summaryrefslogtreecommitdiff
path: root/SRC/sla_geamv.f
diff options
context:
space:
mode:
authorjulie <julielangou@users.noreply.github.com>2008-12-16 17:06:58 +0000
committerjulie <julielangou@users.noreply.github.com>2008-12-16 17:06:58 +0000
commitff981f106bde4ce6a74aa4f4a572c943f5a395b2 (patch)
treea386cad907bcaefd6893535c31d67ec9468e693e /SRC/sla_geamv.f
parente58b61578b55644f6391f3333262b72c1dc88437 (diff)
downloadlapack-ff981f106bde4ce6a74aa4f4a572c943f5a395b2.tar.gz
lapack-ff981f106bde4ce6a74aa4f4a572c943f5a395b2.tar.bz2
lapack-ff981f106bde4ce6a74aa4f4a572c943f5a395b2.zip
Diffstat (limited to 'SRC/sla_geamv.f')
-rw-r--r--SRC/sla_geamv.f271
1 files changed, 271 insertions, 0 deletions
diff --git a/SRC/sla_geamv.f b/SRC/sla_geamv.f
new file mode 100644
index 00000000..45360469
--- /dev/null
+++ b/SRC/sla_geamv.f
@@ -0,0 +1,271 @@
+ SUBROUTINE SLA_GEAMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA,
+ $ Y, INCY )
+*
+* -- LAPACK routine (version 3.2) --
+* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
+* -- Jason Riedy of Univ. of California Berkeley. --
+* -- November 2008 --
+*
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley and NAG Ltd. --
+*
+ IMPLICIT NONE
+* ..
+* .. Scalar Arguments ..
+ REAL ALPHA, BETA
+ INTEGER INCX, INCY, LDA, M, N, TRANS
+* ..
+* .. Array Arguments ..
+ REAL A( LDA, * ), X( * ), Y( * )
+* ..
+*
+* Purpose
+* =======
+*
+* SLA_GEAMV performs one of the matrix-vector operations
+*
+* y := alpha*abs(A)*abs(x) + beta*abs(y),
+* or y := alpha*abs(A)'*abs(x) + beta*abs(y),
+*
+* where alpha and beta are scalars, x and y are vectors and A is an
+* m by n matrix.
+*
+* This function is primarily used in calculating error bounds.
+* To protect against underflow during evaluation, components in
+* the resulting vector are perturbed away from zero by (N+1)
+* times the underflow threshold. To prevent unnecessarily large
+* errors for block-structure embedded in general matrices,
+* "symbolically" zero components are not perturbed. A zero
+* entry is considered "symbolic" if all multiplications involved
+* in computing that entry have at least one zero multiplicand.
+*
+* Parameters
+* ==========
+*
+* TRANS - INTEGER
+* On entry, TRANS specifies the operation to be performed as
+* follows:
+*
+* BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y)
+* BLAS_TRANS y := alpha*abs(A')*abs(x) + beta*abs(y)
+* BLAS_CONJ_TRANS y := alpha*abs(A')*abs(x) + beta*abs(y)
+*
+* Unchanged on exit.
+*
+* M - INTEGER
+* On entry, M specifies the number of rows of the matrix A.
+* M must be at least zero.
+* Unchanged on exit.
+*
+* N - INTEGER
+* On entry, N specifies the number of columns of the matrix A.
+* N must be at least zero.
+* Unchanged on exit.
+*
+* ALPHA - REAL
+* On entry, ALPHA specifies the scalar alpha.
+* Unchanged on exit.
+*
+* A - REAL array of DIMENSION ( LDA, n )
+* Before entry, the leading m by n part of the array A must
+* contain the matrix of coefficients.
+* Unchanged on exit.
+*
+* LDA - INTEGER
+* On entry, LDA specifies the first dimension of A as declared
+* in the calling (sub) program. LDA must be at least
+* max( 1, m ).
+* Unchanged on exit.
+*
+* X - REAL array of DIMENSION at least
+* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
+* and at least
+* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
+* Before entry, the incremented array X must contain the
+* vector x.
+* Unchanged on exit.
+*
+* INCX - INTEGER
+* On entry, INCX specifies the increment for the elements of
+* X. INCX must not be zero.
+* Unchanged on exit.
+*
+* BETA - REAL
+* On entry, BETA specifies the scalar beta. When BETA is
+* supplied as zero then Y need not be set on input.
+* Unchanged on exit.
+*
+* Y - REAL
+* Array of DIMENSION at least
+* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
+* and at least
+* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
+* Before entry with BETA non-zero, the incremented array Y
+* must contain the vector y. On exit, Y is overwritten by the
+* updated vector y.
+*
+* INCY - INTEGER
+* On entry, INCY specifies the increment for the elements of
+* Y. INCY must not be zero.
+* Unchanged on exit.
+*
+* Level 2 Blas routine.
+*
+* ..
+* .. Parameters ..
