Library Functions Manual

NAME¶

tpmlqt - tpmlqt: applies Q

SYNOPSIS¶

Functions¶

subroutine CTPMLQT (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
CTPMLQT subroutine DTPMLQT (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
DTPMLQT subroutine STPMLQT (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
STPMLQT subroutine ZTPMLQT (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
ZTPMLQT

Detailed Description¶

Function Documentation¶

subroutine CTPMLQT (character side, character trans, integer m, integer n, integer k, integer l, integer mb, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer info)¶

CTPMLQT

Purpose:

!>
!> CTPMLQT applies a complex unitary matrix Q obtained from a
!>  complex block reflector H to a general
!> complex matrix C, which consists of two blocks A and B.
!>

Parameters

SIDE

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

TRANS

!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'C':  Conjugate transpose, apply Q**H.
!>

!>          M is INTEGER
!>          The number of rows of the matrix B. M >= 0.
!>

!>          N is INTEGER
!>          The number of columns of the matrix B. N >= 0.
!>

!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q.
!>

!>          L is INTEGER
!>          The order of the trapezoidal part of V.
!>          K >= L >= 0.  See Further Details.
!>

!>          MB is INTEGER
!>          The block size used for the storage of T.  K >= MB >= 1.
!>          This must be the same value of MB used to generate T
!>          in CTPLQT.
!>

!>          V is COMPLEX array, dimension (LDV,K)
!>          The i-th row must contain the vector which defines the
!>          elementary reflector H(i), for i = 1,2,...,k, as returned by
!>          CTPLQT in B.  See Further Details.
!>

LDV

!>          LDV is INTEGER
!>          The leading dimension of the array V. LDV >= K.
!>

!>          T is COMPLEX array, dimension (LDT,K)
!>          The upper triangular factors of the block reflectors
!>          as returned by CTPLQT, stored as a MB-by-K matrix.
!>

LDT

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

!>          A is COMPLEX array, dimension
!>          (LDA,N) if SIDE = 'L' or
!>          (LDA,K) if SIDE = 'R'
!>          On entry, the K-by-N or M-by-K matrix A.
!>          On exit, A is overwritten by the corresponding block of
!>          Q*C or Q**H*C or C*Q or C*Q**H.  See Further Details.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.
!>          If SIDE = 'L', LDA >= max(1,K);
!>          If SIDE = 'R', LDA >= max(1,M).
!>

!>          B is COMPLEX array, dimension (LDB,N)
!>          On entry, the M-by-N matrix B.
!>          On exit, B is overwritten by the corresponding block of
!>          Q*C or Q**H*C or C*Q or C*Q**H.  See Further Details.
!>

LDB

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

WORK

!>          WORK is COMPLEX array. The dimension of WORK is
!>           N*MB if SIDE = 'L', or  M*MB if SIDE = 'R'.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  The columns of the pentagonal matrix V contain the elementary reflectors
!>  H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
!>  trapezoidal block V2:
!>
!>        V = [V1] [V2].
!>
!>
!>  The size of the trapezoidal block V2 is determined by the parameter L,
!>  where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L
!>  rows of a K-by-K upper triangular matrix.  If L=K, V2 is lower triangular;
!>  if L=0, there is no trapezoidal block, hence V = V1 is rectangular.
!>
!>  If SIDE = 'L':  C = [A]  where A is K-by-N,  B is M-by-N and V is K-by-M.
!>                      [B]
!>
!>  If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is K-by-N.
!>
!>  The complex unitary matrix Q is formed from V and T.
!>
!>  If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
!>
!>  If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C.
!>
!>  If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
!>
!>  If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.
!>

Definition at line 197 of file ctpmlqt.f.

subroutine DTPMLQT (character side, character trans, integer m, integer n, integer k, integer l, integer mb, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, integer info)¶

DTPMLQT

Purpose:

!>
!> DTPMQRT applies a real orthogonal matrix Q obtained from a
!>  real block reflector H to a general
!> real matrix C, which consists of two blocks A and B.
!>

Parameters

SIDE

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

TRANS

!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'T':  Transpose, apply Q**T.
!>

!>          M is INTEGER
!>          The number of rows of the matrix B. M >= 0.
!>

!>          N is INTEGER
!>          The number of columns of the matrix B. N >= 0.
!>

!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q.
!>

!>          L is INTEGER
!>          The order of the trapezoidal part of V.
!>          K >= L >= 0.  See Further Details.
!>

!>          MB is INTEGER
!>          The block size used for the storage of T.  K >= MB >= 1.
!>          This must be the same value of MB used to generate T
!>          in DTPLQT.
!>

