gemlqt - Man Page

gemlqt: multiply by Q from gelqt

Synopsis

Functions

subroutine cgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
CGEMLQT
subroutine dgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
DGEMLQT
subroutine sgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
SGEMLQT
subroutine zgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
ZGEMLQT

Detailed Description

Function Documentation

subroutine cgemlqt (character side, character trans, integer m, integer n, integer k, integer mb, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer info)

CGEMLQT

Purpose:

 CGEMLQT overwrites the general complex M-by-N matrix C with

                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      Q C            C Q
 TRANS = 'C':   Q**H C            C Q**H

 where Q is a complex unitary matrix defined as the product of K
 elementary reflectors:

       Q = H(1) H(2) . . . H(K) = I - V T V**H

 generated using the compact WY representation as returned by CGELQT.

 Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'.
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

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

N

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

K

          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.
          If SIDE = 'L', M >= K >= 0;
          if SIDE = 'R', N >= K >= 0.

MB

          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 CGELQT.

V

          V is COMPLEX array, dimension
                               (LDV,M) if SIDE = 'L',
                               (LDV,N) if SIDE = 'R'
          The i-th row must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,...,k, as returned by
          CGELQT in the first K rows of its array argument A.

LDV

          LDV is INTEGER
          The leading dimension of the array V. LDV >= max(1,K).

T

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

LDT

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

C

          C is COMPLEX array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by Q C, Q**H C, C Q**H or C Q.

LDC

          LDC is INTEGER
          The leading dimension of the array C. LDC >= 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.

Definition at line 151 of file cgemlqt.f.

subroutine dgemlqt (character side, character trans, integer m, integer n, integer k, integer mb, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer info)

DGEMLQT  

Purpose:

 DGEMLQT overwrites the general real M-by-N matrix C with

                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      Q C            C Q
 TRANS = 'T':   Q**T C            C Q**T

 where Q is a real orthogonal matrix defined as the product of K
 elementary reflectors:

       Q = H(1) H(2) . . . H(K) = I - V T V**T

 generated using the compact WY representation as returned by DGELQT.

 Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'.
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;
          = 'C':  Transpose, apply Q**T.

M

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

N

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

K

          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.
          If SIDE = 'L', M >= K >= 0;
          if SIDE = 'R', N >= K >= 0.

MB

          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 DGELQT.

V

          V is DOUBLE PRECISION array, dimension
                               (LDV,M) if SIDE = 'L',
                               (LDV,N) if SIDE = 'R'
          The i-th row must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,...,k, as returned by
          DGELQT in the first K rows of its array argument A.

LDV

          LDV is INTEGER
          The leading dimension of the array V.  LDV >= max(1,K).

T

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

LDT

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

C

          C is DOUBLE PRECISION array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by Q C, Q**T C, C Q**T or C Q.

LDC

          LDC is INTEGER
          The leading dimension of the array C. LDC >= 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.

Definition at line 166 of file dgemlqt.f.

subroutine sgemlqt (character side, character trans, integer m, integer n, integer k, integer mb, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer info)

SGEMLQT

Purpose:

 DGEMLQT overwrites the general real M-by-N matrix C with

                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      Q C            C Q
 TRANS = 'T':   Q**T C            C Q**T

 where Q is a real orthogonal matrix defined as the product of K
 elementary reflectors:

       Q = H(1) H(2) . . . H(K) = I - V T V**T

 generated using the compact WY representation as returned by SGELQT.

 Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'.
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;
          = 'C':  Transpose, apply Q**T.

M

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

N

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

K

          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.
          If SIDE = 'L', M >= K >= 0;
          if SIDE = 'R', N >= K >= 0.

MB

          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 SGELQT.

V

          V is REAL array, dimension
                               (LDV,M) if SIDE = 'L',
                               (LDV,N) if SIDE = 'R'
          The i-th row must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,...,k, as returned by
          SGELQT in the first K rows of its array argument A.

LDV

          LDV is INTEGER
          The leading dimension of the array V. LDV >= max(1,K).

T

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

LDT

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

C

          C is REAL array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by Q C, Q**T C, C Q**T or C Q.

LDC

          LDC is INTEGER
          The leading dimension of the array C. LDC >= 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.

Definition at line 151 of file sgemlqt.f.

subroutine zgemlqt (character side, character trans, integer m, integer n, integer k, integer mb, complex*16, dimension( ldv, * ) v, integer ldv, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer info)

ZGEMLQT  

Purpose:

 ZGEMLQT overwrites the general complex M-by-N matrix C with

                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      Q C            C Q
 TRANS = 'C':   Q**H C            C Q**H

 where Q is a complex unitary matrix defined as the product of K
 elementary reflectors:

       Q = H(1) H(2) . . . H(K) = I - V T V**H

 generated using the compact WY representation as returned by ZGELQT.

 Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'.
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

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

N

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

K

          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.
          If SIDE = 'L', M >= K >= 0;
          if SIDE = 'R', N >= K >= 0.

MB

          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 ZGELQT.

V

          V is COMPLEX*16 array, dimension
                               (LDV,M) if SIDE = 'L',
                               (LDV,N) if SIDE = 'R'
          The i-th row must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,...,k, as returned by
          ZGELQT in the first K rows of its array argument A.

LDV

          LDV is INTEGER
          The leading dimension of the array V. LDV >= max(1,K).

T

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

LDT

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

C

          C is COMPLEX*16 array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by Q C, Q**H C, C Q**H or C Q.

LDC

          LDC is INTEGER
          The leading dimension of the array C. LDC >= 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.

Definition at line 166 of file zgemlqt.f.

Author

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Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK