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SUBROUTINE ZLAROR( SIDE, INIT, M, N, A, LDA, ISEED, X, INFO )
* * -- LAPACK auxiliary test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * June 2010 * * .. Scalar Arguments .. CHARACTER INIT, SIDE INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. INTEGER ISEED( 4 ) COMPLEX*16 A( LDA, * ), X( * ) * .. * * Purpose * ======= * * ZLAROR pre- or post-multiplies an M by N matrix A by a random * unitary matrix U, overwriting A. A may optionally be * initialized to the identity matrix before multiplying by U. * U is generated using the method of G.W. Stewart * ( SIAM J. Numer. Anal. 17, 1980, pp. 403-409 ). * (BLAS-2 version) * * Arguments * ========= * * SIDE (input) CHARACTER*1 * SIDE specifies whether A is multiplied on the left or right * by U. * SIDE = 'L' Multiply A on the left (premultiply) by U * SIDE = 'R' Multiply A on the right (postmultiply) by U* * SIDE = 'C' Multiply A on the left by U and the right by U* * SIDE = 'T' Multiply A on the left by U and the right by U' * Not modified. * * INIT (input) CHARACTER*1 * INIT specifies whether or not A should be initialized to * the identity matrix. * INIT = 'I' Initialize A to (a section of) the * identity matrix before applying U. * INIT = 'N' No initialization. Apply U to the * input matrix A. * * INIT = 'I' may be used to generate square (i.e., unitary) * or rectangular orthogonal matrices (orthogonality being * in the sense of ZDOTC): * * For square matrices, M=N, and SIDE many be either 'L' or * 'R'; the rows will be orthogonal to each other, as will the * columns. * For rectangular matrices where M < N, SIDE = 'R' will * produce a dense matrix whose rows will be orthogonal and * whose columns will not, while SIDE = 'L' will produce a * matrix whose rows will be orthogonal, and whose first M * columns will be orthogonal, the remaining columns being * zero. * For matrices where M > N, just use the previous * explanation, interchanging 'L' and 'R' and "rows" and * "columns". * * Not modified. * * M (input) INTEGER * Number of rows of A. Not modified. * * N (input) INTEGER * Number of columns of A. Not modified. * * A COMPLEX*16 array, dimension ( LDA, N ) * Input and output array. Overwritten by U A ( if SIDE = 'L' ) * or by A U ( if SIDE = 'R' ) * or by U A U* ( if SIDE = 'C') * or by U A U' ( if SIDE = 'T') on exit. * * LDA (input) INTEGER * Leading dimension of A. Must be at least MAX ( 1, M ). * Not modified. * * ISEED (input/output) INTEGER array, dimension ( 4 ) * On entry ISEED specifies the seed of the random number * generator. The array elements should be between 0 and 4095; * if not they will be reduced mod 4096. Also, ISEED(4) must * be odd. The random number generator uses a linear * congruential sequence limited to small integers, and so * should produce machine independent random numbers. The * values of ISEED are changed on exit, and can be used in the * next call to ZLAROR to continue the same random number * sequence. * Modified. * * X (workspace) COMPLEX*16 array, dimension ( 3*MAX( M, N ) ) * Workspace. Of length: * 2*M + N if SIDE = 'L', * 2*N + M if SIDE = 'R', * 3*N if SIDE = 'C' or 'T'. * Modified. * * INFO (output) INTEGER * An error flag. It is set to: * 0 if no error. * 1 if ZLARND returned a bad random number (installation * problem) * -1 if SIDE is not L, R, C, or T. * -3 if M is negative. * -4 if N is negative or if SIDE is C or T and N is not equal * to M. * -6 if LDA is less than M. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TOOSML PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, $ TOOSML = 1.0D-20 ) COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), $ CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER IROW, ITYPE, IXFRM, J, JCOL, KBEG, NXFRM DOUBLE PRECISION FACTOR, XABS, XNORM COMPLEX*16 CSIGN, XNORMS * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DZNRM2 COMPLEX*16 ZLARND EXTERNAL LSAME, DZNRM2, ZLARND * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGEMV, ZGERC, ZLACGV, ZLASET, ZSCAL * .. * .. Intrinsic Functions .. INTRINSIC ABS, DCMPLX, DCONJG * .. * .. Executable Statements .. * IF( N.EQ.0 .OR. M.EQ.0 ) $ RETURN * ITYPE = 0 IF( LSAME( SIDE, 'L' ) ) THEN ITYPE = 1 ELSE IF( LSAME( SIDE, 'R' ) ) THEN ITYPE = 2 ELSE IF( LSAME( SIDE, 'C' ) ) THEN ITYPE = 3 ELSE IF( LSAME( SIDE, 'T' ) ) THEN ITYPE = 4 END IF * * Check for argument errors. * INFO = 0 IF( ITYPE.EQ.0 ) THEN INFO = -1 ELSE IF( M.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 .OR. ( ITYPE.EQ.3 .AND. N.NE.M ) ) THEN INFO = -4 ELSE IF( LDA.LT.M ) THEN INFO = -6 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZLAROR', -INFO ) RETURN END IF * IF( ITYPE.EQ.1 ) THEN NXFRM = M ELSE NXFRM = N END IF * * Initialize A to the identity matrix if desired * IF( LSAME( INIT, 'I' ) ) $ CALL ZLASET( 'Full', M, N, CZERO, CONE, A, LDA ) * * If no rotation possible, still multiply by * a random complex number from the circle |x| = 1 * * 2) Compute Rotation by computing Householder * Transformations H(2), H(3), ..., H(n). Note that the * order in which they are computed is irrelevant. * DO 10 J = 1, NXFRM X( J ) = CZERO 10 CONTINUE * DO 30 IXFRM = 2, NXFRM KBEG = NXFRM - IXFRM + 1 * * Generate independent normal( 0, 1 ) random numbers * DO 20 J = KBEG, NXFRM X( J ) = ZLARND( 3, ISEED ) 20 CONTINUE * * Generate a Householder transformation from the random vector X * XNORM = DZNRM2( IXFRM, X( KBEG ), 1 ) XABS = ABS( X( KBEG ) ) IF( XABS.NE.CZERO ) THEN CSIGN = X( KBEG ) / XABS ELSE CSIGN = CONE END IF XNORMS = CSIGN*XNORM X( NXFRM+KBEG ) = -CSIGN FACTOR = XNORM*( XNORM+XABS ) IF( ABS( FACTOR ).LT.TOOSML ) THEN INFO = 1 CALL XERBLA( 'ZLAROR', -INFO ) RETURN ELSE FACTOR = ONE / FACTOR END IF X( KBEG ) = X( KBEG ) + XNORMS * * Apply Householder transformation to A * IF( ITYPE.EQ.1 .OR. ITYPE.EQ.3 .OR. ITYPE.EQ.4 ) THEN * * Apply H(k) on the left of A * CALL ZGEMV( 'C', IXFRM, N, CONE, A( KBEG, 1 ), LDA, $ X( KBEG ), 1, CZERO, X( 2*NXFRM+1 ), 1 ) CALL ZGERC( IXFRM, N, -DCMPLX( FACTOR ), X( KBEG ), 1, $ X( 2*NXFRM+1 ), 1, A( KBEG, 1 ), LDA ) * END IF * IF( ITYPE.GE.2 .AND. ITYPE.LE.4 ) THEN * * Apply H(k)* (or H(k)') on the right of A * IF( ITYPE.EQ.4 ) THEN CALL ZLACGV( IXFRM, X( KBEG ), 1 ) END IF * CALL ZGEMV( 'N', M, IXFRM, CONE, A( 1, KBEG ), LDA, $ X( KBEG ), 1, CZERO, X( 2*NXFRM+1 ), 1 ) CALL ZGERC( M, IXFRM, -DCMPLX( FACTOR ), X( 2*NXFRM+1 ), 1, $ X( KBEG ), 1, A( 1, KBEG ), LDA ) * END IF 30 CONTINUE * X( 1 ) = ZLARND( 3, ISEED ) XABS = ABS( X( 1 ) ) IF( XABS.NE.ZERO ) THEN CSIGN = X( 1 ) / XABS ELSE CSIGN = CONE END IF X( 2*NXFRM ) = CSIGN * * Scale the matrix A by D. * IF( ITYPE.EQ.1 .OR. ITYPE.EQ.3 .OR. ITYPE.EQ.4 ) THEN DO 40 IROW = 1, M CALL ZSCAL( N, DCONJG( X( NXFRM+IROW ) ), A( IROW, 1 ), $ LDA ) 40 CONTINUE END IF * IF( ITYPE.EQ.2 .OR. ITYPE.EQ.3 ) THEN DO 50 JCOL = 1, N CALL ZSCAL( M, X( NXFRM+JCOL ), A( 1, JCOL ), 1 ) 50 CONTINUE END IF * IF( ITYPE.EQ.4 ) THEN DO 60 JCOL = 1, N CALL ZSCAL( M, DCONJG( X( NXFRM+JCOL ) ), A( 1, JCOL ), 1 ) 60 CONTINUE END IF RETURN * * End of ZLAROR * END |