unmr2(3)

Library Functions Manual

unmr2(3)

NAME

unmr2 - {un,or}mr2: step in unmrq

SYNOPSIS

Functions

subroutine cunmr2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
CUNMR2 multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm). subroutine dormr2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
DORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm). subroutine sormr2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
SORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm). subroutine zunmr2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
ZUNMR2 multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm).

Detailed Description

Function Documentation

subroutine cunmr2 (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 info)

CUNMR2 multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm).

Purpose:

!>
!> CUNMR2 overwrites the general complex m-by-n matrix C with
!>
!>       Q * C  if SIDE = 'L' and TRANS = 'N', or
!>
!>       Q**H* C  if SIDE = 'L' and TRANS = 'C', or
!>
!>       C * Q  if SIDE = 'R' and TRANS = 'N', or
!>
!>       C * Q**H if SIDE = 'R' and TRANS = 'C',
!>
!> where Q is a complex unitary matrix defined as the product of k
!> elementary reflectors
!>
!>       Q = H(1)**H H(2)**H . . . H(k)**H
!>
!> as returned by CGERQF. Q is of order m if SIDE = 'L' and of order n
!> if SIDE = 'R'.
!>

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 is INTEGER
!>          The number of rows of the matrix C. M >= 0.
!>

!>          N is INTEGER
!>          The number of columns of the matrix C. N >= 0.
!>

!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q.
!>          If SIDE = 'L', M >= K >= 0;
!>          if SIDE = 'R', N >= K >= 0.
!>

!>          A is COMPLEX array, dimension
!>                               (LDA,M) if SIDE = 'L',
!>                               (LDA,N) if SIDE = 'R'
!>          The i-th row must contain the vector which defines the
!>          elementary reflector H(i), for i = 1,2,...,k, as returned by
!>          CGERQF in the last k rows of its array argument A.
!>          A is modified by the routine but restored on exit.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A. LDA >= max(1,K).
!>

TAU

!>          TAU is COMPLEX array, dimension (K)
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by CGERQF.
!>

!>          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.

Definition at line 157 of file cunmr2.f.

subroutine dormr2 (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 info)

DORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm).

Purpose:

!>
!> DORMR2 overwrites the general real m by n matrix C with
!>
!>       Q * C  if SIDE = 'L' and TRANS = 'N', or
!>
!>       Q**T* C  if SIDE = 'L' and TRANS = 'T', or
!>
!>       C * Q  if SIDE = 'R' and TRANS = 'N', or
!>
!>       C * Q**T if SIDE = 'R' and TRANS = 'T',
!>
!> where Q is a real orthogonal matrix defined as the product of k
!> elementary reflectors
!>
!>       Q = H(1) H(2) . . . H(k)
!>
!> as returned by DGERQF. Q is of order m if SIDE = 'L' and of order n
!> if SIDE = 'R'.
!>

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': apply Q  (No transpose)
!>          = 'T': apply Q' (Transpose)
!>

!>          M is INTEGER
!>          The number of rows of the matrix C. M >= 0.
!>

!>          N is INTEGER
!>          The number of columns of the matrix C. N >= 0.
!>

!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q.
!>          If SIDE = 'L', M >= K >= 0;
!>          if SIDE = 'R', N >= K >= 0.
!>

!>          A is DOUBLE PRECISION array, dimension
!>                               (LDA,M) if SIDE = 'L',
!>                               (LDA,N) if SIDE = 'R'
!>          The i-th row must contain the vector which defines the
!>          elementary reflector H(i), for i = 1,2,...,k, as returned by
!>          DGERQF in the last k rows of its array argument A.
!>          A is modified by the routine but restored on exit.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A. LDA >= max(1,K).
!>

TAU

!>          TAU is DOUBLE PRECISION array, dimension (K)
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by DGERQF.
!>

!>          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.

Definition at line 157 of file dormr2.f.

subroutine sormr2 (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 info)

SORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm).

Purpose:

!>
!> SORMR2 overwrites the general real m by n matrix C with
!>
!>       Q * C  if SIDE = 'L' and TRANS = 'N', or
!>
!>       Q**T* C  if SIDE = 'L' and TRANS = 'T', or
!>
!>       C * Q  if SIDE = 'R' and TRANS = 'N', or
!>
!>       C * Q**T if SIDE = 'R' and TRANS = 'T',
!>
!> where Q is a real orthogonal matrix defined as the product of k
!> elementary reflectors
!>
!>       Q = H(1) H(2) . . . H(k)
!>
!> as returned by SGERQF. Q is of order m if SIDE = 'L' and of order n
!> if SIDE = 'R'.
!>

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': apply Q  (No transpose)
!>          = 'T': apply Q' (Transpose)
!>

!>          M is INTEGER
!>          The number of rows of the matrix C. M >= 0.
!>

!>          N is INTEGER
!>          The number of columns of the matrix C. N >= 0.
!>

!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q.
!>          If SIDE = 'L', M >= K >= 0;
!>          if SIDE = 'R', N >= K >= 0.
!>

!>          A is REAL array, dimension
!>                               (LDA,M) if SIDE = 'L',
!>                               (LDA,N) if SIDE = 'R'
!>          The i-th row must contain the vector which defines the
!>          elementary reflector H(i), for i = 1,2,...,k, as returned by
!>          SGERQF in the last k rows of its array argument A.
!>          A is modified by the routine but restored on exit.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A. LDA >= max(1,K).
!>

TAU

!>          TAU is REAL array, dimension (K)
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by SGERQF.
!>

!>          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.

Definition at line 157 of file sormr2.f.

subroutine zunmr2 (character side, character trans, integer m, integer n, integer k, complex16, dimension( lda, ) a, integer lda, complex16, dimension( ) tau, complex16, dimension( ldc, ) c, integer ldc, complex16, dimension( ) work, integer info)

ZUNMR2 multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm).

Purpose:

!>
!> ZUNMR2 overwrites the general complex m-by-n matrix C with
!>
!>       Q * C  if SIDE = 'L' and TRANS = 'N', or
!>
!>       Q**H* C  if SIDE = 'L' and TRANS = 'C', or
!>
!>       C * Q  if SIDE = 'R' and TRANS = 'N', or
!>
!>       C * Q**H if SIDE = 'R' and TRANS = 'C',
!>
!> where Q is a complex unitary matrix defined as the product of k
!> elementary reflectors
!>
!>       Q = H(1)**H H(2)**H . . . H(k)**H
!>
!> as returned by ZGERQF. Q is of order m if SIDE = 'L' and of order n
!> if SIDE = 'R'.
!>

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 is INTEGER
!>          The number of rows of the matrix C. M >= 0.
!>

!>          N is INTEGER
!>          The number of columns of the matrix C. N >= 0.
!>

!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q.
!>          If SIDE = 'L', M >= K >= 0;
!>          if SIDE = 'R', N >= K >= 0.
!>

!>          A is COMPLEX*16 array, dimension
!>                               (LDA,M) if SIDE = 'L',
!>                               (LDA,N) if SIDE = 'R'
!>          The i-th row must contain the vector which defines the
!>          elementary reflector H(i), for i = 1,2,...,k, as returned by
!>          ZGERQF in the last k rows of its array argument A.
!>          A is modified by the routine but restored on exit.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A. LDA >= max(1,K).
!>

TAU

!>          TAU is COMPLEX*16 array, dimension (K)
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by ZGERQF.
!>

!>          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.

Definition at line 157 of file zunmr2.f.

Author

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