!>          V is DOUBLE PRECISION array, dimension (LDV,K)
!>          The i-th row must contain the vector which defines the
!>          elementary reflector H(i), for i = 1,2,...,k, as returned by
!>          DTPLQT in B.  See Further Details.
!>

LDV

!>          LDV is INTEGER
!>          The leading dimension of the array V. LDV >= K.
!>

!>          T is DOUBLE PRECISION array, dimension (LDT,K)
!>          The upper triangular factors of the block reflectors
!>          as returned by DTPLQT, stored as a MB-by-K matrix.
!>

LDT

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

!>          A is DOUBLE PRECISION array, dimension
!>          (LDA,N) if SIDE = 'L' or
!>          (LDA,K) if SIDE = 'R'
!>          On entry, the K-by-N or M-by-K matrix A.
!>          On exit, A is overwritten by the corresponding block of
!>          Q*C or Q**T*C or C*Q or C*Q**T.  See Further Details.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.
!>          If SIDE = 'L', LDA >= max(1,K);
!>          If SIDE = 'R', LDA >= max(1,M).
!>

!>          B is DOUBLE PRECISION array, dimension (LDB,N)
!>          On entry, the M-by-N matrix B.
!>          On exit, B is overwritten by the corresponding block of
!>          Q*C or Q**T*C or C*Q or C*Q**T.  See Further Details.
!>

LDB

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

WORK

!>          WORK is DOUBLE PRECISION array. The dimension of WORK is
!>           N*MB if SIDE = 'L', or  M*MB if SIDE = 'R'.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  The columns of the pentagonal matrix V contain the elementary reflectors
!>  H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
!>  trapezoidal block V2:
!>
!>        V = [V1] [V2].
!>
!>
!>  The size of the trapezoidal block V2 is determined by the parameter L,
!>  where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L
!>  rows of a K-by-K upper triangular matrix.  If L=K, V2 is lower triangular;
!>  if L=0, there is no trapezoidal block, hence V = V1 is rectangular.
!>
!>  If SIDE = 'L':  C = [A]  where A is K-by-N,  B is M-by-N and V is K-by-M.
!>                      [B]
!>
!>  If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is K-by-N.
!>
!>  The real orthogonal matrix Q is formed from V and T.
!>
!>  If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
!>
!>  If TRANS='T' and SIDE='L', C is on exit replaced with Q**T * C.
!>
!>  If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
!>
!>  If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T.
!>

Definition at line 212 of file dtpmlqt.f.

subroutine STPMLQT (character side, character trans, integer m, integer n, integer k, integer l, integer mb, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldt, * ) t, integer ldt, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer info)¶

STPMLQT

Purpose:

!>
!> STPMLQT applies a real orthogonal matrix Q obtained from a
!>  real block reflector H to a general
!> real matrix C, which consists of two blocks A and B.
!>

Parameters

SIDE

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

TRANS

!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'T':  Transpose, apply Q**T.
!>

!>          M is INTEGER
!>          The number of rows of the matrix B. M >= 0.
!>

!>          N is INTEGER
!>          The number of columns of the matrix B. N >= 0.
!>

!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q.
!>

!>          L is INTEGER
!>          The order of the trapezoidal part of V.
!>          K >= L >= 0.  See Further Details.
!>

!>          MB is INTEGER
!>          The block size used for the storage of T.  K >= MB >= 1.
!>          This must be the same value of MB used to generate T
!>          in STPLQT.
!>

!>          V is REAL array, dimension (LDV,K)
!>          The i-th row must contain the vector which defines the
!>          elementary reflector H(i), for i = 1,2,...,k, as returned by
!>          STPLQT in B.  See Further Details.
!>

LDV

!>          LDV is INTEGER
!>          The leading dimension of the array V. LDV >= K.
!>

!>          T is REAL array, dimension (LDT,K)
!>          The upper triangular factors of the block reflectors
!>          as returned by STPLQT, stored as a MB-by-K matrix.
!>

LDT

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

!>          A is REAL array, dimension
!>          (LDA,N) if SIDE = 'L' or
!>          (LDA,K) if SIDE = 'R'
!>          On entry, the K-by-N or M-by-K matrix A.
!>          On exit, A is overwritten by the corresponding block of
!>          Q*C or Q**T*C or C*Q or C*Q**T.  See Further Details.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.
!>          If SIDE = 'L', LDA >= max(1,K);
!>          If SIDE = 'R', LDA >= max(1,M).
!>

!>          B is REAL array, dimension (LDB,N)
!>          On entry, the M-by-N matrix B.
!>          On exit, B is overwritten by the corresponding block of
!>          Q*C or Q**T*C or C*Q or C*Q**T.  See Further Details.
!>

