NAG Library Function Document

nag_pack_complx_mat_print_comp (x04ddc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     order – Nag_OrderTypeInput

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2:     uplo – Nag_UploTypeInput

On entry: indicates the type of the matrix to be printed

$\mathbf{uplo}=\mathrm{Nag\_Lower}$

The matrix is lower triangular

$\mathbf{uplo}=\mathrm{Nag\_Upper}$

The matrix is upper triangular

Constraint: $\mathbf{uplo}=\mathrm{Nag\_Lower}$ or $\mathrm{Nag\_Upper}$.

3:     diag – Nag_DiagTypeInput

On entry: indicates whether the diagonal elements of the matrix are to be printed.

$\mathbf{diag}=\mathrm{Nag\_NonRefDiag}$

The diagonal elements of the matrix are not referenced and not printed.

$\mathbf{diag}=\mathrm{Nag\_UnitDiag}$

The diagonal elements of the matrix are not referenced, but are assumed all to be unity, and are printed as such.

$\mathbf{diag}=\mathrm{Nag\_NonUnitDiag}$

The diagonal elements of the matrix are referenced and printed.

Constraint: $\mathbf{diag}=\mathrm{Nag\_NonRefDiag}$, $\mathrm{Nag\_UnitDiag}$ or $\mathrm{Nag\_NonUnitDiag}$.

4:     n – IntegerInput

On entry: the number of rows and columns of the matrix to be printed.

If n is less than $1$, nag_pack_complx_mat_print_comp (x04ddc) will exit immediately after printing title; no row or column labels are printed.

5:     a[$\mathit{dim}$] – const ComplexInput

Note: the dimension, dim, of the array a must be at least $\max \left(1,\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right)$.

On entry: the matrix to be printed. Note that a must have space for the diagonal elements of the matrix, even if these are not stored.

The storage of elements $A_{ij}$ depends on the order and uplo arguments as follows:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$ and $\mathbf{uplo}=\mathrm{Nag\_Upper}$,
            $A_{ij}$ is stored in $\mathbf{a}\left[\left(j-1\right)\times j/2+i-1\right]$, for $i\le j$;
• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$ and $\mathbf{uplo}=\mathrm{Nag\_Lower}$,
            $A_{ij}$ is stored in $\mathbf{a}\left[\left(2n-j\right)\times \left(j-1\right)/2+i-1\right]$, for $i\ge j$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$ and $\mathbf{uplo}=\mathrm{Nag\_Upper}$,
            $A_{ij}$ is stored in $\mathbf{a}\left[\left(2n-i\right)\times \left(i-1\right)/2+j-1\right]$, for $i\le j$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$ and $\mathbf{uplo}=\mathrm{Nag\_Lower}$,
            $A_{ij}$ is stored in $\mathbf{a}\left[\left(i-1\right)\times i/2+j-1\right]$, for $i\ge j$.

If $\mathbf{diag}=\mathrm{Nag\_UnitDiag}$, the diagonal elements of $A$ are assumed to be $1$, and are not referenced; the same storage scheme is used whether $\mathbf{diag}=\mathrm{Nag\_NonUnitDiag}$ or $\mathbf{diag}=\mathrm{Nag\_UnitDiag}$.

6:     cmplxform – Nag_ComplexFormTypeInput

On entry: indicates how the value of form is to be used to print matrix elements.

$\mathbf{cmplxform}=\mathrm{Nag\_AboveForm}$

The format code in form is assumed to contain a single real edit-descriptor which is to be used to print the real and imaginary parts of each Complex number one above the other. Each row of the matrix is separated by a blank line, and any row labels are attached only to the real parts. This option means that about twice as many columns can be fitted into ncols characters than if any other cmplxform option is used. A typical value of form for this cmplxform option might be %11.4e.

$\mathbf{cmplxform}=\mathrm{Nag\_BracketForm}$

The format code in form is assumed to contain a single edit-descriptor such as %13.4f, * or NULL, which is used to print the real and imaginary parts of each Complex number separated by a comma, and surrounded by brackets. Thus a matrix element printed with this cmplxform option might look like this: $\left(12.345,-11.323\right)$.

$\mathbf{cmplxform}=\mathrm{Nag\_DirectForm}$

The format code in form is used unaltered to print a Complex number. This cmplxform option allows you flexibility to specify exactly how the number is printed. With this option for cmplxform and a suitable value for form it is possible, for example, to print a Complex number in the form $\left(0.123+3.214i\right)$ or $\left(\text{0.123e−02},\text{0.234e−01}\right)$.

Constraint: $\mathbf{cmplxform}=\mathrm{Nag\_AboveForm}$, $\mathrm{Nag\_BracketForm}$ or $\mathrm{Nag\_DirectForm}$.

7:     form – const char *Input

On entry: a valid C format code. This should be of the form $\%\left[\mathit{flag}\right]ww.pp\left[\mathit{format}\text{ }\mathit{indicator}\right]$, where $\mathit{ww}.pp$ indicates that up to two digits may be used to specify the field width and precision respectively. Only % and $\mathit{format}\text{ }\mathit{indicator}$ must be present. $\mathit{flag}$ can be one of $-$, $+$, $<\text{space}>$ or # and $\mathit{format}\text{ }\mathit{indicator}$ can be e, E, f, g or G. Thus, possible formats include %f, $\%-11.4\mathrm{G}$, %.6e. form is used in conjunction with argument cmplxform, to print elements of the matrix $A$.

