.TH "ungbr" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME ungbr \- {un,or}gbr: generate Q, P from gebrd .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcungbr\fP (vect, m, n, k, a, lda, tau, work, lwork, info)" .br .RI "\fBCUNGBR\fP " .ti -1c .RI "subroutine \fBdorgbr\fP (vect, m, n, k, a, lda, tau, work, lwork, info)" .br .RI "\fBDORGBR\fP " .ti -1c .RI "subroutine \fBsorgbr\fP (vect, m, n, k, a, lda, tau, work, lwork, info)" .br .RI "\fBSORGBR\fP " .ti -1c .RI "subroutine \fBzungbr\fP (vect, m, n, k, a, lda, tau, work, lwork, info)" .br .RI "\fBZUNGBR\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine cungbr (character vect, integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer lwork, integer info)" .PP \fBCUNGBR\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> CUNGBR generates one of the complex unitary matrices Q or P**H !> determined by CGEBRD when reducing a complex matrix A to bidiagonal !> form: A = Q * B * P**H\&. Q and P**H are defined as products of !> elementary reflectors H(i) or G(i) respectively\&. !> !> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q !> is of order M: !> if m >= k, Q = H(1) H(2) \&. \&. \&. H(k) and CUNGBR returns the first n !> columns of Q, where m >= n >= k; !> if m < k, Q = H(1) H(2) \&. \&. \&. H(m-1) and CUNGBR returns Q as an !> M-by-M matrix\&. !> !> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H !> is of order N: !> if k < n, P**H = G(k) \&. \&. \&. G(2) G(1) and CUNGBR returns the first m !> rows of P**H, where n >= m >= k; !> if k >= n, P**H = G(n-1) \&. \&. \&. G(2) G(1) and CUNGBR returns P**H as !> an N-by-N matrix\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIVECT\fP .PP .nf !> VECT is CHARACTER*1 !> Specifies whether the matrix Q or the matrix P**H is !> required, as defined in the transformation applied by CGEBRD: !> = 'Q': generate Q; !> = 'P': generate P**H\&. !> .fi .PP .br \fIM\fP .PP .nf !> M is INTEGER !> The number of rows of the matrix Q or P**H to be returned\&. !> M >= 0\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The number of columns of the matrix Q or P**H to be returned\&. !> N >= 0\&. !> If VECT = 'Q', M >= N >= min(M,K); !> if VECT = 'P', N >= M >= min(N,K)\&. !> .fi .PP .br \fIK\fP .PP .nf !> K is INTEGER !> If VECT = 'Q', the number of columns in the original M-by-K !> matrix reduced by CGEBRD\&. !> If VECT = 'P', the number of rows in the original K-by-N !> matrix reduced by CGEBRD\&. !> K >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX array, dimension (LDA,N) !> On entry, the vectors which define the elementary reflectors, !> as returned by CGEBRD\&. !> On exit, the M-by-N matrix Q or P**H\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= M\&. !> .fi .PP .br \fITAU\fP .PP .nf !> TAU is COMPLEX array, dimension !> (min(M,K)) if VECT = 'Q' !> (min(N,K)) if VECT = 'P' !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i) or G(i), which determines Q or P**H, as !> returned by CGEBRD in its array argument TAUQ or TAUP\&. !> .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 >= max(1,min(M,N))\&. !> For optimum performance LWORK >= min(M,N)*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 .PP Definition at line \fB156\fP of file \fBcungbr\&.f\fP\&. .SS "subroutine dorgbr (character vect, integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)" .PP \fBDORGBR\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> DORGBR generates one of the real orthogonal matrices Q or P**T !> determined by DGEBRD when reducing a real matrix A to bidiagonal !> form: A = Q * B * P**T\&. Q and P**T are defined as products of !> elementary reflectors H(i) or G(i) respectively\&. !> !> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q !> is of order M: !> if m >= k, Q = H(1) H(2) \&. \&. \&. H(k) and DORGBR returns the first n !> columns of Q, where m >= n >= k; !> if m < k, Q = H(1) H(2) \&. \&. \&. H(m-1) and DORGBR returns Q as an !> M-by-M matrix\&. !> !> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T !> is of order N: !> if k < n, P**T = G(k) \&. \&. \&. G(2) G(1) and DORGBR returns the first m !> rows of P**T, where n >= m >= k; !> if k >= n, P**T = G(n-1) \&. \&. \&. G(2) G(1) and DORGBR returns P**T as !> an N-by-N matrix\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIVECT\fP .PP .nf !> VECT is CHARACTER*1 !> Specifies whether the matrix Q or the matrix P**T is !> required, as defined in the transformation applied by DGEBRD: !> = 'Q': generate Q; !> = 'P': generate P**T\&. !> .fi .PP .br \fIM\fP .PP .nf !> M is INTEGER !> The number of rows of the matrix Q or P**T to be returned\&. !> M >= 0\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The number of columns of the matrix Q or P**T to be returned\&. !> N >= 0\&. !> If VECT = 'Q', M >= N >= min(M,K); !> if VECT = 'P', N >= M >= min(N,K)\&. !> .fi .PP .br \fIK\fP .PP .nf !> K is INTEGER !> If VECT = 'Q', the number of columns in the original M-by-K !> matrix reduced by DGEBRD\&. !> If VECT = 'P', the number of rows in the original K-by-N !> matrix reduced by DGEBRD\&. !> K >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, the vectors which define the elementary reflectors, !> as returned by DGEBRD\&. !> On exit, the M-by-N matrix Q or P**T\&. !> .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,K)) if VECT = 'Q' !> (min(N,K)) if VECT = 'P' !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i) or G(i), which determines Q or P**T, as !