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SUBROUTINE DCHKBD( NSIZES, MVAL, NVAL, NTYPES, DOTYPE, NRHS,
$ ISEED, THRESH, A, LDA, BD, BE, S1, S2, X, LDX, $ Y, Z, Q, LDQ, PT, LDPT, U, VT, WORK, LWORK, $ IWORK, NOUT, INFO ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER INFO, LDA, LDPT, LDQ, LDX, LWORK, NOUT, NRHS, $ NSIZES, NTYPES DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER ISEED( 4 ), IWORK( * ), MVAL( * ), NVAL( * ) DOUBLE PRECISION A( LDA, * ), BD( * ), BE( * ), PT( LDPT, * ), $ Q( LDQ, * ), S1( * ), S2( * ), U( LDPT, * ), $ VT( LDPT, * ), WORK( * ), X( LDX, * ), $ Y( LDX, * ), Z( LDX, * ) * .. * * Purpose * ======= * * DCHKBD checks the singular value decomposition (SVD) routines. * * DGEBRD reduces a real general m by n matrix A to upper or lower * bidiagonal form B by an orthogonal transformation: Q' * A * P = B * (or A = Q * B * P'). The matrix B is upper bidiagonal if m >= n * and lower bidiagonal if m < n. * * DORGBR generates the orthogonal matrices Q and P' from DGEBRD. * Note that Q and P are not necessarily square. * * DBDSQR computes the singular value decomposition of the bidiagonal * matrix B as B = U S V'. It is called three times to compute * 1) B = U S1 V', where S1 is the diagonal matrix of singular * values and the columns of the matrices U and V are the left * and right singular vectors, respectively, of B. * 2) Same as 1), but the singular values are stored in S2 and the * singular vectors are not computed. * 3) A = (UQ) S (P'V'), the SVD of the original matrix A. * In addition, DBDSQR has an option to apply the left orthogonal matrix * U to a matrix X, useful in least squares applications. * * DBDSDC computes the singular value decomposition of the bidiagonal * matrix B as B = U S V' using divide-and-conquer. It is called twice * to compute * 1) B = U S1 V', where S1 is the diagonal matrix of singular * values and the columns of the matrices U and V are the left * and right singular vectors, respectively, of B. * 2) Same as 1), but the singular values are stored in S2 and the * singular vectors are not computed. * * For each pair of matrix dimensions (M,N) and each selected matrix * type, an M by N matrix A and an M by NRHS matrix X are generated. * The problem dimensions are as follows * A: M x N * Q: M x min(M,N) (but M x M if NRHS > 0) * P: min(M,N) x N * B: min(M,N) x min(M,N) * U, V: min(M,N) x min(M,N) * S1, S2 diagonal, order min(M,N) * X: M x NRHS * * For each generated matrix, 14 tests are performed: * * Test DGEBRD and DORGBR * * (1) | A - Q B PT | / ( |A| max(M,N) ulp ), PT = P' * * (2) | I - Q' Q | / ( M ulp ) * * (3) | I - PT PT' | / ( N ulp ) * * Test DBDSQR on bidiagonal matrix B * * (4) | B - U S1 VT | / ( |B| min(M,N) ulp ), VT = V' * * (5) | Y - U Z | / ( |Y| max(min(M,N),k) ulp ), where Y = Q' X * and Z = U' Y. * (6) | I - U' U | / ( min(M,N) ulp ) * * (7) | I - VT VT' | / ( min(M,N) ulp ) * * (8) S1 contains min(M,N) nonnegative values in decreasing order. * (Return 0 if true, 1/ULP if false.) * * (9) | S1 - S2 | / ( |S1| ulp ), where S2 is computed without * computing U and V. * * (10) 0 if the true singular values of B are within THRESH of * those in S1. 