unmql(3)

NAME
unmql - {un,or}mql: multiply by Q from geqlf

SYNOPSIS

  Functions
subroutine cunmql (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
CUNMQL
subroutine dormql (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
DORMQL
subroutine sormql (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
SORMQL
subroutine zunmql (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
ZUNMQL

Detailed Description

Function Documentation

  subroutine cunmql (character side, character trans, integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer lwork, integer info)

CUNMQL

Purpose:

     CUNMQL 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(k) . . . H(2) H(1)
     as returned by CGEQLF. 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.

    A

              A is COMPLEX array, dimension (LDA,K)
              The i-th column must contain the vector which defines the
              elementary reflector H(i), for i = 1,2,...,k, as returned by
              CGEQLF in the last k columns of its array argument A.

    LDA

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

    TAU

              TAU is COMPLEX array, dimension (K)
              TAU(i) must contain the scalar factor of the elementary
              reflector H(i), as returned by CGEQLF.

    C

              C is COMPLEX array, dimension (LDC,N)
              On entry, the M-by-N matrix C.
              On exit, C is overwritten by Q*C or Q**H*C or 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, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.
              If SIDE = 'L', LWORK >= max(1,N);
              if SIDE = 'R', LWORK >= max(1,M).
              For good performance, LWORK should generally be larger.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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 cunmql.f.

  subroutine dormql (character side, character trans, integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info)

DORMQL

Purpose:

     DORMQL 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(k) . . . H(2) H(1)
     as returned by DGEQLF. 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;
              = 'T':  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.

    A

              A is DOUBLE PRECISION array, dimension (LDA,K)
              The i-th column must contain the vector which defines the
              elementary reflector H(i), for i = 1,2,...,k, as returned by
              DGEQLF in the last k columns of its array argument A.

    LDA

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

    TAU

              TAU is DOUBLE PRECISION array, dimension (K)
              TAU(i) must contain the scalar factor of the elementary
              reflector H(i), as returned by DGEQLF.

    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 or Q**T*C or 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, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.
              If SIDE = 'L', LWORK >= max(1,N);
              if SIDE = 'R', LWORK >= max(1,M).
              For good performance, LWORK should generally be larger.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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 165 of file dormql.f.

  subroutine sormql (character side, character trans, integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer lwork, integer info)

SORMQL

Purpose:

     SORMQL 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(k) . . . H(2) H(1)
     as returned by SGEQLF. 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;
              = 'T':  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.

    A

              A is REAL array, dimension (LDA,K)
              The i-th column must contain the vector which defines the
              elementary reflector H(i), for i = 1,2,...,k, as returned by
              SGEQLF in the last k columns of its array argument A.

    LDA

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

    TAU

              TAU is REAL array, dimension (K)
              TAU(i) must contain the scalar factor of the elementary
              reflector H(i), as returned by SGEQLF.

    C

              C is REAL array, dimension (LDC,N)
              On entry, the M-by-N matrix C.
              On exit, C is overwritten by Q*C or Q**T*C or 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, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.
              If SIDE = 'L', LWORK >= max(1,N);
              if SIDE = 'R', LWORK >= max(1,M).
              For good performance, LWORK should generally be larger.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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 sormql.f.

  subroutine zunmql (character side, character trans, integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer lwork, integer info)

ZUNMQL

Purpose:

     ZUNMQL 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(k) . . . H(2) H(1)
     as returned by ZGEQLF. 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.

    A

              A is COMPLEX*16 array, dimension (LDA,K)
              The i-th column must contain the vector which defines the
              elementary reflector H(i), for i = 1,2,...,k, as returned by
              ZGEQLF in the last k columns of its array argument A.

    LDA

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

    TAU

              TAU is COMPLEX*16 array, dimension (K)
              TAU(i) must contain the scalar factor of the elementary
              reflector H(i), as returned by ZGEQLF.

    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 or Q**H*C or 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, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.
              If SIDE = 'L', LWORK >= max(1,N);
              if SIDE = 'R', LWORK >= max(1,M).
              For good performance, LWORK should generally be larger.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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 165 of file zunmql.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.