[ccp4bb] AW: [ccp4bb] Extract Euler angles from fractional coordinate matrix
Dear Chen, You have more definitions which are not clearly defined: what do you mean with pseudo-NCS? Either you have NCS or you don’t. Did you mean pseudo crystallographic NCS? In the latter case, you will not have an arbitrary rotational relationship, but a rotation which is (almost) crystallographic, e.g. 60, 90, 120 or 180°. To analyze these, I would use polar rotation angles, which give the direction of the rotation axis (which should be almost parallel to one of the cell axis) and the rotation. When dealing with pseudo crystallographic NCS, you have to be very careful with your definitions, otherwise you can easily get lost. Herman Von: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] Im Auftrag von Chen Zhao Gesendet: Freitag, 5. September 2014 21:46 An: CCP4BB@JISCMAIL.AC.UK Betreff: Re: [ccp4bb] Extract Euler angles from fractional coordinate matrix I am sorry for my carelessness on the definition of Euler angles. I am just thinking of an Euler angle equivalent. Sorry for the confusion I have made. On Fri, Sep 5, 2014 at 3:34 PM, Eleanor Dodson eleanor.dod...@york.ac.ukmailto:eleanor.dod...@york.ac.uk wrote: I don't think Eulerian angles are defined for a non-orthogonal axis system? ? They are defined relative to perpendicular axes X Y Z e.g. Rotate coordinates by gamma about Z, beta about Y', alpha about Z. Eleanor On 5 September 2014 16:27, Chen Zhao c.z...@yale.edumailto:c.z...@yale.edu wrote: Thank you Eleanor for your reply. I am actually considering how to describe a pseudo-NCS with an arbitrary rotational and translational relationship. I don't have to do this but I am just curious. It is more straightforward if I say how the two molecules are related by a rotation around unit cell axis than around orthogonal coordinate axis, which does not have an absolute physical meaning. The command line output after coot superpose prints out the rotational and translational matrices for both the orthogonal and fractional coordinate system. For using coordconv, my concern is that if I deal with a low-symmetry unit cell, which is not orthogonal by itself, the Euler angles for the fractional coordinate system and the orthogonal coordinate system should be different. If I just feed some numbers into coordconv, will it consider them as orthogonal coordinates? Thank you, Chen On Fri, Sep 5, 2014 at 6:24 AM, Eleanor Dodson eleanor.dod...@york.ac.ukmailto:eleanor.dod...@york.ac.uk wrote: Rotation matrices are rarely specified in a fractional coordinate system? The criteria for checking such a matrix is Is the determinant 1? and this only holds for orthogonal matrices. I guess the way I would do this though. You presumably have two sets of fractional coordinates, before and after rotation? There is a ccp4 program - coordconv which will read the fractional coordinates and generate pdb format with the convention ncode = 1 (You may need to fudge the fractional format I suppose..) You can then use superpose to match the two sets of coordinates and the output will tell you the Eulerian angles used for the rotation! Lots of ways to kill cats! Eleanor On 4 September 2014 21:21, Phil Jeffrey pjeff...@princeton.edumailto:pjeff...@princeton.edu wrote: The orthogonal/fractional matrix is outlined here: http://www.iucr.org/__data/assets/pdf_file/0009/7011/19_06_cowtan_coordinate_frames.pdf Sorry to say I apparently ditched my old Fortran o2f and f2o programs to do that. Bear in mind, however, that orthogonal has no fixed orientation with respect to fractional - for most space groups ncode 1 is often used but for primitive monoclinic ncode 3 is sometimes used, and I think the matrix shown in Kevin Cowtan's document above corresponds to ncode 1. Phil Jeffrey Princeton On 9/4/14 3:55 PM, Chen Zhao wrote: I am sorry, just to clarify, the fractional coordinate matrix I referred to is a rotational matrix in the fractional coordinate system. On Thu, Sep 4, 2014 at 3:52 PM, Chen Zhao c.z...