Provided by: liblapack-doc_3.12.0-3build1.1_all 
NAME
unmhr - {un,or}mhr: multiply by Q from gehrd
SYNOPSIS
Functions
subroutine cunmhr (side, trans, m, n, ilo, ihi, a, lda, tau, c, ldc, work, lwork, info)
CUNMHR
subroutine dormhr (side, trans, m, n, ilo, ihi, a, lda, tau, c, ldc, work, lwork, info)
DORMHR
subroutine sormhr (side, trans, m, n, ilo, ihi, a, lda, tau, c, ldc, work, lwork, info)
SORMHR
subroutine zunmhr (side, trans, m, n, ilo, ihi, a, lda, tau, c, ldc, work, lwork, info)
ZUNMHR
Detailed Description
Function Documentation
subroutine cunmhr (character side, character trans, integer m, integer n, integer ilo, integer ihi, complex,
dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer
ldc, complex, dimension( * ) work, integer lwork, integer info)
CUNMHR
Purpose:
CUNMHR 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
where Q is a complex unitary matrix of order nq, with nq = m if
SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
IHI-ILO elementary reflectors, as returned by CGEHRD:
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
Parameters
SIDE
SIDE is CHARACTER*1
= 'L': apply Q or Q**H from the Left;
= 'R': apply Q or Q**H from the Right.
TRANS
TRANS is CHARACTER*1
= 'N': apply Q (No transpose)
= 'C': apply Q**H (Conjugate transpose)
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.
ILO
ILO is INTEGER
IHI
IHI is INTEGER
ILO and IHI must have the same values as in the previous call
of CGEHRD. Q is equal to the unit matrix except in the
submatrix Q(ilo+1:ihi,ilo+1:ihi).
If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
ILO = 1 and IHI = 0, if M = 0;
if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
ILO = 1 and IHI = 0, if N = 0.
A
A is COMPLEX array, dimension
(LDA,M) if SIDE = 'L'
(LDA,N) if SIDE = 'R'
The vectors which define the elementary reflectors, as
returned by CGEHRD.
LDA
LDA is INTEGER
The leading dimension of the array A.
LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
TAU
TAU is COMPLEX array, dimension
(M-1) if SIDE = 'L'
(N-1) if SIDE = 'R'
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGEHRD.
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.
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).
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 dormhr (character side, character trans, integer m, integer n, integer ilo, integer ihi, 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)
DORMHR
Purpose:
DORMHR 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
where Q is a real orthogonal matrix of order nq, with nq = m if
SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
IHI-ILO elementary reflectors, as returned by DGEHRD:
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
Parameters
SIDE
SIDE is CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
TRANS
TRANS is CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**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.
ILO
ILO is INTEGER
IHI
IHI is INTEGER
ILO and IHI must have the same values as in the previous call
of DGEHRD. Q is equal to the unit matrix except in the
submatrix Q(ilo+1:ihi,ilo+1:ihi).
If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
ILO = 1 and IHI = 0, if M = 0;
if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
ILO = 1 and IHI = 0, if N = 0.
A
A is DOUBLE PRECISION array, dimension
(LDA,M) if SIDE = 'L'
(LDA,N) if SIDE = 'R'
The vectors which define the elementary reflectors, as
returned by DGEHRD.
LDA
LDA is INTEGER
The leading dimension of the array A.
LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
TAU
TAU is DOUBLE PRECISION array, dimension
(M-1) if SIDE = 'L'
(N-1) if SIDE = 'R'
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEHRD.
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.
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 sormhr (character side, character trans, integer m, integer n, integer ilo, integer ihi, real,
dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc,
real, dimension( * ) work, integer lwork, integer info)
SORMHR
Purpose:
SORMHR 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
where Q is a real orthogonal matrix of order nq, with nq = m if
SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
IHI-ILO elementary reflectors, as returned by SGEHRD:
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
Parameters
SIDE
SIDE is CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
TRANS
TRANS is CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**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.
ILO
ILO is INTEGER
IHI
IHI is INTEGER
ILO and IHI must have the same values as in the previous call
of SGEHRD. Q is equal to the unit matrix except in the
submatrix Q(ilo+1:ihi,ilo+1:ihi).
If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
ILO = 1 and IHI = 0, if M = 0;
if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
ILO = 1 and IHI = 0, if N = 0.
A
A is REAL array, dimension
(LDA,M) if SIDE = 'L'
(LDA,N) if SIDE = 'R'
The vectors which define the elementary reflectors, as
returned by SGEHRD.
LDA
LDA is INTEGER
The leading dimension of the array A.
LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
TAU
TAU is REAL array, dimension
(M-1) if SIDE = 'L'
(N-1) if SIDE = 'R'
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SGEHRD.
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.
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 zunmhr (character side, character trans, integer m, integer n, integer ilo, integer ihi,
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)
ZUNMHR
Purpose:
ZUNMHR 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
where Q is a complex unitary matrix of order nq, with nq = m if
SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
IHI-ILO elementary reflectors, as returned by ZGEHRD:
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
Parameters
SIDE
SIDE is CHARACTER*1
= 'L': apply Q or Q**H from the Left;
= 'R': apply Q or Q**H from the Right.
TRANS
TRANS is CHARACTER*1
= 'N': apply Q (No transpose)
= 'C': apply Q**H (Conjugate transpose)
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.
ILO
ILO is INTEGER
IHI
IHI is INTEGER
ILO and IHI must have the same values as in the previous call
of ZGEHRD. Q is equal to the unit matrix except in the
submatrix Q(ilo+1:ihi,ilo+1:ihi).
If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
ILO = 1 and IHI = 0, if M = 0;
if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
ILO = 1 and IHI = 0, if N = 0.
A
A is COMPLEX*16 array, dimension
(LDA,M) if SIDE = 'L'
(LDA,N) if SIDE = 'R'
The vectors which define the elementary reflectors, as
returned by ZGEHRD.
LDA
LDA is INTEGER
The leading dimension of the array A.
LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
TAU
TAU is COMPLEX*16 array, dimension
(M-1) if SIDE = 'L'
(N-1) if SIDE = 'R'
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEHRD.
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.
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).
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.
Author
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Version 3.12.0 Fri Aug 9 2024 02:33:22 unmhr(3)