+ REAL ONE, ZERO
+ PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
+* ..
+* .. Local Scalars ..
+ LOGICAL SYMB_ZERO
+ REAL TEMP, SAFE1
+ INTEGER I, INFO, IY, J, JX, KX, KY, LENX, LENY
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA, SLAMCH
+ REAL SLAMCH
+* ..
+* .. External Functions ..
+ EXTERNAL ILATRANS
+ INTEGER ILATRANS
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, ABS, SIGN
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters.
+*
+ INFO = 0
+ IF ( .NOT.( ( TRANS.EQ.ILATRANS( 'N' ) )
+ $ .OR. ( TRANS.EQ.ILATRANS( 'T' ) )
+ $ .OR. ( TRANS.EQ.ILATRANS( 'C' ) ) ) ) THEN
+ INFO = 1
+ ELSE IF( M.LT.0 )THEN
+ INFO = 2
+ ELSE IF( N.LT.0 )THEN
+ INFO = 3
+ ELSE IF( LDA.LT.MAX( 1, M ) )THEN
+ INFO = 6
+ ELSE IF( INCX.EQ.0 )THEN
+ INFO = 8
+ ELSE IF( INCY.EQ.0 )THEN
+ INFO = 11
+ END IF
+ IF( INFO.NE.0 )THEN
+ CALL XERBLA( 'SLA_GEAMV ', INFO )
+ RETURN
+ END IF
+*
+* Quick return if possible.
+*
+ IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
+ $ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
+ $ RETURN
+*
+* Set LENX and LENY, the lengths of the vectors x and y, and set
+* up the start points in X and Y.
+*
+ IF( TRANS.EQ.ILATRANS( 'N' ) )THEN
+ LENX = N
+ LENY = M
+ ELSE
+ LENX = M
+ LENY = N
+ END IF
+ IF( INCX.GT.0 )THEN
+ KX = 1
+ ELSE
+ KX = 1 - ( LENX - 1 )*INCX
+ END IF
+ IF( INCY.GT.0 )THEN
+ KY = 1
+ ELSE
+ KY = 1 - ( LENY - 1 )*INCY
+ END IF
+*
+* Set SAFE1 essentially to be the underflow threshold times the
+* number of additions in each row.
+*
+ SAFE1 = SLAMCH( 'Safe minimum' )
+ SAFE1 = (N+1)*SAFE1
+*
+* Form y := alpha*abs(A)*abs(x) + beta*abs(y).
+*
+* The O(M*N) SYMB_ZERO tests could be replaced by O(N) queries to
+* the inexact flag. Still doesn't help change the iteration order
+* to per-column.
+*
+ IY = KY
+ IF ( INCX.EQ.1 ) THEN
+ DO I = 1, LENY
+ IF ( BETA .EQ. ZERO ) THEN
+ SYMB_ZERO = .TRUE.
+ Y( IY ) = 0.0
+ ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
+ SYMB_ZERO = .TRUE.
+ ELSE
+ SYMB_ZERO = .FALSE.
+ Y( IY ) = BETA * ABS( Y( IY ) )
+ END IF
+ IF ( ALPHA .NE. ZERO ) THEN
+ DO J = 1, LENX
+ IF( TRANS.EQ.ILATRANS( 'N' ) )THEN
+ TEMP = ABS( A( I, J ) )
+ ELSE
+ TEMP = ABS( A( J, I ) )
+ END IF
+
+ SYMB_ZERO = SYMB_ZERO .AND.
+ $ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
+
+ Y( IY ) = Y( IY ) + ALPHA*ABS( X( J ) )*TEMP
+ END DO
+ END IF
+
+ IF ( .NOT.SYMB_ZERO )
+ $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
+
+ IY = IY + INCY
+ END DO
+ ELSE
+ DO I = 1, LENY
+ IF ( BETA .EQ. ZERO ) THEN
+ SYMB_ZERO = .TRUE.
+ Y( IY ) = 0.0
+ ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
+ SYMB_ZERO = .TRUE.
+ ELSE
+ SYMB_ZERO = .FALSE.
+ Y( IY ) = BETA * ABS( Y( IY ) )
+ END IF
+ IF ( ALPHA .NE. ZERO ) THEN
+ JX = KX
+ DO J = 1, LENX
+
+ IF( TRANS.EQ.ILATRANS( 'N' ) )THEN
+ TEMP = ABS( A( I, J ) )
+ ELSE
+ TEMP = ABS( A( J, I ) )
+ END IF
+
+ SYMB_ZERO = SYMB_ZERO .AND.
+ $ ( X( JX ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
+
+ Y( IY ) = Y( IY ) + ALPHA*ABS( X( JX ) )*TEMP
+ JX = JX + INCX
+ END DO
+ END IF
+
+ IF (.NOT.SYMB_ZERO)
+ $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
+
+ IY = IY + INCY
+ END DO
+ END IF
+*
+ RETURN
+*
+* End of SLA_GEAMV
+*
+ END