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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LAPACK                          Version 3.12.0                        unmr3(3)