LDB

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

WORK

!>          WORK is REAL array. The dimension of WORK is
!>           N*MB if SIDE = 'L', or  M*MB if SIDE = 'R'.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  The columns of the pentagonal matrix V contain the elementary reflectors
!>  H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
!>  trapezoidal block V2:
!>
!>        V = [V1] [V2].
!>
!>
!>  The size of the trapezoidal block V2 is determined by the parameter L,
!>  where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L
!>  rows of a K-by-K upper triangular matrix.  If L=K, V2 is lower triangular;
!>  if L=0, there is no trapezoidal block, hence V = V1 is rectangular.
!>
!>  If SIDE = 'L':  C = [A]  where A is K-by-N,  B is M-by-N and V is K-by-M.
!>                      [B]
!>
!>  If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is K-by-N.
!>
!>  The real orthogonal matrix Q is formed from V and T.
!>
!>  If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
!>
!>  If TRANS='T' and SIDE='L', C is on exit replaced with Q**T * C.
!>
!>  If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
!>
!>  If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T.
!>

Definition at line 212 of file stpmlqt.f.

subroutine ZTPMLQT (character side, character trans, integer m, integer n, integer k, integer l, integer mb, complex16, dimension( ldv, ) v, integer ldv, complex16, dimension( ldt, ) t, integer ldt, complex16, dimension( lda, ) a, integer lda, complex16, dimension( ldb, ) b, integer ldb, complex16, dimension( ) work, integer info)¶

ZTPMLQT

Purpose:

!>
!> ZTPMLQT applies a complex unitary matrix Q obtained from a
!>  complex block reflector H to a general
!> complex matrix C, which consists of two blocks A and B.
!>

Parameters

SIDE

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

TRANS

!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'C':  Conjugate transpose, apply Q**H.
!>

!>          M is INTEGER
!>          The number of rows of the matrix B. M >= 0.
!>

!>          N is INTEGER
!>          The number of columns of the matrix B. N >= 0.
!>

!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q.
!>

!>          L is INTEGER
!>          The order of the trapezoidal part of V.
!>          K >= L >= 0.  See Further Details.
!>

!>          MB is INTEGER
!>          The block size used for the storage of T.  K >= MB >= 1.
!>          This must be the same value of MB used to generate T
!>          in ZTPLQT.
!>

!>          V is COMPLEX*16 array, dimension (LDV,K)
!>          The i-th row must contain the vector which defines the
!>          elementary reflector H(i), for i = 1,2,...,k, as returned by
!>          ZTPLQT in B.  See Further Details.
!>

LDV

!>          LDV is INTEGER
!>          The leading dimension of the array V. LDV >= K.
!>

!>          T is COMPLEX*16 array, dimension (LDT,K)
!>          The upper triangular factors of the block reflectors
!>          as returned by ZTPLQT, stored as a MB-by-K matrix.
!>

LDT

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

!>          A is COMPLEX*16 array, dimension
!>          (LDA,N) if SIDE = 'L' or
!>          (LDA,K) if SIDE = 'R'
!>          On entry, the K-by-N or M-by-K matrix A.
!>          On exit, A is overwritten by the corresponding block of
!>          Q*C or Q**H*C or C*Q or C*Q**H.  See Further Details.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.
!>          If SIDE = 'L', LDA >= max(1,K);
!>          If SIDE = 'R', LDA >= max(1,M).
!>

!>          B is COMPLEX*16 array, dimension (LDB,N)
!>          On entry, the M-by-N matrix B.
!>          On exit, B is overwritten by the corresponding block of
!>          Q*C or Q**H*C or C*Q or C*Q**H.  See Further Details.
!>

LDB

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

WORK

!>          WORK is COMPLEX*16 array. The dimension of WORK is
!>           N*MB if SIDE = 'L', or  M*MB if SIDE = 'R'.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  The columns of the pentagonal matrix V contain the elementary reflectors
!>  H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
!>  trapezoidal block V2:
!>
!>        V = [V1] [V2].
!>
!>
!>  The size of the trapezoidal block V2 is determined by the parameter L,
!>  where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L
!>  rows of a K-by-K upper triangular matrix.  If L=K, V2 is lower triangular;
!>  if L=0, there is no trapezoidal block, hence V = V1 is rectangular.
!>
!>  If SIDE = 'L':  C = [A]  where A is K-by-N,  B is M-by-N and V is K-by-M.
!>                      [B]
!>
!>  If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is K-by-N.
!>
!>  The complex unitary matrix Q is formed from V and T.
!>
!>  If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
!>
!>  If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C.
!>
!>  If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
!>
!>  If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.
!>

Definition at line 212 of file ztpmlqt.f.

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