2*THRESH if they are not. (Tested using * DSVDCH) * * Test DBDSQR on matrix A * * (11) | A - (QU) S (VT PT) | / ( |A| max(M,N) ulp ) * * (12) | X - (QU) Z | / ( |X| max(M,k) ulp ) * * (13) | I - (QU)'(QU) | / ( M ulp ) * * (14) | I - (VT PT) (PT'VT') | / ( N ulp ) * * Test DBDSDC on bidiagonal matrix B * * (15) | B - U S1 VT | / ( |B| min(M,N) ulp ), VT = V' * * (16) | I - U' U | / ( min(M,N) ulp ) * * (17) | I - VT VT' | / ( min(M,N) ulp ) * * (18) S1 contains min(M,N) nonnegative values in decreasing order. * (Return 0 if true, 1/ULP if false.) * * (19) | S1 - S2 | / ( |S1| ulp ), where S2 is computed without * computing U and V. * The possible matrix types are * * (1) The zero matrix. * (2) The identity matrix. * * (3) A diagonal matrix with evenly spaced entries * 1, ..., ULP and random signs. * (ULP = (first number larger than 1) - 1 ) * (4) A diagonal matrix with geometrically spaced entries * 1, ..., ULP and random signs. * (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP * and random signs. * * (6) Same as (3), but multiplied by SQRT( overflow threshold ) * (7) Same as (3), but multiplied by SQRT( underflow threshold ) * * (8) A matrix of the form U D V, where U and V are orthogonal and * D has evenly spaced entries 1, ..., ULP with random signs * on the diagonal. * * (9) A matrix of the form U D V, where U and V are orthogonal and * D has geometrically spaced entries 1, ..., ULP with random * signs on the diagonal. * * (10) A matrix of the form U D V, where U and V are orthogonal and * D has "clustered" entries 1, ULP,..., ULP with random * signs on the diagonal. * * (11) Same as (8), but multiplied by SQRT( overflow threshold ) * (12) Same as (8), but multiplied by SQRT( underflow threshold ) * * (13) Rectangular matrix with random entries chosen from (-1,1). * (14) Same as (13), but multiplied by SQRT( overflow threshold ) * (15) Same as (13), but multiplied by SQRT( underflow threshold ) * * Special case: * (16) A bidiagonal matrix with random entries chosen from a * logarithmic distribution on [ulp^2,ulp^(-2)] (I.e., each * entry is e^x, where x is chosen uniformly on * [ 2 log(ulp), -2 log(ulp) ] .) For *this* type: * (a) DGEBRD is not called to reduce it to bidiagonal form. * (b) the bidiagonal is min(M,N) x min(M,N); if M * matrix will be lower bidiagonal, otherwise upper. * (c) only tests 5--8 and 14 are performed. * * A subset of the full set of matrix types may be selected through * the logical array DOTYPE. * * Arguments * ========== * * NSIZES (input) INTEGER * The number of values of M and N contained in the vectors * MVAL and NVAL. The matrix sizes are used in pairs (M,N). * * MVAL (input) INTEGER array, dimension (NM) * The values of the matrix row dimension M. * * NVAL (input) INTEGER array, dimension (NM) * The values of the matrix column dimension N. * * NTYPES (input) INTEGER * The number of elements in DOTYPE. If it is zero, DCHKBD * does nothing. It must be at least zero. If it is MAXTYP+1 * and NSIZES is 1, then an additional type, MAXTYP+1 is * defined, which is to use whatever matrices are in A and