Annotation of rpl/lapack/lapack/zsytrf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZSYTRF( UPLO, N, A, LDA, IPIV, 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: CHARACTER UPLO
! 10: INTEGER INFO, LDA, LWORK, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: INTEGER IPIV( * )
! 14: COMPLEX*16 A( LDA, * ), WORK( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZSYTRF computes the factorization of a complex symmetric matrix A
! 21: * using the Bunch-Kaufman diagonal pivoting method. The form of the
! 22: * factorization is
! 23: *
! 24: * A = U*D*U**T or A = L*D*L**T
! 25: *
! 26: * where U (or L) is a product of permutation and unit upper (lower)
! 27: * triangular matrices, and D is symmetric and block diagonal with
! 28: * with 1-by-1 and 2-by-2 diagonal blocks.
! 29: *
! 30: * This is the blocked version of the algorithm, calling Level 3 BLAS.
! 31: *
! 32: * Arguments
! 33: * =========
! 34: *
! 35: * UPLO (input) CHARACTER*1
! 36: * = 'U': Upper triangle of A is stored;
! 37: * = 'L': Lower triangle of A is stored.
! 38: *
! 39: * N (input) INTEGER
! 40: * The order of the matrix A. N >= 0.
! 41: *
! 42: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
! 43: * On entry, the symmetric matrix A. If UPLO = 'U', the leading
! 44: * N-by-N upper triangular part of A contains the upper
! 45: * triangular part of the matrix A, and the strictly lower
! 46: * triangular part of A is not referenced. If UPLO = 'L', the
! 47: * leading N-by-N lower triangular part of A contains the lower
! 48: * triangular part of the matrix A, and the strictly upper
! 49: * triangular part of A is not referenced.
! 50: *
! 51: * On exit, the block diagonal matrix D and the multipliers used
! 52: * to obtain the factor U or L (see below for further details).
! 53: *
! 54: * LDA (input) INTEGER
! 55: * The leading dimension of the array A. LDA >= max(1,N).
! 56: *
! 57: * IPIV (output) INTEGER array, dimension (N)
! 58: * Details of the interchanges and the block structure of D.
! 59: * If IPIV(k) > 0, then rows and columns k and IPIV(k) were
! 60: * interchanged and D(k,k) is a 1-by-1 diagonal block.
! 61: * If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
! 62: * columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
! 63: * is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) =
! 64: * IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
! 65: * interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
! 66: *
! 67: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
! 68: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 69: *
! 70: * LWORK (input) INTEGER
! 71: * The length of WORK. LWORK >=1. For best performance
! 72: * LWORK >= N*NB, where NB is the block size returned by ILAENV.
! 73: *
! 74: * If LWORK = -1, then a workspace query is assumed; the routine
! 75: * only calculates the optimal size of the WORK array, returns
! 76: * this value as the first entry of the WORK array, and no error
! 77: * message related to LWORK is issued by XERBLA.
! 78: *
! 79: * INFO (output) INTEGER
! 80: * = 0: successful exit
! 81: * < 0: if INFO = -i, the i-th argument had an illegal value
! 82: * > 0: if INFO = i, D(i,i) is exactly zero. The factorization
! 83: * has been completed, but the block diagonal matrix D is
! 84: * exactly singular, and division by zero will occur if it
! 85: * is used to solve a system of equations.
! 86: *
! 87: * Further Details
! 88: * ===============
! 89: *
! 90: * If UPLO = 'U', then A = U*D*U', where
! 91: * U = P(n)*U(n)* ... *P(k)U(k)* ...,
! 92: * i.e., U is a product of terms P(k)*U(k), where k decreases from n to
! 93: * 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
! 94: * and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
! 95: * defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
! 96: * that if the diagonal block D(k) is of order s (s = 1 or 2), then
! 97: *
! 98: * ( I v 0 ) k-s
! 99: * U(k) = ( 0 I 0 ) s
! 100: * ( 0 0 I ) n-k
! 101: * k-s s n-k
! 102: *
! 103: * If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
! 104: * If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
! 105: * and A(k,k), and v overwrites A(1:k-2,k-1:k).
! 106: *
! 107: * If UPLO = 'L', then A = L*D*L', where
! 108: * L = P(1)*L(1)* ... *P(k)*L(k)* ...,
! 109: * i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
! 110: * n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
! 111: * and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
! 112: * defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
! 113: * that if the diagonal block D(k) is of order s (s = 1 or 2), then
! 114: *
! 115: * ( I 0 0 ) k-1
! 116: * L(k) = ( 0 I 0 ) s
! 117: * ( 0 v I ) n-k-s+1
! 118: * k-1 s n-k-s+1
! 119: *
! 120: * If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
! 121: * If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
! 122: * and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
! 123: *
! 124: * =====================================================================
! 125: *
! 126: * .. Local Scalars ..
! 127: LOGICAL LQUERY, UPPER
! 128: INTEGER IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
! 129: * ..
! 130: * .. External Functions ..
! 131: LOGICAL LSAME
! 132: INTEGER ILAENV
! 133: EXTERNAL LSAME, ILAENV
! 134: * ..
! 135: * .. External Subroutines ..
! 136: EXTERNAL XERBLA, ZLASYF, ZSYTF2
! 137: * ..
! 138: * .. Intrinsic Functions ..
! 139: INTRINSIC MAX
! 140: * ..
! 141: * .. Executable Statements ..
! 142: *
! 143: * Test the input parameters.
