unmlq(3)

NAME
unmlq - {un,or}mlq: multiply by Q from gelqf

SYNOPSIS

  Functions
subroutine cunmlq (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
CUNMLQ
subroutine dormlq (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
DORMLQ
subroutine sormlq (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
SORMLQ
subroutine zunmlq (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
ZUNMLQ

Detailed Description

Function Documentation

  subroutine cunmlq (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)

CUNMLQ

Purpose:

     CUNMLQ 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 . . . H(2)**H H(1)**H
     as returned by CGELQF. 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,M) if SIDE = 'L',
                                   (LDA,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
              CGELQF in the first k rows of its array argument A.

    LDA

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

    TAU

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

    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 cunmlq.f.

  subroutine dormlq (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)

DORMLQ

Purpose:

     DORMLQ 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 DGELQF. 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,M) if SIDE = 'L',
                                   (LDA,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
              DGELQF in the first k rows of its array argument A.

    LDA

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

    TAU

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

    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 dormlq.f.

  subroutine sormlq (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)

SORMLQ

Purpose:

     SORMLQ 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 SGELQF. 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,M) if SIDE = 'L',
                                   (LDA,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
              SGELQF in the first k rows of its array argument A.

    LDA

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

    TAU

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

    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 sormlq.f.

  subroutine zunmlq (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)

ZUNMLQ

Purpose:

     ZUNMLQ 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 . . . H(2)**H H(1)**H
     as returned by ZGELQF. 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,M) if SIDE = 'L',
                                   (LDA,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
              ZGELQF in the first k rows of its array argument A.

    LDA

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

    TAU

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

    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 zunmlq.f.

Author

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