Annotation of rpl/lapack/lapack/zlaqps.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1,
! 2: $ VN2, AUXV, F, LDF )
! 3: *
! 4: * -- LAPACK auxiliary routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * .. Scalar Arguments ..
! 10: INTEGER KB, LDA, LDF, M, N, NB, OFFSET
! 11: * ..
! 12: * .. Array Arguments ..
! 13: INTEGER JPVT( * )
! 14: DOUBLE PRECISION VN1( * ), VN2( * )
! 15: COMPLEX*16 A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * ZLAQPS computes a step of QR factorization with column pivoting
! 22: * of a complex M-by-N matrix A by using Blas-3. It tries to factorize
! 23: * NB columns from A starting from the row OFFSET+1, and updates all
! 24: * of the matrix with Blas-3 xGEMM.
! 25: *
! 26: * In some cases, due to catastrophic cancellations, it cannot
! 27: * factorize NB columns. Hence, the actual number of factorized
! 28: * columns is returned in KB.
! 29: *
! 30: * Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
! 31: *
! 32: * Arguments
! 33: * =========
! 34: *
! 35: * M (input) INTEGER
! 36: * The number of rows of the matrix A. M >= 0.
! 37: *
! 38: * N (input) INTEGER
! 39: * The number of columns of the matrix A. N >= 0
! 40: *
! 41: * OFFSET (input) INTEGER
! 42: * The number of rows of A that have been factorized in
! 43: * previous steps.
! 44: *
! 45: * NB (input) INTEGER
! 46: * The number of columns to factorize.
! 47: *
! 48: * KB (output) INTEGER
! 49: * The number of columns actually factorized.
! 50: *
! 51: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
! 52: * On entry, the M-by-N matrix A.
! 53: * On exit, block A(OFFSET+1:M,1:KB) is the triangular
! 54: * factor obtained and block A(1:OFFSET,1:N) has been
! 55: * accordingly pivoted, but no factorized.
! 56: * The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
! 57: * been updated.
! 58: *
! 59: * LDA (input) INTEGER
! 60: * The leading dimension of the array A. LDA >= max(1,M).
! 61: *
! 62: * JPVT (input/output) INTEGER array, dimension (N)
! 63: * JPVT(I) = K <==> Column K of the full matrix A has been
! 64: * permuted into position I in AP.
! 65: *
! 66: * TAU (output) COMPLEX*16 array, dimension (KB)
! 67: * The scalar factors of the elementary reflectors.
! 68: *
! 69: * VN1 (input/output) DOUBLE PRECISION array, dimension (N)
! 70: * The vector with the partial column norms.
! 71: *
! 72: * VN2 (input/output) DOUBLE PRECISION array, dimension (N)
! 73: * The vector with the exact column norms.
! 74: *
! 75: * AUXV (input/output) COMPLEX*16 array, dimension (NB)
! 76: * Auxiliar vector.
! 77: *
! 78: * F (input/output) COMPLEX*16 array, dimension (LDF,NB)
! 79: * Matrix F' = L*Y'*A.
! 80: *
! 81: * LDF (input) INTEGER
! 82: * The leading dimension of the array F. LDF >= max(1,N).
! 83: *
! 84: * Further Details
! 85: * ===============
! 86: *
! 87: * Based on contributions by
! 88: * G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
! 89: * X. Sun, Computer Science Dept., Duke University, USA
! 90: *
! 91: * =====================================================================
! 92: *
! 93: * .. Parameters ..
! 94: DOUBLE PRECISION ZERO, ONE
! 95: COMPLEX*16 CZERO, CONE
! 96: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0,
! 97: $ CZERO = ( 0.0D+0, 0.0D+0 ),
! 98: $ CONE = ( 1.0D+0, 0.0D+0 ) )
! 99: * ..
! 100: * .. Local Scalars ..
! 101: INTEGER ITEMP, J, K, LASTRK, LSTICC, PVT, RK
! 102: DOUBLE PRECISION TEMP, TEMP2, TOL3Z
! 103: COMPLEX*16 AKK
! 104: * ..
! 105: * .. External Subroutines ..
! 106: EXTERNAL ZGEMM, ZGEMV, ZLARFP, ZSWAP
! 107: * ..
! 108: * .. Intrinsic Functions ..
! 109: INTRINSIC ABS, DBLE, DCONJG, MAX, MIN, NINT, SQRT
! 110: * ..
! 111: * .. External Functions ..
! 112: INTEGER IDAMAX
! 113: DOUBLE PRECISION DLAMCH, DZNRM2
! 114: EXTERNAL IDAMAX, DLAMCH, DZNRM2
! 115: * ..
! 116: * .. Executable Statements ..
! 117: *
! 118: LASTRK = MIN( M, N+OFFSET )
! 119: LSTICC = 0
! 120: K = 0
! 121: TOL3Z = SQRT(DLAMCH('Epsilon'))
! 122: *
! 123: * Beginning of while loop.
! 124: *
! 125: 10 CONTINUE
! 126: IF( ( K.LT.NB ) .AND. ( LSTICC.EQ.0 ) ) THEN
! 127: K = K + 1
! 128: RK = OFFSET + K
! 129: *
! 130: * Determine ith pivot column and swap if necessary
! 131: *
! 132: PVT = ( K-1 ) + IDAMAX( N-K+1, VN1( K ), 1 )
! 133: IF( PVT.NE.K ) THEN
! 134: CALL ZSWAP( M, A( 1, PVT ), 1, A( 1, K ), 1 )
! 135: CALL ZSWAP( K-1, F( PVT, 1 ), LDF, F( K, 1 ), LDF )
! 136: ITEMP = JPVT( PVT )
! 137: JPVT( PVT ) = JPVT( K )
! 138: JPVT( K ) = ITEMP
! 139: VN1( PVT ) = VN1( K )
! 140: VN2( PVT ) = VN2( K )
! 141: END IF
! 142: *
! 143: * Apply previous Householder reflectors to column K:
! 144: * A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)'.
