larzb(3)

NAME
larzb - larzb: apply block reflector

SYNOPSIS

  Functions

subroutine clarzb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, c, ldc, work, ldwork)
CLARZB applies a block reflector or its conjugate-transpose to a general matrix.
subroutine dlarzb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, c, ldc, work, ldwork)
DLARZB applies a block reflector or its transpose to a general matrix.
subroutine slarzb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, c, ldc, work, ldwork)
SLARZB applies a block reflector or its transpose to a general matrix.
subroutine zlarzb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, c, ldc, work, ldwork)
ZLARZB applies a block reflector or its conjugate-transpose to a general matrix.

Detailed Description

Function Documentation

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

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

Purpose:

    !>
    !> CLARZB applies a complex block reflector H or its transpose H**H
    !> to a complex distributed M-by-N  C from the left or the right.
    !>
    !> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
    !>

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, not supported yet)
    !>          = '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                        (not supported yet)
    !>          = '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).
    !>

    L

    !>          L is INTEGER
    !>          The number of columns of the matrix V containing the
    !>          meaningful part of the Householder reflectors.
    !>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
    !>

    V

    !>          V is COMPLEX array, dimension (LDV,NV).
    !>          If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of the array V.
    !>          If STOREV = 'C', LDV >= L; 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.

Contributors:
    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

    !>

  subroutine dlarzb (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, 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)

DLARZB applies a block reflector or its transpose to a general matrix.

Purpose:

    !>
    !> DLARZB applies a real block reflector H or its transpose H**T to
    !> a real distributed M-by-N  C from the left or the right.
    !>
    !> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
    !>

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)
    !>          = 'C': 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, not supported yet)
    !>          = '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                        (not supported yet)
    !>          = '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).
    !>

    L

    !>          L is INTEGER
    !>          The number of columns of the matrix V containing the
    !>          meaningful part of the Householder reflectors.
    !>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
    !>

    V

    !>          V is DOUBLE PRECISION array, dimension (LDV,NV).
    !>          If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of the array V.
    !>          If STOREV = 'C', LDV >= L; 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.

Contributors:
    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

    !>

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

SLARZB applies a block reflector or its transpose to a general matrix.

Purpose:

    !>
    !> SLARZB applies a real block reflector H or its transpose H**T to
    !> a real distributed M-by-N  C from the left or the right.
    !>
    !> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
    !>

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)
    !>          = 'C': 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, not supported yet)
    !>          = '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                        (not supported yet)
    !>          = '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).
    !>

    L

    !>          L is INTEGER
    !>          The number of columns of the matrix V containing the
    !>          meaningful part of the Householder reflectors.
    !>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
    !>

    V

    !>          V is REAL array, dimension (LDV,NV).
    !>          If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of the array V.
    !>          If STOREV = 'C', LDV >= L; 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.

Contributors:
    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

    !>

  subroutine zlarzb (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, 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)

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

Purpose:

    !>
    !> ZLARZB applies a complex block reflector H or its transpose H**H
    !> to a complex distributed M-by-N  C from the left or the right.
    !>
    !> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
    !>

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, not supported yet)
    !>          = '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                        (not supported yet)
    !>          = '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).
    !>

    L

    !>          L is INTEGER
    !>          The number of columns of the matrix V containing the
    !>          meaningful part of the Householder reflectors.
    !>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
    !>

    V

    !>          V is COMPLEX*16 array, dimension (LDV,NV).
    !>          If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of the array V.
    !>          If STOREV = 'C', LDV >= L; 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.

Contributors:
    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

    !>

Author

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