Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
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?larfb
Applies a block reflector or its transpose/conjugate-transpose to a general rectangular matrix.
call slarfb( side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork )
call dlarfb( side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork )
call clarfb( side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork )
call zlarfb( side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork )
- mkl.fi
The real flavors of the routine ?larfb apply a real block reflector H or its transpose HT to a real m-by-n matrix C from either left or right.
The complex flavors of the routine ?larfb apply a complex block reflector H or its conjugate transpose HH to a complex m-by-n matrix C from either left or right.
The data types are given for the Fortran interface.
- side
-
CHARACTER*1.
If side = 'L': apply H or HT for real flavors and H or HH for complex flavors from the left.
If side = 'R': apply H or HT for real flavors and H or HH for complex flavors from the right.
- trans
-
CHARACTER*1.
If trans = 'N': apply H (No transpose).
If trans = 'C': apply HH (Conjugate transpose).
If trans = 'T': apply HT (Transpose).
- direct
-
CHARACTER*1.
Indicates how H is formed from a product of elementary reflectors
If direct = 'F': H = H(1)*H(2)*. . . *H(k) (forward)
If direct = 'B': H = H(k)* . . . H(2)*H(1) (backward)
- storev
-
CHARACTER*1.
Indicates how the vectors which define the elementary reflectors are stored:
If storev = 'C': Column-wise
If storev = 'R': Row-wise
- m
-
INTEGER. The number of rows of the matrix C.
- n
-
INTEGER. The number of columns of the matrix C.
- k
-
INTEGER. The order of the matrix T (equal to the number of elementary reflectors whose product defines the block reflector).
- v
-
REAL for slarfb
DOUBLE PRECISION for dlarfb
COMPLEX for clarfb
DOUBLE COMPLEX for zlarfb
Array, DIMENSION
(ldv, k) if storev = 'C'
(ldv, m) if storev = 'R' and side = 'L'
(ldv, n) if storev = 'R' and side = 'R'
The matrix v. See Application Notes below.
- ldv
-
INTEGER. The leading dimension of the array v.
If storev = 'C' and side = 'L', ldv≥ max(1,m);
if storev = 'C' and side = 'R', ldv≥ max(1,n);
if storev = 'R', ldv≥k.
- t
-
REAL for slarfb
DOUBLE PRECISION for dlarfb
COMPLEX for clarfb
DOUBLE COMPLEX for zlarfb
Array, size (ldt,k).
Contains the triangular k-by-k matrix T in the representation of the block reflector.
- ldt
-
INTEGER. The leading dimension of the array t.
ldt≥k.
- c
-
REAL for slarfb
DOUBLE PRECISION for dlarfb
COMPLEX for clarfb
DOUBLE COMPLEX for zlarfb
Array, size (ldc,n).
On entry, the m-by-n matrix C.
- ldc
-
INTEGER. The leading dimension of the array c.
ldc≥ max(1,m).
- work
-
REAL for slarfb
DOUBLE PRECISION for dlarfb
COMPLEX for clarfb
DOUBLE COMPLEX for zlarfb
Workspace array, DIMENSION (ldwork, k).
- ldwork
-
INTEGER. The leading dimension of the array work.
If side = 'L', ldwork≥ max(1, n);
if side = 'R', ldwork≥ max(1, m).
- c
-
On exit, c is overwritten by the product of the following:
H*C, or HT*C, or C*H, or C*HT for real flavors
H*C, or HH*C, or C*H, or C*HH for complex flavors
- info
-
INTEGER.
If info = 0, the execution is successful.
If info = -i, the i-th parameter had an illegal value.
If info = -1011, memory allocation error occurred.
The shape of the matrix V and the storage of the vectors which define the H(i) is best illustrated by the following example with n = 5 and k = 3. The elements equal to 1 are not stored; the corresponding array elements are modified but restored on exit. The rest of the array is not used.