@yale.edumailto:c.z...@yale.edu mailto:c.z...@yale.edumailto:c.z...@yale.edu wrote: Hi all, I am just curious whether there are some tools extracting the Euler angles from a fractional coordinate matrix. I have no luck searching it online. Alternatively, I found the analytical solution for the Euler angles from an orthogonal coordinate matrix. So in the worst case, my problem reduces to calculating the transformation matrix between the fractional and orthogonal coordinate system. I feel a little bit at a loss because it is 6 years since I last studied linear algebra. How can I calculate this for a specific unit cell? Thanks a lot in advance! Sincerely, Chen
Re: [ccp4bb] Extract Euler angles from fractional coordinate matrix
Rotation matrices are rarely specified in a fractional coordinate system? The criteria for checking such a matrix is Is the determinant 1? and this only holds for orthogonal matrices. I guess the way I would do this though. You presumably have two sets of fractional coordinates, before and after rotation? There is a ccp4 program - coordconv which will read the fractional coordinates and generate pdb format with the convention ncode = 1 (You may need to fudge the fractional format I suppose..) You can then use superpose to match the two sets of coordinates and the output will tell you the Eulerian angles used for the rotation! Lots of ways to kill cats! Eleanor On 4 September 2014 21:21, Phil Jeffrey pjeff...@princeton.edu wrote: The orthogonal/fractional matrix is outlined here: http://www.iucr.org/__data/assets/pdf_file/0009/7011/19_ 06_cowtan_coordinate_frames.pdf Sorry to say I apparently ditched my old Fortran o2f and f2o programs to do that. Bear in mind, however, that orthogonal has no fixed orientation with respect to fractional - for most space groups ncode 1 is often used but for primitive monoclinic ncode 3 is sometimes used, and I think the matrix shown in Kevin Cowtan's document above corresponds to ncode 1. Phil Jeffrey Princeton On 9/4/14 3:55 PM, Chen Zhao wrote: I am sorry, just to clarify, the fractional coordinate matrix I referred to is a rotational matrix in the fractional coordinate system. On Thu, Sep 4, 2014 at 3:52 PM, Chen Zhao c.z...@yale.edu mailto:c.z...@yale.edu wrote: Hi all, I am just curious whether there are some tools extracting the Euler angles from a fractional coordinate matrix. I have no luck searching it online. Alternatively, I found the analytical solution for the Euler angles from an orthogonal coordinate matrix. So in the worst case, my problem reduces to calculating the transformation matrix between the fractional and orthogonal coordinate system. I feel a little bit at a loss because it is 6 years since I last studied linear algebra. How can I calculate this for a specific unit cell? Thanks a lot in advance! Sincerely, Chen
Re: [ccp4bb] Extract Euler angles from fractional coordinate matrix
This is just a petty function in CCP4's MMDB library -- Eugene On 4 Sep 2014, at 20:52, Chen Zhao wrote: Hi all, I am just curious whether there are some tools extracting the Euler angles from a fractional coordinate matrix. I have no luck searching it online. Alternatively, I found the analytical solution for the Euler angles from an orthogonal coordinate matrix. So in the worst case, my problem reduces to calculating the transformation matrix between the fractional and orthogonal coordinate system. I feel a little bit at a loss because it is 6 years since I last studied linear algebra. How can I calculate this for a specific unit cell? Thanks a lot in advance! Sincerely, Chen -- Scanned by iCritical.