! 144: *
! 145: INFO = 0
! 146: UPPER = LSAME( UPLO, 'U' )
! 147: LQUERY = ( LWORK.EQ.-1 )
! 148: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 149: INFO = -1
! 150: ELSE IF( N.LT.0 ) THEN
! 151: INFO = -2
! 152: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 153: INFO = -4
! 154: ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
! 155: INFO = -7
! 156: END IF
! 157: *
! 158: IF( INFO.EQ.0 ) THEN
! 159: *
! 160: * Determine the block size
! 161: *
! 162: NB = ILAENV( 1, 'ZSYTRF', UPLO, N, -1, -1, -1 )
! 163: LWKOPT = N*NB
! 164: WORK( 1 ) = LWKOPT
! 165: END IF
! 166: *
! 167: IF( INFO.NE.0 ) THEN
! 168: CALL XERBLA( 'ZSYTRF', -INFO )
! 169: RETURN
! 170: ELSE IF( LQUERY ) THEN
! 171: RETURN
! 172: END IF
! 173: *
! 174: NBMIN = 2
! 175: LDWORK = N
! 176: IF( NB.GT.1 .AND. NB.LT.N ) THEN
! 177: IWS = LDWORK*NB
! 178: IF( LWORK.LT.IWS ) THEN
! 179: NB = MAX( LWORK / LDWORK, 1 )
! 180: NBMIN = MAX( 2, ILAENV( 2, 'ZSYTRF', UPLO, N, -1, -1, -1 ) )
! 181: END IF
! 182: ELSE
! 183: IWS = 1
! 184: END IF
! 185: IF( NB.LT.NBMIN )
! 186: $ NB = N
! 187: *
! 188: IF( UPPER ) THEN
! 189: *
! 190: * Factorize A as U*D*U' using the upper triangle of A
! 191: *
! 192: * K is the main loop index, decreasing from N to 1 in steps of
! 193: * KB, where KB is the number of columns factorized by ZLASYF;
! 194: * KB is either NB or NB-1, or K for the last block
! 195: *
! 196: K = N
! 197: 10 CONTINUE
! 198: *
! 199: * If K < 1, exit from loop
! 200: *
! 201: IF( K.LT.1 )
! 202: $ GO TO 40
! 203: *
! 204: IF( K.GT.NB ) THEN
! 205: *
! 206: * Factorize columns k-kb+1:k of A and use blocked code to
! 207: * update columns 1:k-kb
! 208: *
! 209: CALL ZLASYF( UPLO, K, NB, KB, A, LDA, IPIV, WORK, N, IINFO )
! 210: ELSE
! 211: *
! 212: * Use unblocked code to factorize columns 1:k of A
! 213: *
! 214: CALL ZSYTF2( UPLO, K, A, LDA, IPIV, IINFO )
! 215: KB = K
! 216: END IF
! 217: *
! 218: * Set INFO on the first occurrence of a zero pivot
! 219: *
! 220: IF( INFO.EQ.0 .AND. IINFO.GT.0 )
! 221: $ INFO = IINFO
! 222: *
! 223: * Decrease K and return to the start of the main loop
! 224: *
! 225: K = K - KB
! 226: GO TO 10
! 227: *
! 228: ELSE
! 229: *
! 230: * Factorize A as L*D*L' using the lower triangle of A
! 231: *
! 232: * K is the main loop index, increasing from 1 to N in steps of
! 233: * KB, where KB is the number of columns factorized by ZLASYF;
! 234: * KB is either NB or NB-1, or N-K+1 for the last block
! 235: *
! 236: K = 1
! 237: 20 CONTINUE
! 238: *
! 239: * If K > N, exit from loop
! 240: *
! 241: IF( K.GT.N )
! 242: $ GO TO 40
! 243: *
! 244: IF( K.LE.N-NB ) THEN
! 245: *
! 246: * Factorize columns k:k+kb-1 of A and use blocked code to
! 247: * update columns k+kb:n
! 248: *
! 249: CALL ZLASYF( UPLO, N-K+1, NB, KB, A( K, K ), LDA, IPIV( K ),
! 250: $ WORK, N, IINFO )
! 251: ELSE
! 252: *
! 253: * Use unblocked code to factorize columns k:n of A
! 254: *
! 255: CALL ZSYTF2( UPLO, N-K+1, A( K, K ), LDA, IPIV( K ), IINFO )
! 256: KB = N - K + 1
! 257: END IF
! 258: *
! 259: * Set INFO on the first occurrence of a zero pivot
! 260: *
! 261: IF( INFO.EQ.0 .AND. IINFO.GT.0 )
! 262: $ INFO = IINFO + K - 1
! 263: *
! 264: * Adjust IPIV
! 265: *
! 266: DO 30 J = K, K + KB - 1
! 267: IF( IPIV( J ).GT.0 ) THEN
! 268: IPIV( J ) = IPIV( J ) + K - 1
! 269: ELSE
! 270: IPIV( J ) = IPIV( J ) - K + 1
! 271: END IF
! 272: 30 CONTINUE
! 273: *
! 274: * Increase K and return to the start of the main loop
! 275: *
! 276: K = K + KB
! 277: GO TO 20
! 278: *
! 279: END IF
! 280: *
! 281: 40 CONTINUE
! 282: WORK( 1 ) = LWKOPT
! 283: RETURN
! 284: *
! 285: * End of ZSYTRF
! 286: *
! 287: END
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