Matrix Text File Formats
Matrix Market Exchange Formats
This is the native exchange format for the Matrix Market. We provide only a brief overview of this format on this page; a complete description is provided in the paper The Matrix Market Formats: Initial Design [Gziped PostScript, 51 Kbytes] [PostScript, 189 Kbytes].
The Matrix Market (MM) exchange formats provide a simple mechanism to facilitate the exchange of matrix data. In particular, the objective has been to define a minimal base ASCII file format which can be very easily explained and parsed, but can easily adapted to applications with a more rigid structure, or extended to related data objects. The MM exchange format for matrices is really a collection of affiliated formats which share design elements. In our initial specification, two matrix formats are defined.
Coordinate Format
A file format suitable for representing general sparse matrices. Only nonzero entries are provided, and the coordinates of each nonzero entry is given explicitly. This is illustrated in the example below.
Array Format
A file format suitable for representing general dense matrices. All entries are provided in a pre-defined (column-oriented) order.
Several instances of each of these basic formats are defined. These are obtained by specifying an arithmetic field for the matrix entries (i.e., real, complex, integer, pattern) and a symmetry structure which may reduce the size of the data file (i.e. general, symmetric, skew-symmetric, Hermitian) by storing nonzero entries only on or below the main diagonal.
MM coordinate format is suitable for representing sparse matrices. Only nonzero entries need be encoded, and the coordinates of each are given explicitly. This is illustrated in the following example of a real 5x5 general sparse matrix.
1 0 0 6 0
0 10.5 0 0 0
0 0 .015 0 0
0 250.5 0 -280 33.32
0 0 0 0 12
In MM coordinate format this could be represented as follows.
%%MatrixMarket matrix coordinate real general
%=================================================================================
%
% This ASCII file represents a sparse MxN matrix with L
% nonzeros in the following Matrix Market format:
%
% +----------------------------------------------+
% |%%MatrixMarket matrix coordinate real general | <--- header line
% |% | <--+
% |% comments | |-- 0 or more comment lines
% |% | <--+
% | M N L | <--- rows, columns, entries
% | I1 J1 A(I1, J1) | <--+
% | I2 J2 A(I2, J2) | |
% | I3 J3 A(I3, J3) | |-- L lines
% | . . . | |
% | IL JL A(IL, JL) | <--+
% +----------------------------------------------+
%
% Indices are 1-based, i.e. A(1,1) is the first element.
%
%=================================================================================
5 5 8
1 1 1.000e+00
2 2 1.050e+01
3 3 1.500e-02
1 4 6.000e+00
4 2 2.505e+02
4 4 -2.800e+02
4 5 3.332e+01
5 5 1.200e+01
The first line contains the type code. In this example, it indicates that the object being represented is a matrix in coordinate format and that the numeric data following is real and represented in general form. (By general we mean that the matrix format is not taking advantage of any symmetry properties.)
Variants of the coordinate format are defined for matrices with complex and integer entries, as well as for those in which only the position of the nonzero entries is prescribed (pattern matrices). (These would be indicated by changing real to complex, integer, or pattern, respectively, on the header line). Additional variants are defined for cases in which symmetries can be used to significantly reduce the size of the data: symmetric, skew-symmetric and Hermitian. In these cases, only entries in the lower triangular portion need be supplied. In the skew-symmetric case the diagonal entries are zero, and hence they too are omitted. (These would be indicated by changing general to symmetric, skew-symmetric, or hermitian, respectively, on the header line).
The following software packages are available to aid in reading and writing matrices in Matrix Market format.
Matrix Market I/O in C
Matrix Market I/O in Fortran
Matrix Market I/O in Matlab®
BeBOP Sparse Matrix Conversion Library
Matrix Market I/O in Python
--------------------------------------------------------------------------------
Harwell-Boeing Exchange Format
The Harwell-Boeing format is the most popular mechanism for text-file exchange of sparse matrix data. The following information, taken from User's Guide for the Harwell-Boeing Sparse Matrix Collection provides a specification for this format.
Matrix data is held in an 80-column, fixed-length format for portability. Each matrix begins with a multiple line header block, which is followed by two, three, or four data blocks. The header block contains summary information on the storage formats and space requirements. From the header block alone, the user can determine how much space will be required to store the matrix. Information on the size of the representation in lines is given for ease in skipping past unwanted data.
