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Diffstat (limited to 'src/lib/lapack/dlatrd.f')
| -rw-r--r-- | src/lib/lapack/dlatrd.f | 258 |
1 files changed, 0 insertions, 258 deletions
diff --git a/src/lib/lapack/dlatrd.f b/src/lib/lapack/dlatrd.f deleted file mode 100644 index 27bf9b98..00000000 --- a/src/lib/lapack/dlatrd.f +++ /dev/null @@ -1,258 +0,0 @@ - SUBROUTINE DLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) -* -* -- LAPACK auxiliary routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER LDA, LDW, N, NB -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), E( * ), TAU( * ), W( LDW, * ) -* .. -* -* Purpose -* ======= -* -* DLATRD reduces NB rows and columns of a real symmetric matrix A to -* symmetric tridiagonal form by an orthogonal similarity -* transformation Q' * A * Q, and returns the matrices V and W which are -* needed to apply the transformation to the unreduced part of A. -* -* If UPLO = 'U', DLATRD reduces the last NB rows and columns of a -* matrix, of which the upper triangle is supplied; -* if UPLO = 'L', DLATRD reduces the first NB rows and columns of a -* matrix, of which the lower triangle is supplied. -* -* This is an auxiliary routine called by DSYTRD. -* -* Arguments -* ========= -* -* UPLO (input) CHARACTER*1 -* Specifies whether the upper or lower triangular part of the -* symmetric matrix A is stored: -* = 'U': Upper triangular -* = 'L': Lower triangular -* -* N (input) INTEGER -* The order of the matrix A. -* -* NB (input) INTEGER -* The number of rows and columns to be reduced. -* -* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -* On entry, the symmetric matrix A. If UPLO = 'U', the leading -* n-by-n upper triangular part of A contains the upper -* triangular part of the matrix A, and the strictly lower -* triangular part of A is not referenced. If UPLO = 'L', the -* leading n-by-n lower triangular part of A contains the lower -* triangular part of the matrix A, and the strictly upper -* triangular part of A is not referenced. -* On exit: -* if UPLO = 'U', the last NB columns have been reduced to -* tridiagonal form, with the diagonal elements overwriting -* the diagonal elements of A; the elements above the diagonal -* with the array TAU, represent the orthogonal matrix Q as a -* product of elementary reflectors; -* if UPLO = 'L', the first NB columns have been reduced to -* tridiagonal form, with the diagonal elements overwriting -* the diagonal elements of A; the elements below the diagonal -* with the array TAU, represent the orthogonal matrix Q as a -* product of elementary reflectors. -* See Further Details. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= (1,N). -* -* E (output) DOUBLE PRECISION array, dimension (N-1) -* If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal -* elements of the last NB columns of the reduced matrix; -* if UPLO = 'L', E(1:nb) contains the subdiagonal elements of -* the first NB columns of the reduced matrix. -* -* TAU (output) DOUBLE PRECISION array, dimension (N-1) -* The scalar factors of the elementary reflectors, stored in -* TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. -* See Further Details. -* -* W (output) DOUBLE PRECISION array, dimension (LDW,NB) -* The n-by-nb matrix W required to update the unreduced part -* of A. -* -* LDW (input) INTEGER -* The leading dimension of the array W. LDW >= max(1,N). -* -* Further Details -* =============== -* -* If UPLO = 'U', the matrix Q is represented as a product of elementary -* reflectors -* -* Q = H(n) H(n-1) . . . H(n-nb+1). -* -* Each H(i) has the form -* -* H(i) = I - tau * v * v' -* -* where tau is a real scalar, and v is a real vector with -* v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), -* and tau in TAU(i-1). -* -* If UPLO = 'L', the matrix Q is represented as a product of elementary -* reflectors -* -* Q = H(1) H(2) . . . H(nb). -* -* Each H(i) has the form -* -* H(i) = I - tau * v * v' -* -* where tau is a real scalar, and v is