table of contents
| unmbr(3) | LAPACK | unmbr(3) |
NAME¶
unmbr - {un,or}mbr: multiply by Q, P from gebrd
SYNOPSIS¶
Functions¶
subroutine cunmbr (vect, side, trans, m, n, k, a, lda, tau,
c, ldc, work, lwork, info)
CUNMBR subroutine dormbr (vect, side, trans, m, n, k, a, lda,
tau, c, ldc, work, lwork, info)
DORMBR subroutine sormbr (vect, side, trans, m, n, k, a, lda,
tau, c, ldc, work, lwork, info)
SORMBR subroutine zunmbr (vect, side, trans, m, n, k, a, lda,
tau, c, ldc, work, lwork, info)
ZUNMBR
Detailed Description¶
Function Documentation¶
subroutine cunmbr (character vect, character side, character trans, integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer lwork, integer info)¶
CUNMBR
Purpose:
If VECT = 'Q', CUNMBR overwrites the general complex M-by-N matrix C
with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'C': Q**H * C C * Q**H
If VECT = 'P', CUNMBR overwrites the general complex M-by-N matrix C
with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': P * C C * P
TRANS = 'C': P**H * C C * P**H
Here Q and P**H are the unitary matrices determined by CGEBRD when
reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
and P**H are defined as products of elementary reflectors H(i) and
G(i) respectively.
Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
order of the unitary matrix Q or P**H that is applied.
If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
if nq >= k, Q = H(1) H(2) . . . H(k);
if nq < k, Q = H(1) H(2) . . . H(nq-1).
If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
if k < nq, P = G(1) G(2) . . . G(k);
if k >= nq, P = G(1) G(2) . . . G(nq-1).
Parameters
VECT
VECT is CHARACTER*1
= 'Q': apply Q or Q**H;
= 'P': apply P or P**H.
SIDE
SIDE is CHARACTER*1
= 'L': apply Q, Q**H, P or P**H from the Left;
= 'R': apply Q, Q**H, P or P**H from the Right.
TRANS
TRANS is CHARACTER*1
= 'N': No transpose, apply Q or P;
= 'C': Conjugate transpose, apply Q**H or P**H.
M
M is INTEGER
The number of rows of the matrix C. M >= 0.
N
N is INTEGER
The number of columns of the matrix C. N >= 0.
K
K is INTEGER
If VECT = 'Q', the number of columns in the original
matrix reduced by CGEBRD.
If VECT = 'P', the number of rows in the original
matrix reduced by CGEBRD.
K >= 0.
A
A is COMPLEX array, dimension
(LDA,min(nq,K)) if VECT = 'Q'
(LDA,nq) if VECT = 'P'
The vectors which define the elementary reflectors H(i) and
G(i), whose products determine the matrices Q and P, as
returned by CGEBRD.
LDA
LDA is INTEGER
The leading dimension of the array A.
If VECT = 'Q', LDA >= max(1,nq);
if VECT = 'P', LDA >= max(1,min(nq,K)).
TAU
TAU is COMPLEX array, dimension (min(nq,K))
TAU(i) must contain the scalar factor of the elementary
reflector H(i) or G(i) which determines Q or P, as returned
by CGEBRD in the array argument TAUQ or TAUP.
C
C is COMPLEX array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q
or P*C or P**H*C or C*P or C*P**H.
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK
WORK is COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK.
If SIDE = 'L', LWORK >= max(1,N);
if SIDE = 'R', LWORK >= max(1,M);
if N = 0 or M = 0, LWORK >= 1.
For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L',
and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the
optimal blocksize. (NB = 0 if M = 0 or N = 0.)
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dormbr (character vect, character side, character trans, integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info)¶
DORMBR
Purpose:
If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C
with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q**T * C C * Q**T
If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C
with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': P * C C * P
TRANS = 'T': P**T * C C * P**T
Here Q and P**T are the orthogonal matrices determined by DGEBRD when
reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
P**T are defined as products of elementary reflectors H(i) and G(i)
respectively.
Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
order of the orthogonal matrix Q or P**T that is applied.
If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
if nq >= k, Q = H(1) H(2) . . . H(k);
if nq < k, Q = H(1) H(2) . . . H(nq-1).
If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
if k < nq, P = G(1) G(2) . . . G(k);
if k >= nq, P = G(1) G(2) . . . G(nq-1).
Parameters
VECT
VECT is CHARACTER*1
= 'Q': apply Q or Q**T;
= 'P': apply P or P**T.
SIDE
SIDE is CHARACTER*1
= 'L': apply Q, Q**T, P or P**T from the Left;
= 'R': apply Q, Q**T, P or P**T from the Right.
TRANS
TRANS is CHARACTER*1
= 'N': No transpose, apply Q or P;
= 'T': Transpose, apply Q**T or P**T.
M
M is INTEGER
The number of rows of the matrix C. M >= 0.
N
N is INTEGER
The number of columns of the matrix C. N >= 0.
K
K is INTEGER
If VECT = 'Q', the number of columns in the original
matrix reduced by DGEBRD.
If VECT = 'P', the number of rows in the original
matrix reduced by DGEBRD.
K >= 0.
A
A is DOUBLE PRECISION array, dimension
(LDA,min(nq,K)) if VECT = 'Q'
(LDA,nq) if VECT = 'P'
The vectors which define the elementary reflectors H(i) and
G(i), whose products determine the matrices Q and P, as
returned by DGEBRD.
LDA
LDA is INTEGER
The leading dimension of the array A.
If VECT = 'Q', LDA >= max(1,nq);
if VECT = 'P', LDA >= max(1,min(nq,K)).
TAU
TAU is DOUBLE PRECISION array, dimension (min(nq,K))
TAU(i) must contain the scalar factor of the elementary
reflector H(i) or G(i) which determines Q or P, as returned
by DGEBRD in the array argument TAUQ or TAUP.
C
C is DOUBLE PRECISION array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q
or P*C or P**T*C or C*P or C*P**T.
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK.
If SIDE = 'L', LWORK >= max(1,N);
if SIDE = 'R', LWORK >= max(1,M).
For optimum performance LWORK >= N*NB if SIDE = 'L', and
LWORK >= M*NB if SIDE = 'R', where NB is the optimal
blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine sormbr (character vect, character side, character trans, integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer lwork, integer info)¶
SORMBR
Purpose:
If VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C
with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q**T * C C * Q**T
If VECT = 'P', SORMBR overwrites the general real M-by-N matrix C
with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': P * C C * P
TRANS = 'T': P**T * C C * P**T
Here Q and P**T are the orthogonal matrices determined by SGEBRD when
reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
P**T are defined as products of elementary reflectors H(i) and G(i)
respectively.
Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
order of the orthogonal matrix Q or P**T that is applied.
If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
if nq >= k, Q = H(1) H(2) . . . H(k);
if nq < k, Q = H(1) H(2) . . . H(nq-1).
If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
if k < nq, P = G(1) G(2) . . . G(k);
if k >= nq, P = G(1) G(2) . . . G(nq-1).
Parameters
VECT
VECT is CHARACTER*1
= 'Q': apply Q or Q**T;
= 'P': apply P or P**T.
SIDE
SIDE is CHARACTER*1
= 'L': apply Q, Q**T, P or P**T from the Left;
= 'R': apply Q, Q**T, P or P**T from the Right.
TRANS
TRANS is CHARACTER*1
= 'N': No transpose, apply Q or P;
= 'T': Transpose, apply Q**T or P**T.
M
M is INTEGER
The number of rows of the matrix C. M >= 0.
N
N is INTEGER
The number of columns of the matrix C. N >= 0.
K
K is INTEGER
If VECT = 'Q', the number of columns in the original
matrix reduced by SGEBRD.
