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Diffstat (limited to '2.3-1/src/fortran/lapack/dlaqp2.f')
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diff --git a/2.3-1/src/fortran/lapack/dlaqp2.f b/2.3-1/src/fortran/lapack/dlaqp2.f new file mode 100644 index 00000000..5ce3b162 --- /dev/null +++ b/2.3-1/src/fortran/lapack/dlaqp2.f @@ -0,0 +1,175 @@ + SUBROUTINE DLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, + $ WORK ) +* +* -- LAPACK auxiliary routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + INTEGER LDA, M, N, OFFSET +* .. +* .. Array Arguments .. + INTEGER JPVT( * ) + DOUBLE PRECISION A( LDA, * ), TAU( * ), VN1( * ), VN2( * ), + $ WORK( * ) +* .. +* +* Purpose +* ======= +* +* DLAQP2 computes a QR factorization with column pivoting of +* the block A(OFFSET+1:M,1:N). +* The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. +* +* Arguments +* ========= +* +* M (input) INTEGER +* The number of rows of the matrix A. M >= 0. +* +* N (input) INTEGER +* The number of columns of the matrix A. N >= 0. +* +* OFFSET (input) INTEGER +* The number of rows of the matrix A that must be pivoted +* but no factorized. OFFSET >= 0. +* +* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) +* On entry, the M-by-N matrix A. +* On exit, the upper triangle of block A(OFFSET+1:M,1:N) is +* the triangular factor obtained; the elements in block +* A(OFFSET+1:M,1:N) below the diagonal, together with the +* array TAU, represent the orthogonal matrix Q as a product of +* elementary reflectors. Block A(1:OFFSET,1:N) has been +* accordingly pivoted, but no factorized. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,M). +* +* JPVT (input/output) INTEGER array, dimension (N) +* On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted +* to the front of A*P (a leading column); if JPVT(i) = 0, +* the i-th column of A is a free column. +* On exit, if JPVT(i) = k, then the i-th column of A*P +* was the k-th column of A. +* +* TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) +* The scalar factors of the elementary reflectors. +* +* VN1 (input/output) DOUBLE PRECISION array, dimension (N) +* The vector with the partial column norms. +* +* VN2 (input/output) DOUBLE PRECISION array, dimension (N) +* The vector with the exact column norms. +* +* WORK (workspace) DOUBLE PRECISION array, dimension (N) +* +* Further Details +* =============== +* +* Based on contributions by +* G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain +* X. Sun, Computer Science Dept., Duke University, USA +* +* Partial column norm updating strategy modified by +* Z. Drmac and Z. Bujanovic, Dept. of Mathematics, +* University of Zagreb, Croatia. +* June 2006. +* For more details see LAPACK Working Note 176. +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO, ONE + PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I, ITEMP, J, MN, OFFPI, PVT + DOUBLE PRECISION AII, TEMP, TEMP2, TOL3Z +* .. +* .. External Subroutines .. + EXTERNAL DLARF, DLARFG, DSWAP +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, MIN, SQRT +* .. +* .. External Functions .. + INTEGER IDAMAX + DOUBLE PRECISION DLAMCH, DNRM2 + EXTERNAL IDAMAX, DLAMCH, DNRM2 +* .. +* .. Executable Statements .. +* + MN = MIN( M-OFFSET, N ) + TOL3Z = SQRT(DLAMCH('Epsilon')) +* +* Compute factorization. +* + DO 20 I = 1, MN +* + OFFPI = OFFSET + I +* +* Determine ith pivot column and swap if necessary. +* + PVT = ( I-1 ) + IDAMAX( N-I+1, VN1( I ), 1 ) +* + IF( PVT.NE.I ) THEN + CALL DSWAP( M, A( 1, PVT ), 1, A( 1, I ), 1 ) + ITEMP = JPVT( PVT ) + JPVT( PVT ) = JPVT( I ) + JPVT( I ) = ITEMP + VN1( PVT ) = VN1( I ) + VN2( PVT ) = VN2( I ) + END IF +* +* Generate elementary reflector H(i). +* + IF( OFFPI.LT.M ) THEN + CALL DLARFG( M-OFFPI+1, A( OFFPI, I ), A( OFFPI+1, I ), 1, + $ TAU( I ) ) + ELSE + CALL DLARFG( 1, A( M, I ), A( M, I ), 1, TAU( I ) ) + END IF +* + IF( I.LT.N ) THEN +* +* Apply H(i)' to A(offset+i:m,i+1:n) from the left. +* + AII = A( OFFPI, I ) + A( OFFPI, I ) = ONE + CALL DLARF( 'Left', M-OFFPI+1, N-I, A( OFFPI, I ), 1, + $ TAU( I ), A( OFFPI, I+1 ), LDA, WORK( 1 ) ) + A( OFFPI, I ) = AII + END IF +* +* Update partial column norms. +* + DO 10 J = I + 1, N + IF( VN1( J ).NE.ZERO ) THEN +* +* NOTE: The following 4 lines follow from the analysis in +* Lapack Working Note 176. +* + TEMP = ONE - ( ABS( A( OFFPI, J ) ) / VN1( J ) )**2 + TEMP = MAX( TEMP, ZERO ) + TEMP2 = TEMP*( VN1( J ) / VN2( J ) )**2 + IF( TEMP2 .LE. TOL3Z ) THEN + IF( OFFPI.LT.M ) THEN + VN1( J ) = DNRM2( M-OFFPI, A( OFFPI+1, J ), 1 ) + VN2( J ) = VN1( J ) + ELSE + VN1( J ) = ZERO + VN2( J ) = ZERO + END IF + ELSE + VN1( J ) = VN1( J )*SQRT( TEMP ) + END IF + END IF + 10 CONTINUE +* + 20 CONTINUE +* + RETURN +* +* End of DLAQP2 +* + END |