Annotation of rpl/lapack/lapack/ztzrqf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZTZRQF( M, N, A, LDA, TAU, INFO )
! 2: *
! 3: * -- LAPACK routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: INTEGER INFO, LDA, M, N
! 10: * ..
! 11: * .. Array Arguments ..
! 12: COMPLEX*16 A( LDA, * ), TAU( * )
! 13: * ..
! 14: *
! 15: * Purpose
! 16: * =======
! 17: *
! 18: * This routine is deprecated and has been replaced by routine ZTZRZF.
! 19: *
! 20: * ZTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
! 21: * to upper triangular form by means of unitary transformations.
! 22: *
! 23: * The upper trapezoidal matrix A is factored as
! 24: *
! 25: * A = ( R 0 ) * Z,
! 26: *
! 27: * where Z is an N-by-N unitary matrix and R is an M-by-M upper
! 28: * triangular matrix.
! 29: *
! 30: * Arguments
! 31: * =========
! 32: *
! 33: * M (input) INTEGER
! 34: * The number of rows of the matrix A. M >= 0.
! 35: *
! 36: * N (input) INTEGER
! 37: * The number of columns of the matrix A. N >= M.
! 38: *
! 39: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
! 40: * On entry, the leading M-by-N upper trapezoidal part of the
! 41: * array A must contain the matrix to be factorized.
! 42: * On exit, the leading M-by-M upper triangular part of A
! 43: * contains the upper triangular matrix R, and elements M+1 to
! 44: * N of the first M rows of A, with the array TAU, represent the
! 45: * unitary matrix Z as a product of M elementary reflectors.
! 46: *
! 47: * LDA (input) INTEGER
! 48: * The leading dimension of the array A. LDA >= max(1,M).
! 49: *
! 50: * TAU (output) COMPLEX*16 array, dimension (M)
! 51: * The scalar factors of the elementary reflectors.
! 52: *
! 53: * INFO (output) INTEGER
! 54: * = 0: successful exit
! 55: * < 0: if INFO = -i, the i-th argument had an illegal value
! 56: *
! 57: * Further Details
! 58: * ===============
! 59: *
! 60: * The factorization is obtained by Householder's method. The kth
! 61: * transformation matrix, Z( k ), whose conjugate transpose is used to
! 62: * introduce zeros into the (m - k + 1)th row of A, is given in the form
! 63: *
! 64: * Z( k ) = ( I 0 ),
! 65: * ( 0 T( k ) )
! 66: *
! 67: * where
! 68: *
! 69: * T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ),
! 70: * ( 0 )
! 71: * ( z( k ) )
! 72: *
! 73: * tau is a scalar and z( k ) is an ( n - m ) element vector.
! 74: * tau and z( k ) are chosen to annihilate the elements of the kth row
! 75: * of X.
! 76: *
! 77: * The scalar tau is returned in the kth element of TAU and the vector
! 78: * u( k ) in the kth row of A, such that the elements of z( k ) are
! 79: * in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
! 80: * the upper triangular part of A.
! 81: *
! 82: * Z is given by
! 83: *
! 84: * Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
! 85: *
! 86: * =====================================================================
! 87: *
! 88: * .. Parameters ..
! 89: COMPLEX*16 CONE, CZERO
! 90: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ),
! 91: $ CZERO = ( 0.0D+0, 0.0D+0 ) )
! 92: * ..
! 93: * .. Local Scalars ..
! 94: INTEGER I, K, M1
! 95: COMPLEX*16 ALPHA
! 96: * ..
! 97: * .. Intrinsic Functions ..
! 98: INTRINSIC DCONJG, MAX, MIN
! 99: * ..
! 100: * .. External Subroutines ..
! 101: EXTERNAL XERBLA, ZAXPY, ZCOPY, ZGEMV, ZGERC, ZLACGV,
! 102: $ ZLARFP
! 103: * ..
! 104: * .. Executable Statements ..
! 105: *
! 106: * Test the input parameters.
! 107: *
! 108: INFO = 0
! 109: IF( M.LT.0 ) THEN
! 110: INFO = -1
! 111: ELSE IF( N.LT.M ) THEN
! 112: INFO = -2
! 113: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 114: INFO = -4
! 115: END IF
! 116: IF( INFO.NE.0 ) THEN
! 117: CALL XERBLA( 'ZTZRQF', -INFO )
! 118: RETURN
! 119: END IF
! 120: *
! 121: * Perform the factorization.
! 122: *
! 123: IF( M.EQ.0 )
! 124: $ RETURN
! 125: IF( M.EQ.N ) THEN
! 126: DO 10 I = 1, N
! 127: TAU( I ) = CZERO
! 128: 10 CONTINUE
! 129: ELSE
! 130: M1 = MIN( M+1, N )
! 131: DO 20 K = M, 1, -1
! 132: *
! 133: * Use a Householder reflection to zero the kth row of A.
! 134: * First set up the reflection.
! 135: *
! 136: A( K, K ) = DCONJG( A( K, K ) )
! 137: CALL ZLACGV( N-M, A( K, M1 ), LDA )
! 138: ALPHA = A( K, K )
! 139: CALL ZLARFP( N-M+1, ALPHA, A( K, M1 ), LDA, TAU( K ) )
! 140: A( K, K ) = ALPHA
! 141: TAU( K ) = DCONJG( TAU( K ) )
! 142: *
! 143: IF( TAU( K ).NE.CZERO .AND. K.GT.1 ) THEN
! 144: *
! 145: * We now perform the operation A := A*P( k )'.
! 146: *
! 147: * Use the first ( k - 1 ) elements of TAU to store a( k ),
! 148: * where a( k ) consists of the first ( k - 1 ) elements of
! 149: * the kth column of A. Also let B denote the first
! 150: * ( k - 1 ) rows of the last ( n - m ) columns of A.
! 151: *
! 152: CALL ZCOPY( K-1, A( 1, K ), 1, TAU, 1 )
! 153: *
! 154: * Form w = a( k ) + B*z( k ) in TAU.
! 155: *
! 156: CALL ZGEMV( 'No transpose', K-1, N-M, CONE, A( 1, M1 ),
! 157: $ LDA, A( K, M1 ), LDA, CONE, TAU, 1 )
! 158: *
! 159: * Now form a( k ) := a( k ) - conjg(tau)*w
! 160: * and B := B - conjg(tau)*w*z( k )'.
! 161: *
! 162: CALL ZAXPY( K-1, -DCONJG( TAU( K ) ), TAU, 1, A( 1, K ),
! 163: $ 1 )
! 164: CALL ZGERC( K-1, N-M, -DCONJG( TAU( K ) ), TAU, 1,
! 165: $ A( K, M1 ), LDA, A( 1, M1 ), LDA )
! 166: END IF
! 167: 20 CONTINUE
! 168: END IF
! 169: *
! 170: RETURN
! 171: *
! 172: * End of ZTZRQF
! 173: *
! 174: END
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