If there are no right-hand-side vectors, the matrix has a four-line header block followed by two or three data blocks containing, in order, the column (or element) start pointers, the row (or variable) indices, and the numerical values. If right-hand sides are present, there is a fifth line in the header block and a fourth data block containing the right-hand side(s). The blocks containing the numerical values and right-hand side(s) are optional. The right-hand side(s) can be present only when the numerical values are present. If right-hand sides are present, then vectors for starting guesses and the solution can also be present; if so, they appear as separate full arrays in the right-hand side block following the right-hand side vector(s).
The first line contains the 72-character title and the 8-character identifier by which the matrix is referenced in our documentation. The second line contains the number of lines for each of the following data blocks as well as the total number of lines, excluding the header block. The third line contains a three character string denoting the matrix type as well as the number of rows, columns (or elements), entries, and, in the case of unassembled matrices, the total number of entries in elemental matrices. The fourth line contains the variable Fortran formats for the following data blocks. The fifth line is present only if there are right-hand sides. It contains a one character string denoting the storage format for the right-hand sides as well as the number of right-hand sides, and the number of row index entries (for the assembled case). The exact format is given by the following, where the names of the Fortran variables in the subsequent programs are given in parenthesis:
Line 1 (A72,A8) Col. 1 - 72 Title (TITLE)
Col. 73 - 80 Key (KEY)
Line 2 (5I14) Col. 1 - 14 Total number of lines excluding header (TOTCRD)
Col. 15 - 28 Number of lines for pointers (PTRCRD)
Col. 29 - 42 Number of lines for row (or variable) indices (INDCRD)
Col. 43 - 56 Number of lines for numerical values (VALCRD)
Col. 57 - 70 Number of lines for right-hand sides (RHSCRD)
(including starting guesses and solution vectors if present)
(zero indicates no right-hand side data is present)
Line 3 (A3, 11X, 4I14) Col. 1 - 3 Matrix type (see below) (MXTYPE)
Col. 15 - 28 Number of rows (or variables) (NROW)
Col. 29 - 42 Number of columns (or elements) (NCOL)
Col. 43 - 56 Number of row (or variable) indices (NNZERO)
(equal to number of entries for assembled matrices)
Col. 57 - 70 Number of elemental matrix entries (NELTVL)
(zero in the case of assembled matrices)
Line 4 (2A16, 2A20) Col. 1 - 16 Format for pointers (PTRFMT)
Col. 17 - 32 Format for row (or variable) indices (INDFMT)
Col. 33 - 52 Format for numerical values of coefficient matrix (VALFMT)
Col. 53 - 72 Format for numerical values of right-hand sides (RHSFMT)
Line 5 (A3, 11X, 2I14) Only present if there are right-hand sides present Col. 1 Right-hand side type:
F for full storage or
M for same format as matrix
Col. 2 G if a starting vector(s) (Guess) is supplied. (RHSTYP)
Col. 3 X if an exact solution vector(s) is supplied.
Col. 15 - 28 Number of right-hand sides (NRHS)
Col. 29 - 42 Number of row indices (NRHSIX)
(ignored in case of unassembled matrices)
Note: For matrices in elemental form, the leading two dimensions in the header give the number of variables in the finite element application and the number of elements. It is common that not all of the variables in the application appear in the linear algebra subproblem; hence the matrix represented can be of lower order than the first parameter, described as the "number of variables (NROW)". The finite element variables are numbered from 1 to NROW, but only the subset of variables that actually appear in the list of variables for the elements define the rows and columns of the matrix. The actual order of the square matrix cannot be determined until all of the indices are read.
The three character type field on line 3 describes the matrix type. The following table lists the permitted values for each of the three characters. As an example of the type field, RSA denotes that the matrix is real, symmetric, and assembled.
First Character: R Real matrix
C Complex matrix
P Pattern only (no numerical values supplied)
Second Character: S Symmetric
U Unsymmetric
H Hermitian
Z Skew symmetric
R Rectangular
Third Character: A Assembled
E Elemental matrices (unassembled)
Example Fortran Code for Reading Harwell-Boeing Files
To formalize the logical block structure of the data, we have included two pieces of sample FORTRAN code for reading a matrix in the format of the sparse matrix test collection. Both codes assume the data comes from input unit LUNIT. Neither is a complete code. Real code should include error checking to ensure that the target arrays into which the data are read are large enough. The design allows the arrays to be read by a separate subroutine that can avoid the use of possibly inefficient implicit DO-loops.
First sample fortran code : the standard case, a sparse matrix in standard format with no right-hand sides.
Second sample fortran code : illustrates the full generality of the representation.
The code above outlines the structure of the data. The interpretation of the row (or variable) index arrays will require knowledge of the matrix and right-hand side types, as read in this code.
