upmtr(3)

NAME
upmtr - {up,op}mtr: multiply by Q from hptrd

SYNOPSIS

  Functions

subroutine cupmtr (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)
CUPMTR
subroutine dopmtr (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)
DOPMTR
subroutine sopmtr (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)
SOPMTR
subroutine zupmtr (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)
ZUPMTR

Detailed Description

Function Documentation

  subroutine cupmtr (character side, character uplo, character trans, integer m, integer n, complex, dimension( * ) ap, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer info)

CUPMTR

Purpose:

    !>
    !> CUPMTR 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 CHPTRD using packed
    !> storage:
    !>
    !> 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 triangular packed storage used in previous
    !>                 call to CHPTRD;
    !>          = 'L': Lower triangular packed storage used in previous
    !>                 call to CHPTRD.
    !>

    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.
    !>

    AP

    !>          AP is COMPLEX array, dimension
    !>                               (M*(M+1)/2) if SIDE = 'L'
    !>                               (N*(N+1)/2) if SIDE = 'R'
    !>          The vectors which define the elementary reflectors, as
    !>          returned by CHPTRD.  AP is modified by the routine but
    !>          restored on exit.
    !>

    TAU

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

    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.

  subroutine dopmtr (character side, character uplo, character trans, integer m, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer info)

DOPMTR

Purpose:

    !>
    !> DOPMTR 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 DSPTRD using packed
    !> storage:
    !>
    !> 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 triangular packed storage used in previous
    !>                 call to DSPTRD;
    !>          = 'L': Lower triangular packed storage used in previous
    !>                 call to DSPTRD.
    !>

    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.
    !>

    AP

    !>          AP is DOUBLE PRECISION array, dimension
    !>                               (M*(M+1)/2) if SIDE = 'L'
    !>                               (N*(N+1)/2) if SIDE = 'R'
    !>          The vectors which define the elementary reflectors, as
    !>          returned by DSPTRD.  AP is modified by the routine but
    !>          restored on exit.
    !>

    TAU

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

    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.

  subroutine sopmtr (character side, character uplo, character trans, integer m, integer n, real, dimension( * ) ap, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer info)

SOPMTR

Purpose:

    !>
    !> SOPMTR 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 SSPTRD using packed
    !> storage:
    !>
    !> 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 triangular packed storage used in previous
    !>                 call to SSPTRD;
    !>          = 'L': Lower triangular packed storage used in previous
    !>                 call to SSPTRD.
    !>

    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.
    !>

    AP

    !>          AP is REAL array, dimension
    !>                               (M*(M+1)/2) if SIDE = 'L'
    !>                               (N*(N+1)/2) if SIDE = 'R'
    !>          The vectors which define the elementary reflectors, as
    !>          returned by SSPTRD.  AP is modified by the routine but
    !>          restored on exit.
    !>

    TAU

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

    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.

  subroutine zupmtr (character side, character uplo, character trans, integer m, integer n, complex*16, dimension( * ) ap, complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer info)

ZUPMTR

Purpose:

    !>
    !> ZUPMTR 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 ZHPTRD using packed
    !> storage:
    !>
    !> 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 triangular packed storage used in previous
    !>                 call to ZHPTRD;
    !>          = 'L': Lower triangular packed storage used in previous
    !>                 call to ZHPTRD.
    !>

    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.
    !>

    AP

    !>          AP is COMPLEX*16 array, dimension
    !>                               (M*(M+1)/2) if SIDE = 'L'
    !>                               (N*(N+1)/2) if SIDE = 'R'
    !>          The vectors which define the elementary reflectors, as
    !>          returned by ZHPTRD.  AP is modified by the routine but
    !>          restored on exit.
    !>

    TAU

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

    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.

Author

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