! 145: *
! 146: IF( K.GT.1 ) THEN
! 147: DO 20 J = 1, K - 1
! 148: F( K, J ) = DCONJG( F( K, J ) )
! 149: 20 CONTINUE
! 150: CALL ZGEMV( 'No transpose', M-RK+1, K-1, -CONE, A( RK, 1 ),
! 151: $ LDA, F( K, 1 ), LDF, CONE, A( RK, K ), 1 )
! 152: DO 30 J = 1, K - 1
! 153: F( K, J ) = DCONJG( F( K, J ) )
! 154: 30 CONTINUE
! 155: END IF
! 156: *
! 157: * Generate elementary reflector H(k).
! 158: *
! 159: IF( RK.LT.M ) THEN
! 160: CALL ZLARFP( M-RK+1, A( RK, K ), A( RK+1, K ), 1, TAU( K ) )
! 161: ELSE
! 162: CALL ZLARFP( 1, A( RK, K ), A( RK, K ), 1, TAU( K ) )
! 163: END IF
! 164: *
! 165: AKK = A( RK, K )
! 166: A( RK, K ) = CONE
! 167: *
! 168: * Compute Kth column of F:
! 169: *
! 170: * Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K).
! 171: *
! 172: IF( K.LT.N ) THEN
! 173: CALL ZGEMV( 'Conjugate transpose', M-RK+1, N-K, TAU( K ),
! 174: $ A( RK, K+1 ), LDA, A( RK, K ), 1, CZERO,
! 175: $ F( K+1, K ), 1 )
! 176: END IF
! 177: *
! 178: * Padding F(1:K,K) with zeros.
! 179: *
! 180: DO 40 J = 1, K
! 181: F( J, K ) = CZERO
! 182: 40 CONTINUE
! 183: *
! 184: * Incremental updating of F:
! 185: * F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)'
! 186: * *A(RK:M,K).
! 187: *
! 188: IF( K.GT.1 ) THEN
! 189: CALL ZGEMV( 'Conjugate transpose', M-RK+1, K-1, -TAU( K ),
! 190: $ A( RK, 1 ), LDA, A( RK, K ), 1, CZERO,
! 191: $ AUXV( 1 ), 1 )
! 192: *
! 193: CALL ZGEMV( 'No transpose', N, K-1, CONE, F( 1, 1 ), LDF,
! 194: $ AUXV( 1 ), 1, CONE, F( 1, K ), 1 )
! 195: END IF
! 196: *
! 197: * Update the current row of A:
! 198: * A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)'.
! 199: *
! 200: IF( K.LT.N ) THEN
! 201: CALL ZGEMM( 'No transpose', 'Conjugate transpose', 1, N-K,
! 202: $ K, -CONE, A( RK, 1 ), LDA, F( K+1, 1 ), LDF,
! 203: $ CONE, A( RK, K+1 ), LDA )
! 204: END IF
! 205: *
! 206: * Update partial column norms.
! 207: *
! 208: IF( RK.LT.LASTRK ) THEN
! 209: DO 50 J = K + 1, N
! 210: IF( VN1( J ).NE.ZERO ) THEN
! 211: *
! 212: * NOTE: The following 4 lines follow from the analysis in
! 213: * Lapack Working Note 176.
! 214: *
! 215: TEMP = ABS( A( RK, J ) ) / VN1( J )
! 216: TEMP = MAX( ZERO, ( ONE+TEMP )*( ONE-TEMP ) )
! 217: TEMP2 = TEMP*( VN1( J ) / VN2( J ) )**2
! 218: IF( TEMP2 .LE. TOL3Z ) THEN
! 219: VN2( J ) = DBLE( LSTICC )
! 220: LSTICC = J
! 221: ELSE
! 222: VN1( J ) = VN1( J )*SQRT( TEMP )
! 223: END IF
! 224: END IF
! 225: 50 CONTINUE
! 226: END IF
! 227: *
! 228: A( RK, K ) = AKK
! 229: *
! 230: * End of while loop.
! 231: *
! 232: GO TO 10
! 233: END IF
! 234: KB = K
! 235: RK = OFFSET + KB
! 236: *
! 237: * Apply the block reflector to the rest of the matrix:
! 238: * A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) -
! 239: * A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)'.
! 240: *
! 241: IF( KB.LT.MIN( N, M-OFFSET ) ) THEN
! 242: CALL ZGEMM( 'No transpose', 'Conjugate transpose', M-RK, N-KB,
! 243: $ KB, -CONE, A( RK+1, 1 ), LDA, F( KB+1, 1 ), LDF,
! 244: $ CONE, A( RK+1, KB+1 ), LDA )
! 245: END IF
! 246: *
! 247: * Recomputation of difficult columns.
! 248: *
! 249: 60 CONTINUE
! 250: IF( LSTICC.GT.0 ) THEN
! 251: ITEMP = NINT( VN2( LSTICC ) )
! 252: VN1( LSTICC ) = DZNRM2( M-RK, A( RK+1, LSTICC ), 1 )
! 253: *
! 254: * NOTE: The computation of VN1( LSTICC ) relies on the fact that
! 255: * SNRM2 does not fail on vectors with norm below the value of
! 256: * SQRT(DLAMCH('S'))
! 257: *
! 258: VN2( LSTICC ) = VN1( LSTICC )
! 259: LSTICC = ITEMP
! 260: GO TO 60
! 261: END IF
! 262: *
! 263: RETURN
! 264: *
! 265: * End of ZLAQPS
! 266: *
! 267: END
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