Matlab Procedures for Reading/Writing Harwell-Boeing Files
The developers of the NEP matrix collection have provided a Matlab m-file to write a Matlab sparse matrix in Harwell-Boeing format. A version for complex matrices is also available.
The Berkeley Benchmarking and Optimization (BeBOP) Group has developed a library and standalone utility for converting between Harwell-Boeing, Matrix Market, and MATLAB sparse matrix formats.
--------------------------------------------------------------------------------
Coordinate Text File
Note: This format is being phased out.
The coordinate text format provides a simple and portable method to exchange sparse matrices. Any language or computer system that understands ASCII text can read this file format with a simple read loop. This makes this data accessible not only to users in the Fortran community, but also developers using C, C++, Pascal, or Basic environments.
In coordinate text file format the first line lists three integers: the number of rows m, columns n, and nonzeros nz in the matrix. The nonzero matrix elements are then listed, one per line, by specifying row index i, column index j, and the value a(i,j), in that order. For example,
m m nz
i1 j1 val1
i2 j2 val2
i3 j3 val3
. . .
. . .
. . .
inz jnz valnz
White space is not significant, (i.e. a fixed column is not used). The nonzero values may be in either in fixed or floating point representation, to any precision (although Fortran and C typically parse less than 20 significant digits). For example, the following are each acceptable: 3, 3.141, +3.1415626536E000, 3.1e0.
Experiments show that these coordinate files are approximately 30% larger than corresponding Harwell-Boeing files. Versions compressed with Unix compress or gzip typically exhibits similar ratios.
To represent only structure information of a sparse matrix, a single zero can be placed in the value position, e.g.
M N nz
i1 j1 0
i2 j2 0
i3 j3 0
. . .
. . .
. . .
inz jnz 0
Although more efficient schemes are available, this allows the same routine to read both types of files. The addition of a single byte to each line of the file is typically of little consequence.
Note that there is no implied order for the matrix elements. This allows one to write simple print routines which traverse the sparse matrix in whatever natural order given by the particular storage scheme.
Also note that no annotations are used for storing matrices with special structure. (This keeps the parsing routines simple.) Symmetric matrices can be represented by only their upper or lower triangular portions, but the file format reveals just that --- the reading program sees only a triangular matrix. (The application is responsible for reinterpreting this.)
A MATLAB function (M-file) is available which reads a matrix in coordinate text file format and creates a sparse matrix is available.
This is the native exchange format for the Matrix Market. We provide only a brief overview of this format on this page; a complete description is provided in the paper The Matrix Market Formats: Initial Design [Gziped PostScript, 51 Kbytes] [PostScript, 189 Kbytes].
The Matrix Market (MM) exchange formats provide a simple mechanism to facilitate the exchange of matrix data. In particular, the objective has been to define a minimal base ASCII file format which can be very easily explained and parsed, but can easily adapted to applications with a more rigid structure, or extended to related data objects. The MM exchange format for matrices is really a collection of affiliated formats which share design elements. In our initial specification, two matrix formats are defined.
Coordinate Format
A file format suitable for representing general sparse matrices. Only nonzero entries are provided, and the coordinates of each nonzero entry is given explicitly. This is illustrated in the example below.
Array Format
A file format suitable for representing general dense matrices. All entries are provided in a pre-defined (column-oriented) order.
Several instances of each of these basic formats are defined. These are obtained by specifying an arithmetic field for the matrix entries (i.e., real, complex, integer, pattern) and a symmetry structure which may reduce the size of the data file (i.e. general, symmetric, skew-symmetric, Hermitian) by storing nonzero entries only on or below the main diagonal.
MM coordinate format is suitable for representing sparse matrices. Only nonzero entries need be encoded, and the coordinates of each are given explicitly. This is illustrated in the following example of a real 5x5 general sparse matrix.
1 0 0 6 0
0 10.5 0 0 0
0 0 .015 0 0
0 250.5 0 -280 33.32
0 0 0 0 12
In MM coordinate format this could be represented as follows.
%%MatrixMarket matrix coordinate real general
%=================================================================================
%
% This ASCII file represents a sparse MxN matrix with L
% nonzeros in the following Matrix Market format:
%
% +----------------------------------------------+
% |%%MatrixMarket matrix coordinate real general | <--- header line
% |% | <--+
% |% comments | |-- 0 or more comment lines
% |% | <--+
% | M N L | <--- rows, columns, entries
% | I1 J1 A(I1, J1) | <--+
% | I2 J2 A(I2, J2) | |
% | I3 J3 A(I3, J3) | |-- L lines
% | . . . | |
% | IL JL A(IL, JL) | <--+
% +----------------------------------------------+
%
% Indices are 1-based, i.e. A(1,1) is the first element.
