.TH "gerqf" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME gerqf \- gerqf: RQ factor .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcgerqf\fP (m, n, a, lda, tau, work, lwork, info)" .br .RI "\fBCGERQF\fP " .ti -1c .RI "subroutine \fBdgerqf\fP (m, n, a, lda, tau, work, lwork, info)" .br .RI "\fBDGERQF\fP " .ti -1c .RI "subroutine \fBsgerqf\fP (m, n, a, lda, tau, work, lwork, info)" .br .RI "\fBSGERQF\fP " .ti -1c .RI "subroutine \fBzgerqf\fP (m, n, a, lda, tau, work, lwork, info)" .br .RI "\fBZGERQF\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine cgerqf (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer lwork, integer info)" .PP \fBCGERQF\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> CGERQF computes an RQ factorization of a complex M-by-N matrix A: !> A = R * Q\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf !> M is INTEGER !> The number of rows of the matrix A\&. M >= 0\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The number of columns of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX array, dimension (LDA,N) !> On entry, the M-by-N matrix A\&. !> On exit, !> if m <= n, the upper triangle of the subarray !> A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; !> if m >= n, the elements on and above the (m-n)-th subdiagonal !> contain the M-by-N upper trapezoidal matrix R; !> the remaining elements, with the array TAU, represent the !> unitary matrix Q as a product of min(m,n) elementary !> reflectors (see Further Details)\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,M)\&. !> .fi .PP .br \fITAU\fP .PP .nf !> TAU is COMPLEX array, dimension (min(M,N)) !> The scalar factors of the elementary reflectors (see Further !> Details)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is COMPLEX array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The dimension of the array WORK\&. !> LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise\&. !> For optimum performance LWORK >= M*NB, where NB is !> the optimal blocksize\&. !> !> 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\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf !> !> The matrix Q is represented as a product of elementary reflectors !> !> Q = H(1)**H H(2)**H \&. \&. \&. H(k)**H, where k = min(m,n)\&. !> !> Each H(i) has the form !> !> H(i) = I - tau * v * v**H !> !> where tau is a complex scalar, and v is a complex vector with !> v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on !> exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i)\&. !> .fi .PP .RE .PP .PP Definition at line \fB138\fP of file \fBcgerqf\&.f\fP\&. .SS "subroutine dgerqf (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)" .PP \fBDGERQF\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> DGERQF computes an RQ factorization of a real M-by-N matrix A: !> A = R * Q\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf !> M is INTEGER !> The number of rows of the matrix A\&. M >= 0\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The number of columns of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, the M-by-N matrix A\&. !> On exit, !> if m <= n, the upper triangle of the subarray !> A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; !> if m >= n, the elements on and above the (m-n)-th subdiagonal !> contain the M-by-N upper trapezoidal matrix R; !> the remaining elements, with the array TAU, represent the !> orthogonal matrix Q as a product of min(m,n) elementary !> reflectors (see Further Details)\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,M)\&. !> .fi .PP .br \fITAU\fP .PP .nf !> TAU is DOUBLE PRECISION array, dimension (min(M,N)) !> The scalar factors of the elementary reflectors (see Further !> Details)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The dimension of the array WORK\&. !> LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise\&. !> For optimum performance LWORK >= M*NB, where NB is !> the optimal blocksize\&. !> !> 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\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf !> !> The matrix Q is represented as a product of elementary reflectors !> !> Q = H(1) H(2) \&. \&. \&. H(k), where k = min(m,n)\&. !> !> Each H(i) has the form !> !> H(i) = I - tau * v * v**T !> !> where tau is a real scalar, and v is a real vector with !> v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in !> A(m-k+i,1:n-k+i-1), and tau in TAU(i)\&. !> .fi .PP .RE .PP .PP Definition at line \fB138\fP of file \fBdgerqf\&.f\fP\&. .SS "subroutine sgerqf (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)" .PP \fBSGERQF\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> SGERQF computes an RQ factorization of a real M-by-N matrix A: !> A = R * Q\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf !> M is INTEGER !> The number of rows of the matrix A\&. M >= 0\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The number of columns of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is REAL array, dimension (LDA,N) !> On entry, the M-by-N matrix A\&. !> On exit, !> if m <= n, the upper triangle of the subarray !> A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; !> if m >= n, the elements on and above the (m-n)-th subdiagonal !> contain the M-by-N upper trapezoidal matrix R; !> the remaining elements, with the array TAU, represent the !> orthogonal matrix Q as a product of min(m,n) elementary !> reflectors (see Further Details)\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,M)\&. !> .fi .PP .br \fITAU\fP .PP .nf !> TAU is REAL array, dimension (min(M,N)) !> The scalar factors of the elementary reflectors (see Further !> Details)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is REAL array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The dimension of the array WORK\&. !> LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise\&. !> For optimum performance LWORK >= M*NB, where NB is !> the optimal blocksize\&. !> !> 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\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf !> !> The matrix Q is represented as a product of elementary reflectors !> !> Q = H(1) H(2) \&. \&. \&. H(k), where k = min(m,n)\&. !> !> Each H(i) has the form !> !> H(i) = I - tau * v * v**T !> !> where tau is a real scalar, and v is a real vector with !> v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in !> A(m-k+i,1:n-k+i-1), and tau in TAU(i)\&. !> .fi .PP .RE .PP .PP Definition at line \fB138\fP of file \fBsgerqf\&.f\fP\&. .SS "subroutine zgerqf (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)" .PP \fBZGERQF\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> ZGERQF computes an RQ factorization of a complex M-by-N matrix A: !> A = R * Q\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf !> M is INTEGER !> The number of rows of the matrix A\&. M >= 0\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The number of columns of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the M-by-N matrix A\&. !> On exit, !> if m <= n, the upper triangle of the subarray !> A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; !> if m >= n, the elements on and above the (m-n)-th subdiagonal !> contain the M-by-N upper trapezoidal matrix R; !> the remaining elements, with the array TAU, represent the !> unitary matrix Q as a product of min(m,n) elementary !> reflectors (see Further Details)\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,M)\&. !> .fi .PP .br \fITAU\fP .PP .nf !> TAU is COMPLEX*16 array, dimension (min(M,N)) !> The scalar factors of the elementary reflectors (see Further !> Details)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The dimension of the array WORK\&. !> LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise\&. !> For optimum performance LWORK >= M*NB, where NB is !> the optimal blocksize\&. !> !> 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\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf !> !> The matrix Q is represented as a product of elementary reflectors !> !> Q = H(1)**H H(2)**H \&. \&. \&. H(k)**H, where k = min(m,n)\&. !> !> Each H(i) has the form !> !> H(i) = I - tau * v * v**H !> !> where tau is a complex scalar, and v is a complex vector with !> v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on !> exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i)\&. !> .fi .PP .RE .PP .PP Definition at line \fB138\fP of file \fBzgerqf\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.