Re: [ccp4bb] Extract Euler angles from fractional coordinate matrix
Thank you Eleanor for your reply. I am actually considering how to describe a pseudo-NCS with an arbitrary rotational and translational relationship. I don't have to do this but I am just curious. It is more straightforward if I say how the two molecules are related by a rotation around unit cell axis than around orthogonal coordinate axis, which does not have an absolute physical meaning. The command line output after coot superpose prints out the rotational and translational matrices for both the orthogonal and fractional coordinate system. For using coordconv, my concern is that if I deal with a low-symmetry unit cell, which is not orthogonal by itself, the Euler angles for the fractional coordinate system and the orthogonal coordinate system should be different. If I just feed some numbers into coordconv, will it consider them as orthogonal coordinates? Thank you, Chen On Fri, Sep 5, 2014 at 6:24 AM, Eleanor Dodson eleanor.dod...@york.ac.uk wrote: Rotation matrices are rarely specified in a fractional coordinate system? The criteria for checking such a matrix is Is the determinant 1? and this only holds for orthogonal matrices. I guess the way I would do this though. You presumably have two sets of fractional coordinates, before and after rotation? There is a ccp4 program - coordconv which will read the fractional coordinates and generate pdb format with the convention ncode = 1 (You may need to fudge the fractional format I suppose..) You can then use superpose to match the two sets of coordinates and the output will tell you the Eulerian angles used for the rotation! Lots of ways to kill cats! Eleanor On 4 September 2014 21:21, Phil Jeffrey pjeff...@princeton.edu wrote: The orthogonal/fractional matrix is outlined here: http://www.iucr.org/__data/assets/pdf_file/0009/7011/19_ 06_cowtan_coordinate_frames.pdf Sorry to say I apparently ditched my old Fortran o2f and f2o programs to do that. Bear in mind, however, that orthogonal has no fixed orientation with respect to fractional - for most space groups ncode 1 is often used but for primitive monoclinic ncode 3 is sometimes used, and I think the matrix shown in Kevin Cowtan's document above corresponds to ncode 1. Phil Jeffrey Princeton On 9/4/14 3:55 PM, Chen Zhao wrote: I am sorry, just to clarify, the fractional coordinate matrix I referred to is a rotational matrix in the fractional coordinate system. On Thu, Sep 4, 2014 at 3:52 PM, Chen Zhao c.z...@yale.edu mailto:c.z...@yale.edu wrote: Hi all, I am just curious whether there are some tools extracting the Euler angles from a fractional coordinate matrix. I have no luck searching it online. Alternatively, I found the analytical solution for the Euler angles from an orthogonal coordinate matrix. So in the worst case, my problem reduces to calculating the transformation matrix between the fractional and orthogonal coordinate system. I feel a little bit at a loss because it is 6 years since I last studied linear algebra. How can I calculate this for a specific unit cell? Thanks a lot in advance! Sincerely, Chen
Re: [ccp4bb] Extract Euler angles from fractional coordinate matrix
I don't think Eulerian angles are defined for a non-orthogonal axis system? ? They are defined relative to perpendicular axes X Y Z e.g. Rotate coordinates by gamma about Z, beta about Y', alpha about Z. Eleanor On 5 September 2014 16:27, Chen Zhao c.z...@yale.edu wrote: Thank you Eleanor for your reply. I am actually considering how to describe a pseudo-NCS with an arbitrary rotational and translational relationship. I don't have to do this but I am just curious. It is more straightforward if I say how the two molecules are related by a rotation around unit cell axis than around orthogonal coordinate axis, which does not have an absolute physical meaning. The command line output after coot superpose prints out the rotational and translational matrices for both the orthogonal and fractional coordinate system. For using coordconv, my concern is that if I deal with a low-symmetry unit cell, which is not orthogonal by itself, the Euler angles for the fractional coordinate system and the orthogonal coordinate system should be different. If I just feed some numbers into coordconv, will it consider them as orthogonal coordinates? Thank you, Chen On Fri, Sep 5, 2014 at 6:24 AM, Eleanor Dodson eleanor.dod...