B. * This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and * DOTYPE(MAXTYP+1) is .TRUE. . * * DOTYPE (input) LOGICAL array, dimension (NTYPES) * If DOTYPE(j) is .TRUE., then for each size (m,n), a matrix * of type j will be generated. If NTYPES is smaller than the * maximum number of types defined (PARAMETER MAXTYP), then * types NTYPES+1 through MAXTYP will not be generated. If * NTYPES is larger than MAXTYP, DOTYPE(MAXTYP+1) through * DOTYPE(NTYPES) will be ignored. * * NRHS (input) INTEGER * The number of columns in the "right-hand side" matrices X, Y, * and Z, used in testing DBDSQR. If NRHS = 0, then the * operations on the right-hand side will not be tested. * NRHS must be at least 0. * * 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 values of ISEED are changed on exit, and can be * used in the next call to DCHKBD to continue the same random * number sequence. * * THRESH (input) DOUBLE PRECISION * The threshold value for the test ratios. A result is * included in the output file if RESULT >= THRESH. To have * every test ratio printed, use THRESH = 0. Note that the * expected value of the test ratios is O(1), so THRESH should * be a reasonably small multiple of 1, e.g., 10 or 100. * * A (workspace) DOUBLE PRECISION array, dimension (LDA,NMAX) * where NMAX is the maximum value of N in NVAL. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,MMAX), * where MMAX is the maximum value of M in MVAL. * * BD (workspace) DOUBLE PRECISION array, dimension * (max(min(MVAL(j),NVAL(j)))) * * BE (workspace) DOUBLE PRECISION array, dimension * (max(min(MVAL(j),NVAL(j)))) * * S1 (workspace) DOUBLE PRECISION array, dimension * (max(min(MVAL(j),NVAL(j)))) * * S2 (workspace) DOUBLE PRECISION array, dimension * (max(min(MVAL(j),NVAL(j)))) * * X (workspace) DOUBLE PRECISION array, dimension (LDX,NRHS) * * LDX (input) INTEGER * The leading dimension of the arrays X, Y, and Z. * LDX >= max(1,MMAX) * * Y (workspace) DOUBLE PRECISION array, dimension (LDX,NRHS) * * Z (workspace) DOUBLE PRECISION array, dimension (LDX,NRHS) * * Q (workspace) DOUBLE PRECISION array, dimension (LDQ,MMAX) * * LDQ (input) INTEGER * The leading dimension of the array Q. LDQ >= max(1,MMAX). * * PT (workspace) DOUBLE PRECISION array, dimension (LDPT,NMAX) * * LDPT (input) INTEGER * The leading dimension of the arrays PT, U, and V. * LDPT >= max(1, max(min(MVAL(j),NVAL(j)))). * * U (workspace) DOUBLE PRECISION array, dimension * (LDPT,max(min(MVAL(j),NVAL(j)))) * * V (workspace) DOUBLE PRECISION array, dimension * (LDPT,max(min(MVAL(j),NVAL(j)))) * * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) * * LWORK (input) INTEGER * The number of entries in WORK. This must be at least * 3(M+N) and M(M + max(M,N,k) + 1) + N*min(M,N) for all * pairs (M,N)=(MM(j),NN(j)) * * IWORK (workspace) INTEGER array, dimension at least 8*min(M,N) * * NOUT (input) INTEGER * The FORTRAN unit number for printing out error messages * (e.g., if a routine returns IINFO not equal to 0.) * * INFO (output) INTEGER * If 0, then everything ran OK. * -1: NSIZES < 0 * -2: Some MM(j) < 0 * -3: Some NN(j) < 0 * -4: NTYPES < 0 * -6: NRHS < 0 * -8: THRESH < 0 * -11: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ). * -17: LDB < 1 or LDB < MMAX. * -21: LDQ < 1 or LDQ < MMAX. * -23: LDPT< 1 or LDPT< MNMAX. * -27: LWORK too small. * If DLATMR, SLATMS, DGEBRD, DORGBR, or DBDSQR, * returns an error code, the * absolute value of it is returned. * *----------------------------------------------------------------------- * * Some Local Variables and Parameters: * ---- ----- --------- --- ---------- * * ZERO, ONE Real 0 and 1. * MAXTYP The number of types defined. * NTEST The number of tests performed, or which can * be performed so far, for the current matrix. * MMAX Largest value in NN. * NMAX Largest value in NN. * MNMIN min(MM(j), NN(j)) (the dimension of the bidiagonal * matrix.) * MNMAX The maximum value of MNMIN for j=1,...,NSIZES. * NFAIL The number of tests which have exceeded THRESH * COND, IMODE Values to be passed to the matrix generators. * ANORM Norm of A; passed to matrix generators. * * OVFL, UNFL Overflow and underflow thresholds. * RTOVFL, RTUNFL Square roots of the previous 2 values. * ULP, ULPINV Finest relative precision and its inverse. * * The following four arrays decode JTYPE: * KTYPE(j) The general type (1-10) for type "j". * KMODE(j) The MODE value to be passed to the matrix * generator for type "j". * KMAGN(j) The order of magnitude ( O(1), * O(overflow^(1/2) ), O(underflow^(1/2) ) * * ====================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TWO, HALF PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, $ HALF = 0.5D0 ) INTEGER MAXTYP PARAMETER ( MAXTYP = 16 ) * .. * .. Local Scalars .. LOGICAL BADMM, BADNN, BIDIAG CHARACTER UPLO CHARACTER*3 PATH INTEGER I, IINFO, IMODE, ITYPE, J, JCOL, JSIZE, JTYPE, $ LOG2UI, M, MINWRK, MMAX, MNMAX, MNMIN, MQ, $ MTYPES, N, NFAIL, NMAX, NTEST DOUBLE PRECISION AMNINV, ANORM, COND, OVFL, RTOVFL, RTUNFL, $ TEMP1, TEMP2, ULP, ULPINV, UNFL * .. * .. Local Arrays .. INTEGER IDUM( 1 ), IOLDSD( 4 ), KMAGN( MAXTYP ), $ KMODE( MAXTYP ), KTYPE( MAXTYP ) DOUBLE PRECISION DUM( 1 ), DUMMA( 1 ), RESULT( 19 ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLARND EXTERNAL DLAMCH, DLARND * .. * .. External Subroutines .. EXTERNAL ALASUM, DBDSDC, DBDSQR, DBDT01, DBDT02, DBDT03, $ DCOPY, DGEBRD, DGEMM, DLABAD, DLACPY, DLAHD2, $ DLASET, DLATMR, DLATMS, DORGBR, DORT01, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, EXP, INT, LOG, MAX, MIN, SQRT * .. * .. Scalars in Common .. LOGICAL LERR, OK CHARACTER*32 SRNAMT INTEGER INFOT, NUNIT * .. * .. Common blocks .. COMMON / INFOC / INFOT, NUNIT, OK, LERR COMMON / SRNAMC / SRNAMT * .. * .. Data statements .. DATA KTYPE / 1, 2, 5*4, 5*6, 3*9, 10 / DATA KMAGN / 2*1, 3*1, 2, 3, 3*1, 2, 3, 1, 2, 3, 0 / DATA KMODE / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0, $ 0, 0, 0 / * .. * .. Executable Statements .. * * Check for errors * INFO = 0 * BADMM = .FALSE. BADNN = .FALSE. MMAX = 1 NMAX = 1 MNMAX = 1 MINWRK = 1 DO 10 J = 1, NSIZES MMAX = MAX( MMAX, MVAL( J ) ) IF( MVAL( J ).LT.0 ) $ BADMM = .TRUE. NMAX = MAX( NMAX, NVAL( J ) ) IF( NVAL( J ).LT.0 ) $ BADNN = .TRUE. MNMAX = MAX( MNMAX, MIN( MVAL( J ), NVAL( J ) ) ) MINWRK = MAX( MINWRK, 3*( MVAL( J )+NVAL( J ) ), $ MVAL( J )*( MVAL( J )+MAX( MVAL( J ), NVAL( J ), $ NRHS )+1 )+NVAL( J )*MIN( NVAL( J ), MVAL( J ) ) ) 10 CONTINUE * * Check for errors * IF( NSIZES.LT.0 ) THEN INFO = -1 ELSE IF( BADMM ) THEN INFO = -2 ELSE IF( BADNN ) THEN INFO = -3 ELSE IF( NTYPES.LT.0 ) THEN INFO = -4 ELSE IF( NRHS.LT.0 ) THEN INFO = -6 ELSE IF( LDA.LT.MMAX ) THEN INFO = -11 ELSE IF( LDX.LT.MMAX ) THEN INFO = -17 ELSE IF( LDQ.LT.MMAX ) THEN INFO = -21 ELSE IF( LDPT.LT.MNMAX ) THEN INFO = -23 ELSE IF( MINWRK.GT.LWORK ) THEN INFO = -27 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DCHKBD', -INFO ) RETURN END IF * * Initialize constants * PATH( 1: 1 ) = 'Double precision' PATH( 2: 3 ) = 'BD' NFAIL = 0 NTEST = 0 UNFL = DLAMCH( 'Safe minimum' ) OVFL = DLAMCH( 'Overflow' ) CALL DLABAD( UNFL, OVFL ) ULP = DLAMCH( 'Precision' ) ULPINV = ONE / ULP LOG2UI = INT( LOG( ULPINV ) / LOG( TWO ) ) RTUNFL = SQRT( UNFL ) RTOVFL = SQRT( OVFL ) INFOT = 0 * * Loop over sizes, types * DO 200 JSIZE = 1, NSIZES M = MVAL( JSIZE ) N = NVAL( JSIZE ) MNMIN = MIN( M, N ) AMNINV = ONE / MAX( M, N, 1 ) * IF( NSIZES.NE.1 ) THEN MTYPES = MIN( MAXTYP, NTYPES ) ELSE MTYPES = MIN( MAXTYP+1, NTYPES ) END IF * DO 190 JTYPE = 1, MTYPES IF( .NOT.DOTYPE( JTYPE ) ) $ GO TO 190 * DO 20 J = 1, 4 IOLDSD( J ) = ISEED( J ) 20 CONTINUE * DO 30 J = 1, 14 RESULT( J ) = -ONE 30 CONTINUE * UPLO = ' ' * * Compute "A" * * Control parameters: * * KMAGN KMODE KTYPE * =1 O(1) clustered 1 zero * =2 large clustered 2 identity * =3 small exponential (none) * =4 arithmetic diagonal, (w/ eigenvalues) * =5 random symmetric, w/ eigenvalues * =6 nonsymmetric, w/ singular values * =7 random diagonal * =8 random symmetric * =9 random nonsymmetric * =10 random bidiagonal (log. distrib.) * IF( MTYPES.GT.MAXTYP ) $ GO TO 100 * ITYPE = KTYPE( JTYPE ) IMODE = KMODE( JTYPE ) * * Compute norm * GO TO ( 40, 50, 60 )KMAGN( JTYPE ) * 40 CONTINUE ANORM = ONE GO TO 70 * 50 CONTINUE ANORM = ( RTOVFL*ULP )*AMNINV GO TO 70 * 60 CONTINUE ANORM = RTUNFL*MAX( M, N )*ULPINV GO TO 70 * 70 CONTINUE * CALL DLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA ) IINFO = 0 COND = ULPINV * BIDIAG = .FALSE. IF( ITYPE.EQ.1 ) THEN * * Zero matrix * IINFO = 0 * ELSE IF( ITYPE.EQ.2 ) THEN * * Identity * DO 80 JCOL = 1, MNMIN A( JCOL, JCOL ) = ANORM 80 CONTINUE * ELSE IF( ITYPE.EQ.4 ) THEN * * Diagonal Matrix, [Eigen]values Specified * CALL DLATMS( MNMIN, MNMIN, 'S', ISEED, 'N', WORK, IMODE, $ COND, ANORM, 0, 0, 'N', A, LDA, $ WORK( MNMIN+1 ), IINFO ) * ELSE IF( ITYPE.EQ.5 ) THEN * * Symmetric, eigenvalues specified * CALL DLATMS( MNMIN, MNMIN, 'S', ISEED, 'S', WORK, IMODE, $ COND, ANORM, M, N, 'N', A, LDA, $ WORK( MNMIN+1 ), IINFO ) * ELSE IF( ITYPE.EQ.6 ) THEN * * Nonsymmetric, singular values specified * CALL DLATMS( M, N, 'S', ISEED, 'N', WORK, IMODE, COND, $ ANORM, M, N, 'N', A, LDA, WORK( MNMIN+1 ), $ IINFO ) * ELSE IF( ITYPE.EQ.7 ) THEN * * Diagonal, random entries * CALL DLATMR( MNMIN, MNMIN, 'S', ISEED, 'N', WORK, 6, ONE, $ ONE, 'T', 'N', WORK( MNMIN+1 ), 1, ONE, $ WORK( 2*MNMIN+1 ), 1, ONE, 'N', IWORK, 0, 0, $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO ) * ELSE IF( ITYPE.EQ.8 ) THEN * * Symmetric, random