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.\" RCSid "$Id$" |
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.TH RMTXOP 1 7/8/97 RADIANCE |
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.TH RMTXOP 1 5/31/2014 RADIANCE |
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.SH NAME |
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rmtxop - concatenate, add, multiply, divide, transpose, scale, and convert matrices |
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.SH SYNOPSIS |
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][ |
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.B \-t |
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][ |
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.B "\-c ce .." |
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][ |
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.B "\-s sf .." |
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][ |
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.B "\-c ce .." |
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.B "\-rf|\-rb" |
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] |
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.B m1 |
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[ |
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NROWS={number of rows} |
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NCOLS={number of columns} |
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NCOMP={number of components} |
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FORMAT={ascii|float|double|32-bit_rle_rgbe|32-bit_rle_xyze} |
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.sp |
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FORMAT={ascii|float|double|32-bit_rle_rgbe|32-bit_rle_xyze|Radiance_spectra} |
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.fi |
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.sp |
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The number of components indicates that each matrix element is actually |
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composed of multiple elements, most commonly an RGB triple. |
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This is essentially dividing the matrix into planes, where each component |
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using quotes and a beginning exclamation point ('!'). |
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.PP |
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Two special cases are handled for component matrices that are either |
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XML files containing BTDF data, or Radiance picture files. |
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In the first case, a BSDF library is used to load and interpret the |
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transmission matrix. |
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XML files containing BSDF data, or Radiance picture files. |
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In the first case, the BSDF library loads and interprets the |
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transmission matrix by default. |
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Alternatively, the front (normal-side) reflectance is selected if the |
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.I \-rf |
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option precedes the file name, or the backside reflectance if |
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.I \-rb |
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is specified. |
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(XML files cannot be read from the standard input or from a command.)\0 |
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In the second case, the RGBE or XYZE values are loaded in a 3-component |
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matrix where the number of columns match the X-dimension of the picture, and |
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the number of rows match the Y-dimension. |
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The picture must be in standard pixel ordering, and the first row |
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is at the top with the first column on the left. |
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Any exposure changes that were applied to the pictures before |
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.I rmtxop |
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will be undone, similar to the |
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.I pcomb(1) |
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.I \-o |
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option. |
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Radiance spectral pictures with more than 3 components are also supported. |
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These are typically produced by |
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.I rtrace(1) |
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or |
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.I rfluxmtx(1). |
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.PP |
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Before each file, the |
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.I \-t |
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and |
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– |
.I \-s |
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or |
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.I \-c |
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and/or |
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.I \-s |
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options may be used to modify the matrix. |
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The |
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.I \-t |
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option transposes the matrix, swapping rows and columns. |
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The |
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.I \-s |
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option applies the given scalar factor(s) to the elements of the matrix. |
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If only one factor is provided, |
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it will be used for all components. |
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If multiple factors are given, their number must match the number of matrix |
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components. |
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Alternatively, the |
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.I \-c |
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option may be used to "transform" the element values, possibly changing |
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option can "transform" the element values, possibly changing |
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the number of components in the matrix. |
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For example, a 3-component matrix can be transformed into a single-component |
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matrix by using |
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yield the second new component. |
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Note that the number of coefficients must be an even multiple of the number |
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of original components. |
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The |
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Alternatively, a set of symbolic output components can be specified as capital |
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letters, with the following definitions: |
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.sp |
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.nf |
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R - red channel |
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G - green channel |
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B - blue channel |
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X - CIE X channel |
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Y - CIE Y channel (aka., luminance or illuminance) |
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Z - CIE Z channel |
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S - scotopic luminance or illuminance |
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M - melanopic luminance or illuminance |
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.fi |
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.sp |
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These letters may be given in any order as a single string, and if |
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.I "-c RGB" |
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or |
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.I "-c XYZ" |
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is specified along with a |
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.I "-fc" |
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option, the output will be written as a RGBE or XYZE picture, respectively. |
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Note that conversion from a float or RGBE color space applies a conversion |
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of 179 lumens/watt (for CIE or melanopic output) or 412 (for scotopic output), |
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and the reverse happens for conversion from XYZE input to RGB or RGBE output. |
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.PP |
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Additionally, the |
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.I \-s |
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and |
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option applies the given scalar factor(s) to the elements of the matrix. |
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If only one factor is provided, |
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it will be used for all components. |
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If multiple factors are given, their number must match the number of matrix |
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components |
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.I after |
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application of any |
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.I \-c |
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options are mutually exclusive, insofar as they cannot be applied together |
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to the same input matrix. |
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option for this input matrix or picture. |
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.PP |
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If present, the second and subsequent matrices on the command |
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line are concatenated to the result unless separated by a plus ('+'), |
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line are concatenated together, unless separated by a plus ('+'), |
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asterisk ('*'), or forward slash ('/') symbol, |
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in which case the matrix elements are added, multiplied, or divided together, |
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respectively. |
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(Note that the asterisk must be quoted or escaped in most shells.)\0 |
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in which case the individual matrix elements are added, |
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multiplied, or divided, respectively. |
