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unmr3(3) Library Functions Manual unmr3(3)

NAME

unmr3 - {un,or}mr3: step in unmrz

SYNOPSIS

Functions


subroutine CUNMR3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info)
CUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm). subroutine DORMR3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info)
DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm). subroutine SORMR3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info)
SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm). subroutine ZUNMR3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info)
ZUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm).

Detailed Description

Function Documentation

subroutine CUNMR3 (character side, character trans, integer m, integer n, integer k, integer l, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer info)

CUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm).

Purpose:

!>
!> CUNMR3 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(2) . . . H(k)
!>
!> as returned by CTZRZF. 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

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

L

!>          L is INTEGER
!>          The number of columns of the matrix A containing
!>          the meaningful part of the Householder reflectors.
!>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
!>

A

!>          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
!>          CTZRZF 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 CTZRZF.
!>

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.

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

!>

Definition at line 176 of file cunmr3.f.

subroutine DORMR3 (character side, character trans, integer m, integer n, integer k, integer l, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer info)

DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

Purpose:

!>
!> DORMR3 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 = 'C', or
!>
!>       C * Q  if SIDE = 'R' and TRANS = 'N', or
!>
!>       C * Q**T if SIDE = 'R' and TRANS = 'C',
!>
!> 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 DTZRZF. 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**T (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.
!>

K

!>          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.
!>

L

!>          L is INTEGER
!>          The number of columns of the matrix A containing
!>          the meaningful part of the Householder reflectors.
!>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
!>

A

!>          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
!>          DTZRZF 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 DTZRZF.
!>

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.

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

!>

Definition at line 176 of file dormr3.f.

subroutine SORMR3 (character side, character trans, integer m, integer n, integer k, integer l, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer info)

SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

Purpose:

!>
!> SORMR3 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 = 'C', or
!>
!>       C * Q  if SIDE = 'R' and TRANS = 'N', or
!>
!>       C * Q**T if SIDE = 'R' and TRANS = 'C',
!>
!> 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 STZRZF. 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**T (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.
!>

K

!>          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.
!>

L

!>          L is INTEGER
!>          The number of columns of the matrix A containing
!>          the meaningful part of the Householder reflectors.
!>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
!>

A

!>          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
!>          STZRZF 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 STZRZF.
!>

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.

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

!>

Definition at line 176 of file sormr3.f.

subroutine ZUNMR3 (character side, character trans, integer m, integer n, integer k, integer l, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer info)

ZUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm).

Purpose:

!>
!> ZUNMR3 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(2) . . . H(k)
!>
!> as returned by ZTZRZF. 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

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

L

!>          L is INTEGER
!>          The number of columns of the matrix A containing
!>          the meaningful part of the Householder reflectors.
!>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
!>

A

!>          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
!>          ZTZRZF 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 ZTZRZF.
!>

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.

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

!>

Definition at line 176 of file zunmr3.f.

Author

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