Man page - upmtr(3)

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Manual

upmtr

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cupmtr (character side, character uplo, character trans, integerm, integer n, complex, dimension( * ) ap, complex, dimension( * ) tau,complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * )work, integer info)
subroutine dopmtr (character side, character uplo, character trans, integerm, integer n, double precision, dimension( * ) ap, double precision,dimension( * ) tau, double precision, dimension( ldc, * ) c, integerldc, double precision, dimension( * ) work, integer info)
subroutine sopmtr (character side, character uplo, character trans, integerm, integer n, real, dimension( * ) ap, real, dimension( * ) tau, real,dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integerinfo)
subroutine zupmtr (character side, character uplo, character trans, integerm, integer n, complex*16, dimension( * ) ap, complex*16, dimension( * )tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16,dimension( * ) work, integer info)
Author

NAME

upmtr - {up,op}mtr: multiply by Q from hptrd

SYNOPSIS

Functions

subroutine cupmtr (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)
CUPMTR
subroutine dopmtr (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)
DOPMTR
subroutine sopmtr (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)
SOPMTR
subroutine zupmtr (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)
ZUPMTR

Detailed Description

Function Documentation

subroutine cupmtr (character side, character uplo, character trans, integerm, integer n, complex, dimension( * ) ap, complex, dimension( * ) tau,complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * )work, integer info)

CUPMTR

Purpose:

CUPMTR 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
nq-1 elementary reflectors, as returned by CHPTRD using packed
storage:

if UPLO = ’U’, Q = H(nq-1) . . . H(2) H(1);

if UPLO = ’L’, Q = H(1) H(2) . . . H(nq-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.

UPLO

UPLO is CHARACTER*1
= ’U’: Upper triangular packed storage used in previous
call to CHPTRD;
= ’L’: Lower triangular packed storage used in previous
call to CHPTRD.

TRANS

TRANS is CHARACTER*1
= ’N’: No transpose, apply Q;
= ’C’: Conjugate transpose, apply Q**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.

AP

AP is COMPLEX array, dimension
(M*(M+1)/2) if SIDE = ’L’
(N*(N+1)/2) if SIDE = ’R’
The vectors which define the elementary reflectors, as
returned by CHPTRD. AP is modified by the routine but
restored on exit.

TAU

TAU is COMPLEX array, dimension (M-1) if SIDE = ’L’
or (N-1) if SIDE = ’R’
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CHPTRD.

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
(N) if SIDE = ’L’
(M) if SIDE = ’R’

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 dopmtr (character side, character uplo, character trans, integerm, integer n, double precision, dimension( * ) ap, double precision,dimension( * ) tau, double precision, dimension( ldc, * ) c, integerldc, double precision, dimension( * ) work, integer info)

DOPMTR

Purpose:

DOPMTR 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
nq-1 elementary reflectors, as returned by DSPTRD using packed
storage:

if UPLO = ’U’, Q = H(nq-1) . . . H(2) H(1);

if UPLO = ’L’, Q = H(1) H(2) . . . H(nq-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.

UPLO

UPLO is CHARACTER*1
= ’U’: Upper triangular packed storage used in previous
call to DSPTRD;
= ’L’: Lower triangular packed storage used in previous
call to DSPTRD.

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.

AP

AP is DOUBLE PRECISION array, dimension
(M*(M+1)/2) if SIDE = ’L’
(N*(N+1)/2) if SIDE = ’R’
The vectors which define the elementary reflectors, as
returned by DSPTRD. AP is modified by the routine but
restored on exit.

TAU

TAU is DOUBLE PRECISION array, dimension (M-1) if SIDE = ’L’
or (N-1) if SIDE = ’R’
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DSPTRD.

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
(N) if SIDE = ’L’
(M) if SIDE = ’R’

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 sopmtr (character side, character uplo, character trans, integerm, integer n, real, dimension( * ) ap, real, dimension( * ) tau, real,dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integerinfo)

SOPMTR

Purpose:

SOPMTR 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
nq-1 elementary reflectors, as returned by SSPTRD using packed
storage:

if UPLO = ’U’, Q = H(nq-1) . . . H(2) H(1);

if UPLO = ’L’, Q = H(1) H(2) . . . H(nq-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.

UPLO

UPLO is CHARACTER*1
= ’U’: Upper triangular packed storage used in previous
call to SSPTRD;
= ’L’: Lower triangular packed storage used in previous
call to SSPTRD.

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.

AP

AP is REAL array, dimension
(M*(M+1)/2) if SIDE = ’L’
(N*(N+1)/2) if SIDE = ’R’
The vectors which define the elementary reflectors, as
returned by SSPTRD. AP is modified by the routine but
restored on exit.

TAU

TAU is REAL array, dimension (M-1) if SIDE = ’L’
or (N-1) if SIDE = ’R’
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SSPTRD.

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
(N) if SIDE = ’L’
(M) if SIDE = ’R’

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 zupmtr (character side, character uplo, character trans, integerm, integer n, complex*16, dimension( * ) ap, complex*16, dimension( * )tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16,dimension( * ) work, integer info)

ZUPMTR

Purpose:

ZUPMTR 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
nq-1 elementary reflectors, as returned by ZHPTRD using packed
storage:

if UPLO = ’U’, Q = H(nq-1) . . . H(2) H(1);

if UPLO = ’L’, Q = H(1) H(2) . . . H(nq-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.

UPLO

UPLO is CHARACTER*1
= ’U’: Upper triangular packed storage used in previous
call to ZHPTRD;
= ’L’: Lower triangular packed storage used in previous
call to ZHPTRD.

TRANS

TRANS is CHARACTER*1
= ’N’: No transpose, apply Q;
= ’C’: Conjugate transpose, apply Q**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.

AP

AP is COMPLEX*16 array, dimension
(M*(M+1)/2) if SIDE = ’L’
(N*(N+1)/2) if SIDE = ’R’
The vectors which define the elementary reflectors, as
returned by ZHPTRD. AP is modified by the routine but
restored on exit.

TAU

TAU is COMPLEX*16 array, dimension (M-1) if SIDE = ’L’
or (N-1) if SIDE = ’R’
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZHPTRD.

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
(N) if SIDE = ’L’
(M) if SIDE = ’R’

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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