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SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) |
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IMPLICIT NONE |
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* |
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* -- LAPACK auxiliary routine (version 3.2) -- |
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* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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* November 2006 |
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* |
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* .. Scalar Arguments .. |
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CHARACTER DIRECT, STOREV |
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INTEGER K, LDT, LDV, N |
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* .. |
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* .. Array Arguments .. |
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DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) |
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* .. |
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* |
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* Purpose |
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* ======= |
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* |
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* DLARFT forms the triangular factor T of a real block reflector H |
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* of order n, which is defined as a product of k elementary reflectors. |
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* |
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* If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; |
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* |
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* If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. |
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* |
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* If STOREV = 'C', the vector which defines the elementary reflector |
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* H(i) is stored in the i-th column of the array V, and |
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* |
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* H = I - V * T * V' |
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* |
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* If STOREV = 'R', the vector which defines the elementary reflector |
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* H(i) is stored in the i-th row of the array V, and |
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* |
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* H = I - V' * T * V |
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* |
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* Arguments |
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* ========= |
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* |
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* DIRECT (input) CHARACTER*1 |
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* Specifies the order in which the elementary reflectors are |
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* multiplied to form the block reflector: |
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* = 'F': H = H(1) H(2) . . . H(k) (Forward) |
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* = 'B': H = H(k) . . . H(2) H(1) (Backward) |
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* |
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* STOREV (input) CHARACTER*1 |
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* Specifies how the vectors which define the elementary |
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* reflectors are stored (see also Further Details): |
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* = 'C': columnwise |
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* = 'R': rowwise |
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* |
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* N (input) INTEGER |
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* The order of the block reflector H. N >= 0. |
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* |
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* K (input) INTEGER |
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* The order of the triangular factor T (= the number of |
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* elementary reflectors). K >= 1. |
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* |
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* V (input/output) DOUBLE PRECISION array, dimension |
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* (LDV,K) if STOREV = 'C' |
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* (LDV,N) if STOREV = 'R' |
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* The matrix V. See further details. |
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* |
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* LDV (input) INTEGER |
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* The leading dimension of the array V. |
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* If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. |
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* |
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* TAU (input) DOUBLE PRECISION array, dimension (K) |
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* TAU(i) must contain the scalar factor of the elementary |
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* reflector H(i). |
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* |
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* T (output) DOUBLE PRECISION array, dimension (LDT,K) |
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* The k by k triangular factor T of the block reflector. |
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* If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is |
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* lower triangular. The rest of the array is not used. |
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* |
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* LDT (input) INTEGER |
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* The leading dimension of the array T. LDT >= K. |
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* |
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* Further Details |
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* =============== |
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* |
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* The shape of the matrix V and the storage of the vectors which define |
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* the H(i) is best illustrated by the following example with n = 5 and |
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* k = 3. The elements equal to 1 are not stored; the corresponding |
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* array elements are modified but restored on exit. The rest of the |
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* array is not used. |
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* |
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* DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': |
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* |
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* V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) |
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* ( v1 1 ) ( 1 v2 v2 v2 ) |
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* ( v1 v2 1 ) ( 1 v3 v3 ) |
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* ( v1 v2 v3 ) |
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* ( v1 v2 v3 ) |
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* |
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* DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': |
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* |
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* V = ( v1 v2 v3 ) V = ( v1 v1 1 ) |
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* ( v1 v2 v3 ) ( v2 v2 v2 1 ) |
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* ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) |
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* ( 1 v3 ) |
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* ( 1 ) |
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* |
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* ===================================================================== |
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* |
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* .. Parameters .. |
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DOUBLE PRECISION ONE, ZERO |
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
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* .. |
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* .. Local Scalars .. |
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INTEGER I, J, PREVLASTV, LASTV |
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DOUBLE PRECISION VII |
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* .. |
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* .. External Subroutines .. |
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EXTERNAL DGEMV, DTRMV |
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* .. |
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* .. External Functions .. |
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LOGICAL LSAME |
