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version 1.7, 2016/08/27 15:34:46
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version 1.8, 2017/06/17 10:54:10
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| * |
* |
| * =========== DOCUMENTATION =========== |
* =========== DOCUMENTATION =========== |
| * |
* |
| * Online html documentation available at |
* Online html documentation available at |
| * http://www.netlib.org/lapack/explore-html/ |
* http://www.netlib.org/lapack/explore-html/ |
| * |
* |
| *> \htmlonly |
*> \htmlonly |
| *> Download ZGEQRT3 + dependencies |
*> Download ZGEQRT3 + dependencies |
| *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgeqrt3.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgeqrt3.f"> |
| *> [TGZ]</a> |
*> [TGZ]</a> |
| *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgeqrt3.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgeqrt3.f"> |
| *> [ZIP]</a> |
*> [ZIP]</a> |
| *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgeqrt3.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgeqrt3.f"> |
| *> [TXT]</a> |
*> [TXT]</a> |
| *> \endhtmlonly |
*> \endhtmlonly |
| * |
* |
| * Definition: |
* Definition: |
| * =========== |
* =========== |
| * |
* |
| * RECURSIVE SUBROUTINE ZGEQRT3( M, N, A, LDA, T, LDT, INFO ) |
* RECURSIVE SUBROUTINE ZGEQRT3( M, N, A, LDA, T, LDT, INFO ) |
| * |
* |
| * .. Scalar Arguments .. |
* .. Scalar Arguments .. |
| * INTEGER INFO, LDA, M, N, LDT |
* INTEGER INFO, LDA, M, N, LDT |
| * .. |
* .. |
| * .. Array Arguments .. |
* .. Array Arguments .. |
| * COMPLEX*16 A( LDA, * ), T( LDT, * ) |
* COMPLEX*16 A( LDA, * ), T( LDT, * ) |
| * .. |
* .. |
| * |
* |
| * |
* |
| *> \par Purpose: |
*> \par Purpose: |
| * ============= |
* ============= |
| *> |
*> |
| *> \verbatim |
*> \verbatim |
| *> |
*> |
| *> ZGEQRT3 recursively computes a QR factorization of a complex M-by-N |
*> ZGEQRT3 recursively computes a QR factorization of a complex M-by-N |
| *> matrix A, using the compact WY representation of Q. |
*> matrix A, using the compact WY representation of Q. |
| *> |
*> |
| *> Based on the algorithm of Elmroth and Gustavson, |
*> Based on the algorithm of Elmroth and Gustavson, |
| *> IBM J. Res. Develop. Vol 44 No. 4 July 2000. |
*> IBM J. Res. Develop. Vol 44 No. 4 July 2000. |
| *> \endverbatim |
*> \endverbatim |
| * |
* |
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| *> \param[in,out] A |
*> \param[in,out] A |
| *> \verbatim |
*> \verbatim |
| *> A is COMPLEX*16 array, dimension (LDA,N) |
*> A is COMPLEX*16 array, dimension (LDA,N) |
| *> On entry, the complex M-by-N matrix A. On exit, the elements on |
*> On entry, the complex M-by-N matrix A. On exit, the elements on |
| *> and above the diagonal contain the N-by-N upper triangular matrix R; |
*> and above the diagonal contain the N-by-N upper triangular matrix R; |
| *> the elements below the diagonal are the columns of V. See below for |
*> the elements below the diagonal are the columns of V. See below for |
| *> further details. |
*> further details. |
|
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| * Authors: |
* Authors: |
| * ======== |
* ======== |
| * |
* |
| *> \author Univ. of Tennessee |
*> \author Univ. of Tennessee |
| *> \author Univ. of California Berkeley |
*> \author Univ. of California Berkeley |
| *> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
| *> \author NAG Ltd. |
*> \author NAG Ltd. |
| * |
* |
