unmtr(3)

NAME
unmtr - {un,or}mtr: multiply by Q from hetrd

SYNOPSIS

  Functions
subroutine cunmtr (side, uplo, trans, m, n, a, lda, tau, c, ldc, work, lwork, info)
CUNMTR
subroutine dormtr (side, uplo, trans, m, n, a, lda, tau, c, ldc, work, lwork, info)
DORMTR
subroutine sormtr (side, uplo, trans, m, n, a, lda, tau, c, ldc, work, lwork, info)
SORMTR
subroutine zunmtr (side, uplo, trans, m, n, a, lda, tau, c, ldc, work, lwork, info)
ZUNMTR

Detailed Description

Function Documentation

  subroutine cunmtr (character side, character uplo, character trans, integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer lwork, integer info)

CUNMTR

Purpose:

    !>
    !> CUNMTR 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 CHETRD:
    !>
    !> 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 triangle of A contains elementary reflectors
    !>                 from CHETRD;
    !>          = 'L': Lower triangle of A contains elementary reflectors
    !>                 from CHETRD.
    !>

    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.
    !>

    A

    !>          A is COMPLEX array, dimension
    !>                               (LDA,M) if SIDE = 'L'
    !>                               (LDA,N) if SIDE = 'R'
    !>          The vectors which define the elementary reflectors, as
    !>          returned by CHETRD.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.
    !>          LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
    !>

    TAU

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

    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 (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK.
    !>          If SIDE = 'L', LWORK >= max(1,N);
    !>          if SIDE = 'R', LWORK >= max(1,M).
    !>          For optimum performance LWORK >= N*NB if SIDE = 'L', and
    !>          LWORK >=M*NB if SIDE = 'R', where NB is the optimal
    !>          blocksize.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the optimal size of the WORK array, returns
    !>          this value as the first entry of the WORK array, and no error
    !>          message related to LWORK is issued by XERBLA.
    !>

    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 170 of file cunmtr.f.

  subroutine dormtr (character side, character uplo, character trans, integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info)

DORMTR

Purpose:

    !>
    !> DORMTR 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 DSYTRD:
    !>
    !> 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 triangle of A contains elementary reflectors
    !>                 from DSYTRD;
    !>          = 'L': Lower triangle of A contains elementary reflectors
    !>                 from DSYTRD.
    !>

    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.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension
    !>                               (LDA,M) if SIDE = 'L'
    !>                               (LDA,N) if SIDE = 'R'
    !>          The vectors which define the elementary reflectors, as
    !>          returned by DSYTRD.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.
    !>          LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
    !>

    TAU

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

    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 (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK.
    !>          If SIDE = 'L', LWORK >= max(1,N);
    !>          if SIDE = 'R', LWORK >= max(1,M).
    !>          For optimum performance LWORK >= N*NB if SIDE = 'L', and
    !>          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
    !>          blocksize.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the optimal size of the WORK array, returns
    !>          this value as the first entry of the WORK array, and no error
    !>          message related to LWORK is issued by XERBLA.
    !>

    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 169 of file dormtr.f.

  subroutine sormtr (character side, character uplo, character trans, integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer lwork, integer info)

SORMTR

Purpose:

    !>
    !> SORMTR 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 SSYTRD:
    !>
    !> 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 triangle of A contains elementary reflectors
    !>                 from SSYTRD;
    !>          = 'L': Lower triangle of A contains elementary reflectors
    !>                 from SSYTRD.
    !>

    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.
    !>

    A

    !>          A is REAL array, dimension
    !>                               (LDA,M) if SIDE = 'L'
    !>                               (LDA,N) if SIDE = 'R'
    !>          The vectors which define the elementary reflectors, as
    !>          returned by SSYTRD.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.
    !>          LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
    !>

    TAU

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

    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 (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK.
    !>          If SIDE = 'L', LWORK >= max(1,N);
    !>          if SIDE = 'R', LWORK >= max(1,M).
    !>          For optimum performance LWORK >= N*NB if SIDE = 'L', and
    !>          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
    !>          blocksize.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the optimal size of the WORK array, returns
    !>          this value as the first entry of the WORK array, and no error
    !>          message related to LWORK is issued by XERBLA.
    !>

    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 170 of file sormtr.f.

  subroutine zunmtr (character side, character uplo, character trans, integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer lwork, integer info)

ZUNMTR

Purpose:

    !>
    !> ZUNMTR 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 ZHETRD:
    !>
    !> 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 triangle of A contains elementary reflectors
    !>                 from ZHETRD;
    !>          = 'L': Lower triangle of A contains elementary reflectors
    !>                 from ZHETRD.
    !>

    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.
    !>

    A

    !>          A is COMPLEX*16 array, dimension
    !>                               (LDA,M) if SIDE = 'L'
    !>                               (LDA,N) if SIDE = 'R'
    !>          The vectors which define the elementary reflectors, as
    !>          returned by ZHETRD.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.
    !>          LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
    !>

    TAU

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

    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 (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK.
    !>          If SIDE = 'L', LWORK >= max(1,N);
    !>          if SIDE = 'R', LWORK >= max(1,M).
    !>          For optimum performance LWORK >= N*NB if SIDE = 'L', and
    !>          LWORK >=M*NB if SIDE = 'R', where NB is the optimal
    !>          blocksize.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the optimal size of the WORK array, returns
    !>          this value as the first entry of the WORK array, and no error
    !>          message related to LWORK is issued by XERBLA.
    !>

    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 169 of file zunmtr.f.

Author

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