unmqr(3)

NAME
unmqr - {un,or}mqr: multiply by Q from geqrf

SYNOPSIS

  Functions
subroutine cunmqr (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
CUNMQR
subroutine dormqr (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
DORMQR
subroutine sormqr (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
SORMQR
subroutine zunmqr (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
ZUNMQR

Detailed Description

Function Documentation

  subroutine cunmqr (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)

CUNMQR

Purpose:

    !>
    !> CUNMQR 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)
    !>
    !> as returned by CGEQRF. 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
    !>          CGEQRF in the first 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 CGEQRF.
    !>

    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 cunmqr.f.

  subroutine dormqr (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)

DORMQR

Purpose:

    !>
    !> DORMQR 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)
    !>
    !> as returned by DGEQRF. 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
    !>          DGEQRF in the first 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 DGEQRF.
    !>

    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 dormqr.f.

  subroutine sormqr (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)

SORMQR

Purpose:

    !>
    !> SORMQR 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)
    !>
    !> as returned by SGEQRF. 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
    !>          SGEQRF in the first 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 SGEQRF.
    !>

    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 sormqr.f.

  subroutine zunmqr (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)

ZUNMQR

Purpose:

    !>
    !> ZUNMQR 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)
    !>
    !> as returned by ZGEQRF. 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
    !>          ZGEQRF in the first 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 ZGEQRF.
    !>

    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 zunmqr.f.

Author

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