| *> \date June 2016 |
*> \date June 2016 |
| * |
* |
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| * ===================================================================== |
* ===================================================================== |
| RECURSIVE SUBROUTINE ZGEQRT3( M, N, A, LDA, T, LDT, INFO ) |
RECURSIVE SUBROUTINE ZGEQRT3( M, N, A, LDA, T, LDT, INFO ) |
| * |
* |
| * -- LAPACK computational routine (version 3.6.1) -- |
* -- LAPACK computational routine (version 3.7.0) -- |
| * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
| * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
| * June 2016 |
* June 2016 |
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| * Compute Householder transform when N=1 |
* Compute Householder transform when N=1 |
| * |
* |
| CALL ZLARFG( M, A(1,1), A( MIN( 2, M ), 1 ), 1, T(1,1) ) |
CALL ZLARFG( M, A(1,1), A( MIN( 2, M ), 1 ), 1, T(1,1) ) |
| * |
* |
| ELSE |
ELSE |
| * |
* |
| * Otherwise, split A into blocks... |
* Otherwise, split A into blocks... |
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| T( I, J+N1 ) = A( I, J+N1 ) |
T( I, J+N1 ) = A( I, J+N1 ) |
| END DO |
END DO |
| END DO |
END DO |
| CALL ZTRMM( 'L', 'L', 'C', 'U', N1, N2, ONE, |
CALL ZTRMM( 'L', 'L', 'C', 'U', N1, N2, ONE, |
| & A, LDA, T( 1, J1 ), LDT ) |
& A, LDA, T( 1, J1 ), LDT ) |
| * |
* |
| CALL ZGEMM( 'C', 'N', N1, N2, M-N1, ONE, A( J1, 1 ), LDA, |
CALL ZGEMM( 'C', 'N', N1, N2, M-N1, ONE, A( J1, 1 ), LDA, |
|
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| CALL ZTRMM( 'L', 'U', 'C', 'N', N1, N2, ONE, |
CALL ZTRMM( 'L', 'U', 'C', 'N', N1, N2, ONE, |
| & T, LDT, T( 1, J1 ), LDT ) |
& T, LDT, T( 1, J1 ), LDT ) |
| * |
* |
| CALL ZGEMM( 'N', 'N', M-N1, N2, N1, -ONE, A( J1, 1 ), LDA, |
CALL ZGEMM( 'N', 'N', M-N1, N2, N1, -ONE, A( J1, 1 ), LDA, |
| & T( 1, J1 ), LDT, ONE, A( J1, J1 ), LDA ) |
& T( 1, J1 ), LDT, ONE, A( J1, J1 ), LDA ) |
| * |
* |
| CALL ZTRMM( 'L', 'L', 'N', 'U', N1, N2, ONE, |
CALL ZTRMM( 'L', 'L', 'N', 'U', N1, N2, ONE, |
|
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| * |
* |
| * Compute A(J1:M,J1:N) <- (Y2,R2,T2) where Q2 = I - Y2 T2 Y2^H |
* Compute A(J1:M,J1:N) <- (Y2,R2,T2) where Q2 = I - Y2 T2 Y2^H |
| * |
* |
| CALL ZGEQRT3( M-N1, N2, A( J1, J1 ), LDA, |
CALL ZGEQRT3( M-N1, N2, A( J1, J1 ), LDA, |
| & T( J1, J1 ), LDT, IINFO ) |
& T( J1, J1 ), LDT, IINFO ) |
| * |
* |
| * Compute T3 = T(1:N1,J1:N) = -T1 Y1^H Y2 T2 |
* Compute T3 = T(1:N1,J1:N) = -T1 Y1^H Y2 T2 |
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| CALL ZTRMM( 'R', 'L', 'N', 'U', N1, N2, ONE, |
CALL ZTRMM( 'R', 'L', 'N', 'U', N1, N2, ONE, |
| & A( J1, J1 ), LDA, T( 1, J1 ), LDT ) |
& A( J1, J1 ), LDA, T( 1, J1 ), LDT ) |
| * |
* |
| CALL ZGEMM( 'C', 'N', N1, N2, M-N, ONE, A( I1, 1 ), LDA, |
CALL ZGEMM( 'C', 'N', N1, N2, M-N, ONE, A( I1, 1 ), LDA, |
| & A( I1, J1 ), LDA, ONE, T( 1, J1 ), LDT ) |
& A( I1, J1 ), LDA, ONE, T( 1, J1 ), LDT ) |
| * |
* |
| CALL ZTRMM( 'L', 'U', 'N', 'N', N1, N2, -ONE, T, LDT, |
CALL ZTRMM( 'L', 'U', 'N', 'N', N1, N2, -ONE, T, LDT, |
| & T( 1, J1 ), LDT ) |
& T( 1, J1 ), LDT ) |
| * |
* |
| CALL ZTRMM( 'R', 'U', 'N', 'N', N1, N2, ONE, |
CALL ZTRMM( 'R', 'U', 'N', 'N', N1, N2, ONE, |
| & T( J1, J1 ), LDT, T( 1, J1 ), LDT ) |
& T( J1, J1 ), LDT, T( 1, J1 ), LDT ) |
| * |
* |
| * Y = (Y1,Y2); R = [ R1 A(1:N1,J1:N) ]; T = [T1 T3] |
* Y = (Y1,Y2); R = [ R1 A(1:N1,J1:N) ]; T = [T1 T3] |
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