%
%=================================================================================
5 5 8
1 1 1.000e+00
2 2 1.050e+01
3 3 1.500e-02
1 4 6.000e+00
4 2 2.505e+02
4 4 -2.800e+02
4 5 3.332e+01
5 5 1.200e+01
The first line contains the type code. In this example, it indicates that the object being represented is a matrix in coordinate format and that the numeric data following is real and represented in general form. (By general we mean that the matrix format is not taking advantage of any symmetry properties.)
Variants of the coordinate format are defined for matrices with complex and integer entries, as well as for those in which only the position of the nonzero entries is prescribed (pattern matrices). (These would be indicated by changing real to complex, integer, or pattern, respectively, on the header line). Additional variants are defined for cases in which symmetries can be used to significantly reduce the size of the data: symmetric, skew-symmetric and Hermitian. In these cases, only entries in the lower triangular portion need be supplied. In the skew-symmetric case the diagonal entries are zero, and hence they too are omitted. (These would be indicated by changing general to symmetric, skew-symmetric, or hermitian, respectively, on the header line).
The following software packages are available to aid in reading and writing matrices in Matrix Market format.
Matrix Market I/O in C
Matrix Market I/O in Fortran
Matrix Market I/O in Matlab®
BeBOP Sparse Matrix Conversion Library
Matrix Market I/O in Python
--------------------------------------------------------------------------------
Harwell-Boeing Exchange Format
The Harwell-Boeing format is the most popular mechanism for text-file exchange of sparse matrix data. The following information, taken from User's Guide for the Harwell-Boeing Sparse Matrix Collection provides a specification for this format.
Matrix data is held in an 80-column, fixed-length format for portability. Each matrix begins with a multiple line header block, which is followed by two, three, or four data blocks. The header block contains summary information on the storage formats and space requirements. From the header block alone, the user can determine how much space will be required to store the matrix. Information on the size of the representation in lines is given for ease in skipping past unwanted data.
If there are no right-hand-side vectors, the matrix has a four-line header block followed by two or three data blocks containing, in order, the column (or element) start pointers, the row (or variable) indices, and the numerical values. If right-hand sides are present, there is a fifth line in the header block and a fourth data block containing the right-hand side(s). The blocks containing the numerical values and right-hand side(s) are optional. The right-hand side(s) can be present only when the numerical values are present. If right-hand sides are present, then vectors for starting guesses and the solution can also be present; if so, they appear as separate full arrays in the right-hand side block following the right-hand side vector(s).
The first line contains the 72-character title and the 8-character identifier by which the matrix is referenced in our documentation. The second line contains the number of lines for each of the following data blocks as well as the total number of lines, excluding the header block. The third line contains a three character string denoting the matrix type as well as the number of rows, columns (or elements), entries, and, in the case of unassembled matrices, the total number of entries in elemental matrices. The fourth line contains the variable Fortran formats for the following data blocks. The fifth line is present only if there are right-hand sides. It contains a one character string denoting the storage format for the right-hand sides as well as the number of right-hand sides, and the number of row index entries (for the assembled case). The exact format is given by the following, where the names of the Fortran variables in the subsequent programs are given in parenthesis:
Line 1 (A72,A8) Col. 1 - 72 Title (TITLE)
Col. 73 - 80 Key (KEY)
Line 2 (5I14) Col. 1 - 14 Total number of lines excluding header (TOTCRD)
Col. 15 - 28 Number of lines for pointers (PTRCRD)
Col. 29 - 42 Number of lines for row (or variable) indices (INDCRD)
Col. 43 - 56 Number of lines for numerical values (VALCRD)
Col. 57 - 70 Number of lines for right-hand sides (RHSCRD)
(including starting guesses and solution vectors if present)
(zero indicates no right-hand side data is present)
Line 3 (A3, 11X, 4I14) Col. 1 - 3 Matrix type (see below) (MXTYPE)
Col. 15 - 28 Number of rows (or variables) (NROW)
Col. 29 - 42 Number of columns (or elements) (NCOL)
Col. 43 - 56 Number of row (or variable) indices (NNZERO)
(equal to number of entries for assembled matrices)
Col. 57 - 70 Number of elemental matrix entries (NELTVL)
(zero in the case of assembled matrices)
Line 4 (2A16, 2A20) Col. 1 - 16 Format for pointers (PTRFMT)
Col. 17 - 32 Format for row (or variable) indices (INDFMT)
Col. 33 - 52 Format for numerical values of coefficient matrix (VALFMT)
Col. 53 - 72 Format for numerical values of right-hand sides (RHSFMT)
Line 5 (A3, 11X, 2I14) Only present if there are right-hand sides present Col. 1 Right-hand side type:
F for full storage or
M for same format as matrix
Col. 2 G if a starting vector(s) (Guess) is supplied. (RHSTYP)
Col. 3 X if an exact solution vector(s) is supplied.
