larfb(3)

NAME
larfb - larfb: apply block Householder reflector

SYNOPSIS

  Functions
subroutine clarfb (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.
subroutine dlarfb (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
DLARFB applies a block reflector or its transpose to a general rectangular matrix.
subroutine slarfb (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
SLARFB applies a block reflector or its transpose to a general rectangular matrix.
subroutine zlarfb (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.

Detailed Description

Function Documentation

  subroutine clarfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( ldwork, * ) work, integer ldwork)

CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.

Purpose:

    !>
    !> CLARFB applies a complex block reflector H or its transpose H**H to a
    !> complex M-by-N matrix C, from either the left or the right.
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply H or H**H from the Left
    !>          = 'R': apply H or H**H from the Right
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N': apply H (No transpose)
    !>          = 'C': apply H**H (Conjugate transpose)
    !>

    DIRECT

    !>          DIRECT is CHARACTER*1
    !>          Indicates how H is formed from a product of elementary
    !>          reflectors
    !>          = 'F': H = H(1) H(2) . . . H(k) (Forward)
    !>          = 'B': H = H(k) . . . H(2) H(1) (Backward)
    !>

    STOREV

    !>          STOREV is CHARACTER*1
    !>          Indicates how the vectors which define the elementary
    !>          reflectors are stored:
    !>          = 'C': Columnwise
    !>          = 'R': Rowwise
    !>

    M

    !>          M is INTEGER
    !>          The number of rows of the matrix C.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix C.
    !>

    K

    !>          K is INTEGER
    !>          The order of the matrix T (= the number of elementary
    !>          reflectors whose product defines the block reflector).
    !>          If SIDE = 'L', M >= K >= 0;
    !>          if SIDE = 'R', N >= K >= 0.
    !>

    V

    !>          V is COMPLEX array, dimension
    !>                                (LDV,K) if STOREV = 'C'
    !>                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
    !>                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
    !>          The matrix V. See Further Details.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of the array V.
    !>          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
    !>          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
    !>          if STOREV = 'R', LDV >= K.
    !>

    T

    !>          T is COMPLEX array, dimension (LDT,K)
    !>          The triangular K-by-K matrix T in the representation of the
    !>          block reflector.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T. LDT >= K.
    !>

    C

    !>          C is COMPLEX array, dimension (LDC,N)
    !>          On entry, the M-by-N matrix C.
    !>          On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (LDWORK,K)
    !>

    LDWORK

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  The shape of the matrix V and the storage of the vectors which define
    !>  the H(i) is best illustrated by the following example with n = 5 and
    !>  k = 3. The triangular part of V (including its diagonal) is not
    !>  referenced.
    !>
    !>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
    !>
    !>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )
    !>                   ( v1  1    )                     (     1 v2 v2 v2 )
    !>                   ( v1 v2  1 )                     (        1 v3 v3 )
    !>                   ( v1 v2 v3 )
    !>                   ( v1 v2 v3 )
    !>
    !>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
    !>
    !>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
    !>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
    !>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
    !>                   (     1 v3 )
    !>                   (        1 )
    !>

Definition at line 194 of file clarfb.f.

  subroutine dlarfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( ldwork, * ) work, integer ldwork)

DLARFB applies a block reflector or its transpose to a general rectangular matrix.

Purpose:

    !>
    !> DLARFB applies a real block reflector H or its transpose H**T to a
    !> real m by n matrix C, from either the left or the right.
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply H or H**T from the Left
    !>          = 'R': apply H or H**T from the Right
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N': apply H (No transpose)
    !>          = 'T': apply H**T (Transpose)
    !>

    DIRECT

    !>          DIRECT is CHARACTER*1
    !>          Indicates how H is formed from a product of elementary
    !>          reflectors
    !>          = 'F': H = H(1) H(2) . . . H(k) (Forward)
    !>          = 'B': H = H(k) . . . H(2) H(1) (Backward)
    !>

    STOREV

    !>          STOREV is CHARACTER*1
    !>          Indicates how the vectors which define the elementary
    !>          reflectors are stored:
    !>          = 'C': Columnwise
    !>          = 'R': Rowwise
    !>

    M

    !>          M is INTEGER
    !>          The number of rows of the matrix C.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix C.
    !>

    K

    !>          K is INTEGER
    !>          The order of the matrix T (= the number of elementary
    !>          reflectors whose product defines the block reflector).
    !>          If SIDE = 'L', M >= K >= 0;
    !>          if SIDE = 'R', N >= K >= 0.
    !>

    V

    !>          V is DOUBLE PRECISION array, dimension
    !>                                (LDV,K) if STOREV = 'C'
    !>                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
    !>                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
    !>          The matrix V. See Further Details.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of the array V.
    !>          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
    !>          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
    !>          if STOREV = 'R', LDV >= K.
    !>

    T

    !>          T is DOUBLE PRECISION array, dimension (LDT,K)
    !>          The triangular k by k matrix T in the representation of the
    !>          block reflector.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T. LDT >= K.
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (LDC,N)
    !>          On entry, the m by n matrix C.
    !>          On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (LDWORK,K)
    !>

    LDWORK

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  The shape of the matrix V and the storage of the vectors which define
    !>  the H(i) is best illustrated by the following example with n = 5 and
    !>  k = 3. The triangular part of V (including its diagonal) is not
    !>  referenced.
    !>
    !>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
    !>
    !>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )
    !>                   ( v1  1    )                     (     1 v2 v2 v2 )
    !>                   ( v1 v2  1 )                     (        1 v3 v3 )
    !>                   ( v1 v2 v3 )
    !>                   ( v1 v2 v3 )
    !>
    !>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
    !>
    !>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
    !>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
    !>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
    !>                   (     1 v3 )
    !>                   (        1 )
    !>

Definition at line 194 of file dlarfb.f.

  subroutine slarfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldc, * ) c, integer ldc, real, dimension( ldwork, * ) work, integer ldwork)

SLARFB applies a block reflector or its transpose to a general rectangular matrix.