a real vector with -* v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), -* and tau in TAU(i). -* -* The elements of the vectors v together form the n-by-nb matrix V -* which is needed, with W, to apply the transformation to the unreduced -* part of the matrix, using a symmetric rank-2k update of the form: -* A := A - V*W' - W*V'. -* -* The contents of A on exit are illustrated by the following examples -* with n = 5 and nb = 2: -* -* if UPLO = 'U': if UPLO = 'L': -* -* ( a a a v4 v5 ) ( d ) -* ( a a v4 v5 ) ( 1 d ) -* ( a 1 v5 ) ( v1 1 a ) -* ( d 1 ) ( v1 v2 a a ) -* ( d ) ( v1 v2 a a a ) -* -* where d denotes a diagonal element of the reduced matrix, a denotes -* an element of the original matrix that is unchanged, and vi denotes -* an element of the vector defining H(i). -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE, HALF - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, HALF = 0.5D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, IW - DOUBLE PRECISION ALPHA -* .. -* .. External Subroutines .. - EXTERNAL DAXPY, DGEMV, DLARFG, DSCAL, DSYMV -* .. -* .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DDOT - EXTERNAL LSAME, DDOT -* .. -* .. Intrinsic Functions .. - INTRINSIC MIN -* .. -* .. Executable Statements .. -* -* Quick return if possible -* - IF( N.LE.0 ) - $ RETURN -* - IF( LSAME( UPLO, 'U' ) ) THEN -* -* Reduce last NB columns of upper triangle -* - DO 10 I = N, N - NB + 1, -1 - IW = I - N + NB - IF( I.LT.N ) THEN -* -* Update A(1:i,i) -* - CALL DGEMV( 'No transpose', I, N-I, -ONE, A( 1, I+1 ), - $ LDA, W( I, IW+1 ), LDW, ONE, A( 1, I ), 1 ) - CALL DGEMV( 'No transpose', I, N-I, -ONE, W( 1, IW+1 ), - $ LDW, A( I, I+1 ), LDA, ONE, A( 1, I ), 1 ) - END IF - IF( I.GT.1 ) THEN -* -* Generate elementary reflector H(i) to annihilate -* A(1:i-2,i) -* - CALL DLARFG( I-1, A( I-1, I ), A( 1, I ), 1, TAU( I-1 ) ) - E( I-1 ) = A( I-1, I ) - A( I-1, I ) = ONE -* -* Compute W(1:i-1,i) -* - CALL DSYMV( 'Upper', I-1, ONE, A, LDA, A( 1, I ), 1, - $ ZERO, W( 1, IW ), 1 ) - IF( I.LT.N ) THEN - CALL DGEMV( 'Transpose', I-1, N-I, ONE, W( 1, IW+1 ), - $ LDW, A( 1, I ), 1, ZERO, W( I+1, IW ), 1 ) - CALL DGEMV( 'No transpose', I-1, N-I, -ONE, - $ A( 1, I+1 ), LDA, W( I+1, IW ), 1, ONE, - $ W( 1, IW ), 1 ) - CALL DGEMV( 'Transpose', I-1, N-I, ONE, A( 1, I+1 ), - $ LDA, A( 1, I ), 1, ZERO, W( I+1, IW ), 1 ) - CALL DGEMV( 'No transpose', I-1, N-I, -ONE, - $ W( 1, IW+1 ), LDW, W( I+1, IW ), 1, ONE, - $ W( 1, IW ), 1 ) - END IF - CALL DSCAL( I-1, TAU( I-1 ), W( 1, IW ), 1 ) - ALPHA = -HALF*TAU( I-1 )*DDOT( I-1, W( 1, IW ), 1, - $ A( 1, I ), 1 ) - CALL DAXPY( I-1, ALPHA, A( 1, I ), 1, W( 1, IW ), 1 ) - END IF -* - 10 CONTINUE - ELSE -* -* Reduce first NB columns of lower triangle -* - DO 20 I = 1, NB -* -* Update A(i:n,i) -* - CALL DGEMV( 'No transpose', N-I+1, I-1, -ONE, A( I, 1 ), - $ LDA, W( I, 1 ), LDW, ONE, A( I, I ), 1 ) - CALL DGEMV( 'No transpose', N-I+1, I-1, -ONE, W( I, 1 ), - $ LDW, A( I, 1 ), LDA, ONE, A( I, I ), 1 ) - IF( I.LT.N ) THEN -* -* Generate elementary reflector H(i) to annihilate -* A(i+2:n,i) -* - CALL DLARFG( N-I, A( I+1, I ), A( MIN( I+2, N ), I ), 1, - $ TAU( I ) ) - E( I ) = A( I+1, I ) - A( I+1, I ) = ONE -* -* Compute W(i+1:n,i) -* - CALL DSYMV( 'Lower', N-I, ONE, A( I+1, I+1 ), LDA, - $ A( I+1, I ), 1, ZERO, W( I+1, I ), 1 ) - CALL DGEMV( 'Transpose', N-I, I-1, ONE, W( I+1, 1 ), LDW, - $ A( I+1, I ), 1, ZERO, W( 1, I ), 1 ) - CALL DGEMV( 'No transpose', N-I, I-1, -ONE, A( I+1, 1 ), - $ LDA, W( 1, I ), 1, ONE, W( I+1, I ), 1 ) - CALL DGEMV( 'Transpose', N-I, I-1, ONE, A( I+1, 1 ), LDA, - $ A( I+1, I ), 1, ZERO, W( 1, I ), 1 ) - CALL DGEMV( 'No transpose', N-I, I-1, -ONE, W( I+1, 1 ), - $ LDW, W( 1, I ), 1, ONE, W( I+1, I ), 1 ) - CALL DSCAL( N-I, TAU( I ), W( I+1, I ), 1 ) - ALPHA = -HALF*TAU( I )*DDOT( N-I, W( I+1, I ), 1, - $ A( I+1, I ), 1 ) - CALL DAXPY( N-I, ALPHA, A( I+1, I ), 1, W( I+1, I ), 1 ) - END IF -* - 20 CONTINUE - END IF -* - RETURN -* -* End of DLATRD -* - END |