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 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.

          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 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 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 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.

          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 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 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 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.

          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 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 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, complex16, dimension( lda, ) a, integer lda, complex16, dimension( ) tau, complex16, dimension( ldc, ) c, integer ldc, complex16, 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 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.

          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 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 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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