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Featured Threads. Log in Register. Search titles only. Search Advanced searchâ€¦. Log in. JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding. Thread starter se Start date Apr 15, I have a function to calculate the determinant already, and I am trying to write one to find the cofactor of a given element.

I run the program to calculate all the cofactors of a given 3x3 matrix, and for some reason they come out transposed ie, the cofactor the program gives for the element m 1,2 is what I calculate to be the cofactor for the element m 2,1.

### Fortran - Vector and Matrix Multiplication Functions

I've been through the maths a load of times and I can't see what I've done that would cause this, so I just need someone else to have a look please. I know there are probably other ways of calculating the cofactors, but I have only been programming since September last year and can't really do anything too complicated, hence why I have tried to use such a simple function here.

So I just really want help on what the problem is with what I have written myself, as opposed to offering alternatives. Many thanks in advance. You must log in or register to reply here. Last Post Sep 11, Replies 1 Views 3K.

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Last Post May 25, Replies 3 Views 5K. Fortran Fortran undefined symbol fThis worksheet makes use of several examples programs that are all available for download from this website. Among these are some which are specifically aimed at working with matrices and vectors. This program is also an example of dynamic memory allocation. Write a program to read in 2 square matrices of any size.

Confirm that the matrices obey the rule. Write a program that will read a 3 X 3 matrix from a data file. In the program, include a subroutine that will generate any cofactor cof of the matrix mat. Call the subroutine cofactor and use these arguments:. Use the program you developed Exercise 7.

Unlike most of the exercises in these worksheets, REAL programs tend to be rather large. In large programs, the underlying logic can often be difficult to follow. It helps, therefore, both in the devising of a program and later in its maintenance, to have a plan of what you intend the program to do.

The flowchart is shown on the next page. The logic of the program, as a whole, is clear. Details like what will happen in the subroutines is glossed over at this stage.

In commercial programming, flowcharts are usually formalized, with specific shapes for boxes that do different things. That need not concern us here. Worksheet 7 - Advanced Topics. This worksheet is also available in PDF format.

## PROGRAMS WRITTEN IN FORTRAN PROGRAMMING LANGUAGE

Aims By the end of this worksheet you will be able to: Use array functions Create larger programs aided by "Flow Charts". Privacy and cookies policy. Sum of all the elements of an array, or of all the elements along a specified dimension of an array.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

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I have done a program to calculate a determinant of a matrix. My program works, but the problem is that it takes long time to calculate, especially for big matrix. Could you tell me how can a perform my program in order to calculate the determinant in the shortest possible time? One simple way is to do an LU decomposition and then multiply the determinants of the resulting matrices, because. I should mention that answer is just if you are writing this for your own edification.

If you actually need to use such a routine in some application, you should follow Yuval Filmus's advice and find a library routine. Use the Gaussian algorithm to get an upper triangle matrix, and multiply its elements in the diagonal.

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Determinant of a big matrix Ask Question. Asked 7 years, 6 months ago. Active 7 years, 6 months ago.

Viewed 4k times. Bek Bek 1 1 gold badge 3 3 silver badges 9 9 bronze badges. Always try to use a library routine when doing calculations with matrices. In this case, there is no LAPACK routine for determinant, but you can use some of the decomposition routines to get access to the eigenvalue. See for example the link in my comment to Berci's answer. Active Oldest Votes. There are faster but more complicated ways. Potato Potato I have a function to calculate the determinant already, and I am trying to write one to find the cofactor of a given element.

So far I have the following as a function where ii is the dummy variable representing the row number of the element,jj is the column number and mm is the 3x3 matrix in question:. The if statements utilise the cyclical nature of the cofactor calculation and the alternating minus and plus signs on each cofactor can be left out because of this.

I run the program to calculate all the cofactors of a given 3x3 matrix, and for some reason they come out transposed ie, the cofactor the program gives for the element m 1,2 is what I calculate to be the cofactor for the element m 2,1.

I've been through the maths a load of times and I can't see what I've done that would cause this, so I just need someone else to have a look please. I know there are probably other ways of calculating the cofactors, but I have only been programming since September last year and can't really do anything too complicated, hence why I have tried to use such a simple function here.

So I just really want help on what the problem is with what I have written myself, as opposed to offering alternatives. You have to remember one important thing about Fortran: it stores the values in memory this way column major :. Depending how you loaded up your matrix, it may be transposed from your point of view if you count on the jj index to cycle before the ii does.

What seems obvious is which you basically evaluate the determinant of the minor matrix for this term and not the different factors necessary to make a cofactor matrix.

Many thanks in advance. Answer Save. Vincent G Lv 7. You have to remember one important thing about Fortran: it stores the values in memory this way column major : mm 1,1 ,mm 2,1 ,mm 3,1 ,mm 1,2 ,mm 2, There are other languages like C for instance that store arrays in row major order.

Still have questions? Get your answers by asking now.Arrays can store a fixed-size sequential collection of elements of the same type. An array is used to store a collection of data, but it is often more useful to think of an array as a collection of variables of the same type.

All arrays consist of contiguous memory locations. The lowest address corresponds to the first element and the highest address to the last element.