entries * CALL DLATMR( MNMIN, MNMIN, 'S', ISEED, 'S', WORK, 6, ONE, $ ONE, 'T', 'N', WORK( MNMIN+1 ), 1, ONE, $ WORK( M+MNMIN+1 ), 1, ONE, 'N', IWORK, M, N, $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO ) * ELSE IF( ITYPE.EQ.9 ) THEN * * Nonsymmetric, random entries * CALL DLATMR( M, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE, $ 'T', 'N', WORK( MNMIN+1 ), 1, ONE, $ WORK( M+MNMIN+1 ), 1, ONE, 'N', IWORK, M, N, $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO ) * ELSE IF( ITYPE.EQ.10 ) THEN * * Bidiagonal, random entries * TEMP1 = -TWO*LOG( ULP ) DO 90 J = 1, MNMIN BD( J ) = EXP( TEMP1*DLARND( 2, ISEED ) ) IF( J.LT.MNMIN ) $ BE( J ) = EXP( TEMP1*DLARND( 2, ISEED ) ) 90 CONTINUE * IINFO = 0 BIDIAG = .TRUE. IF( M.GE.N ) THEN UPLO = 'U' ELSE UPLO = 'L' END IF ELSE IINFO = 1 END IF * IF( IINFO.EQ.0 ) THEN * * Generate Right-Hand Side * IF( BIDIAG ) THEN CALL DLATMR( MNMIN, NRHS, 'S', ISEED, 'N', WORK, 6, $ ONE, ONE, 'T', 'N', WORK( MNMIN+1 ), 1, $ ONE, WORK( 2*MNMIN+1 ), 1, ONE, 'N', $ IWORK, MNMIN, NRHS, ZERO, ONE, 'NO', Y, $ LDX, IWORK, IINFO ) ELSE CALL DLATMR( M, NRHS, 'S', ISEED, 'N', WORK, 6, ONE, $ ONE, 'T', 'N', WORK( M+1 ), 1, ONE, $ WORK( 2*M+1 ), 1, ONE, 'N', IWORK, M, $ NRHS, ZERO, ONE, 'NO', X, LDX, IWORK, $ IINFO ) END IF END IF * * Error Exit * IF( IINFO.NE.0 ) THEN WRITE( NOUT, FMT = 9998 )'Generator', IINFO, M, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) RETURN END IF * 100 CONTINUE * * Call DGEBRD and DORGBR to compute B, Q, and P, do tests. * IF( .NOT.BIDIAG ) THEN * * Compute transformations to reduce A to bidiagonal form: * B := Q' * A * P. * CALL DLACPY( ' ', M, N, A, LDA, Q, LDQ ) CALL DGEBRD( M, N, Q, LDQ, BD, BE, WORK, WORK( MNMIN+1 ), $ WORK( 2*MNMIN+1 ), LWORK-2*MNMIN, IINFO ) * * Check error code from DGEBRD. * IF( IINFO.NE.0 ) THEN WRITE( NOUT, FMT = 9998 )'DGEBRD', IINFO, M, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) RETURN END IF * CALL DLACPY( ' ', M, N, Q, LDQ, PT, LDPT ) IF( M.GE.N ) THEN UPLO = 'U' ELSE UPLO = 'L' END IF * * Generate Q * MQ = M IF( NRHS.LE.0 ) $ MQ = MNMIN CALL DORGBR( 'Q', M, MQ, N, Q, LDQ, WORK, $ WORK( 2*MNMIN+1 ), LWORK-2*MNMIN, IINFO ) * * Check error code from DORGBR. * IF( IINFO.NE.0 ) THEN WRITE( NOUT, FMT = 9998 )'DORGBR(Q)', IINFO, M, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) RETURN END IF * * Generate P' * CALL DORGBR( 'P', MNMIN, N, M, PT, LDPT, WORK( MNMIN+1 ), $ WORK( 2*MNMIN+1 ), LWORK-2*MNMIN, IINFO ) * * Check error code from DORGBR. * IF( IINFO.NE.0 ) THEN WRITE( NOUT, FMT = 9998 )'DORGBR(P)', IINFO, M, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) RETURN END IF * * Apply Q' to an M by NRHS matrix X: Y := Q' * X. * CALL DGEMM( 'Transpose', 'No transpose', M, NRHS, M, ONE, $ Q, LDQ, X, LDX, ZERO, Y, LDX ) * * Test 1: Check the decomposition A := Q * B * PT * 2: Check the orthogonality of Q * 3: Check the orthogonality of PT * CALL DBDT01( M, N, 1, A, LDA, Q, LDQ, BD, BE, PT, LDPT, $ WORK, RESULT( 1 ) ) CALL DORT01( 'Columns', M, MQ, Q, LDQ, WORK, LWORK, $ RESULT( 2 ) ) CALL DORT01( 'Rows', MNMIN, N, PT, LDPT, WORK, LWORK, $ RESULT( 3 ) ) END IF * * Use