@york.ac.uk wrote: Rotation matrices are rarely specified in a fractional coordinate system? The criteria for checking such a matrix is Is the determinant 1? and this only holds for orthogonal matrices. I guess the way I would do this though. You presumably have two sets of fractional coordinates, before and after rotation? There is a ccp4 program - coordconv which will read the fractional coordinates and generate pdb format with the convention ncode = 1 (You may need to fudge the fractional format I suppose..) You can then use superpose to match the two sets of coordinates and the output will tell you the Eulerian angles used for the rotation! Lots of ways to kill cats! Eleanor On 4 September 2014 21:21, Phil Jeffrey pjeff...@princeton.edu wrote: The orthogonal/fractional matrix is outlined here: http://www.iucr.org/__data/assets/pdf_file/0009/7011/19_ 06_cowtan_coordinate_frames.pdf Sorry to say I apparently ditched my old Fortran o2f and f2o programs to do that. Bear in mind, however, that orthogonal has no fixed orientation with respect to fractional - for most space groups ncode 1 is often used but for primitive monoclinic ncode 3 is sometimes used, and I think the matrix shown in Kevin Cowtan's document above corresponds to ncode 1. Phil Jeffrey Princeton On 9/4/14 3:55 PM, Chen Zhao wrote: I am sorry, just to clarify, the fractional coordinate matrix I referred to is a rotational matrix in the fractional coordinate system. On Thu, Sep 4, 2014 at 3:52 PM, Chen Zhao c.z...@yale.edu mailto:c.z...@yale.edu wrote: Hi all, I am just curious whether there are some tools extracting the Euler angles from a fractional coordinate matrix. I have no luck searching it online. Alternatively, I found the analytical solution for the Euler angles from an orthogonal coordinate matrix. So in the worst case, my problem reduces to calculating the transformation matrix between the fractional and orthogonal coordinate system. I feel a little bit at a loss because it is 6 years since I last studied linear algebra. How can I calculate this for a specific unit cell? Thanks a lot in advance! Sincerely, Chen
Re: [ccp4bb] Extract Euler angles from fractional coordinate matrix
I am sorry for my carelessness on the definition of Euler angles. I am just thinking of an Euler angle equivalent. Sorry for the confusion I have made. On Fri, Sep 5, 2014 at 3:34 PM, Eleanor Dodson eleanor.dod...@york.ac.uk wrote: I don't think Eulerian angles are defined for a non-orthogonal axis system? ? They are defined relative to perpendicular axes X Y Z e.g. Rotate coordinates by gamma about Z, beta about Y', alpha about Z. Eleanor On 5 September 2014 16:27, Chen Zhao c.z...@yale.edu wrote: Thank you Eleanor for your reply. I am actually considering how to describe a pseudo-NCS with an arbitrary rotational and translational relationship. I don't have to do this but I am just curious. It is more straightforward if I say how the two molecules are related by a rotation around unit cell axis than around orthogonal coordinate axis, which does not have an absolute physical meaning. The command line output after coot superpose prints out the rotational and translational matrices for both the orthogonal and fractional coordinate system. For using coordconv, my concern is that if I deal with a low-symmetry unit cell, which is not orthogonal by itself, the Euler angles for the fractional coordinate system and the orthogonal coordinate system should be different. If I just feed some numbers into coordconv, will it consider them as orthogonal coordinates? Thank you, Chen On Fri, Sep 5, 2014 at 6:24 AM, Eleanor Dodson eleanor.dod...@york.ac.uk wrote: Rotation matrices are rarely specified in a fractional coordinate system? The criteria for checking such a matrix is Is the determinant 1? and this only holds for orthogonal matrices. I guess the way I would do this though. You presumably have two sets of fractional coordinates, before and after rotation? There is a ccp4 program - coordconv which will read the fractional coordinates and generate pdb format with the convention ncode = 1 (You may need to fudge the fractional format I suppose..) You can then use superpose to match the two sets of coordinates and the output will tell you the Eulerian angles used for the rotation! Lots of ways to kill cats! Eleanor On 4 September 2014 21:21, Phil Jeffrey pjeff...