is distributed with the NAG Foundation
+          Library software and should be available on-line.
+\end{verbatim}
+\endscroll
+\end{page}
+\begin{page}{manpageXXx05abf}{NAG On-line Documentation: x05abf}
+\beginscroll
+\begin{verbatim}
+
+
+
+     X05ABF(3NAG)      Foundation Library (12/10/92)      X05ABF(3NAG)
+
+
+
+          X05 -- Date and Time Utilities                             X05ABF
+                  X05ABF -- NAG Foundation Library Routine Document
+
+          Note: Before using this routine, please read the Users' Note for
+          your implementation to check implementation-dependent details.
+          The symbol (*) after a NAG routine name denotes a routine that is
+          not included in the Foundation Library.
+
+          1. Purpose
+
+          X05ABF converts from a seven-integer format time and date, as
+          returned by X05AAF, into a character string, returned via the
+          routine name.
+
+          2. Specification
+
+                 CHARACTER*30 FUNCTION X05ABF (ITIME)
+                 INTEGER          ITIME(7)
+
+          3. Description
+
+          X05ABF returns a character string of length 30 which contains the
+          date and time as supplied in argument ITIME. On exit, the
+          character string has the following format:
+
+
+                `DAY XXTH MTH YEAR HR:MN:SC.MIL',
+
+
+            where  DAY   is one of 'Sun', 'Mon', 'Tue', 'Wed', 'Thu',
+                         'Fri', 'Sat',
+
+                   XX    is an integer denoting the day of the month,
+
+                   TH    is one of 'st', 'nd', 'rd', 'th',
+
+                   MTH   is one of 'Jan', 'Feb', 'Mar', 'Apr', 'May',
+                         'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec',
+
+                   YEAR  is the year as a four digit integer,
+
+                   HR    is the hour,
+
+                   MN    is the minute,
+
+                   SC    is the second,
+
+                   MIL   is the millisecond.
+
+          If on entry the date in ITIME is invalid, the string returned is
+
+          4. References
+
+          None.
+
+          5. Parameters
+
+           1:  ITIME(7) -- INTEGER array                              Input
+               On entry: a date and time in the format returned by X05AAF,
+               as follows:
+                   ITIME   must contain the year as a positive integer.
+                   (1)
+
+                   ITIME   must contain the month, in the range 1-12.
+                   (2)
+
+                   ITIME   must contain the day, in the range 1 to p, where
+                   (3)     p = 28, 29, 30 or 31, depending on the month and
+                           year.
+
+                   ITIME   must contain the hour, in the range 0-23.
+                   (4)
+
+                   ITIME   must contain the minute, in the range 0-59.
+                   (5)
+
+                   ITIME   must contain the second, in the range 0-59.
+                   (6)
+
+                   ITIME   must contain the millisecond, in the range 0-
+                   (7)     999.
+
+          6. Error Indicators and Warnings
+
+          None.
+
+          7. Accuracy
+
+          The day name included as part of the character string returned by
+          this routine is calculated assuming that the date is part of the
+          Gregorian calendar. This calendar has been in operation in Europe
+          since October the 15th 1582, and in Great Britain since September
+          the 14th 1752. Entry to this routine with a date earlier than
+          these will therefore not return a day name that is historically
+          accurate.
+
+          8. Further Comments
+
+          Two dates stored in character string format, as returned by this
+          routine, may be compared by X05ACF.
+
+          9. Example
+
+          This program initialises a time in ITIME, and converts it to
+          character format by a call to X05ABF.
+
+          The example program is not reproduced here. The source code for
+          all example programs is distributed with the NAG Foundation
+          Library software and should be available on-line.
+\end{verbatim}
+\endscroll
+\end{page}
+\begin{page}{manpageXXx05acf}{NAG On-line Documentation: x05acf}
+\beginscroll
+\begin{verbatim}
+
+
+
+     X05ACF(3NAG)      Foundation Library (12/10/92)      X05ACF(3NAG)
+
+
+
+          X05 -- Date and Time Utilities                             X05ACF
+                  X05ACF -- NAG Foundation Library Routine Document
+
+          Note: Before using this routine, please read the Users' Note for
+          your implementation to check implementation-dependent details.
+          The symbol (*) after a NAG routine name denotes a routine that is
+          not included in the Foundation Library.
+
+          1. Purpose
+
+          X05ACF compares two date/time character strings, each stored in
+          the format returned by X05ABF.
