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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