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Diffstat (limited to 'src/lib/lapack/dlasyf.f')
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1 files changed, 0 insertions, 587 deletions
diff --git a/src/lib/lapack/dlasyf.f b/src/lib/lapack/dlasyf.f deleted file mode 100644 index 67b9c147..00000000 --- a/src/lib/lapack/dlasyf.f +++ /dev/null @@ -1,587 +0,0 @@ - SUBROUTINE DLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO ) -* -* -- LAPACK routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, KB, LDA, LDW, N, NB -* .. -* .. Array Arguments .. - INTEGER IPIV( * ) - DOUBLE PRECISION A( LDA, * ), W( LDW, * ) -* .. -* -* Purpose -* ======= -* -* DLASYF computes a partial factorization of a real symmetric matrix A -* using the Bunch-Kaufman diagonal pivoting method. The partial -* factorization has the form: -* -* A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: -* ( 0 U22 ) ( 0 D ) ( U12' U22' ) -* -* A = ( L11 0 ) ( D 0 ) ( L11' L21' ) if UPLO = 'L' -* ( L21 I ) ( 0 A22 ) ( 0 I ) -* -* where the order of D is at most NB. The actual order is returned in -* the argument KB, and is either NB or NB-1, or N if N <= NB. -* -* DLASYF is an auxiliary routine called by DSYTRF. It uses blocked code -* (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or -* A22 (if UPLO = 'L'). -* -* 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. N >= 0. -* -* NB (input) INTEGER -* The maximum number of columns of the matrix A that should be -* factored. NB should be at least 2 to allow for 2-by-2 pivot -* blocks. -* -* KB (output) INTEGER -* The number of columns of A that were actually factored. -* KB is either NB-1 or NB, or N if N <= NB. -* -* 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, A contains details of the partial factorization. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,N). -* -* IPIV (output) INTEGER array, dimension (N) -* Details of the interchanges and the block structure of D. -* If UPLO = 'U', only the last KB elements of IPIV are set; -* if UPLO = 'L', only the first KB elements are set. -* -* If IPIV(k) > 0, then rows and columns k and IPIV(k) were -* interchanged and D(k,k) is a 1-by-1 diagonal block. -* If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and -* columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) -* is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = -* IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were -* interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -* -* W (workspace) DOUBLE PRECISION array, dimension (LDW,NB) -* -* LDW (input) INTEGER -* The leading dimension of the array W. LDW >= max(1,N). -* -* INFO (output) INTEGER -* = 0: successful exit -* > 0: if INFO = k, D(k,k) is exactly zero. The factorization -* has been completed, but the block diagonal matrix D is -* exactly singular. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) - DOUBLE PRECISION EIGHT, SEVTEN - PARAMETER ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER IMAX, J, JB, JJ, JMAX, JP, K, KK, KKW, KP, - $ KSTEP, KW - DOUBLE PRECISION ABSAKK, ALPHA, COLMAX, D11, D21, D22, R1, - $ ROWMAX, T -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER IDAMAX - EXTERNAL LSAME, IDAMAX -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DGEMM, DGEMV, DSCAL, DSWAP -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN, SQRT -* .. -* .. Executable Statements .. -* - INFO = 0 -* -* Initialize ALPHA for use in choosing pivot block size. -* - ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT -* - IF( LSAME( UPLO, 'U' ) ) THEN -* -* Factorize the trailing columns of A using the upper triangle -* of A and working backwards, and compute the matrix W = U12*D -* for use in updating A11 -* -* K is the main loop index, decreasing from N in steps of 1 or 2 -* -* KW is the column of W which corresponds to column K of A -* - K = N - 10 CONTINUE - KW = NB + K - N -* -* Exit from loop -* - IF( ( K.LE.N-NB+1 .AND. NB.LT.N ) .OR. K.LT.1 ) - $ GO TO 30 -* -* Copy column K of A to column KW of W and update it -* - CALL DCOPY( K, A( 1, K ), 1, W( 1, KW ), 1 ) - IF( K.LT.N ) - $ CALL DGEMV( 'No transpose', K, N-K, -ONE, A( 1, K+1 ), LDA, - $ W( K, KW+1 ), LDW, ONE, W( 1, KW ), 1 ) -* - KSTEP = 1 -* -* Determine rows and columns to be interchanged and whether -* a 1-by-1 or 2-by-2 pivot block will be used -* - ABSAKK = ABS( W( K, KW ) ) -* -* IMAX is the row-index of the largest off-diagonal element in -* column K, and COLMAX is its absolute value -* - IF( K.GT.1 ) THEN - IMAX = IDAMAX( K-1, W( 1, KW ), 1 ) - COLMAX = ABS( W( IMAX, KW ) ) - ELSE - COLMAX = ZERO - END IF -* - IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN -* -* Column K is zero: set INFO and continue -* - IF( INFO.EQ.0 ) - $ INFO = K - KP = K - ELSE - IF( ABSAKK.GE.ALPHA*COLMAX ) THEN -* -* no interchange, use 1-by-1 pivot block -* - KP = K - ELSE -* -* Copy column IMAX to column KW-1 of W and update it -* - CALL DCOPY( IMAX, A( 1, IMAX ), 1, W( 1, KW-1 ), 1 ) - CALL DCOPY( K-IMAX, A( IMAX, IMAX+1 ), LDA, - $ W( IMAX+1, KW-1 ), 1 ) - IF( K.LT.N ) - $ CALL DGEMV( 'No transpose', K, N-K, -ONE, A( 1, K+1 ), - $ LDA, W( IMAX, KW+1 ), LDW, ONE, - $ W( 1, KW-1 ), 1 ) -* -* JMAX is the column-index of the largest off-diagonal -* element in row IMAX, and ROWMAX is its absolute value -* - JMAX = IMAX + IDAMAX( K-IMAX, W( IMAX+1, KW-1 ), 1 ) - ROWMAX = ABS( W( JMAX, KW-1 ) ) - IF( IMAX.GT.1 ) THEN - JMAX = IDAMAX( IMAX-1, W( 1, KW-1 ), 1 ) - ROWMAX = MAX( ROWMAX, ABS( W( JMAX, KW-1 ) ) ) - END IF -* - IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN -* -* no interchange, use 1-by-1 pivot block -* - KP = K - ELSE IF( ABS( W( IMAX, KW-1 ) ).GE.ALPHA*ROWMAX ) THEN -* -* interchange rows and columns K and IMAX, use 1-by-1 -* pivot block -* - KP = IMAX -* -* copy column KW-1 of W to column KW -* - CALL DCOPY( K, W( 1, KW-1 ), 1, W( 1, KW ), 1 ) - ELSE -* -* interchange rows and columns K-1 and IMAX, use 2-by-2 -* pivot block -* - KP = IMAX - KSTEP = 2 - END IF - END IF -* - KK = K - KSTEP + 1 - KKW = NB + KK - N -* -* Updated column KP is already stored in column KKW of W -* - IF( KP.NE.KK ) THEN -* -* Copy non-updated column KK to column KP -* - A( KP, K ) = A( KK, K ) - CALL DCOPY( K-1-KP, A( KP+1, KK ), 1, A( KP, KP+1 ), - $ LDA ) - CALL DCOPY( KP, A( 1, KK ), 1, A( 1, KP ), 1 ) -* -* Interchange rows KK and KP in last KK columns of A and W -* - CALL DSWAP( N-KK+1, A( KK, KK ), LDA, A( KP, KK ), LDA ) - CALL DSWAP( N-KK+1, W( KK, KKW ), LDW, W( KP, KKW ), - $ LDW ) - END IF -* - IF( KSTEP.EQ.1 ) THEN -* -* 1-by-1 pivot block D(k): column KW of W now holds -* -* W(k) = U(k)*D(k) -* -* where U(k) is the k-th column of U -* -* Store U(k) in column k of A -* - CALL DCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 ) - R1 = ONE / A( K, K ) - CALL DSCAL( K-1, R1, A( 1, K ), 1 ) - ELSE -* -* 2-by-2 pivot block D(k): columns KW and KW-1 of W now -* hold -* -* ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k) -* -* where