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EXTERNAL LSAME |
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* .. |
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* .. Executable Statements .. |
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* |
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* Quick return if possible |
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* |
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IF( N.EQ.0 ) |
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$ RETURN |
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* |
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IF( LSAME( DIRECT, 'F' ) ) THEN |
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PREVLASTV = N |
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DO 20 I = 1, K |
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PREVLASTV = MAX( I, PREVLASTV ) |
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IF( TAU( I ).EQ.ZERO ) THEN |
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* |
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* H(i) = I |
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* |
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DO 10 J = 1, I |
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T( J, I ) = ZERO |
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10 CONTINUE |
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ELSE |
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* |
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* general case |
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* |
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VII = V( I, I ) |
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V( I, I ) = ONE |
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IF( LSAME( STOREV, 'C' ) ) THEN |
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! Skip any trailing zeros. |
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DO LASTV = N, I+1, -1 |
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IF( V( LASTV, I ).NE.ZERO ) EXIT |
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END DO |
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J = MIN( LASTV, PREVLASTV ) |
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* |
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* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)' * V(i:j,i) |
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* |
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CALL DGEMV( 'Transpose', J-I+1, I-1, -TAU( I ), |
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$ V( I, 1 ), LDV, V( I, I ), 1, ZERO, |
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$ T( 1, I ), 1 ) |
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ELSE |
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! Skip any trailing zeros. |
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DO LASTV = N, I+1, -1 |
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IF( V( I, LASTV ).NE.ZERO ) EXIT |
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END DO |
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J = MIN( LASTV, PREVLASTV ) |
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* |
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* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)' |
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* |
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CALL DGEMV( 'No transpose', I-1, J-I+1, -TAU( I ), |
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$ V( 1, I ), LDV, V( I, I ), LDV, ZERO, |
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$ T( 1, I ), 1 ) |
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END IF |
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V( I, I ) = VII |
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* |
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* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) |
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* |
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CALL DTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T, |
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$ LDT, T( 1, I ), 1 ) |
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T( I, I ) = TAU( I ) |
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IF( I.GT.1 ) THEN |
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PREVLASTV = MAX( PREVLASTV, LASTV ) |
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ELSE |
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PREVLASTV = LASTV |
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END IF |
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END IF |
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20 CONTINUE |
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ELSE |
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PREVLASTV = 1 |
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DO 40 I = K, 1, -1 |
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IF( TAU( I ).EQ.ZERO ) THEN |
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* |
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* H(i) = I |
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* |
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DO 30 J = I, K |
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T( J, I ) = ZERO |
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30 CONTINUE |
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ELSE |
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* |
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* general case |
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* |
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IF( I.LT.K ) THEN |
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IF( LSAME( STOREV, 'C' ) ) THEN |
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VII = V( N-K+I, I ) |
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V( N-K+I, I ) = ONE |
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! Skip any leading zeros. |
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DO LASTV = 1, I-1 |
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IF( V( LASTV, I ).NE.ZERO ) EXIT |
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END DO |
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J = MAX( LASTV, PREVLASTV ) |
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* |
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* T(i+1:k,i) := |
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* - tau(i) * V(j:n-k+i,i+1:k)' * V(j:n-k+i,i) |
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* |
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CALL DGEMV( 'Transpose', N-K+I-J+1, K-I, -TAU( I ), |
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$ V( J, I+1 ), LDV, V( J, I ), 1, ZERO, |
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$ T( I+1, I ), 1 ) |
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V( N-K+I, I ) = VII |
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ELSE |
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VII = V( I, N-K+I ) |
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V( I, N-K+I ) = ONE |
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! Skip any leading zeros. |
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DO LASTV = 1, I-1 |
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IF( V( I, LASTV ).NE.ZERO ) EXIT |
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END DO |
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J = MAX( LASTV, PREVLASTV ) |
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* |
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* T(i+1:k,i) := |
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* - tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)' |
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* |
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CALL DGEMV( 'No transpose', K-I, N-K+I-J+1, |
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$ -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV, |
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$ ZERO, T( I+1, I ), 1 ) |
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V( I, N-K+I ) = VII |
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END IF |
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* |
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* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) |
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* |
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CALL DTRMV( 'Lower', 'No transpose', 'Non-unit', K-I, |
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$ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) |
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IF( I.GT.1 ) THEN |
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PREVLASTV = MIN( PREVLASTV, LASTV ) |
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ELSE |
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PREVLASTV = LASTV |
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END IF |
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END IF |
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T( I, I ) = TAU( I ) |
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END IF |
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40 CONTINUE |
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END IF |
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RETURN |
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* |
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* End of DLARFT |
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* |
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END |