Man page - unmhr(3)

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Manual

unmhr

NAME
SYNOPSIS
Functions
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, integerldc, complex, dimension( * ) work, integer lwork, integer info)
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)
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)
subroutine zunmhr (character side, character trans, integer m, integer n,integer ilo, integer ihi, complex*16, dimension( lda, * ) a, integerlda, complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c,integer ldc, complex*16, dimension( * ) work, integer lwork, integerinfo)
Author

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, integerldc, 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, integerlda, complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c,integer ldc, complex*16, dimension( * ) work, integer lwork, integerinfo)

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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