U(k) and U(k-1) are the k-th and (k-1)-th columns -* of U -* - IF( K.GT.2 ) THEN -* -* Store U(k) and U(k-1) in columns k and k-1 of A -* - D21 = W( K-1, KW ) - D11 = W( K, KW ) / D21 - D22 = W( K-1, KW-1 ) / D21 - T = ONE / ( D11*D22-ONE ) - D21 = T / D21 - DO 20 J = 1, K - 2 - A( J, K-1 ) = D21*( D11*W( J, KW-1 )-W( J, KW ) ) - A( J, K ) = D21*( D22*W( J, KW )-W( J, KW-1 ) ) - 20 CONTINUE - END IF -* -* Copy D(k) to A -* - A( K-1, K-1 ) = W( K-1, KW-1 ) - A( K-1, K ) = W( K-1, KW ) - A( K, K ) = W( K, KW ) - END IF - END IF -* -* Store details of the interchanges in IPIV -* - IF( KSTEP.EQ.1 ) THEN - IPIV( K ) = KP - ELSE - IPIV( K ) = -KP - IPIV( K-1 ) = -KP - END IF -* -* Decrease K and return to the start of the main loop -* - K = K - KSTEP - GO TO 10 -* - 30 CONTINUE -* -* Update the upper triangle of A11 (= A(1:k,1:k)) as -* -* A11 := A11 - U12*D*U12' = A11 - U12*W' -* -* computing blocks of NB columns at a time -* - DO 50 J = ( ( K-1 ) / NB )*NB + 1, 1, -NB - JB = MIN( NB, K-J+1 ) -* -* Update the upper triangle of the diagonal block -* - DO 40 JJ = J, J + JB - 1 - CALL DGEMV( 'No transpose', JJ-J+1, N-K, -ONE, - $ A( J, K+1 ), LDA, W( JJ, KW+1 ), LDW, ONE, - $ A( J, JJ ), 1 ) - 40 CONTINUE -* -* Update the rectangular superdiagonal block -* - CALL DGEMM( 'No transpose', 'Transpose', J-1, JB, N-K, -ONE, - $ A( 1, K+1 ), LDA, W( J, KW+1 ), LDW, ONE, - $ A( 1, J ), LDA ) - 50 CONTINUE -* -* Put U12 in standard form by partially undoing the interchanges -* in columns k+1:n -* - J = K + 1 - 60 CONTINUE - JJ = J - JP = IPIV( J ) - IF( JP.LT.0 ) THEN - JP = -JP - J = J + 1 - END IF - J = J + 1 - IF( JP.NE.JJ .AND. J.LE.N ) - $ CALL DSWAP( N-J+1, A( JP, J ), LDA, A( JJ, J ), LDA ) - IF( J.LE.N ) - $ GO TO 60 -* -* Set KB to the number of columns factorized -* - KB = N - K -* - ELSE -* -* Factorize the leading columns of A using the lower triangle -* of A and working forwards, and compute the matrix W = L21*D -* for use in updating A22 -* -* K is the main loop index, increasing from 1 in steps of 1 or 2 -* - K = 1 - 70 CONTINUE -* -* Exit from loop -* - IF( ( K.GE.NB .AND. NB.LT.N ) .OR. K.GT.N ) - $ GO TO 90 -* -* Copy column K of A to column K of W and update it -* - CALL DCOPY( N-K+1, A( K, K ), 1, W( K, K ), 1 ) - CALL DGEMV( 'No transpose', N-K+1, K-1, -ONE, A( K, 1 ), LDA, - $ W( K, 1 ), LDW, ONE, W( K, K ), 1 ) -* - KSTEP = 1 -* -* Determine rows and columns to be interchanged and whether -* a 1-by-1 or 2-by-2 pivot block will be used -* - ABSAKK = ABS( W( K, K ) ) -* -* IMAX is the row-index of the largest off-diagonal element in -* column K, and COLMAX is its absolute value -* - IF( K.LT.N ) THEN - IMAX = K + IDAMAX( N-K, W( K+1, K ), 1 ) - COLMAX = ABS( W( IMAX, K ) ) - ELSE - COLMAX = ZERO - END IF -* - IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN -* -* Column K is zero: set INFO and continue -* - IF( INFO.EQ.0 ) - $ INFO = K - KP = K - ELSE - IF( ABSAKK.GE.ALPHA*COLMAX ) THEN -* -* no interchange, use 1-by-1 pivot block -* - KP = K - ELSE -* -* Copy column IMAX to column K+1 of W and update it -* - CALL DCOPY( IMAX-K, A( IMAX, K ), LDA, W( K, K+1 ), 1 ) - CALL DCOPY( N-IMAX+1, A( IMAX, IMAX ), 1, W( IMAX, K+1 ), - $ 1 ) - CALL DGEMV( 'No transpose', N-K+1, K-1, -ONE, A( K, 1 ), - $ LDA, W( IMAX, 1 ), LDW, ONE, W( K, K+1 ), 1 ) -* -* JMAX is the column-index of the largest off-diagonal -* element in row IMAX, and ROWMAX is its absolute value -* - JMAX = K - 1 + IDAMAX( IMAX-K, W( K, K+1 ), 1 ) - ROWMAX = ABS( W( JMAX, K+1 ) ) - IF( IMAX.LT.N ) THEN - JMAX = IMAX + IDAMAX( N-IMAX, W( IMAX+1, K+1 ), 1 ) - ROWMAX = MAX( ROWMAX, ABS( W( JMAX, K+1 ) ) ) - END IF -* - IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN -* -* no interchange, use 1-by-1 pivot block -* - KP = K - ELSE IF( ABS( W( IMAX, K+1 ) ).GE.ALPHA*ROWMAX ) THEN -* -* interchange rows and columns K and IMAX, use 1-by-1 -* pivot block -* - KP = IMAX -* -* copy column K+1 of W to column K -* - CALL DCOPY( N-K+1, W( K, K+1 ), 1, W( K, K ), 1 ) - ELSE -* -* interchange rows and columns K+1 and IMAX, use 2-by-2 -* pivot block -* - KP = IMAX - KSTEP = 2 - END IF - END IF -* - KK = K + KSTEP - 1 -* -* Updated column KP is already stored in column KK of W -* - IF( KP.NE.KK ) THEN -* -* Copy non-updated column KK to column KP -* - A( KP, K ) = A( KK, K ) - CALL DCOPY( KP-K-1, A( K+1, KK ), 1, A( KP, K+1 ), LDA ) - CALL DCOPY( N-KP+1, A( KP, KK ), 1, A( KP, KP ), 1 ) -* -* Interchange rows KK and KP in first KK columns of A and W -* - CALL DSWAP( KK, A( KK, 1 ), LDA, A( KP, 1 ), LDA ) - CALL DSWAP( KK, W( KK, 1 ), LDW, W( KP, 1 ), LDW ) - END IF -* - IF( KSTEP.EQ.1 ) THEN -* -* 1-by-1 pivot block D(k): column k of W now holds -* -* W(k) = L(k)*D(k) -* -* where L(k) is the k-th column of L -* -* Store L(k) in column k of A -* - CALL DCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 ) - IF( K.LT.N ) THEN - R1 = ONE / A( K, K ) - CALL DSCAL( N-K, R1, A( K+1, K ), 1 ) - END IF - ELSE -* -* 2-by-2 pivot block D(k): columns k and k+1 of W now hold -* -* ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k) -* -* where L(k) and L(k+1) are the k-th and (k+1)-th columns -* of L -* - IF( K.LT.N-1 ) THEN -* -* Store L(k) and L(k+1) in columns k and k+1 of A -* - D21 = W( K+1, K ) - D11 = W( K+1, K+1 ) / D21 - D22 = W( K, K ) / D21 - T = ONE / ( D11*D22-ONE ) - D21 = T / D21 - DO 80 J = K + 2, N - A( J, K ) = D21*( D11*W( J, K )-W( J, K+1 ) ) - A( J, K+1 ) = D21*( D22*W( J, K+1 )-W( J, K ) ) - 80 CONTINUE - END IF -* -* Copy D(k) to A -* - A( K, K ) = W( K, K ) - A( K+1, K ) = W( K+1, K ) - A( K+1, K+1 ) = W( K+1, K+1 ) - END IF - END IF -* -* Store details of the interchanges in IPIV -* - IF( KSTEP.EQ.1 ) THEN - IPIV( K ) = KP - ELSE - IPIV( K ) = -KP - IPIV( K+1 ) = -KP - END IF -* -* Increase K and return to the start of the main loop -* - K = K + KSTEP - GO TO 70 -* - 90 CONTINUE -* -* Update the lower triangle of A22 (= A(k:n,k:n)) as -* -* A22 := A22 - L21*D*L21' = A22 - L21*W' -* -* computing blocks of NB columns at a time -* - DO 110 J = K, N, NB - JB = MIN( NB, N-J+1 ) -* -* Update the lower triangle of the diagonal block -* - DO 100 JJ = J, J + JB - 1 - CALL DGEMV( 'No transpose', J+JB-JJ, K-1, -ONE, - $ A( JJ, 1 ), LDA, W( JJ, 1 ), LDW, ONE, - $ A( JJ, JJ ), 1 ) - 100 CONTINUE -* -* Update the rectangular subdiagonal block -* - IF( J+JB.LE.N ) - $ CALL DGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB, - $ K-1, -ONE, A( J+JB, 1 ), LDA, W( J, 1 ), LDW, - $ ONE, A( J+JB, J ), LDA ) - 110 CONTINUE -* -* Put L21 in standard form by partially undoing the interchanges -* in columns 1:k-1 -* - J = K - 1 - 120 CONTINUE - JJ = J - JP = IPIV( J ) - IF( JP.LT.0 ) THEN - JP = -JP - J = J - 1 - END IF - J = J - 1 - IF( JP.NE.JJ .AND. J.GE.1 ) - $ CALL DSWAP( J, A( JP, 1 ), LDA, A( JJ, 1 ), LDA ) - IF( J.GE.1 ) - $ GO TO 120 -* -* Set KB to the number of columns factorized -* - KB = K - 1 -* - END IF - RETURN -* -* End of DLASYF -* - END |