Library Functions Manual

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

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

!>          K is INTEGER
!>          The order of the matrix T (= the number of elementary
!>          reflectors whose product defines the block reflector).
!>

!>          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 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 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 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:

!>

Definition at line 181 of file clarzb.f.

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

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

!>          K is INTEGER
!>          The order of the matrix T (= the number of elementary
!>          reflectors whose product defines the block reflector).
!>

!>          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 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 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 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:

!>

Definition at line 181 of file dlarzb.f.

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

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

!>          K is INTEGER
!>          The order of the matrix T (= the number of elementary
!>          reflectors whose product defines the block reflector).
!>

!>          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 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 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 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:

!>

Definition at line 181 of file slarzb.f.

subroutine ZLARZB (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, complex16, dimension( ldv, ) v, integer ldv, complex16, dimension( ldt, ) t, integer ldt, complex16, dimension( ldc, ) c, integer ldc, complex16, 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 is INTEGER
!>          The number of rows of the matrix C.
!>

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

!>          K is INTEGER
!>          The order of the matrix T (= the number of elementary
!>          reflectors whose product defines the block reflector).
!>

!>          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 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 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 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:

!>

Definition at line 181 of file zlarzb.f.

Author¶

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