+
+          2. Specification
+
+                 INTEGER FUNCTION X05ACF (CTIME1, CTIME2)
+                 CHARACTER*(*)    CTIME1, CTIME2
+
+          3. Description
+
+          X05ACF compares two date/time character strings, and returns an
+          integer that specifies which one is the earliest. The result is
+          an integer returned through the routine name, with meaning as
+          follows:
+
+               X05ACF = -1: the first date/time string is earlier than the
+               second.
+
+               X05ACF = 0: the two date/time strings are equivalent.
+
+               X05ACF = 1: the first date/time string is later than the
+               second.
+
+          4. References
+
+          None.
+
+          5. Parameters
+
+           1:  CTIME1 -- CHARACTER*(*)                                Input
+
+           2:  CTIME2 -- CHARACTER*(*)                                Input
+               On entry: the date/time strings to be compared. These are
+               expected be in the format returned by X05ABF, although
+               X05ACF will still attempt to interpret the strings if they
+               vary slightly from this format. See Section 8 for further
+               details.
+
+          6. Error Indicators and Warnings
+
+          None.
+
+          7. Accuracy
+
+          Not applicable.
+
+          8. Further Comments
+
+          For flexibility, X05ACF will accept various formats for the two
+          date/time strings CTIME1 and CTIME2.
+
+          The strings do not have to be the same length. It is permissible,
+          for example, to enter with one or both of the strings truncated
+          to a smaller length, in which case missing fields are treated as
+          zero.
+
+          Each character string may be of any length, but everything after
+          character 80 is ignored.
+
+          Each string may or may not include an alphabetic day name, such
+          as 'Wednesday', at its start. These day names are ignored, and no
+          check is made that the day name corresponds correctly to the rest
+          of the date.
+
+          The month name may contain any number of characters provided it
+          uniquely identifies the month, however all characters that are
+          supplied are significant.
+
+          Each field in the character string must be separated by one or
+          more spaces.
+
+          The case of all alphabetic characters is insignificant.
+
+          Any field in a date time string that is indecipherable according
+          to the above rules will be converted to a zero value internally.
+          Thus two strings that are completely indecipherable will compare
+          equal.
+
+          According to these rules, all the following date/time strings are
+          equivalent:
+
+              'Thursday 10th July 1958 12:43:17.320'
+
+              'THU 10th JULY 1958 12:43:17.320'
+
+              '10th Jul 1958 12:43:17.320'
+
+          9. Example
+
+          This program initialises two date/time strings, and compares them
+          by a call to X05ACF.
+
+
+          The example program is not reproduced here. The source code for
+          all example programs is distributed with the NAG Foundation
+          Library software and should be available on-line.
+
+\end{verbatim}
+\endscroll
+\end{page}
+\begin{page}{manpageXXx05baf}{NAG On-line Documentation: x05baf}
+\beginscroll
+\begin{verbatim}
+
+
+
+     X05BAF(3NAG)      Foundation Library (12/10/92)      X05BAF(3NAG)
+
+
+
+          X05 -- Date and Time Utilities                             X05BAF
+                  X05BAF -- NAG Foundation Library Routine Document
+
+          Note: Before using this routine, please read the Users' Note for
+          your implementation to check implementation-dependent details.
+          The symbol (*) after a NAG routine name denotes a routine that is
+          not included in the Foundation Library.
+
+          1. Purpose
+
+          X05BAF returns the amount of processor time used since an
+          unspecified previous time, via the routine name.
+
+          2. Specification
+
+                 DOUBLE PRECISION FUNCTION X05BAF ()
+
+          3. Description
+
+          X05BAF returns the number of seconds of processor time used since
+          some previous time. The previous time is system dependent, but
+          may be, for example, the time the current job or the current
+          program started running.
+
+          If the system clock of the host machine is inaccessible for any
+          reason, X05BAF returns the value zero.
+
+          4. References
+
+          None.
+
+          5. Parameters
+
+          None.
+
+          6. Error Indicators and Warnings
+
+          None.
+
+          7. Accuracy
+
+          The accuracy of the value returned depends on the accuracy of the
+          system clock on the host machine.
+
+          8. Further Comments
+
+          Since the value returned by X05BAF is the amount of processor
+          time since some unspecified earlier time, no significance should
+          be placed on the value other than as a marker to be compared with
+          some later figure returned by X05BAF. The amount of processor
+          time that has elapsed between two calls of X05BAF can be simply
+          calculated as the earlier value subtracted from the later value.
+
+          9. Example
+
+          This program makes a call to X05BAF, performs some computations,
+          makes another call to X05BAF, and gives the time used by the
+          computations as the difference between the two returned values.
+
+          The example program is not reproduced here. The source code for
+          all example programs is distributed with the NAG Foundation
+          Library software and should be available on-line.
+\end{verbatim}
+\endscroll
+\end{page}