Annotation of rpl/lapack/lapack/zgelqf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, 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, LWORK, M, N
! 10: * ..
! 11: * .. Array Arguments ..
! 12: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
! 13: * ..
! 14: *
! 15: * Purpose
! 16: * =======
! 17: *
! 18: * ZGELQF computes an LQ factorization of a complex M-by-N matrix A:
! 19: * A = L * Q.
! 20: *
! 21: * Arguments
! 22: * =========
! 23: *
! 24: * M (input) INTEGER
! 25: * The number of rows of the matrix A. M >= 0.
! 26: *
! 27: * N (input) INTEGER
! 28: * The number of columns of the matrix A. N >= 0.
! 29: *
! 30: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
! 31: * On entry, the M-by-N matrix A.
! 32: * On exit, the elements on and below the diagonal of the array
! 33: * contain the m-by-min(m,n) lower trapezoidal matrix L (L is
! 34: * lower triangular if m <= n); the elements above the diagonal,
! 35: * with the array TAU, represent the unitary matrix Q as a
! 36: * product of elementary reflectors (see Further Details).
! 37: *
! 38: * LDA (input) INTEGER
! 39: * The leading dimension of the array A. LDA >= max(1,M).
! 40: *
! 41: * TAU (output) COMPLEX*16 array, dimension (min(M,N))
! 42: * The scalar factors of the elementary reflectors (see Further
! 43: * Details).
! 44: *
! 45: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
! 46: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 47: *
! 48: * LWORK (input) INTEGER
! 49: * The dimension of the array WORK. LWORK >= max(1,M).
! 50: * For optimum performance LWORK >= M*NB, where NB is the
! 51: * optimal blocksize.
! 52: *
! 53: * If LWORK = -1, then a workspace query is assumed; the routine
! 54: * only calculates the optimal size of the WORK array, returns
! 55: * this value as the first entry of the WORK array, and no error
! 56: * message related to LWORK is issued by XERBLA.
! 57: *
! 58: * INFO (output) INTEGER
! 59: * = 0: successful exit
! 60: * < 0: if INFO = -i, the i-th argument had an illegal value
! 61: *
! 62: * Further Details
! 63: * ===============
! 64: *
! 65: * The matrix Q is represented as a product of elementary reflectors
! 66: *
! 67: * Q = H(k)' . . . H(2)' H(1)', where k = min(m,n).
! 68: *
! 69: * Each H(i) has the form
! 70: *
! 71: * H(i) = I - tau * v * v'
! 72: *
! 73: * where tau is a complex scalar, and v is a complex vector with
! 74: * v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
! 75: * A(i,i+1:n), and tau in TAU(i).
! 76: *
! 77: * =====================================================================
! 78: *
! 79: * .. Local Scalars ..
! 80: LOGICAL LQUERY
! 81: INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB,
! 82: $ NBMIN, NX
! 83: * ..
! 84: * .. External Subroutines ..
! 85: EXTERNAL XERBLA, ZGELQ2, ZLARFB, ZLARFT
! 86: * ..
! 87: * .. Intrinsic Functions ..
! 88: INTRINSIC MAX, MIN
! 89: * ..
! 90: * .. External Functions ..
! 91: INTEGER ILAENV
! 92: EXTERNAL ILAENV
! 93: * ..
! 94: * .. Executable Statements ..
! 95: *
! 96: * Test the input arguments
! 97: *
! 98: INFO = 0
! 99: NB = ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 )
! 100: LWKOPT = M*NB
! 101: WORK( 1 ) = LWKOPT
! 102: LQUERY = ( LWORK.EQ.-1 )
! 103: IF( M.LT.0 ) THEN
! 104: INFO = -1
! 105: ELSE IF( N.LT.0 ) THEN
! 106: INFO = -2
! 107: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 108: INFO = -4
! 109: ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN
! 110: INFO = -7
! 111: END IF
! 112: IF( INFO.NE.0 ) THEN
! 113: CALL XERBLA( 'ZGELQF', -INFO )
! 114: RETURN
! 115: ELSE IF( LQUERY ) THEN
! 116: RETURN
! 117: END IF
! 118: *
! 119: * Quick return if possible
! 120: *
! 121: K = MIN( M, N )
! 122: IF( K.EQ.0 ) THEN
! 123: WORK( 1 ) = 1
! 124: RETURN
! 125: END IF
! 126: *
! 127: NBMIN = 2
! 128: NX = 0
! 129: IWS = M
! 130: IF( NB.GT.1 .AND. NB.LT.K ) THEN
! 131: *
! 132: * Determine when to cross over from blocked to unblocked code.
! 133: *
! 134: NX = MAX( 0, ILAENV( 3, 'ZGELQF', ' ', M, N, -1, -1 ) )
! 135: IF( NX.LT.K ) THEN
! 136: *
! 137: * Determine if workspace is large enough for blocked code.
! 138: *
! 139: LDWORK = M
! 140: IWS = LDWORK*NB
! 141: IF( LWORK.LT.IWS ) THEN
! 142: *
! 143: * Not enough workspace to use optimal NB: reduce NB and
! 144: * determine the minimum value of NB.
! 145: *
! 146: NB = LWORK / LDWORK
! 147: NBMIN = MAX( 2, ILAENV( 2, 'ZGELQF', ' ', M, N, -1,
! 148: $ -1 ) )
! 149: END IF
! 150: END IF
! 151: END IF
! 152: *
! 153: IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
! 154: *
! 155: * Use blocked code initially
! 156: *
! 157: DO 10 I = 1, K - NX, NB
! 158: IB = MIN( K-I+1, NB )
! 159: *
! 160: * Compute the LQ factorization of the current block
! 161: * A(i:i+ib-1,i:n)
! 162: *
! 163: CALL ZGELQ2( IB, N-I+1, A( I, I ), LDA, TAU( I ), WORK,
! 164: $ IINFO )
! 165: IF( I+IB.LE.M ) THEN
! 166: *
! 167: * Form the triangular factor of the block reflector
! 168: * H = H(i) H(i+1) . . . H(i+ib-1)
! 169: *
! 170: CALL ZLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ),
! 171: $ LDA, TAU( I ), WORK, LDWORK )
! 172: *
! 173: * Apply H to A(i+ib:m,i:n) from the right
! 174: *
! 175: CALL ZLARFB( 'Right', 'No transpose', 'Forward',
! 176: $ 'Rowwise', M-I-IB+1, N-I+1, IB, A( I, I ),
! 177: $ LDA, WORK, LDWORK, A( I+IB, I ), LDA,
! 178: $ WORK( IB+1 ), LDWORK )
! 179: END IF
! 180: 10 CONTINUE
! 181: ELSE
! 182: I = 1
! 183: END IF
! 184: *
! 185: * Use unblocked code to factor the last or only block.
! 186: *
! 187: IF( I.LE.K )
! 188: $ CALL ZGELQ2( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK,
! 189: $ IINFO )
! 190: *
! 191: WORK( 1 ) = IWS
! 192: RETURN
! 193: *
! 194: * End of ZGELQF
! 195: *
! 196: END
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