DBDSQR to form the SVD of the bidiagonal matrix B: * B := U * S1 * VT, and compute Z = U' * Y. * CALL DCOPY( MNMIN, BD, 1, S1, 1 ) IF( MNMIN.GT.0 ) $ CALL DCOPY( MNMIN-1, BE, 1, WORK, 1 ) CALL DLACPY( ' ', M, NRHS, Y, LDX, Z, LDX ) CALL DLASET( 'Full', MNMIN, MNMIN, ZERO, ONE, U, LDPT ) CALL DLASET( 'Full', MNMIN, MNMIN, ZERO, ONE, VT, LDPT ) * CALL DBDSQR( UPLO, MNMIN, MNMIN, MNMIN, NRHS, S1, WORK, VT, $ LDPT, U, LDPT, Z, LDX, WORK( MNMIN+1 ), IINFO ) * * Check error code from DBDSQR. * IF( IINFO.NE.0 ) THEN WRITE( NOUT, FMT = 9998 )'DBDSQR(vects)', IINFO, M, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) IF( IINFO.LT.0 ) THEN RETURN ELSE RESULT( 4 ) = ULPINV GO TO 170 END IF END IF * * Use DBDSQR to compute only the singular values of the * bidiagonal matrix B; U, VT, and Z should not be modified. * CALL DCOPY( MNMIN, BD, 1, S2, 1 ) IF( MNMIN.GT.0 ) $ CALL DCOPY( MNMIN-1, BE, 1, WORK, 1 ) * CALL DBDSQR( UPLO, MNMIN, 0, 0, 0, S2, WORK, VT, LDPT, U, $ LDPT, Z, LDX, WORK( MNMIN+1 ), IINFO ) * * Check error code from DBDSQR. * IF( IINFO.NE.0 ) THEN WRITE( NOUT, FMT = 9998 )'DBDSQR(values)', IINFO, M, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) IF( IINFO.LT.0 ) THEN RETURN ELSE RESULT( 9 ) = ULPINV GO TO 170 END IF END IF * * Test 4: Check the decomposition B := U * S1 * VT * 5: Check the computation Z := U' * Y * 6: Check the orthogonality of U * 7: Check the orthogonality of VT * CALL DBDT03( UPLO, MNMIN, 1, BD, BE, U, LDPT, S1, VT, LDPT, $ WORK, RESULT( 4 ) ) CALL DBDT02( MNMIN, NRHS, Y, LDX, Z, LDX, U, LDPT, WORK, $ RESULT( 5 ) ) CALL DORT01( 'Columns', MNMIN, MNMIN, U, LDPT, WORK, LWORK, $ RESULT( 6 ) ) CALL DORT01( 'Rows', MNMIN, MNMIN, VT, LDPT, WORK, LWORK, $ RESULT( 7 ) ) * * Test 8: Check that the singular values are sorted in * non-increasing order and are non-negative * RESULT( 8 ) = ZERO DO 110 I = 1, MNMIN - 1 IF( S1( I ).LT.S1( I+1 ) ) $ RESULT( 8 ) = ULPINV IF( S1( I ).LT.ZERO ) $ RESULT( 8 ) = ULPINV 110 CONTINUE IF( MNMIN.GE.1 ) THEN IF( S1( MNMIN ).LT.ZERO ) $ RESULT( 8 ) = ULPINV END IF * * Test 9: Compare DBDSQR with and without singular vectors * TEMP2 = ZERO * DO 120 J = 1, MNMIN TEMP1 = ABS( S1( J )-S2( J ) ) / $ MAX( SQRT( UNFL )*MAX( S1( 1 ), ONE ), $ ULP*MAX( ABS( S1( J ) ), ABS( S2( J ) ) ) ) TEMP2 = MAX( TEMP1, TEMP2 ) 120 CONTINUE * RESULT( 9 ) = TEMP2 * * Test 10: Sturm sequence test of singular values * Go up by factors of two until it succeeds * TEMP1 = THRESH*( HALF-ULP ) * DO 130 J = 0, LOG2UI * CALL DSVDCH( MNMIN, BD, BE, S1, TEMP1, IINFO ) IF( IINFO.EQ.0 ) $ GO TO 140 TEMP1 = TEMP1*TWO 130 CONTINUE * 140 CONTINUE RESULT( 10 ) = TEMP1 * * Use DBDSQR to form the decomposition A := (QU) S (VT PT) * from the bidiagonal form A := Q B PT. * IF( .NOT.BIDIAG ) THEN CALL DCOPY( MNMIN, BD, 1, S2, 1 ) IF( MNMIN.GT.0 ) $ CALL DCOPY( MNMIN-1, BE, 1, WORK, 1 ) * CALL DBDSQR( UPLO, MNMIN, N, M, NRHS, S2, WORK, PT, LDPT, $ Q, LDQ, Y, LDX, WORK( MNMIN+1 ), IINFO ) * * Test 11: Check the decomposition A := Q*U * S2 * VT*PT * 12: Check the computation Z := U' * Q' * X * 13: Check the orthogonality of Q*U * 14: Check the orthogonality of VT*PT * CALL DBDT01( M, N, 