If VECT = 'P', the number of rows in the original
matrix reduced by SGEBRD.
K >= 0.
A
A is REAL array, dimension
(LDA,min(nq,K)) if VECT = 'Q'
(LDA,nq) if VECT = 'P'
The vectors which define the elementary reflectors H(i) and
G(i), whose products determine the matrices Q and P, as
returned by SGEBRD.
LDA
LDA is INTEGER
The leading dimension of the array A.
If VECT = 'Q', LDA >= max(1,nq);
if VECT = 'P', LDA >= max(1,min(nq,K)).
TAU
TAU is REAL array, dimension (min(nq,K))
TAU(i) must contain the scalar factor of the elementary
reflector H(i) or G(i) which determines Q or P, as returned
by SGEBRD in the array argument TAUQ or TAUP.
C
C is REAL array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q
or P*C or P**T*C or C*P or C*P**T.
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK
WORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK.
If SIDE = 'L', LWORK >= max(1,N);
if SIDE = 'R', LWORK >= max(1,M).
For optimum performance LWORK >= N*NB if SIDE = 'L', and
LWORK >= M*NB if SIDE = 'R', where NB is the optimal
blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zunmbr (character vect, character side, character trans, integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer lwork, integer info)¶
ZUNMBR
Purpose:
If VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C
with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'C': Q**H * C C * Q**H
If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C
with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': P * C C * P
TRANS = 'C': P**H * C C * P**H
Here Q and P**H are the unitary matrices determined by ZGEBRD when
reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
and P**H are defined as products of elementary reflectors H(i) and
G(i) respectively.
Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
order of the unitary matrix Q or P**H that is applied.
If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
if nq >= k, Q = H(1) H(2) . . . H(k);
if nq < k, Q = H(1) H(2) . . . H(nq-1).
If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
if k < nq, P = G(1) G(2) . . . G(k);
if k >= nq, P = G(1) G(2) . . . G(nq-1).
Parameters
VECT
VECT is CHARACTER*1
= 'Q': apply Q or Q**H;
= 'P': apply P or P**H.
SIDE
SIDE is CHARACTER*1
= 'L': apply Q, Q**H, P or P**H from the Left;
= 'R': apply Q, Q**H, P or P**H from the Right.
TRANS
TRANS is CHARACTER*1
= 'N': No transpose, apply Q or P;
= 'C': Conjugate transpose, apply Q**H or P**H.
M
M is INTEGER
The number of rows of the matrix C. M >= 0.
N
N is INTEGER
The number of columns of the matrix C. N >= 0.
K
K is INTEGER
If VECT = 'Q', the number of columns in the original
matrix reduced by ZGEBRD.
If VECT = 'P', the number of rows in the original
matrix reduced by ZGEBRD.
K >= 0.
A
A is COMPLEX*16 array, dimension
(LDA,min(nq,K)) if VECT = 'Q'
(LDA,nq) if VECT = 'P'
The vectors which define the elementary reflectors H(i) and
G(i), whose products determine the matrices Q and P, as
returned by ZGEBRD.
LDA
LDA is INTEGER
The leading dimension of the array A.
If VECT = 'Q', LDA >= max(1,nq);
if VECT = 'P', LDA >= max(1,min(nq,K)).
TAU
TAU is COMPLEX*16 array, dimension (min(nq,K))
TAU(i) must contain the scalar factor of the elementary
reflector H(i) or G(i) which determines Q or P, as returned
by ZGEBRD in the array argument TAUQ or TAUP.
C
C is COMPLEX*16 array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q
or P*C or P**H*C or C*P or C*P**H.
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK
WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK.
If SIDE = 'L', LWORK >= max(1,N);
if SIDE = 'R', LWORK >= max(1,M);
if N = 0 or M = 0, LWORK >= 1.
For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L',
and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the
optimal blocksize. (NB = 0 if M = 0 or N = 0.)
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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