Arrays can be one- dimensional like vectorstwo-dimensional like matrices and Fortran allows you to create up to 7-dimensional arrays. For example, to declare a one-dimensional array named number, of real numbers containing 5 elements, you write. The individual elements of arrays are referenced by specifying their subscripts. The first element of an array has a subscript of one. The array numbers contains five real variables â€”numbers 1numbers 2numbers 3numbers 4and numbers 5.

### Matrix cofactors in F95/F90

One-dimensional array elements can be directly assigned values using a short hand symbol, called array constructor, like. You can pass an array to a procedure as an argument. In the above example, the subroutine fillArray and printArray can only be called with arrays with dimension 5.

So far we have referred to the whole array, Fortran provides an easy way to refer several elements, or a section of an array, using a single statement. To access an array section, you need to provide the lower and the upper bound of the section, as well as a stride incrementfor all the dimensions. This notation is called a subscript triplet:. When no lower and upper bounds are mentioned, it defaults to the extents you declared, and stride value defaults to 1.

Fortran - Arrays Advertisements. Previous Page. Next Page. Live Demo. Previous Page Print Page. It is the number of dimensions an array has. For example, for the array named matrix, rank is 2, and for the array named numbers, rank is 1. It is the number of elements along a dimension.

For example, the array numbers has extent 5 and the array named matrix has extent 3 in both dimensions. The shape of an array is a one-dimensional integer array, containing the number of elements the extent in each dimension.

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For example, for the array matrix, shape is 3, 3 and the array numbers it is 5. It is the number of elements an array contains.

For the array matrix, it is 9, and for the array numbers, it is 5.There is a large a number of intrinsic functions and five intrinsic subroutines in Fortran I treat the numeric and mathematical routines very shortly, since they are not changed from Fortran 77 and therefore should be well-known.

This section is based on section 13 of the ISO standardwhich contains a more formal treatment. We follow the arrangement of the different functions and subroutines in the standard, but explain directly in the list. For a more detailed treatment we refer to Metcalf and Reid When a parameter below is optional it is given in lower case characters. When an argument list contains several arguments the function can be called either by position related arguments or by a keyword.

Keyword must be used if some previous argument is not included. Keywords are normally the names that are given below. We have not always given all the natural limitations to the variables, for example that the rank is not permitted to be negative. The use is illustrated in the example program in chapter 8 of the main text.

Only the last one is difficult to explain, which is most easily done with the examples from ISO A historic fact is that the numerical functions in Fortran 66 had to have specific different names in different precisions, and these explicit names are still the only ones which can be used when a function name is passed as an argument.

A complete table of all the numerical functions follow. On the other hand, some functions do not have any specific name. Below I use C for complex floating point values, D for floating point values in double precision, I for integers, and R for floating point values in single precision. Truncation is towards zero, INT Inner product DPROD on the other hand is a very useful function which gives the product of two numbers in single precision as a double precision number.

It is both fast and accurate.

Same as in Fortran All trigonometric functions work in radians. A historic fact is that the mathematical functions in Fortran 66 had to have specific different names in different precisions, and these explicit names are still the only ones which can be used when a function name is passed as an argument. A complete table of all the mathematical functions follow.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

The dark mode beta is finally here. Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. This code in fortran calculates the determinant of a nxn matrix using the laplacian formula expansion by minors. I understand fully how this process works.

But could somebody give me an insight into how the following code operates over, say a given iteration, this section of the code contains the recursive function determinant matrix - assume some nxn matrix is read in and passed through and another function to call the cofactor.

There are aspects of the code I understand but its the recursion that is confusing me profoundly. I've tried to run through step by step with a 3x3 matrix but to no avail. The main section im struggling with is these two calls and the operation of the respective cofactor calculation. Any input for an explanation would be greatly appreciated like i said an example of one iteration.

This is my first post in stack-overflow as most of my question reside in mathstack as you can probably tell by the mathematical nature of the question. Although I do have experience programming, the concept of recursion especially in this example is really boggling my mind.

More specifically, one passes the above 3x3 matrix to cofactor to get a 2x2 sub-matrix by removing the i -th row and 1st column of the matrix. The obtained 2x2 sub-matrix cf is then passed to determinant in the next line to calculate the co-factor corresponding to this sub-matrix.

So, in this first iterations we are trying to calculate. Note here that the three determinants in the right-hand side are yet to be calculated by subsequent calls of determinant. Let us consider one such subsequent call, e. We are passing the following sub-matrix stored in cf. Then, the same procedure as described above is repeated again and independently of the Laplace expansion for the parent 3x3 matrix. Note that the i in this subsequent call is different from the i of the previous call; they are all local variables living inside a particular call of a routine and are totally independent from each other.

Also note that the index of dummy array argument like matrix :,: always start from 1 in Fortran unless otherwise specified. This kind of operations are repeated until the size of the sub-matrix becomes 1. For example, we can insert a lot of print statements as. BTW, the code in the Rossetta page seems much simpler than the OP's code by creating a sub-matrix directly as a local array. The simplified version of the code reads.

Note that the Laplace expansion is made along the first row, and that the submat is assigned using array sections.

**Linear Algebra 14TBD: The Direct Algebraic Definition of the Determinant**

The assignment can also be written simply as. The latter form is used in the Rosetta page.

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