> returned by DGEBRD in its array argument TAUQ or TAUP\&. !> .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 >= max(1,min(M,N))\&. !> For optimum performance LWORK >= min(M,N)*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 .PP Definition at line \fB156\fP of file \fBdorgbr\&.f\fP\&. .SS "subroutine sorgbr (character vect, integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)" .PP \fBSORGBR\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> SORGBR generates one of the real orthogonal matrices Q or P**T !> determined by SGEBRD when reducing a real matrix A to bidiagonal !> form: A = Q * B * P**T\&. Q and P**T are defined as products of !> elementary reflectors H(i) or G(i) respectively\&. !> !> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q !> is of order M: !> if m >= k, Q = H(1) H(2) \&. \&. \&. H(k) and SORGBR returns the first n !> columns of Q, where m >= n >= k; !> if m < k, Q = H(1) H(2) \&. \&. \&. H(m-1) and SORGBR returns Q as an !> M-by-M matrix\&. !> !> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T !> is of order N: !> if k < n, P**T = G(k) \&. \&. \&. G(2) G(1) and SORGBR returns the first m !> rows of P**T, where n >= m >= k; !> if k >= n, P**T = G(n-1) \&. \&. \&. G(2) G(1) and SORGBR returns P**T as !> an N-by-N matrix\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIVECT\fP .PP .nf !> VECT is CHARACTER*1 !> Specifies whether the matrix Q or the matrix P**T is !> required, as defined in the transformation applied by SGEBRD: !> = 'Q': generate Q; !> = 'P': generate P**T\&. !> .fi .PP .br \fIM\fP .PP .nf !> M is INTEGER !> The number of rows of the matrix Q or P**T to be returned\&. !> M >= 0\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The number of columns of the matrix Q or P**T to be returned\&. !> N >= 0\&. !> If VECT = 'Q', M >= N >= min(M,K); !> if VECT = 'P', N >= M >= min(N,K)\&. !> .fi .PP .br \fIK\fP .PP .nf !> K is INTEGER !> If VECT = 'Q', the number of columns in the original M-by-K !> matrix reduced by SGEBRD\&. !> If VECT = 'P', the number of rows in the original K-by-N !> matrix reduced by SGEBRD\&. !> K >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is REAL array, dimension (LDA,N) !> On entry, the vectors which define the elementary reflectors, !> as returned by SGEBRD\&. !> On exit, the M-by-N matrix Q or P**T\&. !> .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,K)) if VECT = 'Q' !> (min(N,K)) if VECT = 'P' !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i) or G(i), which determines Q or P**T, as !> returned by SGEBRD in its array argument TAUQ or TAUP\&. !> .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 >= max(1,min(M,N))\&. !> For optimum performance LWORK >= min(M,N)*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 .PP Definition at line \fB156\fP of file \fBsorgbr\&.f\fP\&. .SS "subroutine zungbr (character vect, integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)" .PP \fBZUNGBR\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> ZUNGBR generates one of the complex unitary matrices Q or P**H !> determined by ZGEBRD when reducing a complex matrix A to bidiagonal !> form: A = Q * B * P**H\&. Q and P**H are defined as products of !> elementary reflectors H(i) or G(i) respectively\&. !> !> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q !> is of order M: !> if m >= k, Q = H(1) H(2) \&. \&. \&. H(k) and ZUNGBR returns the first n !> columns of Q, where m >= n >= k; !> if m < k, Q = H(1) H(2) \&. \&. \&. H(m-1) and ZUNGBR returns Q as an !> M-by-M matrix\&. !> !> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H !> is of order N: !> if k < n, P**H = G(k) \&. \&. \&. G(2) G(1) and ZUNGBR returns the first m !> rows of P**H, where n >= m >= k; !> if k >= n, P**H = G(n-1) \&. \&. \&. G(2) G(1) and ZUNGBR returns P**H as !> an N-by-N matrix\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIVECT\fP .PP .nf !> VECT is CHARACTER*1 !> Specifies whether the matrix Q or the matrix P**H is !> required, as defined in the transformation applied by ZGEBRD: !> = 'Q': generate Q; !> = 'P': generate P**H\&. !> .fi .PP .br \fIM\fP .PP .nf !> M is INTEGER !> The number of rows of the matrix Q or P**H to be returned\&. !> M >= 0\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The number of columns of the matrix Q or P**H to be returned\&. !> N >= 0\&. !> If VECT = 'Q', M >= N >= min(M,K); !> if VECT = 'P', N >= M >= min(N,K)\&. !> .fi .PP .br \fIK\fP .PP .nf !> K is INTEGER !> If VECT = 'Q', the number of columns in the original M-by-K !> matrix reduced by ZGEBRD\&. !> If VECT = 'P', the number of rows in the original K-by-N !> matrix reduced by ZGEBRD\&. !> K >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the vectors which define the elementary reflectors, !> as returned by ZGEBRD\&. !> On exit, the M-by-N matrix Q or P**H\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= M\&. !> .fi .PP .br \fITAU\fP .PP .nf !> TAU is COMPLEX*16 array, dimension !> (min(M,K)) if VECT = 'Q' !> (min(N,K)) if VECT = 'P' !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i) or G(i), which determines Q or P**H, as !> returned by ZGEBRD in its array argument TAUQ or TAUP\&. !> .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 >= max(1,min(M,N))\&. !> For optimum performance LWORK >= min(M,N)*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 .PP Definition at line \fB156\fP of file \fBzungbr\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.