Visible to Intel only — GUID: GUID-DE4A61A9-578D-415C-AD5F-F6D99586FD04
Visible to Intel only — GUID: GUID-DE4A61A9-578D-415C-AD5F-F6D99586FD04
?opmtr
Multiplies a real matrix by the real orthogonal matrix Q determined by ?sptrd.
Syntax
call sopmtr(side, uplo, trans, m, n, ap, tau, c, ldc, work, info)
call dopmtr(side, uplo, trans, m, n, ap, tau, c, ldc, work, info)
call opmtr(ap, tau, c [,side] [,uplo] [,trans] [,info])
Include Files
- mkl.fi, lapack.f90
Description
The routine multiplies a real matrix C by Q or QT, where Q is the orthogonal matrix Q formed by sptrd when reducing a packed real symmetric matrix A to tridiagonal form: A = Q*T*QT. Use this routine after a call to ?sptrd.
Depending on the parameters side and trans, the routine can form one of the matrix products Q*C, QT*C, C*Q, or C*QT (overwriting the result on C).
Input Parameters
In the descriptions below, r denotes the order of Q:
If side = 'L', r = m; if side = 'R', r = n.
- side
-
CHARACTER*1. Must be either 'L' or 'R'.
If side = 'L', Q or QT is applied to C from the left.
If side = 'R', Q or QT is applied to C from the right.
- uplo
-
CHARACTER*1. Must be 'U' or 'L'.
Use the same uplo as supplied to ?sptrd.
- trans
-
CHARACTER*1. Must be either 'N' or 'T'.
If trans = 'N', the routine multiplies C by Q.
If trans = 'T', the routine multiplies C by QT.
- m
-
INTEGER. The number of rows in the matrix C (m≥ 0).
- n
-
INTEGER. The number of columns in C (n≥ 0).
- ap, tau, c, work
-
REAL for sopmtr
DOUBLE PRECISION for dopmtr.
ap and tau are the arrays returned by ?sptrd.
The dimension of ap must be at least max(1, r(r+1)/2).
The dimension of tau must be at least max(1, r-1).
c(ldc,*) contains the matrix C.
The second dimension of c must be at least max(1, n)
work(*) is a workspace array.
The dimension of work must be at least
max(1, n) if side = 'L';
max(1, m) if side = 'R'.
- ldc
-
INTEGER. The leading dimension of c; ldc≥ max(1, n) .
Output Parameters
- c
-
Overwritten by the product Q*C, QT*C, C*Q, or C*QT (as specified by side and trans).
- info
-
INTEGER.
If info = 0, the execution is successful.
If info = -i, the i-th parameter had an illegal value.
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see LAPACK 95 Interface Conventions.
Specific details for the routine opmtr interface are the following:
- ap
-
Holds the array A of size (r*(r+1)/2), where
r = m if side = 'L'.
r = n if side = 'R'.
- tau
-
Holds the vector with the number of elements r - 1.
- c
-
Holds the matrix C of size (m,n).
- side
-
Must be 'L' or 'R'. The default value is 'L'.
- uplo
-
Must be 'U' or 'L'. The default value is 'U'.
- trans
-
Must be 'N', 'C', or 'T'. The default value is 'N'.
Application Notes
The computed product differs from the exact product by a matrix E such that ||E||2 = O(ε) ||C||2, where ε is the machine precision.
The total number of floating-point operations is approximately 2*m2*n if side = 'L', or 2*n2*m if side = 'R'.
The complex counterpart of this routine is upmtr.