Col. 15 - 28 Number of right-hand sides (NRHS)
Col. 29 - 42 Number of row indices (NRHSIX)
(ignored in case of unassembled matrices)
Note: For matrices in elemental form, the leading two dimensions in the header give the number of variables in the finite element application and the number of elements. It is common that not all of the variables in the application appear in the linear algebra subproblem; hence the matrix represented can be of lower order than the first parameter, described as the "number of variables (NROW)". The finite element variables are numbered from 1 to NROW, but only the subset of variables that actually appear in the list of variables for the elements define the rows and columns of the matrix. The actual order of the square matrix cannot be determined until all of the indices are read.
The three character type field on line 3 describes the matrix type. The following table lists the permitted values for each of the three characters. As an example of the type field, RSA denotes that the matrix is real, symmetric, and assembled.
First Character: R Real matrix
C Complex matrix
P Pattern only (no numerical values supplied)
Second Character: S Symmetric
U Unsymmetric
H Hermitian
Z Skew symmetric
R Rectangular
Third Character: A Assembled
E Elemental matrices (unassembled)
Example Fortran Code for Reading Harwell-Boeing Files
To formalize the logical block structure of the data, we have included two pieces of sample FORTRAN code for reading a matrix in the format of the sparse matrix test collection. Both codes assume the data comes from input unit LUNIT. Neither is a complete code. Real code should include error checking to ensure that the target arrays into which the data are read are large enough. The design allows the arrays to be read by a separate subroutine that can avoid the use of possibly inefficient implicit DO-loops.
First sample fortran code : the standard case, a sparse matrix in standard format with no right-hand sides.
Second sample fortran code : illustrates the full generality of the representation.
The code above outlines the structure of the data. The interpretation of the row (or variable) index arrays will require knowledge of the matrix and right-hand side types, as read in this code.
Matlab Procedures for Reading/Writing Harwell-Boeing Files
The developers of the NEP matrix collection have provided a Matlab m-file to write a Matlab sparse matrix in Harwell-Boeing format. A version for complex matrices is also available.
The Berkeley Benchmarking and Optimization (BeBOP) Group has developed a library and standalone utility for converting between Harwell-Boeing, Matrix Market, and MATLAB sparse matrix formats.
--------------------------------------------------------------------------------
Coordinate Text File
Note: This format is being phased out.
The coordinate text format provides a simple and portable method to exchange sparse matrices. Any language or computer system that understands ASCII text can read this file format with a simple read loop. This makes this data accessible not only to users in the Fortran community, but also developers using C, C++, Pascal, or Basic environments.
In coordinate text file format the first line lists three integers: the number of rows m, columns n, and nonzeros nz in the matrix. The nonzero matrix elements are then listed, one per line, by specifying row index i, column index j, and the value a(i,j), in that order. For example,
m m nz
i1 j1 val1
i2 j2 val2
i3 j3 val3
. . .
. . .
. . .
inz jnz valnz
White space is not significant, (i.e. a fixed column is not used). The nonzero values may be in either in fixed or floating point representation, to any precision (although Fortran and C typically parse less than 20 significant digits). For example, the following are each acceptable: 3, 3.141, +3.1415626536E000, 3.1e0.
Experiments show that these coordinate files are approximately 30% larger than corresponding Harwell-Boeing files. Versions compressed with Unix compress or gzip typically exhibits similar ratios.
To represent only structure information of a sparse matrix, a single zero can be placed in the value position, e.g.
M N nz
i1 j1 0
i2 j2 0
i3 j3 0
. . .
. . .
. . .
inz jnz 0
Although more efficient schemes are available, this allows the same routine to read both types of files. The addition of a single byte to each line of the file is typically of little consequence.
Note that there is no implied order for the matrix elements. This allows one to write simple print routines which traverse the sparse matrix in whatever natural order given by the particular storage scheme.
Also note that no annotations are used for storing matrices with special structure. (This keeps the parsing routines simple.) Symmetric matrices can be represented by only their upper or lower triangular portions, but the file format reveals just that --- the reading program sees only a triangular matrix. (The application is responsible for reinterpreting this.)
A MATLAB function (M-file) is available which reads a matrix in coordinate text file format and creates a sparse matrix is available.
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