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The concatenation operator ('.') is the default and need not be specified. |
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Note also that the asterisk must be quoted or escaped in most shells. |
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In the case of addition, the two matrices involved must have the same number |
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of components. |
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If subtraction is desired, use addition ('+') with a scaling parameter of -1 |
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for the second matrix (the |
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.I \-s |
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option). |
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For element-wise multiplication and division, the second matrix is |
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permitted instead to have a single component per element, which will be |
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permitted to have a single component per element, which will be |
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applied equally to all components of the first matrix. |
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If element-wise division is specified, any zero elements in the second |
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matrix will result in a warning and the corresponding component(s) in the |
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first matrix will be set to zero. |
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.PP |
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The number of components in the new matrix after applying any |
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Evaluation proceeds from left to right, and all operations have |
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the same precedence. |
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If a different evaluation order is desired, pipe the result of one |
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.I rmtxop |
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command into another, as shown in one of the examples below. |
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.PP |
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The number of components in the next matrix after applying any |
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.I -c |
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transform must agree with the prior result. |
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For concatenation (matrix multiplication), the number of columns |
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in the prior result must equal the number of rows in the new matrix, and |
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in the prior result must equal the number of rows in the next matrix, and |
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the result will have the number of rows of the previous and the number |
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of columns of the new matrix. |
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of columns of the next matrix. |
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In the case of addition, multiplication, and division, |
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the number of rows and columns of the prior result and the |
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new matrix must match, and will not be changed by the operation. |
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next matrix must match, and will not be changed by the operation. |
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.PP |
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A final transpose or transform/scaling operation may be applied to |
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the results by appending the |
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.I \-t |
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and |
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.I \-c |
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and/or |
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.I \-s |
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options after the last matrix on the command line. |
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.PP |
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Results are sent to the standard output. |
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By default, the values will be written in the lowest resolution format |
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among the inputs, but the |
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.I \-f |
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option may be used to explicitly output components |
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as ASCII (-fa), binary doubles (-fd), floats (-ff), or RGBE colors (-fc). |
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as ASCII (-fa), binary doubles (-fd), floats (-ff), or common-exponent |
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colors/spectra (-fc). |
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In the latter case, the actual matrix dimensions are written in the resolution |
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string rather than the header. |
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Also, matrix results written as Radiance pictures must have either one |
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Also, matrix results will be written as standard |
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Radiance pictures if they have either one |
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or three components. |
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In the one-component case, the output is written as grayscale. |
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If more than 3 components are in the final matrix and |
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.I -fc |
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is specified, the output will be a Radiance spectral picture. |
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.PP |
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The |
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.I \-v |
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.IP "" .2i |
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rmtxop -fc blinds.xml > blinds.hdr |
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.PP |
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To extract the luminance values from a picture as an ASCII matrix: |
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.IP "" .2i |
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rmtxop -fa -c .265 .670 .065 image.hdr > image_lum.mtx |
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.PP |
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To render a melanopic illuminance image with |
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.I rtrace\: |
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.IP "" .2i |
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vwrays -ff -x 1024 -y 1024 -vf myview.vf | |
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rtrace -fff -cs 18 -co+ -i+ `vwrays -x 1024 -y 1024 -vf myview.vf -d` scene.oct | |
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rmtxop -fc -c M - > scene_meli.hdr |
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.PP |
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To scale a matrix by 4 and add it to the transpose of another matrix: |
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.IP "" .2i |
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rmtxop -s 4 left.mtx + -t right.mtx > result.mtx |
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rmtxop -s 4 first.mtx + -t second.mtx > result.mtx |
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.PP |
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To multiply elements of two matrices, then concatenate with a third, |
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applying a final transpose to the result: |
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.IP "" .2i |
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rmtxop first.mtx \\* second.mtx . third.mtx -t > result.mtx |
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.PP |
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To left-multiply the element-wise division of two matrices: |
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.IP "" .2i |
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rmtxop -fd numerator.mtx / denominator.mtx | rmtxop left.mtx - > result.mtx |
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.PP |
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To send the elements of a binary matrix to |
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.I rcalc(1) |
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for further processing: |
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.IP "" .2i |
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rmtxop -fa orig.mtx | rcollate -ho -oc 1 | rcalc [operations] |
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.SH NOTES |
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Matrix multiplication is associative but not commutative, so order |
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Matrix concatenation is associative but not commutative, so order |
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matters to the result. |
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.I Rmtxop |
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takes advantage of the associative property to evaluate the |
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implicit equation from right to left when this reduces the |
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number of basic operations. |
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takes advantage of this associative property to concatenate |
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from right to left when it reduces the number of basic operations. |
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If the rightmost matrix is a column vector for example, it is |
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much faster to concatenate from the right, and the result should |
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much faster to concatenate from the right, and the result will |
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be the same. |
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This only applies to matrix multiplication. |
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Element-wise addition, multiplication, and division are still |
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Note that this only applies to concatenation; |
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element-wise addition, multiplication, and division are always |
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evaluated from left to right. |
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.SH AUTHOR |
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Greg Ward |
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.SH "SEE ALSO" |
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cnt(1), getinfo(1), histo(1), neaten(1), rcalc(1), rcollate(1), |
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rcontrib(1), rfluxmtx(1), rlam(1), |
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rsplit(1), tabfunc(1), total(1), wrapBSDF(1) |
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cnt(1), getinfo(1), histo(1), neaten(1), pcomb(1), |
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ra_xyze(1), rcalc(1), |
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rcollate(1), rcontrib(1), rcrop(1), rfluxmtx(1), rlam(1), |
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rsplit(1), rtrace(1), tabfunc(1), total(1), vwrays(1), |
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wrapBSDF(1) |
