--- rpl/lapack/lapack/zggqrf.f 2011/07/22 07:38:14 1.8
+++ rpl/lapack/lapack/zggqrf.f 2011/11/21 20:43:10 1.9
@@ -1,10 +1,224 @@
+*> \brief \b ZGGQRF
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZGGQRF + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZGGQRF( N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK,
+* LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER INFO, LDA, LDB, LWORK, M, N, P
+* ..
+* .. Array Arguments ..
+* COMPLEX*16 A( LDA, * ), B( LDB, * ), TAUA( * ), TAUB( * ),
+* $ WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZGGQRF computes a generalized QR factorization of an N-by-M matrix A
+*> and an N-by-P matrix B:
+*>
+*> A = Q*R, B = Q*T*Z,
+*>
+*> where Q is an N-by-N unitary matrix, Z is a P-by-P unitary matrix,
+*> and R and T assume one of the forms:
+*>
+*> if N >= M, R = ( R11 ) M , or if N < M, R = ( R11 R12 ) N,
+*> ( 0 ) N-M N M-N
+*> M
+*>
+*> where R11 is upper triangular, and
+*>
+*> if N <= P, T = ( 0 T12 ) N, or if N > P, T = ( T11 ) N-P,
+*> P-N N ( T21 ) P
+*> P
+*>
+*> where T12 or T21 is upper triangular.
+*>
+*> In particular, if B is square and nonsingular, the GQR factorization
+*> of A and B implicitly gives the QR factorization of inv(B)*A:
+*>
+*> inv(B)*A = Z**H * (inv(T)*R)
+*>
+*> where inv(B) denotes the inverse of the matrix B, and Z**H denotes the
+*> conjugate transpose of matrix Z.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of rows of the matrices A and B. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The number of columns of the matrix A. M >= 0.
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*> P is INTEGER
+*> The number of columns of the matrix B. P >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,M)
+*> On entry, the N-by-M matrix A.
+*> On exit, the elements on and above the diagonal of the array
+*> contain the min(N,M)-by-M upper trapezoidal matrix R (R is
+*> upper triangular if N >= M); the elements below the diagonal,
+*> with the array TAUA, represent the unitary matrix Q as a
+*> product of min(N,M) elementary reflectors (see Further
+*> Details).
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] TAUA
+*> \verbatim
+*> TAUA is COMPLEX*16 array, dimension (min(N,M))
+*> The scalar factors of the elementary reflectors which
+*> represent the unitary matrix Q (see Further Details).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is COMPLEX*16 array, dimension (LDB,P)
+*> On entry, the N-by-P matrix B.
+*> On exit, if N <= P, the upper triangle of the subarray
+*> B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;
+*> if N > P, the elements on and above the (N-P)-th subdiagonal
+*> contain the N-by-P upper trapezoidal matrix T; the remaining
+*> elements, with the array TAUB, represent the unitary
+*> matrix Z as a product of elementary reflectors (see Further
+*> Details).
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] TAUB
+*> \verbatim
+*> TAUB is COMPLEX*16 array, dimension (min(N,P))
+*> The scalar factors of the elementary reflectors which
+*> represent the unitary matrix Z (see Further Details).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The dimension of the array WORK. LWORK >= max(1,N,M,P).
+*> For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3),
+*> where NB1 is the optimal blocksize for the QR factorization
+*> of an N-by-M matrix, NB2 is the optimal blocksize for the
+*> RQ factorization of an N-by-P matrix, and NB3 is the optimal
+*> blocksize for a call of ZUNMQR.
+*>
+*> 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.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup complex16OTHERcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> The matrix Q is represented as a product of elementary reflectors
+*>
+*> Q = H(1) H(2) . . . H(k), where k = min(n,m).
+*>
+*> Each H(i) has the form
+*>
+*> H(i) = I - taua * v * v**H
+*>
+*> where taua is a complex scalar, and v is a complex vector with
+*> v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
+*> and taua in TAUA(i).
+*> To form Q explicitly, use LAPACK subroutine ZUNGQR.
+*> To use Q to update another matrix, use LAPACK subroutine ZUNMQR.
+*>
+*> The matrix Z is represented as a product of elementary reflectors
+*>
+*> Z = H(1) H(2) . . . H(k), where k = min(n,p).
+*>
+*> Each H(i) has the form
+*>
+*> H(i) = I - taub * v * v**H
+*>
+*> where taub is a complex scalar, and v is a complex vector with
+*> v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in
+*> B(n-k+i,1:p-k+i-1), and taub in TAUB(i).
+*> To form Z explicitly, use LAPACK subroutine ZUNGRQ.
+*> To use Z to update another matrix, use LAPACK subroutine ZUNMRQ.