0, A, LDA, Q, LDQ, S2, DUMMA, PT, $ LDPT, WORK, RESULT( 11 ) ) CALL DBDT02( M, NRHS, X, LDX, Y, LDX, Q, LDQ, WORK, $ RESULT( 12 ) ) CALL DORT01( 'Columns', M, MQ, Q, LDQ, WORK, LWORK, $ RESULT( 13 ) ) CALL DORT01( 'Rows', MNMIN, N, PT, LDPT, WORK, LWORK, $ RESULT( 14 ) ) END IF * * Use DBDSDC to form the SVD of the bidiagonal matrix B: * B := U * S1 * VT * CALL DCOPY( MNMIN, BD, 1, S1, 1 ) IF( MNMIN.GT.0 ) $ CALL DCOPY( MNMIN-1, BE, 1, WORK, 1 ) CALL DLASET( 'Full', MNMIN, MNMIN, ZERO, ONE, U, LDPT ) CALL DLASET( 'Full', MNMIN, MNMIN, ZERO, ONE, VT, LDPT ) * CALL DBDSDC( UPLO, 'I', MNMIN, S1, WORK, U, LDPT, VT, LDPT, $ DUM, IDUM, WORK( MNMIN+1 ), IWORK, IINFO ) * * Check error code from DBDSDC. * IF( IINFO.NE.0 ) THEN WRITE( NOUT, FMT = 9998 )'DBDSDC(vects)', IINFO, M, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) IF( IINFO.LT.0 ) THEN RETURN ELSE RESULT( 15 ) = ULPINV GO TO 170 END IF END IF * * Use DBDSDC to compute only the singular values of the * bidiagonal matrix B; U and VT should not be modified. * CALL DCOPY( MNMIN, BD, 1, S2, 1 ) IF( MNMIN.GT.0 ) $ CALL DCOPY( MNMIN-1, BE, 1, WORK, 1 ) * CALL DBDSDC( UPLO, 'N', MNMIN, S2, WORK, DUM, 1, DUM, 1, $ DUM, IDUM, WORK( MNMIN+1 ), IWORK, IINFO ) * * Check error code from DBDSDC. * IF( IINFO.NE.0 ) THEN WRITE( NOUT, FMT = 9998 )'DBDSDC(values)', IINFO, M, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) IF( IINFO.LT.0 ) THEN RETURN ELSE RESULT( 18 ) = ULPINV GO TO 170 END IF END IF * * Test 15: Check the decomposition B := U * S1 * VT * 16: Check the orthogonality of U * 17: Check the orthogonality of VT * CALL DBDT03( UPLO, MNMIN, 1, BD, BE, U, LDPT, S1, VT, LDPT, $ WORK, RESULT( 15 ) ) CALL DORT01( 'Columns', MNMIN, MNMIN, U, LDPT, WORK, LWORK, $ RESULT( 16 ) ) CALL DORT01( 'Rows', MNMIN, MNMIN, VT, LDPT, WORK, LWORK, $ RESULT( 17 ) ) * * Test 18: Check that the singular values are sorted in * non-increasing order and are non-negative * RESULT( 18 ) = ZERO DO 150 I = 1, MNMIN - 1 IF( S1( I ).LT.S1( I+1 ) ) $ RESULT( 18 ) = ULPINV IF( S1( I ).LT.ZERO ) $ RESULT( 18 ) = ULPINV 150 CONTINUE IF( MNMIN.GE.1 ) THEN IF( S1( MNMIN ).LT.ZERO ) $ RESULT( 18 ) = ULPINV END IF * * Test 19: Compare DBDSQR with and without singular vectors * TEMP2 = ZERO * DO 160 J = 1, MNMIN TEMP1 = ABS( S1( J )-S2( J ) ) / $ MAX( SQRT( UNFL )*MAX( S1( 1 ), ONE ), $ ULP*MAX( ABS( S1( 1 ) ), ABS( S2( 1 ) ) ) ) TEMP2 = MAX( TEMP1, TEMP2 ) 160 CONTINUE * RESULT( 19 ) = TEMP2 * * End of Loop -- Check for RESULT(j) > THRESH * 170 CONTINUE DO 180 J = 1, 19 IF( RESULT( J ).GE.THRESH ) THEN IF( NFAIL.EQ.0 ) $ CALL DLAHD2( NOUT, PATH ) WRITE( NOUT, FMT = 9999 )M, N, JTYPE, IOLDSD, J, $ RESULT( J ) NFAIL = NFAIL + 1 END IF 180 CONTINUE IF( .NOT.BIDIAG ) THEN NTEST = NTEST + 19 ELSE NTEST = NTEST + 5 END IF * 190 CONTINUE 200 CONTINUE * * Summary * CALL ALASUM( PATH, NOUT, NFAIL, NTEST, 0 ) * RETURN * * End of DCHKBD * 9999 FORMAT( ' M=', I5, ', N=', I5, ', type ', I2, ', seed=', $ 4( I4, ',' ), ' test(', I2, ')=', G11.4 ) 9998 FORMAT( ' DCHKBD: ', A, ' returned INFO=', I6, '.', / 9X, 'M=', $ I6, ', N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), $ I5, ')' ) * END |