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 elements equal to 1 are not stored; the corresponding
      array elements are modified but restored on exit. The rest of the
      array is not used.
      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 195 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 elements equal to 1 are not stored; the corresponding
      array elements are modified but restored on exit. The rest of the
      array is not used.
      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 195 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 elements equal to 1 are not stored; the corresponding
      array elements are modified but restored on exit. The rest of the
      array is not used.
      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 195 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 elements equal to 1 are not stored; the corresponding
      array elements are modified but restored on exit. The rest of the
      array is not used.
      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 195 of file zlarfb.f.

Author

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