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE ZGGQRF( N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK,
$ LWORK, INFO )
*
-* -- LAPACK routine (version 3.3.1) --
+* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* -- April 2011 --
+* November 2011
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LWORK, M, N, P
@@ -14,133 +228,6 @@
$ WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* ZGGQRF computes a generalized QR factorization of an N-by-M matrix A
-* and an N-by-P matrix B:
-*
-* A = Q*R, B = Q*T*Z,
-*
-* where Q is an N-by-N unitary matrix, Z is a P-by-P unitary matrix,
-* and R and T assume one of the forms:
-*
-* if N >= M, R = ( R11 ) M , or if N < M, R = ( R11 R12 ) N,
-* ( 0 ) N-M N M-N
-* M
-*
-* where R11 is upper triangular, and
-*
-* if N <= P, T = ( 0 T12 ) N, or if N > P, T = ( T11 ) N-P,
-* P-N N ( T21 ) P
-* P
-*
-* where T12 or T21 is upper triangular.
-*
-* In particular, if B is square and nonsingular, the GQR factorization
-* of A and B implicitly gives the QR factorization of inv(B)*A:
-*
-* inv(B)*A = Z**H * (inv(T)*R)
-*
-* where inv(B) denotes the inverse of the matrix B, and Z**H denotes the
-* conjugate transpose of matrix Z.
-*
-* Arguments
-* =========
-*
-* N (input) INTEGER
-* The number of rows of the matrices A and B. N >= 0.
-*
-* M (input) INTEGER
-* The number of columns of the matrix A. M >= 0.
-*
-* P (input) INTEGER
-* The number of columns of the matrix B. P >= 0.
-*
-* A (input/output) COMPLEX*16 array, dimension (LDA,M)
-* On entry, the N-by-M matrix A.
-* On exit, the elements on and above the diagonal of the array
-* contain the min(N,M)-by-M upper trapezoidal matrix R (R is
-* upper triangular if N >= M); the elements below the diagonal,
-* with the array TAUA, represent the unitary matrix Q as a
-* product of min(N,M) elementary reflectors (see Further
-* Details).
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* TAUA (output) COMPLEX*16 array, dimension (min(N,M))
-* The scalar factors of the elementary reflectors which
-* represent the unitary matrix Q (see Further Details).
-*
-* B (input/output) COMPLEX*16 array, dimension (LDB,P)
-* On entry, the N-by-P matrix B.
-* On exit, if N <= P, the upper triangle of the subarray
-* B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;
-* if N > P, the elements on and above the (N-P)-th subdiagonal
-* contain the N-by-P upper trapezoidal matrix T; the remaining
-* elements, with the array TAUB, represent the unitary
-* matrix Z as a product of elementary reflectors (see Further
-* Details).
-*
-* LDB (input) INTEGER
-* The leading dimension of the array B. LDB >= max(1,N).
-*
-* TAUB (output) COMPLEX*16 array, dimension (min(N,P))
-* The scalar factors of the elementary reflectors which
-* represent the unitary matrix Z (see Further Details).
-*
-* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
-* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
-*
-* LWORK (input) INTEGER
-* The dimension of the array WORK. LWORK >= max(1,N,M,P).
-* For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3),
-* where NB1 is the optimal blocksize for the QR factorization
-* of an N-by-M matrix, NB2 is the optimal blocksize for the
-* RQ factorization of an N-by-P matrix, and NB3 is the optimal
-* blocksize for a call of ZUNMQR.
-*
-* 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 (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value.
-*
-* Further Details
-* ===============
-*
-* The matrix Q is represented as a product of elementary reflectors
-*
-* Q = H(1) H(2) . . . H(k), where k = min(n,m).
-*
-* Each H(i) has the form
-*
-* H(i) = I - taua * v * v**H
-*
-* where taua is a complex scalar, and v is a complex vector with
-* v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
-* and taua in TAUA(i).
-* To form Q explicitly, use LAPACK subroutine ZUNGQR.
-* To use Q to update another matrix, use LAPACK subroutine ZUNMQR.
-*
-* The matrix Z is represented as a product of elementary reflectors
-*
-* Z = H(1) H(2) . . . H(k), where k = min(n,p).
-*
-* Each H(i) has the form
-*
-* H(i) = I - taub * v * v**H
-*
-* where taub is a complex scalar, and v is a complex vector with
-* v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in
-* B(n-k+i,1:p-k+i-1), and taub in TAUB(i).
-* To form Z explicitly, use LAPACK subroutine ZUNGRQ.
-* To use Z to update another matrix, use LAPACK subroutine ZUNMRQ.
-*
* =====================================================================
*
* .. Local Scalars ..