Purpose:

    !>
    !> SLARFB applies a real block reflector H or its transpose H**T to a
    !> real m by n matrix C, from either the left or the right.
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply H or H**T from the Left
    !>          = 'R': apply H or H**T from the Right
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N': apply H (No transpose)
    !>          = 'T': apply H**T (Transpose)
    !>

    DIRECT

    !>          DIRECT is CHARACTER*1
    !>          Indicates how H is formed from a product of elementary
    !>          reflectors
    !>          = 'F': H = H(1) H(2) . . . H(k) (Forward)
    !>          = 'B': H = H(k) . . . H(2) H(1) (Backward)
    !>

    STOREV

    !>          STOREV is CHARACTER*1
    !>          Indicates how the vectors which define the elementary
    !>          reflectors are stored:
    !>          = 'C': Columnwise
    !>          = 'R': Rowwise
    !>

    M

    !>          M is INTEGER
    !>          The number of rows of the matrix C.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix C.
    !>

    K

    !>          K is INTEGER
    !>          The order of the matrix T (= the number of elementary
    !>          reflectors whose product defines the block reflector).
    !>          If SIDE = 'L', M >= K >= 0;
    !>          if SIDE = 'R', N >= K >= 0.
    !>

    V

    !>          V is REAL array, dimension
    !>                                (LDV,K) if STOREV = 'C'
    !>                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
    !>                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
    !>          The matrix V. See Further Details.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of the array V.
    !>          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
    !>          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
    !>          if STOREV = 'R', LDV >= K.
    !>

    T

    !>          T is REAL array, dimension (LDT,K)
    !>          The triangular k by k matrix T in the representation of the
    !>          block reflector.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T. LDT >= K.
    !>

    C

    !>          C is REAL array, dimension (LDC,N)
    !>          On entry, the m by n matrix C.
    !>          On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          WORK is REAL array, dimension (LDWORK,K)
    !>

    LDWORK

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  The shape of the matrix V and the storage of the vectors which define
    !>  the H(i) is best illustrated by the following example with n = 5 and
    !>  k = 3. The triangular part of V (including its diagonal) is not
    !>  referenced.
    !>
    !>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
    !>
    !>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )
    !>                   ( v1  1    )                     (     1 v2 v2 v2 )
    !>                   ( v1 v2  1 )                     (        1 v3 v3 )
    !>                   ( v1 v2 v3 )
    !>                   ( v1 v2 v3 )
    !>
    !>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
    !>
    !>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
    !>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
    !>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
    !>                   (     1 v3 )
    !>                   (        1 )
    !>

Definition at line 194 of file slarfb.f.

  subroutine zlarfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, complex*16, dimension( ldv, * ) v, integer ldv, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( ldwork, * ) work, integer ldwork)

ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.

Purpose:

    !>
    !> ZLARFB applies a complex block reflector H or its transpose H**H to a
    !> complex M-by-N matrix C, from either the left or the right.
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply H or H**H from the Left
    !>          = 'R': apply H or H**H from the Right
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N': apply H (No transpose)
    !>          = 'C': apply H**H (Conjugate transpose)
    !>

    DIRECT

    !>          DIRECT is CHARACTER*1
    !>          Indicates how H is formed from a product of elementary
    !>          reflectors
    !>          = 'F': H = H(1) H(2) . . . H(k) (Forward)
    !>          = 'B': H = H(k) . . . H(2) H(1) (Backward)
    !>

    STOREV

    !>          STOREV is CHARACTER*1
    !>          Indicates how the vectors which define the elementary
    !>          reflectors are stored:
    !>          = 'C': Columnwise
    !>          = 'R': Rowwise
    !>

    M

    !>          M is INTEGER
    !>          The number of rows of the matrix C.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix C.
    !>

    K

    !>          K is INTEGER
    !>          The order of the matrix T (= the number of elementary
    !>          reflectors whose product defines the block reflector).
    !>          If SIDE = 'L', M >= K >= 0;
    !>          if SIDE = 'R', N >= K >= 0.
    !>

    V

    !>          V is COMPLEX*16 array, dimension
    !>                                (LDV,K) if STOREV = 'C'
    !>                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
    !>                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
    !>          See Further Details.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of the array V.
    !>          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
    !>          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
    !>          if STOREV = 'R', LDV >= K.
    !>

    T

    !>          T is COMPLEX*16 array, dimension (LDT,K)
    !>          The triangular K-by-K matrix T in the representation of the
    !>          block reflector.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T. LDT >= K.
    !>

    C

    !>          C is COMPLEX*16 array, dimension (LDC,N)
    !>          On entry, the M-by-N matrix C.
    !>          On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (LDWORK,K)
    !>

    LDWORK

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  The shape of the matrix V and the storage of the vectors which define
    !>  the H(i) is best illustrated by the following example with n = 5 and
    !>  k = 3. The triangular part of V (including its diagonal) is not
    !>  referenced.
    !>
    !>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
    !>
    !>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )
    !>                   ( v1  1    )                     (     1 v2 v2 v2 )
    !>                   ( v1 v2  1 )                     (        1 v3 v3 )
    !>                   ( v1 v2 v3 )
    !>                   ( v1 v2 v3 )
    !>
    !>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
    !>
    !>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
    !>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
    !>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
    !>                   (     1 v3 )
    !>                   (        1 )
    !>

Definition at line 194 of file zlarfb.f.

Author

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