In addition, nag_pack_complx_mat_print_comp (x04ddc) chooses its own format code when form is NULL or $\mathbf{form}=\text{'*'}$.

If $\mathbf{form}=\mathbf{NULL}$, nag_pack_complx_mat_print_comp (x04ddc) will choose a format code such that numbers will be printed with either a %8.4f, a %11.4f or a %13.4e format. The %8.4f code is chosen if the sizes of all the matrix elements to be printed lie between $0.001$ and $1.0$. The %11.4f code is chosen if the sizes of all the matrix elements to be printed lie between $0.001$ and $9999.9999$. Otherwise the %13.4e code is chosen.

If $\mathbf{form}=\text{'*'}$, nag_pack_complx_mat_print_comp (x04ddc) will choose a format code such that numbers will be printed to as many significant digits as are necessary to distinguish between neighbouring machine numbers. Thus any two numbers that are stored with different internal representations should look different on output.

More complicated values of form, to print a Complex number in a desired form, may be used. See the description of argument cmplxform above for more details.

Constraint: if $\mathbf{cmplxform}=\mathrm{Nag\_AboveForm}$ or $\mathrm{Nag\_BracketForm}$, form must be of the form $\%\left[\mathit{flag}\right]ww.pp\left[\mathit{format}\text{ }\mathit{indicator}\right]$.

8:     title – const char *Input

On entry: a title to be printed above the matrix, or name of the matrix.

If $\mathbf{title}=\mathbf{NULL}$, no title (and no blank line) will be printed.

If title contains more than ncols characters, the contents of title will be wrapped onto more than one line, with the break after ncols characters.

Any trailing blank characters in title are ignored.

9:     labrow – Nag_LabelTypeInput

On entry: indicates the type of labelling to be applied to the rows of the matrix.

$\mathbf{labrow}=\mathrm{Nag\_NoLabels}$

Prints no row labels.

$\mathbf{labrow}=\mathrm{Nag\_IntegerLabels}$

Prints integer row labels.

$\mathbf{labrow}=\mathrm{Nag\_CharacterLabels}$

Prints character labels, which must be supplied in array rlabs.

Constraint: $\mathbf{labrow}=\mathrm{Nag\_NoLabels}$, $\mathrm{Nag\_IntegerLabels}$ or $\mathrm{Nag\_CharacterLabels}$.

10:   rlabs[$\mathit{dim}$] – const char *Input

Note: the dimension, dim, of the array rlabs must be at least

• $\mathbf{n}$ when $\mathbf{labrow}=\mathrm{Nag\_CharacterLabels}$;
• otherwise rlabs may be NULL.

On entry: if $\mathbf{labrow}=\mathrm{Nag\_CharacterLabels}$, rlabs must contain labels for the rows of the matrix; otherwise rlabs is not referenced and may be NULL.

Labels are right-justified when output, in a field which is as wide as necessary to hold the longest row label. Note that this field width is subtracted from the number of usable columns, ncols.

11:   labcol – Nag_LabelTypeInput

On entry: indicates the type of labelling to be applied to the columns of the matrix.

$\mathbf{labcol}=\mathrm{Nag\_NoLabels}$

Prints no column labels.

$\mathbf{labcol}=\mathrm{Nag\_IntegerLabels}$

Prints integer column labels.

$\mathbf{labcol}=\mathrm{Nag\_CharacterLabels}$

Prints character labels, which must be supplied in array clabs.

Constraint: $\mathbf{labcol}=\mathrm{Nag\_NoLabels}$, $\mathrm{Nag\_IntegerLabels}$ or $\mathrm{Nag\_CharacterLabels}$.

12:   clabs[$\mathit{dim}$] – const char *Input

Note: the dimension, dim, of the array clabs must be at least

• $\mathbf{n}$ when $\mathbf{labcol}=\mathrm{Nag\_CharacterLabels}$;
• otherwise clabs may be NULL.

On entry: if $\mathbf{labcol}=\mathrm{Nag\_CharacterLabels}$, clabs must contain labels for the columns of the matrix; otherwise clabs is not referenced and may be NULL.

Labels are right-justified when output. Any label that is too long for the column width, which is determined by form, is truncated.

13:   ncols – IntegerInput

On entry: the maximum output record length. If the number of columns of the matrix is too large to be accommodated in ncols characters, the matrix will be printed in parts, containing the largest possible number of matrix columns, and each part separated by a blank line.

ncols must be large enough to hold at least one column of the matrix using the format specifier in form. If a value less than or equal to 0 or greater than $132$ is supplied for ncols, then the value $80$ is used instead.

14:   indent – IntegerInput

On entry: the number of columns by which the matrix (and any title and labels) should be indented. The effective value of ncols is reduced by indent columns. If a value less than $0$ or greater than ncols is supplied for indent, the value $0$ is used instead.

15:   outfile – const char *Input

On entry: the name of a file to which output will be directed. If outfile is NULL the output will be directed to standard output.

16:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Memory allocation failed.

NE_BAD_PARAM

On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.

NE_COL_WIDTH

$⟨\mathit{\text{value}}⟩$ is not wide enough to hold at least one matrix column. $\mathbf{ncols}=⟨\mathit{\text{value}}⟩$ and $\mathbf{indent}=⟨\mathit{\text{value}}⟩$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

NE_INVALID_FORMAT

The string  has not been recognized as a valid format.

NE_NOT_APPEND_FILE

Cannot open file  for appending.

NE_NOT_CLOSE_FILE

Cannot close file .

NE_NOT_WRITE_FILE

Cannot open file  for writing.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example