@princeton.edu wrote: The orthogonal/fractional matrix is outlined here: http://www.iucr.org/__data/assets/pdf_file/0009/7011/19_ 06_cowtan_coordinate_frames.pdf Sorry to say I apparently ditched my old Fortran o2f and f2o programs to do that. Bear in mind, however, that orthogonal has no fixed orientation with respect to fractional - for most space groups ncode 1 is often used but for primitive monoclinic ncode 3 is sometimes used, and I think the matrix shown in Kevin Cowtan's document above corresponds to ncode 1. Phil Jeffrey Princeton On 9/4/14 3:55 PM, Chen Zhao wrote: I am sorry, just to clarify, the fractional coordinate matrix I referred to is a rotational matrix in the fractional coordinate system. On Thu, Sep 4, 2014 at 3:52 PM, Chen Zhao c.z...@yale.edu mailto:c.z...@yale.edu wrote: Hi all, I am just curious whether there are some tools extracting the Euler angles from a fractional coordinate matrix. I have no luck searching it online. Alternatively, I found the analytical solution for the Euler angles from an orthogonal coordinate matrix. So in the worst case, my problem reduces to calculating the transformation matrix between the fractional and orthogonal coordinate system. I feel a little bit at a loss because it is 6 years since I last studied linear algebra. How can I calculate this for a specific unit cell? Thanks a lot in advance! Sincerely, Chen
[ccp4bb] Extract Euler angles from fractional coordinate matrix
Hi all, I am just curious whether there are some tools extracting the Euler angles from a fractional coordinate matrix. I have no luck searching it online. Alternatively, I found the analytical solution for the Euler angles from an orthogonal coordinate matrix. So in the worst case, my problem reduces to calculating the transformation matrix between the fractional and orthogonal coordinate system. I feel a little bit at a loss because it is 6 years since I last studied linear algebra. How can I calculate this for a specific unit cell? Thanks a lot in advance! Sincerely, Chen
Re: [ccp4bb] Extract Euler angles from fractional coordinate matrix
I am sorry, just to clarify, the fractional coordinate matrix I referred to is a rotational matrix in the fractional coordinate system. On Thu, Sep 4, 2014 at 3:52 PM, Chen Zhao c.z...@yale.edu wrote: Hi all, I am just curious whether there are some tools extracting the Euler angles from a fractional coordinate matrix. I have no luck searching it online. Alternatively, I found the analytical solution for the Euler angles from an orthogonal coordinate matrix. So in the worst case, my problem reduces to calculating the transformation matrix between the fractional and orthogonal coordinate system. I feel a little bit at a loss because it is 6 years since I last studied linear algebra. How can I calculate this for a specific unit cell? Thanks a lot in advance! Sincerely, Chen
Re: [ccp4bb] Extract Euler angles from fractional coordinate matrix
The orthogonal/fractional matrix is outlined here: http://www.iucr.org/__data/assets/pdf_file/0009/7011/19_06_cowtan_coordinate_frames.pdf Sorry to say I apparently ditched my old Fortran o2f and f2o programs to do that. Bear in mind, however, that orthogonal has no fixed orientation with respect to fractional - for most space groups ncode 1 is often used but for primitive monoclinic ncode 3 is sometimes used, and I think the matrix shown in Kevin Cowtan's document above corresponds to ncode 1. Phil Jeffrey Princeton On 9/4/14 3:55 PM, Chen Zhao wrote: I am sorry, just to clarify, the fractional coordinate matrix I referred to is a rotational matrix in the fractional coordinate system. On Thu, Sep 4, 2014 at 3:52 PM, Chen Zhao c.z...@yale.edu mailto:c.z...@yale.edu wrote: Hi all, I am just curious whether there are some tools extracting the Euler angles from a fractional coordinate matrix. I have no luck searching it online. Alternatively, I found the analytical solution for the Euler angles from an orthogonal coordinate matrix. So in the worst case, my problem reduces to calculating the transformation matrix between the fractional and orthogonal coordinate system. I feel a little bit at a loss because it is 6 years since I last studied linear algebra. How can I calculate this for a specific unit cell? Thanks a lot in advance! Sincerely, Chen
